National Numeracy and Mathematics Progression Framework BEGIN

Transcription

1 National Numeracy and Mathematics Progression Framework BEGIN

2 Main menu Please choose an organiser below to find out more: National Numeracy Progression Framework ESTIMATION AND ROUNDING NUMBER AND NUMBER PROCESSES FRACTIONS, DECIMAL FRACTIONS AND PERCENTAGES MONEY TIME MEASUREMENT DATA AND ANALYSIS IDEAS OF CHANCE AND UNCERTAINTY National Mathematics Progression Framework EXPRESSIONS AND EQUATIONS ANGLES, SYMMETRY AND TRANSFORMATION MULTIPLES, FACTORS AND PRIMES PATTERNS AND RELATIONSHIPS POWERS AND ROOTS PROPERTIES OF 2D SHAPES AND 3D OBJECTS MATHEMATICS ITS IMPACT ON THE WORLD PAST, PRESENT AND FUTURE

3 Estimation and rounding Awareness of size and amount Concept of estimation Concept of rounding Accuracy within rounding Tolerance

4 Estimation and rounding Awareness of size and amount Awareness of size and amount Comparing size and amount supports the development of appropriate language relating to quantities. This also Concept supports of an understanding Concept of where of numbers sit Accuracy on a within estimation number line. rounding rounding Awareness of size and amount Tolerance

5 Estimation and rounding Awareness of size and amount Awareness of size and amount Comparing different sizes and amounts (quantities) using appropriate vocabulary to describe them in relation to each other. Previous knowledge and understanding Demonstrate an ability Comparing to compare size items, and shapes amount and supports groups the development In play, can group or sort items by own criteria of appropriate language relating to quantities. This also AwarenessCan talk about items, shapes or groups in own words, with some evidence of comparative Concept supports language, of understanding e.g. taller, smaller, Concept of longer, where of numbers sit Accuracy on a within of size and shorter estimation number line. rounding rounding amount Tolerance Awareness of size and amount

6 Estimation and rounding Concept of estimation Awareness of size and amount Early estimation skills allow for more refined comparisons and for approximations to be made. Estimating is the Concept interpretation of of relative size Concept and quantities. of Accuracy within estimation rounding rounding Concept of estimation Tolerance

7 Estimation and rounding Awareness of size and amount Concept of estimation Concept of estimation As this skill becomes more refined, learners will be able to predict solutions and check the accuracy of calculations. Previous knowledge and understanding Can apply knowledge Early estimation of number in skills relation allow to quantities for more refined comparisons Is able to group and or segregate for approximations items to a given to criteria be made. Estimating is the Can talk about Concept items, shapes interpretation of or groups and can of relative size Concept use and quantities. of Accuracy within comparative language estimation rounding rounding Concept of estimation Tolerance

8 Estimation and rounding Concept of rounding Awareness of size and amount The ability to round supports the development of mental agility. It also allows for quick estimations to be made in Concept calculations of and to check Concept the reasonableness of of a Accuracy solution. within estimation rounding rounding Tolerance Concept of rounding

9 Estimation and rounding Concept of rounding The concept of rounding is the application of understanding of Concept place value and of knowing rounding what is the most appropriate whole number (or decimal fraction) to round it to, within a given context. Awareness of size and amount Previous knowledge and understanding Have an understanding of place value Have an understanding of estimation and approximate values The ability to round supports the development of mental agility. It also allows for quick estimations to be made in Concept calculations of and to check Concept the reasonableness of of a Accuracy solution. within estimation rounding rounding Tolerance Concept of rounding

10 Estimation and rounding Accuracy within rounding Awareness of size and amount Rounding accurately is an essential component of determining the reasonableness of a solution. In different MAIN MENU Concept contexts of there will be different Concept degrees of of accuracy Accuracy within estimation required. rounding rounding Tolerance Accuracy with rounding

11 Accuracy within rounding Estimation and rounding As this skill becomes more refined, learners will be able to predict solutions and check the accuracy of calculations. Awareness of size and amount Previous knowledge and understanding Understand that a rounded Accuracy value is not within equal to rounding the original value Can use knowledge of place value to make a decision on how a number should be rounded Can explain what rounding means using vocabulary of estimation, e.g. about, nearly, roughly Can select and apply appropriate rounding strategy in a given situation, e.g. measurement, time, money Using knowledge of number, is able to give an increasingly accurate estimation of the quantity of a given set Can determine the reasonableness of an outcome Rounding accurately is an essential component of determining the reasonableness of a solution. In different Concept contexts of there will be different Concept degrees of of accuracy Accuracy within estimation required. rounding rounding Tolerance Accuracy with rounding

12 Estimation and rounding Tolerance Awareness of size and amount To understand that there are acceptable degrees of accuracy required in calculations, including with measurement and Concept of Concept of Accuracy within real-life contexts. estimation rounding rounding Tolerance Tolerance

13 Tolerance Tolerance intervals are the differences between the greatest and least Estimation and rounding acceptable values of the measurement. Tolerance is the maximum range of variation allowed within particular situations and contexts and supports the understanding of inaccuracy. Awareness of size and amount Tolerance Previous knowledge and understanding Knows that depending on the situation, degrees of accuracy in rounding may differ, e.g. when measuring room for a carpet, rounding up should be Why applied is it to important? ensure enough carpet is purchased Display an awareness of appropriateness of rounding, e.g. when preparing to arrive for a train journey, rounding up would be inappropriate Understand that measurements are not always accurate to varying degrees To understand that there are acceptable degrees of accuracy required in calculations, including with measurement and Concept of Concept of Accuracy within real-life contexts. estimation rounding rounding Tolerance Tolerance

14 Number and number processes Numerals Awareness of number Counting Quantity Place value Addition and Subtraction Multiplication and Division Order of operations Negative numbers Fractions, decimal fractions and percentages Applying across contexts Mental agility

15 Number and number processes Numerals Awareness of number Awareness of number Counting Quantities Mental agility Numbers are all around us and they are used in many different ways. Developing an understanding of numbers and their role Add\Subtract in the description of quantities is fundamental to forming the connections needed to describe a group of objects. Order To be of confident and comfortable Place value with numbers, it is necessary to operations understand how the number system works and how numbers relate to each other. It is important to understand Multiply/Divide numbers can be classified into sets called number systems, e.g. natural numbers and real numbers. All numbers can be expressed using the digits: 0,1,2,3,4,5,6,7,8 and 9. Awareness of number Negative numbers Fractions, decimal fractions and percentages Applying across contexts

16 Number and number processes Awareness of number Awareness of number Numerals Quantities Mental agility Awareness of number Learners need to have an awareness of what numbers are through understanding and application of the meaning of numbers the relationship between numbers comparison Counting and contrast between the relative size (magnitude of numbers) Here are video exemplars: Numbers are all around us and they are used in many different ways. Developing an understanding of numbers and their role Add\Subtract in the description of quantities is fundamental to forming the connections needed to describe a group of objects. Order To be of confident and comfortable Place value with numbers, it is necessary to operations understand how the number system works and how numbers relate to each other. It is important to understand Multiply/Divide numbers can be classified into sets called number systems e.g. natural numbers and real numbers. All numbers can be expressed using the digits; 0,1,2,3,4,5,6,7,8 and 9. learnerstalkingaboutnumbersoutsideschool1.asp learnerstalkingaboutnumbersoutsideschool2.asp learnerstalkingaboutnumbers.asp Awareness of number Negative numbers Fractions, decimal fractions and percentages Applying across contexts

17 Number and number processes Numerals Numerals Awareness of number Counting Quantities Add\Subtract Developing an understanding that we have both words and symbols Order of Place for all value the numbers we use needs to be understood. operations This ensures the ability to count accurately and understand one to one correspondence. Numerals Multiply/Divide Negative numbers Fractions, decimal fractions and percentages Applying across contexts Mental agility

18 Number and number processes Numerals Awareness of number A numeral is a symbol that represents a number. The move from Numerals the real object to the symbols of numbers is one of the Numerals first and most abstract concepts that learners meet. Digits make up numbers. Here are video exemplars: Counting Quantities hiddennumbers.asp Add\Subtract Developing an understanding that we have both words and symbols Order of Place for all value the numbers we use needs to be understood. operations This ensures the ability to count accurately and understand one to one correspondence. matchingnumberwithquantity.asp numeralsdotpatterns.asp Numerals Multiply/Divide Negative numbers Fractions, decimal fractions and percentages Applying across contexts Mental agility

19 Number and number processes Numerals Counting Awareness of number Counting Quantities Mental agility Develop the ability to count with understanding of one to one Add\Subtract correspondence is crucial to develop future ability to carry out the four operations quickly and efficiently. Place value Counting Developing counting skills The importance Multiply/Divide of zero Language Order of operations One-to-one correspondence Counting forwards and backwards Negative numbers Fractions, decimal fractions and percentages Applying across contexts

20 Number and number processes Awareness of number Counting Counting is more than reciting numbers in order. It involves understanding of the number system and being able to apply this knowledge. Using a one-to-one Counting Quantities Mental agility Counting correspondence to link numbers to their amounts or quantities enables the development of counting with understanding. Numerals Zero should be included when learning about numbers, to build understanding for future work in developing understanding of place value and decimal fractions. Develop the ability to count with understanding of one to one Add\Subtract correspondence is crucial to develop future ability to carry out the four operations quickly and efficiently. Here is a video exemplar: Place value Counting Developing counting skills The importance Multiply/Divide of zero Language Order of operations One-to-one correspondence Counting forwards and backwards Negative numbers Fractions, decimal fractions and percentages Applying across contexts

21 Number and number processes The importance of zero Awareness of number Numerals Counting Quantities Mental agility Counting Leaners should be learners in counting from zero and understanding the importance of zero as a quantity and numeral digit used to represent that number (0). Leaners should also understand the value of zero. Here are video exemplars: Develop the ability to count with understanding of one to one theimportanceofzero.asp Add\Subtract correspondence is crucial to develop future ability to carry out the four operations quickly and efficiently. Place value Counting Developing counting skills theimportanceofzerochoir.asp The importance Multiply/Divide of zero Language Order of operations One-to-one correspondence Counting forwards and backwards Negative numbers Fractions, decimal fractions and percentages Applying across contexts

22 Number and number processes One-to-one correspondence Numerals Counting Learners need to understand that each object must be counted only once and as the number name is identified by the learner. Here are video exemplars: countingonetoonevideo1.asp Awareness of number Counting Quantities Mental agility Develop the ability to count with understanding of one to one Add\Subtract countingonetoonevideo2.asp correspondence is crucial to develop future ability to carry out the four operations quickly and efficiently. countingonetoonevideo3.asp Place value Counting Developing counting skills The importance Multiply/Divide of zero Language Order of operations One-to-one correspondence Counting forwards and backwards Negative numbers Fractions, decimal fractions and percentages Applying across contexts

23 Number and number processes Awareness of number Developing counting skills When counting a group of items, and then re-counting the same group starting with a different item, the total remains unchanged. This concept is Counting Quantities Mental agility Counting the conservation of number-the arrangement of a group of items does not affect the total. Numerals The last number said in a count indicates how many items there are in a group; it does not describe the last item counted. As counting develops, within a known range Why of is numbers it important? and beyond, other techniques can be learned, e.g. counting in jumps, e.g. 2,4,6,8 or 5,10,15,20 etc. Develop the ability to count with understanding of one to one Add\Subtract correspondence is crucial to develop future ability to carry out the four operations quickly and efficiently. Here are video exemplars: Place value developingcountingskillsalearnerusingjumpcountingskills1.asp Counting developingcountingskillsalearnerusingjumpcountingskills2.asp Developing counting skills The importance Multiply/Divide of zero Language Order of operations One-to-one correspondence Counting forwards and backwards Negative numbers Fractions, decimal fractions and percentages Applying across contexts

24 Number and number processes Numerals Counting Awareness of number Counting Quantities Mental agility Develop the ability to count with understanding of one to one Add\Subtract correspondence Language is crucial to develop future ability to carry out the four operations quickly and efficiently. Place value Language should be developed in order to compare size and quantity. Counting Developing counting skills The importance Multiply/Divide of zero Here is a video exemplar: countinglanguage.asp Language Order of operations One-to-one correspondence Counting forwards and backwards Negative numbers Fractions, decimal fractions and percentages Applying across contexts

25 Number and number processes Numerals Counting Counting forwards and backwards Awareness of number Counting Quantities Mental agility Place value Add\Subtract Develop the ability to count with understanding of one to one correspondence is crucial to develop future ability to carry out the four operations quickly and efficiently. Counting Developing counting skills The importance Multiply/Divide of zero Language Order of operations One-to-one correspondence Counting forwards and backwards Negative numbers This enables learners to use the counting system to count forwards or backwards from any number (including zero). Here are video exemplars: countingforwardsandbackwards1.asp countingforwardsandbackwards2.asp Fractions, decimal fractions and percentages Applying across contexts

26 Number and number processes Numerals Quantity Awareness of number Counting Quantities Place value Add\Subtract The concept of quantity enables the communication of value, amount, size and number of objects. Quantity Multiply/Divide Subitising Order of operations Arrays Negative numbers Fractions, decimal fractions and percentages Applying across contexts Mental agility Groupings

27 Number and number processes Awareness of number Numerals Quantity An amount. Quantities Quantity Here Counting are video exemplars: Place value Add\Subtract The concept of quantity enables the communication of value, amount, size and number of objects. Quantity Multiply/Divide Subitising Order of operations Arrays Negative numbers Fractions, decimal fractions and percentages Applying across contexts Mental agility Groupings

28 Number and number processes Subitising Numerals Quantity Recognising a quantity without counting, simply by looking. Here are video exemplars: Awareness of number Counting Quantities Place value Add\Subtract The concept of quantity enables the communication of value, amount, size and quantitysubitising3.asp number of objects. Quantity quantitysubitising1.asp quantitysubitising2.asp Multiply/Divide Subitising Order of operations Arrays Negative numbers Fractions, decimal fractions and percentages Applying across contexts Mental agility Groupings

29 Number and number processes Numerals Quantity Arrays Identify quantities and patterns to make quick estimates. Awareness of number Counting Quantities Place value Add\Subtract The concept of quantity enables the communication of value, amount, size and number of objects. quantityarrays2.asp Quantity Here are video exemplars: quantityarrays1.asp Multiply/Divide Subitising Order of operations Arrays Negative numbers Fractions, decimal fractions and percentages Applying across contexts Mental agility Groupings

30 Number and number processes Numerals Quantity Awareness of number Groupings What Counting is it? Quantities Add\Subtract The concept of quantity enables the communication of value, amount, size and number of objects. Recognise the amount of objects in a group and use this information to estimate the amount of objects in a larger Place value group. Here are video exemplars: Quantity Multiply/Divide Subitising Order of operations Arrays Negative numbers Fractions, decimal fractions and percentages Applying across contexts Mental agility Groupings

31 Number and number processes Numerals Mental agility Awareness of number Counting Quantities Add\Subtract Being able to visualise, hold and manipulate numbers helps to demonstrate Order of Place value an understanding of the number system and how operations it works. Multiply/Divide Mental agility Negative numbers Fractions, decimal fractions and percentages Applying across contexts Mental agility

32 Number and number processes Awareness of number Mental agility Numerals Counting Quantities Mental agility Mental agility is developed through understanding how to use and select appropriate strategies. The preferred method is often selected until the learner has developed confidence in identifying the most efficient method. Add\Subtract Being able to visualise, hold and manipulate number helps to demonstrate Order of Place value an understanding of the number system and how operations it works. Here is a video exemplar: mentalagility.asp Mental agility Multiply/Divide Negative numbers Fractions, decimal fractions and percentages Applying across contexts Mental agility

33 Number and number processes Numerals Place value Awareness of number Counting Quantities Mental agility The language to be used in place value is important for Add\Subtract communicating the value of a digit and its place within the number system. Place value Place value Grouping and partitioning Zero as a Multiply/Divide place holder Working with decimal fractions Order of operations Language of place value Mental agility Negative numbers Fractions, decimal fractions and percentages Applying across contexts

34 Number and number processes Awareness of number Place value What Numerals is it? Counting Quantities Mental agility Place value It is understanding how a number is composed and knowing its relationship to Why other is numbers. it important? It is the place of each of the digit or digits which makes a difference to the value of the number both in whole numbers and decimal fractions. The language to be used in place value is important for Add\Subtract communicating the value of a digit and its place within the number system. Here is a video exemplar: Place value Place value Grouping and partitioning Zero as a Multiply/Divide place holder Working with decimal fractions Order of operations Language of place value Mental agility Negative numbers Fractions, decimal fractions and percentages Applying across contexts

35 Number and number processes Zero as a place holder Awareness of number Numerals Counting Quantities Mental agility Place value The language to be used in place value is important for zeroplaceholder2.asp Add\Subtract communicating the value of a digit and its place within the number system. Place value Place value Grouping and partitioning The position of a digit gives its value and zero acts as a place holder and determines the value of the number. Here are video exemplars: zeroplaceholder1.asp zeroasaplaceholder3.asp Zero as a Multiply/Divide place holder Working with decimal fractions Order of operations Language of place value Mental agility Negative numbers Fractions, decimal fractions and percentages Applying across contexts

36 Number and number processes Language of place value Awareness of number Numerals Counting Quantities Mental agility Place value The language to be used in place value is important for Add\Subtract languageofplacevalue2.asp communicating the value of a digit and its place within the number system. Place value Place value Grouping and partitioning It is the place of the digit or digits which indicates the value of the number, whether a whole number or a decimal fraction. Learners need to be able to work with ones, tens, hundreds etc and tenths, hundredths and thousandths etc. Here are video exemplars: languageofplacevalue1.asp Zero as a Multiply/Divide place holder Working with decimal fractions languageofplacevalue3.asp Order of operations Language of place value Mental agility Negative numbers Fractions, decimal fractions and percentages Applying across contexts

37 Number and number processes Numerals Place value Awareness of number Grouping and The partitioning language to be used in place value is important for What Add\Subtract Counting is it? communicating the value of a digit and its place within the Both standard (e.g. 76 = ) and non-standard (e.g. number system. 76 = or ) partitioning should be taught as both will assist learners in Place their mental value calculations. Here is a video exemplar: Quantities Place value groupingandpartitioning.asp Mental agility Grouping and partitioning Zero as a Multiply/Divide place holder Working with decimal fractions Order of operations Language of place value Mental agility Negative numbers Fractions, decimal fractions and percentages Applying across contexts

38 Number and number processes Awareness of number Numerals Counting Quantities Mental agility Place value Working with decimal fractions It is the place of a digit or digits which determines the value of the number, whether a whole number or decimal fraction. Zero within a decimal fraction acts as a place The language holder. to The be decimal used point place separates value the is whole important numbers for Add\Subtract communicating from the the fractions value e.g. of it separates a digit and the units (or place ones) within from the the tenths. The decimal point does not move. number system. Here are video exemplars: Place value Place value Grouping and partitioning workingwithdecimalfractions1.asp Zero as a Multiply/Divide place holder workingwithdecimalfractions2.asp Working with decimal fractions Order of operations Language of place value Mental agility Negative numbers Fractions, decimal fractions and percentages Applying across contexts

39 Number and number processes Awareness of number Numerals Counting Quantities Mental agility Place value Mental agility The language to be used in place value is important for Add\Subtract communicating the value of a digit and its place within the within their mental calculations. number system. Place value Place value Grouping and partitioning Zero as a Multiply/Divide place holder Working with decimal fractions Order of operations Language of place value Mental agility Negative numbers Developing the ability to use efficient methods to calculate mentally and confidently using knowledge of place value Here are video exemplars: pvmentalagility1.asp pvmentalagility2.asp Fractions, decimal fractions and percentages Applying across contexts

40 Number and number processes Numerals Addition and Subtraction Awareness of number Counting Quantities Mental agility Add\Subtract Being able to add and subtract mentally and on paper is a key Order of life skill Place and value provides the foundation for the understanding of operations multiplication and division. Addition and Subtraction Multiply/Divide Relationship between addition and subtraction Algorithms Negative numbers Fractions, decimal fractions and percentages Applying across contexts

41 Number and number processes Addition and subtraction Awareness of number These are inverse operations and must be taught together. Numerals Addition is the process of combining two or more quantities Addition to calculate and their sum subtraction or total. Subtraction is the difference between two quantities. Learners should carry out calculations to solve real life problems in familiar Why practical is it important? contexts and become Add\Subtract increasingly Counting fluent in addition and subtraction. Quantities Mental agility Being able to add and subtract mentally and on paper is a key Order of life skill Place and value provides the foundation for the understanding of operations Here is a video exemplar: additionandsubtraction.asp multiplication and division. Addition and Subtraction Multiply/Divide Relationship between addition and subtraction Algorithms Negative numbers Fractions, decimal fractions and percentages Applying across contexts

42 Number and number processes Awareness of number Numerals Counting Quantities Mental agility Relationship between addition and subtraction Exploring the relationship between addition and subtraction. Addition and subtraction need to be taught together e.g. highlighting that subtraction can be calculated by adding on. Recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve Addition missing and number subtraction problems. Here are video exemplars: relationshipbetweenadditionandsubtraction1.asp Add\Subtract Being able to add and subtract mentally and on paper is a key relationshipbetweenadditionandsubtraction2.asp Order of life skill Place and value provides the foundation for the understanding of operations multiplication and division. Addition and subtraction relationshipbetweenadditionandsubtraction3.asp Multiply/Divide Relationship between addition and subtraction Algorithms Negative numbers Fractions, decimal fractions and percentages Applying across contexts

43 Number and number processes Algorithms Awareness of number Numerals Counting Quantities Mental agility Addition and subtraction Algorithms should be introduced after practical experiences and understanding the concepts of addition and subtraction. Reading, writing and interrogating mathematical statements involving +, -, = signs. This includes working out the missing number in a mathematical statement. Written methods Negative support Add\Subtract place value and working with larger numbers. numbers Being able to add and subtract mentally and on paper is a key Order of life skill Place and value provides the foundation for the understanding of operations multiplication and division. Addition and subtraction Multiply/Divide Relationship between addition and subtraction Here is a video exemplar: Algorithms Fractions, decimal fractions and percentages Applying across contexts

44 Number and number processes Multiplication and Division Awareness of number Numerals Counting Quantity Mental agility Grouping and sharing small quantities to develop understanding of multiplication and division. Doubling number quantities and finding simple fractions of Add\Subtract objects, numbers and quantities. Multiplication and division are inverse operations which should be taught together. Multiplication and division are Order linked of initially Place value with repeated addition approaches involving increasing operations sets or amounts. Division is initially linked to repeated subtraction and involves decreasing quantities Multiply/Divide by set amounts or sharing equally. Symbols are used to represent multiplication and division (x, ). Multiplication and Division Relationship between multiplication and division Negative numbers Fractions, decimal fractions and percentages Applying across contexts

45 Number and number processes Awareness of number Multiplication and Division Quantities Mental agility Multiplication and division Grouping and sharing small quantities to develop Numerals understanding of multiplication and division. Doubling number quantities and finding simple fractions of objects, numbers and quantities. Multiplication and division are inverse operations which should be taught together. Multiplication and division is linked initially with repeated addition approaches involving increasing Countingsets or amounts. Division is initially linked to repeated subtraction and involves decreasing quantities by set amounts or sharing equally. Symbols are used to represent multiplication and division (x, ). Being able to multiply and divide mentally and on paper is Add\Subtract a key life skill. Learners should understand the relationship between multiplication divisions to be able to carry out Order of calculations Place value efficiently including work with fractions. operations It is important that children are taught to appreciate and make use of this mathematical Multiply/Divide relationship when developing and using mental calculation strategies. Here is a video exemplar: multiplicationanddivision.asp Multiplication and Division Relationship between multiplication and division Negative numbers Fractions, decimal fractions and percentages Applying across contexts

46 Number and number processes Awareness of number Numerals Counting Quantity Mental agility Relationship between multiplication and division Knowing how to find multiplication and division facts, including use of partitioning and the inverse operation. Being able to recall a particular multiplication fact and being able to use this to solve related multiplication and division tasks. The set of related facts is known as a fact family. Using relationships to support recall and being able to manipulate numbers facts mentally, accurately and confidently. Using knowledge of division when working with fractions e.g. ½ of 40. The relationship between digits in the decimals system should be highlighted when multiplying and dividing by 10, 100, 1000 etc. Multiplication Here are video exemplars: and division Being able to multiply and divide mentally and on paper is Add\Subtract a key life skill. icationanddivision2.asp Learners should understand the relationship between multiplication divisions to be able to carry out icationanddivision3.asp Order of calculations Place value efficiently including work with fractions. operations It is important that icationanddivision4.asp children are taught to appreciate and make use of this mathematical Multiply/Divide relationship when developing and using mental icationanddivision5.asp calculation strategies. Multiplication and Division licationanddivisionmandd.asp icationanddivision1.asp Relationship between multiplication and division Negative numbers Fractions, decimal fractions and percentages MAIN MENU Applying across contexts

47 Number and number processes Numerals Order of operations Awareness of number Counting Quantity Mental agility Add\Subtract An understanding of commutative, distributive and associative properties enables the development of more Order of efficient Place calculations. value Rules established to support operations carrying out calculations that involve more than one operation. Order of operations Multiply/Divide Understanding and application of the order of operations Commutative, distributive and associative properties Negative numbers Fractions, decimal fractions and percentages Applying across contexts

48 Number and number processes Awareness of number Numerals Order of operations Quantities Mental agility Order of operations There is a set order of operations used within calculations involving more than one operation, e.g. + and x. Counting Here are video exemplars: Add\Subtract An understanding of commutative, distributive and associative properties enables the development of more Order of efficient Place calculations. value Rules established to support operations carrying out calculations that involve more than one operation. orderofoperations1.asp orderofoperations2.asp Order of operations Multiply/Divide Understanding and application of the order of operations Commutative, distributive and associative properties Negative numbers Fractions, decimal fractions and percentages Applying across contexts

49 Number and number processes Understanding and application of the order of operations Awareness of number Numerals Counting Quantity Mental agility At the introductory stage the order of operations applies to the four basic operations, where multiplication and division have equal priority and addition and subtraction have equal priority. Order of operations This can then be extended to include brackets and indices. The use of mnemonics such as BODMAS, BIDMAS and BOMDAS are often used when deciding on the order of operations. Here are video exemplars: Add\Subtract An understanding numeracyacrosslearningapplication.asp of commutative, distributive and associative properties enables the development of more Order of efficient Place calculations. value understandingandapplication1.asp Rules established to support operations carrying out calculations that involve more than one operation. Order of operations understandingandapplication2.asp Multiply/Divide Understanding and application of the order of operations Commutative, distributive and associative properties Negative numbers Fractions, decimal fractions and percentages Applying across contexts

50 Number and number processes Awareness of number Numerals Counting Quantity Mental agility Order of operations Add\Subtract An understanding of commutative, Here are video exemplars: distributive and associative properties enables the development of more Order of efficient Place calculations. value Rules established to support operations carrying out calculations that involve more than one operation. Order of operations Commutative, distributive and associative properties The commutative law states that you can swap numbers around (within a calculation) and still get the correct answer. The commutative law and inverse relationship develops multiplicative reasoning. The distributive law states that multiplying a number by a group of numbers added together is the same as doing each multiplication separately. The associative law states: It doesn t matter how you group the numbers when you add It doesn t matter how you group the numbers when you multiply Multiply/Divide Understanding and application of the order of operations Commutative, distributive and associative properties Negative numbers Fractions, decimal fractions and percentages Applying across contexts

51 Number and number processes Numerals Negative numbers Awareness of number Counting Quantity Mental agility Understanding negative Add\Subtract numbers is important for real life applications such as temperature measurements, graphs and charts and budgeting. Place value Negative numbers Calculations Multiply/Divide Integers Application in real life contexts Order of operations Ordering Negative numbers Fractions, decimal fractions and percentages Applying across contexts

52 Number and number processes Numerals Negative numbers Awareness of number Negative numbers Numbers which are Understanding less than zero. negative Add\Subtract numbers is important for real life Counting Here is a video applications exemplar: such as temperature measurements, graphs and negativenumbers.asp charts and budgeting. Quantity Mental agility Place value Negative numbers Calculations Multiply/Divide Integers Application in real life contexts Order of operations Ordering Negative numbers Fractions, decimal fractions and percentages Applying across contexts

53 Number and number processes Awareness of number Numerals Counting Quantity Mental agility Integers Negative numbers The term integer is used when working with positive and negative whole numbers. Integer calculations set in a context involve an understanding of how to deal with Understanding negative negative numbers within Add\Subtract numbers the 4 operations. is important for real life applications such Here as is a temperature video exemplar: measurements, graphs and charts and budgeting. Place value Negative numbers Calculations Multiply/Divide Integers Application in real life contexts Order of operations Ordering Negative numbers Fractions, decimal fractions and percentages Applying across contexts

54 Number and number processes Numerals Negative numbers Ordering Awareness of number Counting Quantity Mental agility Understanding negative Add\Subtract numbers line is or important measuring device. for real life applications such as temperature measurements, Here is a video exemplar: graphs and charts and budgeting. Place value Negative numbers Calculations Multiply/Divide Integers Application in real life contexts Recognising the position of negative numbers on a number Order of operations Ordering Negative numbers Fractions, decimal fractions and percentages Applying across contexts

55 Number and number processes Numerals Negative numbers Awareness of number Calculations Counting Mental agility Understanding negative Add\Subtract numbers is important for real life applications such as temperature measurements, graphs and charts and budgeting. Effect of negative numbers within calculations involving Place value the 4 operations, e.g. double negatives. Here is a video exemplar: Quantities Negative numbers Calculations Multiply/Divide Integers Application in real life contexts Order of operations Ordering Negative numbers Fractions, decimal fractions and percentages Applying across contexts

56 Number and number processes Numerals Negative numbers Awareness of number Counting Quantity Mental agility Understanding negative Add\Subtract numbers is important for real life applications Application such as in temperature real life contexts measurements, graphs and charts and budgeting. Order of Place Applying value knowledge and understanding of negative operations numbers within real life contexts. Here is a video exemplar: Negative numbers Multiply/Divide Integers Ordering Calculations applicationinreallife.asp Application in real life contexts Negative numbers Fractions, decimal fractions and percentages Applying across contexts

57 Number and number processes Numerals Fractions, decimal fractions and percentages Awareness of number Counting Quantity Mental agility Add\Subtract The ability to see fractions, decimal fraction and percentages Order of as operators Place value rather than just a number. The ability to solve operations problems involving fractions, decimal fractions and percentages using a wide variety of methods is an important life skill. Fractions, decimal fractions and percentages Multiply/Divide Inter-relationship Negative numbers Fractions, decimal fractions and percentages Applying across contexts

58 Number and number processes Awareness of number Numerals Fractions, decimal fractions and percentages and percentages Working with fractions involves using times tables skills and Counting Quantities Mental agility Fractions, decimal fractions the links between Why multiplication is it important? and division facts. Understanding of place value is crucial. Add\Subtract The ability to see fractions, decimal fraction and percentages Here are video exemplars: Order of as operators Place value rather than just a number. The ability to solve operations problems involving fractions, decimal fractions and percentages using a wide variety of methods is an important life skill. Fractions, decimal fractions and percentages Multiply/Divide Inter-relationship Negative numbers Fractions, decimal fractions and percentages Applying across contexts

59 Number and number processes Numerals Fractions, decimal fractions and percentages Inter-relationship Awareness of number Counting Quantity Mental agility Add\Subtract The ability to see fractions, decimal fraction and percentages Order of as operators Place value rather and how than to convert just a from number.the one form to another. ability to solve operations problems involving fractions, Here is a video decimal exemplar: fractions and percentages using a wide variety of methods is an important life skill. Fractions, decimal fractions and percentages Being able to express and understand the inter-relationship between fractions, decimal fractions and percentages. Knowing that numbers can be expressed in different forms Multiply/Divide fdfandpinterrelationships.asp Inter-relationship Negative numbers Fractions, decimal fractions and percentages Applying across contexts

60 Number and number processes Numerals Applying across contexts Awareness of number Counting Quantity Mental agility Being able to apply numeracy Add\Subtract skills across a variety of real life contexts leads to being numerate and being able to function Order of Place responsibly value in everyday life, contribute effectively to society and increase our opportunities within operations the world of work. Applying across contexts Multiply/Divide Negative numbers Fractions, decimal fractions and percentages Applying across contexts

61 Number and number processes Awareness of number Applying across contexts Numerals Counting Quantities Mental agility Applying across contexts Exposure to a range of different strategies and methods for applying number Why processes. is it important? Application of the correct strategy to solve one step and multi-step problems using the most efficient methods. Being able to apply numeracy Add\Subtract skills across a variety of real life contexts leads to being numerate and being able to function Order of Place responsibly value in everyday life, contribute effectively to society and increase our opportunities within operations the world of work. Here are video exemplars: applyingacrosscontextslearner2.asp applyingacrosscontexts.asp Applying across contexts Multiply/Divide Negative numbers Fractions, decimal fractions and percentages Applying across contexts

62 Fractions, decimal fractions and percentages Decimal fractions and place value Concept of a whole and parts Concept of a fraction Fractional notation and vocabulary Relationship between fractions, multiplication and division Fractions Equivalent forms Relationships that link fractions, decimal fractions and percentages Applying across contexts Percentages

63 Fractions, decimal fractions and percentages Concept of a whole and parts To develop an understanding of fractions learners must have knowledge and understanding of what is meant by a whole or a part. Decimal fractions and place values Concept of a whole and parts Concept of a fraction Concept of a whole Fractional and parts notation and vocabulary Equal parts Relationship One object, shape or A group of items between quantity can be Equivalent fractions, shared into parts can be shared out Fractions forms multiplication and division Percentages Relationships that link fractions, decimal fractions and percentages Applying across contexts

64 Fractions, decimal fractions and percentages Concept of a whole Concept or a partof a whole and parts A whole can represent Why one is item important? a group of items. Previous knowledge To develop and understanding understanding of fractions learners must have Awareness of vocabulary knowledge related and to understanding wholes partsof what is meant by a whole Awareness that or a part a part. of an object, shape or group is less than the whole Decimal fractions and place values Concept of a whole and parts Concept of a fraction Concept of Fractional a whole or a part notation and vocabulary Equal parts Relationship One object, shape or A group of items between quantity can be Equivalent fractions, shared into parts can be shared out Fractions forms multiplication and division Percentages Relationships that link fractions, decimal fractions and percentages Applying across contexts

65 Fractions, decimal fractions and percentages splitting into tenths and each part is an equal 10th. Concept of a whole or a part Concept of a whole and parts Concept of a fraction One object, shape or quantity can be shared into equal parts When an object, shape or quantity is split into two equal parts then each part is one half. When an item is split into two unequal parts then these two parts are not halves. This principle applies to all unitary fractions, e.g. Previous knowledge and understanding Awareness that a part of an object, shape or group is less than the Why whole is it important? Understand and demonstrate the concept of sharing Understand and demonstrate the concept of sharing fairly knowledge Have experience and understanding of sharing real of life what situations, is meant by a whole Decimal e.g. with siblings, in or play a part. situations fractions and place values To develop an understanding of fractions learners must have Concept of Fractional a whole or a part notation and vocabulary Equal parts Relationship One object, shape or A group of items between quantity can be Equivalent fractions, shared into parts can be shared out Fractions forms multiplication and division Percentages Relationships that link fractions, decimal fractions and percentages Applying across contexts

66 Fractions, decimal fractions and percentages Concept of a whole and parts Concept of a whole and parts Concept of a fraction Concept of Fractional a whole or a part notation and vocabulary Previous knowledge and understanding Awareness of sharing fairly and splitting a group of items Have experience Decimal of sharing out items in a variety of contexts fractions and place values To develop an understanding of fractions learners must have knowledge and understanding of what is meant by a whole or a part. Equal parts A group of items can be shared out Sharing a collection of items into equal groups and into groups which are not equal. Relationship One object, shape or A group of items between quantity can be Equivalent fractions, shared into parts can be shared out Fractions forms multiplication and division Percentages Relationships that link fractions, decimal fractions and percentages Applying across contexts

67 Fractions, decimal fractions and percentages Concept of a whole and parts Concept of a whole and parts Equal partsto develop an understanding of fractions learners must have knowledge and understanding of what is meant by a whole Decimal Equal parts can or form a part. a whole. fractions and place values Previous knowledge and understanding Is able to identify and Concept explain ofwhen Relationship an object, One object, shape or A group of items Fractional Concept of a a whole or a part between quantity can be shape or quantity has not been split/shared Equivalent notation and fractions, shared into parts can be shared out Fractions fraction equally. forms vocabulary multiplication and division Equal parts Percentages Relationships that link fractions, decimal fractions and percentages Applying across contexts

68 Fractions, decimal fractions and percentages Concept of a fraction Understanding this concept is needed to appreciate the notation of fractions. When working with a fraction it is essential to understand that the denominator denotes the number of equal parts. Decimal fractions and place values Concept of a whole and parts Concept of a fraction Fractional Concept of notation a fraction and vocabulary Relationship between Fractions with fractions, equal parts multiplication and division Fractions Sharing with a remainder Equivalent forms Relationships that link fractions, decimal fractions and percentages Applying across contexts Equal sharing Percentages

69 Fractions, decimal fractions and percentages Concept of a Concept fraction of a fraction Concept of a whole and parts That a whole can be separated into equal parts. These parts are called fractions. Understanding this concept is needed to appreciate the Previous knowledge notation and of understanding fractions. When working with a fraction it is Understand that a whole can be split into smaller essential to understand that the denominator denotes the parts number of equal parts. Understand the term equal Concept of a fraction Fractional Concept of notation a fraction and vocabulary Equal sharing Relationship between Fractions with fractions, equal parts multiplication and division Decimal fractions and place values Fractions Percentages Sharing with a remainder Equivalent forms Relationships that link fractions, decimal fractions and percentages Applying across contexts

70 Fractions, decimal fractions and percentages Fractions with equal parts Concept of a fraction Concept of a whole and parts Concept of a fraction Understanding that fractions of a whole are equal parts. Previous knowledge and understanding Understand that a whole can be split into smaller parts Understand the term equal Decimal Is aware of the relationship between equal fractions and the fractions and whole place values Understanding this concept is needed to appreciate the notation of fractions. When working with a fraction it is essential to understand that the denominator denotes the number of equal parts. Fractional Concept of notation a fraction and vocabulary Equal sharing Relationship between Fractions with fractions, equal parts multiplication and division Fractions Percentages Sharing with a remainder Equivalent forms Relationships that link fractions, decimal fractions and percentages Applying across contexts

71 Fractions, decimal fractions and percentages Concept of a fraction Concept of a whole and parts Concept of a fraction Fractional Concept of notation a fraction and vocabulary Relationship between Fractions with fractions, equal parts multiplication and division Previous knowledge and understanding Experience of one to one correspondence Understand equal sharing Decimal Experience of sharing out items in a variety of fractions and contexts place values Understanding this concept is needed to appreciate the notation of fractions. When working with a fraction it is essential to understand that the denominator denotes the number of equal parts. Equal sharing Sharing with a remainder Awareness that when a group of items is shared equally there may be some left over. This is known as the remainder. Fractions Percentages Sharing with a remainder Equivalent forms Relationships that link fractions, decimal fractions and percentages Applying across contexts

72 Fractions, decimal fractions Concept of a whole and parts and percentages Concept of a fraction Equal sharing Understanding this concept is needed to appreciate the Splitting a group notation of items of equally fractions. into a number When working with a fraction it is of smaller groups. essential This underpins to understand the concept that of the denominator denotes the fractions. number of equal parts. Previous knowledge and understanding Relationship Understand the Fractional term Concept equal of Concept of a between Fractions with Have experience notation of a sharing fraction and out items fraction fractions, in a variety equal parts of contexts vocabulary multiplication and division Decimal fractions and place values Fractions Sharing with no remainder Equivalent forms Relationships that link fractions, decimal fractions and percentages Applying across contexts Equal sharing Percentages

73 Fractions, decimal fractions and percentages Fractional notation and vocabulary Concept of a whole and parts Concept of a fraction Understanding fractional notation aids communication, reinforces the concept of equal sharing Decimal and can be developed further to investigate equivalent fractions. Understanding what place values the two numbers that make up a fraction represent, allows for calculations to be made. Fractional notation and vocabulary Fractional notation and vocabulary Relationship between fractions, Fractions multiplication Numerator and and division denominator Equivalent forms Relationships that link fractions, decimal fractions and percentages Applying across contexts Percentages

74 Fractions, decimal fractions and percentages Concept of a whole and parts Concept of a fraction Fractional notation and vocabulary Fractional notation and vocabulary Fractional notation Why is is used it important? to find, name and write fractions of a length, shape, object or quantity. Understanding fractional notation aids communication, reinforces the concept of equal sharing Decimal Previous knowledge and understanding and can be developed Awareness that further fractional to investigate notation has equivalent a top and fractions. Understanding what place values bottom number, the two e.g. 1/2 numbers that make up a fraction represent, allows for calculations to be made. Fractional notation and vocabulary Fractional notation and vocabulary Relationship between fractions, Fractions multiplication Numerator and and division denominator Percentages Equivalent forms Relationships that link fractions, decimal fractions and percentages Applying across contexts

75 Fractions, decimal fractions and percentages Numerator and denominator Concept of a whole and parts Concept of a fraction Fractional notation and vocabulary Numerator indicates the number of equal parts. Denominator indicates the number of equal parts the unit is divided into. The greater the numerator the more parts there are. The greater the denominator the more parts the whole has been divided Decimal into. fractions and Previous knowledge and understanding place values Understand that the top and bottom number of a fraction mean Relationship different things Fractional between Equivalent notation and fractions, Fractions forms vocabulary Fractional notation multiplication Numerator and and vocabulary and division denominator Understanding fractional notation aids communication, reinforces the concept of equal sharing and can be developed further to investigate equivalent fractions. Understanding what the two numbers that make up a fraction represent, allows for calculations to be made. Percentages Relationships that link fractions, decimal fractions and percentages Applying across contexts

76 Fractions, decimal fractions and percentages Relationship between fractions, multiplication and division Concept of a whole and parts Concept of a fraction Decimal Understanding the link between fractions fractions and and multiplication leads to an understanding of percentages place and values the application of multiplication and division in calculations such as those involving ratio. Relationship Fractional between notation and fractions, vocabulary multiplication Relationship between and fractions, division multiplication and divisions Fractions Equivalent forms Relationships that link fractions, decimal fractions and percentages Applying across contexts Percentages

77 Fractions, decimal fractions and percentages Relationship between fractions, multiplication Concept of a whole and parts and division Relationship between fractions, multiplication and division There is a direct link between finding a fraction of an object or a quantity and multiplication and division. Understanding the link between fractions and multiplication leads to an understanding of percentages and the application of multiplication and division in calculations such as those Decimal Previous knowledge and understanding fractions and Apply multiplication facts and corresponding division facts place values (inverse operations) to whole numbers Understand Relationship involving the role of Fractional ratio. numerator and denominator in a fraction Concept of a between notation and fractions, Fractions fraction vocabulary multiplication Relationship between and fractions, division multiplication and divisions Percentages Equivalent forms Relationships that link fractions, decimal fractions and percentages Applying across contexts

78 Fractions, decimal fractions and percentages Decimal fractions and place value Concept of a whole and parts Concept of a fraction Understanding decimal fractions is important Decimal for conversion in measurement and understanding what fractions proportion and of a whole place values is represented. It is also important relative to interpreting answers generated through the use of calculators. Fractional notation and Decimal vocabulary fractions and place value Relationship between fractions, Fractions multiplication The decimal point and division Equivalent forms Relationships that link fractions, decimal fractions and percentages Applying across contexts Percentages

79 Fractions, decimal fractions Decimal fractions and place value and What percentages is it? Learning and teaching about decimal fractions is an extension of learners understanding of place value. There is a multiplicative relationship between the Decimal fractions and place value decimal places and the value of the positions increases in powers of 10 from right to left. Moving left from the decimal point the powers of 10 increase and moving right from the decimal point the powers of 10 decrease. There are many contexts for learning about decimal fractions, e.g. money and measurement. Understanding decimal fractions is important for conversion in measurement and understanding what proportion of a whole is represented. It is also important relative to interpreting answers generated through the use of calculators. Decimal Previous knowledge and understanding fractions and Have a knowledge of place value and its role in calculation place values Have an awareness that not all numbers are whole numbers Relationship Concept of a Fractional Concept of a between whole notation and fractions, Fractions fraction and parts Decimal vocabulary fractions multiplication The decimal point and place value and division Percentages Equivalent forms Relationships that link fractions, decimal fractions and percentages Applying across contexts

80 Fractions, decimal fractions and percentages Concept of a whole and parts Concept of a fraction The decimal point In order to successfully manipulate numbers, learners need to have a conceptual understanding of place value, including the role of the decimal point. The decimal point separates the whole numbers from the fractions and is placed between the units (or ones) and the tenths. It is important to ensure that when multiplying or dividing by multiples of 10, learners understand that the decimal point does not move. Decimal fractions and place value Understanding decimal fractions is important for conversion in measurement and understanding what proportion of a whole is represented. It is also important relative to interpreting answers generated through the use of calculators. Previous knowledge and understanding Decimal Can talk about the multiplicative relationship fractions and between the digits in whole numbers place values Can give examples of where the decimal point can be seen in real life contexts, Relationship e.g. money 2.39, measurement 2.5l of paint Fractional between Equivalent notation and fractions, Fractions forms Decimal vocabulary fractions multiplication The decimal point and place value and division Percentages Relationships that link fractions, decimal fractions and percentages Applying across contexts

81 Fractions, decimal fractions and percentages Fractions Concept of a whole and parts Concept of a fraction Decimal Working with fractions is an important fractions skill and in the world of work and daily life. place values Fractional notation Fractions and vocabulary Relationship between fractions, multiplication and division Fractions Equivalent forms Relationships that link fractions, decimal fractions and percentages Applying across contexts Percentages

82 Fractions A proper fraction is when the numerator is less than the denominator e.g ½. An improper fraction is when the numerator is more than the denominator, e.g. 3/2. A fraction expresses a part of a whole. When carrying out calculations, the most appropriate form of a fraction Fractions, decimal fractions should be used, e.g. 6/100 of 500 (calculate 1/100 then multiply by 6, rather than 3/50 which is the fraction in its simplest form). and percentages Previous knowledge and understanding Apply multiplication facts and corresponding division facts (inverse operations) to whole numbers Fractions Know that the numerator is the number on the top of a fraction Know that the denominator is the number on the bottom of a fraction Know that the numerator shows Why the number is it important? of equal parts Decimal Know that the denominator shows the total number of parts the whole has fractions been split and into Understand that the larger the denominator is, the greater the number of of work and daily life. place parts values the whole has been split into Concept of a whole and parts Concept of a fraction Working with fractions is an important skill in the world Fractional notation Fractions and vocabulary Relationship between fractions, multiplication and division Fractions Percentages Equivalent forms Relationships that link fractions, decimal fractions and percentages Applying across contexts

83 Fractions, decimal fractions and percentages Percentages Concept of a whole and parts Concept of a fraction Percentages are used in a wide variety of contexts, many Decimal of which are used in everyday life. Understanding that fractions and percentages are a specific way of representing place values fractions with a denominator of 100 can support understanding of the relationships between fractions, decimal fractions. Fractional notation and vocabulary Percentages Relationship between fractions, multiplication and division Fractions Equivalent forms Relationships that link fractions, decimal fractions and percentages Applying across contexts Percentages

84 Fractions, decimal fractions and percentages Percentages Concept of a whole and parts Percentages Percent means out of 100 therefore 100% is equivalent to one whole. Percentages are used in a wide variety of contexts, many Previous knowledge Decimal of and which understanding are used in everyday life. Understanding that Have a knowledge of fractions and decimal fractions fractions and percentages are a specific way of representing place values fractions with Can give examples of where they have experienced percentages in real a denominator life, e.g. 2% battery of 100 left, can 50% support off sale understanding of the relationships between Relationship Have a knowledge of fractions, decimal fractions. Fractional place value and its role in calculation Concept of a between Equivalent notation and fractions, Fractions fraction forms vocabulary multiplication Percentages and division Percentages Relationships that link fractions, decimal fractions and percentages Applying across contexts

85 Fractions, decimal fractions Concept of a whole and parts Concept of a fraction and percentages Equivalent forms This understanding leads to confidence when using fractions in calculations and in relation to decimal fractions and percentages. Knowledge and understanding Decimal of equivalences can help to make calculations simpler fractions when and carrying out calculations in relation to fractions, place decimal values fractions and percentages. Fractional notation and vocabulary Equivalent forms Relationship between fractions, multiplication and division Fractions Equivalent forms Relationships that link fractions, decimal fractions and percentages Applying across contexts Percentages

86 Fractions, decimal fractions Equivalent forms and percentages Equivalent forms Fractions which have the same value, even though they may Concept of a whole and parts look different, e.g. 1/2 and 2/4 are equivalent, because they are both equal to a half. The simplest form of a fraction can be used to support efficient calculation skills. Understanding that fractions expressed in different ways can be equal in value. This understanding leads to confidence when using fractions in calculations and in relation to decimal fractions and percentages. Knowledge and understanding of equivalences can help to make calculations simpler when carrying out calculations in relation to fractions, decimal fractions and percentages. Previous knowledge and understanding Decimal Apply multiplication facts and corresponding division facts fractions and (inverse operations) to whole numbers place values Know that equivalent means an equal value Know and understand fractional notation Relationship and know the Fractional Concept relationship of a between fractions, decimal between fractions and notation and fractions, Fractions fraction percentages, e.g. 3/4= 3 divided by 4 = 0.75 = 75% vocabulary multiplication and division Equivalent forms Percentages Equivalent forms Relationships that link fractions, decimal fractions and percentages Applying across contexts

87 Fractions, decimal fractions and percentages Relationships that link fractions, decimal fractions and percentages Concept of a whole and parts Concept of a fraction Decimal The ability to interchange between fractions a fraction, and decimal fraction and percentage is a skill that place allows values for different ways to solve problems efficiently, including mental calculations. Relationship Fractional between notation and Relationships that link fractions, Comparisons Fractions between fractions, vocabulary decimal fractions multiplication fractions, decimal fractions and percentagesand division and percentages Equivalent forms Relationships that link fractions, decimal fractions and percentages Applying across contexts Percentages

88 Fractions, decimal Understand the relationship between fractions, decimal fractions and percentages. Ability to change between the different forms for the and percentages most efficient ways of carrying out calculations, in different contexts. Concept of a whole and parts Relationships that link fractions, decimal fractions and percentages Previous knowledge and understanding Is aware that hundredths can be written as a fraction, decimal fraction or a percentage fractions and percentages Can multiply and divide whole numbers and decimal fractions by multiples of 10 Be able to place fractions, decimal fractions and percentages on Decimal a number line fractions and Know and understand fractional notation specifically that e.g. place 3/4 = values 3 divided by 4 = 0.75 etc. Concept of a fraction Relationships that link fractions, decimal The ability to interchange between a fraction, decimal fraction and percentage is a skill that allows for different ways to solve problems efficiently, including mental calculations. Relationship Fractional between notation and Relationships that link fractions, Comparisons Fractions between fractions, vocabulary decimal fractions multiplication fractions, decimal fractions and percentagesand division and percentages Percentages Equivalent forms Relationships that link fractions, decimal fractions and percentages Applying across contexts

89 Fractions, Comparisons between fractions, decimal fractions and percentages and percentages Concept of a whole and parts Concept of a fraction Being able to place different forms in order on a number line and know the Relationships relative value that of each link one. fractions, decimal fractions and percentages Previous knowledge and understanding When given different representations can convert to most appropriate form Have a knowledge of place value Decimal with decimals and whole numbers Be able to order decimals on fractions a number and line Knowledge of the concept of place hundredths values and its equivalent forms Can place examples of the same form in order Relationships Relationship Fractional that link between Equivalent notation and fractions, Relationships that link fractions, Comparisons Fractions between forms vocabulary decimal fractions, decimal fractions multiplication fractions, decimal fractions fractions and and percentagesand division and percentages percentages The ability to interchange between a fraction, decimal fraction and percentage is a skill that allows for different ways to solve problems efficiently, including mental calculations. Applying across contexts Percentages

90 Fractions, decimal fractions and percentages Applying across contexts Concept of a whole and parts Concept of a fraction Being able to carry out calculations and Decimal move between different forms is an important skill. fractions Choosing and the most place values important form to display the answer depends on context. Relationship Fractional between Equivalent notation Applying and across fractions, Linking fractions Fractions forms vocabulary contexts multiplication Proportion and ratio and division Relationships that link fractions, decimal fractions and percentages Applying across contexts Percentages

91 Fractions, decimal fractions display the answer depends on context. and percentages Concept of a whole and parts Applying across contexts Being able to carry out calculations and move between different forms is an important skill. Choosing the most important form to Previous knowledge and understanding Has experience of fractions, decimal fractions and percentages in a range of contexts including new and unfamiliar situations Applying across contexts Can place examples of the same form in order Can convert between Why forms is it to important? assist ordering a variety of fractions, decimal fractions and percentages Can select the most appropriate strategy when approaching a Decimal calculation fractions and Can convert between fractions, decimal fractions and place values percentages to assist ordering when written in different forms Relationship Fractional Concept of a between notation and fractions, Fractions fraction Applying across Linking fractions vocabulary contexts multiplication and ratio and division Being able to carry out calculations and move between different forms is an important skill. Choosing the most important form to display the answer depends on context. Percentages Equivalent Proportion forms Relationships that link fractions, decimal fractions and percentages Applying across contexts

92 Fractions, decimal Linking fractions and ratios fractions and percentages comparisons and carry out calculations. Concept of a whole and parts Concept of a fraction Understanding how ratio links to fractions. Numbers in a given ratio can be expressed in fractional form. In its fractional form it is easier to make Applying across contexts Previous knowledge and understanding Apply multiplication facts and corresponding division facts (inverse operations) to whole numbers Being Know able how to carry construct out a calculations ratio from a problem and Decimal move in context between Apply knowledge of fractions to problems different forms is an important skill. fractions in context Choosing and the most Awareness of real life examples of ratio place vocabulary, values e.g. diluting juice important Knowledge form and role to display of numerator the answer and denominator depends on context. Relationship Fractional between Equivalent notation Applying and across fractions, Linking fractions Fractions forms vocabulary contexts multiplication Proportion and ratio and division Percentages Relationships that link fractions, decimal fractions and percentages Applying across contexts

93 Fractions, decimal Proportion fractions and percentages Concept of a whole and parts Concept of a fraction Applying across contexts Fractional notation Applying and across vocabulary contexts Two variables are proportional if a change in one is always accompanied by a change in the other. As one quantity increases or decreases another quantity increases or decreases in proportion. Previous knowledge and understanding Awareness that multiplication and division are inverse operations Apply multiplication facts and corresponding division facts (inverse operations) to whole numbers Decimal Awareness of practical concept of proportion fractions and Apply multiplication facts and corresponding division facts place values (inverse operations) to fractions Being able to carry out calculations and move between different forms is an important skill. Choosing the most important form to display the answer depends on context. Relationship between fractions, Linking fractions Fractions multiplication and ratio and division Equivalent Proportion forms Relationships that link fractions, decimal fractions and percentages Applying across contexts Percentages

94 Money Exchange money for goods and services Awareness of money Coins and notes Understanding money in a digital world Understanding risks and rewards Analyse the impact of financial decisions Money calculations Developing financial capability

95 Money Awareness of money Awareness of money Exchange money for goods and services An early appreciation of the contexts in which money is used is Understanding Understanding Coins important. and This includes an awareness that money is valuable money in a risks and notes and there is a need to keep it safe. In doing so young people will digital world rewards appreciate the difference between needs and wants. Awareness of money Money calculations Analyse the impact of financial decisions Developing financial capability

96 Money Awareness of money Awareness of money Exchange Working with Awareness money is the application of money money for of numbers in a specific context. Understanding goods that and money can be used in exchange Why is for it goods important? and services. services An early appreciation of the contexts in which money is used. Previous knowledge and understanding Understanding Understanding Coins This and includes an awareness that money is valuable and there is a Knowledge of the existence of money money in a risks and Awareness notes need of buying to keep and it selling safe. In doing so young people will appreciate the digital world rewards difference between needs and wants. Awareness of money Money calculations Analyse the impact of financial decisions Developing financial capability

97 Money Coins and notes Exchange money for Using notes and goods coins and is an everyday life skill. In many transactions change services should be given/received. Awareness of money Coins and notes Coins and notes Using coins and notes Understanding money in a digital world Understanding risks and rewards Relevant contexts Analyse the impact of financial decisions The interrelationship between different sets of coins and notes Money calculations Developing financial capability

98 Money Coins and notes Coins and notes have different monetary values and are used to buy products and services, as well as being used to save. Coins and notes Previous knowledge and understanding Awareness that Why money is it important? takes various Exchange forms, e.g. coins, notes, cards and vouchers money for Using notes and goods coins and is an everyday life skill. In many Know that money is used in real life to buy items and servicestransactions change services should be given/received. Awareness of money Coins and notes Coins and notes Using coins and notes Understanding money in a digital world Understanding risks and rewards Relevant contexts Analyse the impact of financial decisions The interrelationship between different sets of coins and notes Money calculations Developing financial capability

99 Money Awareness of money Coins and notes Previous Exchange knowledge and understanding money for Using notes Know and goods coins and understand and is everyday whole number life skill. addition In many and subtraction transactions change services should be given/received. Understand the notion of saving Coins and notes Using coins and notes The relationship between the value of coins and the cost of goods that are exchanged leads to understanding that different coins and notes have varying values. The ability to exchange an appropriate amount of money for goods or services and estimate/ calculate the amount payable and change. Coins and notes The interrelationship between different sets of coins and notes Money calculations Using coins and notes Understanding money in a digital world Understanding risks and rewards Relevant contexts Analyse the impact of financial decisions Developing financial capability

100 Money Awareness of money Coins and notes Previous knowledge and understanding Recognise that there are different ways to make Exchange exact amounts of money Be able to make exact combinations of simple money for Using notes and goods coins and is an everyday amounts life skill. using In mental many strategies transactions change services should be given/received. Have experienced the concept of giving and receiving change Coins and notes Coins and notes The interrelationship between different sets of coins and notes Money calculations Relevant contexts Apply the knowledge of coins in play and in real life situations. Using coins and notes Understanding money in a digital world Understanding risks and rewards Relevant contexts Analyse the impact of financial decisions Developing financial capability

101 Money The inter-relationship between different sets of coins and notes Understanding Coins that different and combinations notes of coins/ notes create a total amount, e.g. five 20p coins have the same value Why as a 1 is it coin, important? two Exchange 10 notes have the same value as a 20. money for Using notes and goods coins and is an everyday life skill. In many Previous knowledge transactions and understanding change services should be given/received. Be able to use a range of addition and subtraction strategies with money Understanding Understanding Awareness of Knowledge Coins and and understanding of whole numbers money in a risks and money and their relative notes Using coins Coins values and notes digital worldrelevant contexts rewards Awareness of the units of money and notes Coins and notes The interrelationship between different sets of coins and notes Money calculations Analyse the impact of financial decisions Developing financial capability

102 Money Awareness of money Exchange money for goods and services Exchange money for goods and services Understanding that, in order to purchase goods or services, money has to be exchanged. Developing Understanding awareness Understanding of Coins and money in a risks and notes where money comes from. Awareness of the difference between needs and wants. digital world rewards Exchange money for goods and services Money calculations Application in everyday life Analyse the impact of financial decisions Developing financial capability

103 Money Exchange money for goods and services Knowing how much money is available and what can be purchased with Exchange it. money Exchange for goods and services money for Previous knowledge Why and is it understanding important? goods and Understand that money includes coins, services notes, cards and vouchers Understanding that, in order to purchase goods or services, Be able to calculate money the has costs to of be items exchanged. by adding the Developing Understanding awareness Understanding of Awareness of Coins and prices together money in a risks and money notes where using the this most money appropriate comes strategies from. Awareness of the difference Be able to use a between range of strategies needs and to add wants. and subtract digital world rewards Be able to confidently use vocabulary: more, less etc. Money calculations Exchange money for goods and services Application in everyday life Analyse the impact of financial decisions Developing financial capability

104 Money Awareness of money Application in everyday life The ability to solve contextualised problems. Applying mental agility skills to solve abstract problems. When exchanging money for goods or services, being able to calculate change. Exchange money Exchange for goods and services money for Why is Previous it important? knowledge goods and and understanding Has experience services of working with money through relevant Understanding contextsthat, in order to purchase goods or services, money has Is able to be to estimate exchanged. and calculate Developing Understanding costs awareness Understanding of Coins and money in a risks and notes where this Is able money to estimate comes and from. calculate Awareness change of the difference Understands that affordability between needs and wants. digital is based world on money rewards available Exchange money for goods and services Money calculations Application in everyday life Analyse the impact of financial decisions Developing financial capability

105 Money Awareness of money Exchange money for goods and services Money calculations Developing confidence in mental Understanding written calculations Understanding Coins and money in a risks and notes involving money is an important skill in everyday life. digital world rewards Money calculations Money calculations Applying the four operations in calculations involving money Analyse the impact of financial decisions Developing financial capability

106 Money Money calculations Money calculations are any calculations involving addition, subtraction, multiplication or division (or a combination of these operations.) Mental strategies can involve rounding. Written calculations can involve decimal fractions. Exchange Previous knowledge and understanding money for Use a range of Money strategies to calculations be able to add, subtract, multiply and divide using whole numbers goods and Understand that Why monetary is it important? amounts services can be written with no more than 2 decimal places Developing confidence in mental Understanding written calculations Understanding Awareness of Use a range Coins of strategies and to be able to add, subtract, money in a risks and money multiply and divide notes involving numbers money to 2 decimal is an important places skill in everyday life. digital world rewards Analyse the impact of financial decisions Money calculations Money calculations Applying the four operations in calculations involving money Developing financial capability

107 Money Awareness of money Applying the four operations in calculations involving money Using money as a context for the application of number skills, including decimal fractions and percentages. Estimation Exchange or calculating the total cost of goods or services Money purchased. calculations money for goods and Why is it Previous important? services knowledge and understanding Use a range of strategies to be able to add, subtract, Developing confidence in mental Understanding written calculations Understanding Coins and multiply and divide numbers to 2 decimal places money in a risks and notes involving money Estimate is an amounts important using rounding skill everyday strategies life. digital world rewards Money calculations Money calculations Applying the four operations in calculations involving money Analyse the impact of financial decisions Developing financial capability

108 Money Awareness of money Exchange money for goods and The increased variety servicesof methods of payment has changed money from a concrete to a more abstract concept. Understanding money in a digital world Coins and notes Understanding money in a digital world Understanding money in a digital world Money calculations Online shopping Understanding risks and rewards Online banking Analyse the impact of financial decisions Best value Developing financial capability

109 Money Understanding money in a digital world Recognising the advantages Understanding disadvantages Exchange money of debit in and a digital world credit cards. money for goods and Previous knowledge and understanding The increased variety services Understand the various methods of paying of for methods goods and of payment has changed services money from a concrete to a more Understanding abstract concept. Understanding Awareness of Understand Coins the and terms credit/debit and debt money in a risks and money notes digital world rewards Understanding money in a digital world Money calculations Online shopping Online banking Analyse the impact of financial decisions Best value Developing financial capability

110 Money Awareness of money Online shopping Understanding money in a digital world Exchange Using cards to make payments for goods online. Making money for Why is comparisons it important? between different websites and shops. goods and The increased variety services Previous knowledge of methods and understanding of payment has changed money from Use a a range concrete of strategies to a more add/subtract/multiply Understanding abstract concept. Understanding Coins and divide numbers to 2 decimal places to compare costs money in a risks and notes digital world rewards Understanding money in a digital world Money calculations Online shopping Online banking Analyse the impact of financial decisions Best value Developing financial capability

111 Money Awareness of money using cards (including contactless technologies) and Understanding Exchange money withdrawals in a from digital ATMs. world money for goods and Previous knowledge and understanding services Recognise and understand how to read a bank balance The increased variety of methods of payment has changed statement money from a concrete to a more Use Understanding IT abstract to login to concept. secure Understanding websites Understanding Analyse the impact money a of importance risks of online and security of financial decisions digital world rewards Coins and notes Understanding money in a digital world Money calculations Online banking This involves keeping track of online banking, transactions Online shopping Online banking Best value Developing financial capability

112 Money Understanding money in a digital world Best value Exchange money for goods and Making comparisons between different websites, shops and The increased variety servicesof methods of payment has changed online savings accounts. money from a concrete to a more Understanding abstract concept. Understanding Awareness of Previous knowledge Coins and and understanding money in a risks and money Use a range notes of strategies add/subtract/multiply and digital world rewards divide numbers to 2 Understanding decimal places to compare costs Understand the concept money in of a benefits digital Money and comparing Online shopping these Online banking with overall costs world calculations Analyse the impact of financial decisions Best value Developing financial capability

113 Money Awareness of money Understanding risks and rewards Exchange money for goods and Spending and saving services money responsibly involves budgeting, incomes and expenditure over a period of time. Understanding money in a digital world Coins and notes Understanding risks and rewards Money calculations Risks and rewards of online shopping Personal financial products Understanding risks and rewards Analyse the impact of financial decisions Borrowing Developing financial capability

114 Money Understanding risks and rewards Recognising that there are a range of rewards for saving and investing money, as well as risks involved in borrowing. This includes calculations involving varying rates of interest and transactions. Awareness of money Understanding risks and rewards Previous knowledge and understanding Understand the terms save, invest Exchange and borrow Understand the concept of debt money for Use a range of Why strategies is it add/subtract/multiply important? goods and and divide numbers Spending to 2 decimal and places saving services money responsibly involves budgeting, Use knowledge incomes of percentages and expenditure to calculate interest over a and period of time. compare costs Understanding Coins and money in a notes digital world Understanding risks and rewards Money calculations Risks and rewards of online shopping Personal financial products Understanding risks and rewards Analyse the impact of financial decisions Borrowing Developing financial capability

115 Money Awareness of money Understanding risks and rewards charges. Exchange Previous knowledge money forand understanding Use a range goods of strategies and add/subtract/multiply and Spending divide and numbers saving services money to 2 decimal responsibly places to involves compare costs budgeting, incomes Able and to expenditure use literacy skills over to a determine period of hidden time. costs such as delivery Understanding money in a digital world Coins and notes Risks and rewards of online shopping There can be financial benefits of purchasing goods and services online. There can be hidden costs e.g. delivery Understanding risks and rewards Money calculations Risks and rewards of online shopping Personal financial products Understanding risks and rewards Analyse the impact of financial decisions Borrowing Developing financial capability

116 Money Awareness of money Understanding risks and rewards Previous knowledge and understanding Exchange Understand the terms associated with financial products money for Use knowledge of percentages to calculate interest and goods and apply as interest Spending and saving services money Understand responsibly the involves concept budgeting, of insurance incomes and expenditure over Use a knowledge period of of time. vague, robust and misleading information Understanding to inform choices Understanding money in a risks and digital world rewards Coins and notes Understanding risks and rewards Money calculations Personal financial products Making informed choices around basic bank accounts, insurance products, credit/debit cards, investments and loans. Risks and rewards of online shopping Personal financial products Analyse the impact of financial decisions Borrowing Developing financial capability

117 Money Understanding risks and rewards Borrowing Exchange money for Borrowing money can be appropriate goods if the and benefits that come from the expenditure Spending are and in saving line services with money the loan responsibly period. involves budgeting, incomes and expenditure over a period of time. Understanding Understanding Awareness Previous of knowledge Coins and and understanding money in a risks and money Use knowledge notes of vague, robust and misleading information to inform digital world rewards Understanding choices risks Risks and rewards of Personal financial Use knowledge of percentages and rewardsto calculate Money online interest shopping and products apply as interest calculations Analyse the impact of financial decisions Borrowing Developing financial capability

118 Money Awareness of money Exchange money for goods and services Analyse the impact of financial decisions Understanding Coins The and ability to analyse the impact Understanding of financial decisions ensures money in a risks and notes greater responsibility for individual economic wellbeing. digital world rewards Money calculations Analyse the impact of financial decisions Analyse the impact of financial decisions Developing financial capability

119 Money Analyse the impact of financial decisions Financial decisions impact on the development of financial capability. This includes being able to analyse the impact of individual financial decisions on others as well as the impact that the financial decisions of others Exchange have on individuals. Analyse the money impact for of financial decisions Previous knowledge and understanding goods and An understanding of ethical trading, tax (including direct services and indirect taxation), National Insurance Applying understanding Understanding Understanding Awareness of Coins The and ability of to financial analyse services, the impact saving, of financial decisions ensures borrowing, overspending, online spending, debit, credit money in a risks and money and scams to notes greater make financial responsibility decisions for individual economic wellbeing. digital world rewards Analyse the impact of financial decisions Money calculations Analyse the impact of financial decisions Developing financial capability

120 Money Awareness of money Developing financial capability Developing financial capability Exchange involves; Financial understanding money for Financial competence goods and Financial responsibility services Financial enterprise Understanding Understanding Coins and money in a risks and These notes four aspects are interconnected and mutually supportive digital world rewards and outline a framework for developing skills, attitudes and behaviours that will support learners as employees, employers, Money entrepreneurs or voluntary workers. calculations The ability to make decisions on spending and saving money is vital in order to balance lifestyle with the cost of living. Analyse the impact of financial decisions Financial understanding Financial competence Financial responsibility Financial enterprise Developing financial capability

121 Money Financial understanding Developing financial capability Developing financial understanding is the first step in ensuring young people Developing leaving school financial have capability the Exchange skills involves; required to deal confidently Financial with everyday understanding financial money issues. for It will also help them to make Financial informed competence decisions goods and choices and about their personal finances. Financial responsibility services Financial enterprise This milestone includes knowledge, understanding and Understanding Understanding Awareness of Coins and skills from across the curriculum money in a risks and money These notes four aspects are interconnected and mutually supportive digital world rewards and outline This video clip highlights a framework the impact for of developing Financial Education skills, attitudes and behaviours that will support on young people and learners their families. as employees, It includes employers, learners Money entrepreneurs or voluntary workers. conversations with advice and support for practitioners. calculations The ability to make decisions on spending and saving money is vital in order to balance lifestyle with the cost of living. Analyse the impact of financial decisions Financial understanding Financial competence Financial responsibility Financial enterprise Developing financial capability

122 Money Awareness of money Financial competence Developing financial capability This means being able to apply knowledge and Why is understanding it important? of financial matters across a range of Developing contexts, financial using digital capability Exchange technologies involves; where appropriate. Financial Being financially understanding competent includes being able to money for identify and tackle problems or issues with confidence and Financial competence goods and being able to manage financial situations effectively and Financial efficiently. responsibility services Financial enterprise Understanding Understanding Coins This andmilestone includes knowledge, understanding and money in a risks and These notes skills from across the curriculum four aspects are interconnected and mutually supportive digital world rewards and outline a framework This video for clip developing highlights the skills, impact attitudes of Financial and Education behaviours that will support learners on as young employees, people and employers, their Money families. entrepreneurs It includes learners or voluntary workers. conversations with calculations advice and support for practitioners. The ability to make decisions on spending and saving money is vital in order to balance lifestyle with the cost of living. Analyse the impact of financial decisions Financial understanding Financial competence Financial responsibility Financial enterprise Developing financial capability

123 Money Awareness of money Developing financial capability Financial responsibility Developing financial capability Exchange This involves; means having a caring and responsible attitude Financial understanding money with for regard to the use of resources. Children and young Financial competence goods people and who budget wisely and plan for the future will be Financial responsibility services responsible citizens who look after themselves. Financial enterprise This milestone Understanding includes knowledge, Understanding understanding and Coins and skills from across money the curriculum in a risks and These notes four aspects are interconnected and mutually supportive digital world rewards and outline a framework for developing This skills, video attitudes clip highlights and behaviours the impact of that Financial will support Education learners as employees, employers, Money young entrepreneurs people and their or families. voluntary It includes workers. learners calculations conversations with advice and support for practitioners. The ability to make decisions on spending and saving money is vital in order to balance lifestyle with the cost of living. Analyse the impact of financial decisions Financial understanding Financial competence Financial responsibility Financial enterprise Developing financial capability

124 Money Awareness of money Developing financial capability Financial enterprise Financial enterprise is about being able to deploy resources Developing financial capability Exchange involves; in an imaginative and confident manner. Financially Financial understanding money for enterprising behaviours will involve recognising risks and Financial competence rewards and making decisions based on informed thought goods and enabling children and young people to contribute effectively Financial responsibility services to the development of Scotland s wealth. Financial enterprise Understanding Understanding Coins and This milestone includes Analyse the impact money in a risks and knowledge, understanding and These notes four aspects are interconnected and mutually skills supportive from across the of financial decisions digital world rewards and curriculum outline a framework for developing skills, attitudes and behaviours that will support learners as employees, employers, Money entrepreneurs This or video voluntary clip highlights workers. the impact of Financial Education on young people and their families. It includes learners calculations conversations with advice and support for practitioners. The ability to make decisions on spending and saving money is vital in order to balance lifestyle with the cost of living. Financial understanding Financial competence Financial responsibility Financial enterprise Developing financial capability

125 Time Recording and displaying Units of time Converting units of time Concept of time Telling the time Time, calculations including more complex durations Time/speed/ distance Time management Duration of time Using appropriate units of time Calendars

126 Time Recording and displaying Concept of time Concept of time Converting units of time Why Units is of it time important? Developing an understanding of time and the passing of time supports the skills necessary for calculating durations and recording time. Telling the time Concept of time Time, calculations including more complex durations Time/speed/ distance Time management Duration of time Using appropriate units of time Calendars

127 Time Concept of time Recording and Concept of time displaying Awareness of patterns of time and the passing of time in Concept of time relation to years, seasons, months, weeks, days, hours, Converting minutes and seconds. units of time Why Units is of it time Previous knowledge and understanding important? Have experience Developing of routines, e.g. an understanding night day, of time and the passing of time routines at home supports the skills necessary for calculating durations and Recognise and understand that clocks, watches, digital Time, displays etc. are recording used to tell time. the time Telling the time Concept of time calculations including more complex durations Time/speed/ distance Time management Duration of time Using appropriate units of time Calendars

128 Time Recording and displaying Concept of time Converting Recording and dislaying time units of time Units of time Recording and displaying the time is an essential life skill that allows organisation of events and activities. Time, calculations Telling the Time/speed/ including time Recording and distance more complex displaying time durations Time management Duration of time Using appropriate units of time Calendars

129 Time Recording and displaying time Recording time involves Recording expressing and time using numbers and words. Displaying time is representing displaying the time on a clock face or on a digital display. Concept of time Previous knowledge and understanding Converting Be able to recognise Recording and understand and that clocks, dislaying watches time units and of time digital displays are used Units to tell of time the time Be able to recognise Why and understand is it important? that calendars and diaries are used for recording events in time Be able to recognise Recording the numerals and 1-12, displaying 1-24 then the 1-60 time as is an essential life skill that appropriate to learning allows as required organisation of events and activities. Time, calculations Telling the including time Recording and more complex displaying time durations Time/speed/ distance Time management Duration of time Using appropriate units of time Calendars

130 Time Recording and displaying Concept of time Units of time Converting units of time Why Units is of it time important? Use of units of time allows communication using a common language and understanding. Time, calculations Telling the Time/speed/ including time distance Units of time Relationships more complex Appropriate use durations Time management Duration of time Using appropriate units of time Calendars

131 Time Concept of time Units of time The ways in which we record time using the appropriate vocabulary. Knowledge of the relationship between different Recording units of time. and displaying Previous knowledge and understanding Understand routines Units of time Recognise and understand that there are different Converting styles of clocks, e.g. analogue and digital units of time Recognise and Why Units understand is of it time when calendars and important? diaries are used Be able to name Use the of days units of of the time weekallows communication using a common Be able to name language the months and of understanding. the year Be able to name the seasons Time, calculations including Telling the time more complex durations Units of time Relationships Appropriate use Time/speed/ distance Time management Duration of time Using appropriate units of time Calendars

132 Time Concept of time Relationships The relationship between different units of time e.g. Recording number and of days in a year, minutes in an hour etc. displaying Previous knowledge and understanding Know key time vocabulary, e.g. seconds, hours, Units of decades, time millennia etc. Converting Know the ordinal number units of the of time months, e.g. Why Units is of it time January 1st month important? Have an awareness of a variety of patterns of time, Use of units e.g. of time day follows allows night, communication Monday follows using Sunday, a common language and December understanding. follows November, Autumn follows Summer Time, calculations Telling the Time/speed/ including time distance Units of time Relationships more complex Appropriate use durations Time management Duration of time Using appropriate units of time Calendars

133 Time Concept of time Appropriate use Using the appropriate unit of time depending on the context and situation. Recording and Previous knowledge and understanding displaying Know the days of the week Know the numbers 1-60 Know time facts such as: there are 7 days in a week, Units of time Converting 365 days a year and 366 in a leap year, 4 seasons units in the of year timeetc. Why Units is of it time important? Know the reason why there is a leap year Understand the terms seconds, minutes, hours, Use of units of time allows communication days, weeks, using months, a common years language and understanding. Interpret a variety of date formats, e.g , 12th Time, March 2015 calculations Telling the Time/speed/ Time including time distance management Units of time Relationships more complex Appropriate use durations Duration of time Using appropriate units of time Calendars

134 Time Recording and displaying Telling the time Units of time Converting units of time Concept of time Supports the development of skills in effective time management. Time, calculations Telling the including time Analogue more and Telling the time complex digitaldurations Time/speed/ distance Time management Duration of time Using appropriate units of time Calendars

135 Time Telling the time Understanding time displays of various types and being able to express this using the correct vocabulary and in relation to specific times of the day e.g. morning or afternoon. Recording and Previous knowledge and displaying understanding Know the numbers 1-60, e.g for hours on an analogue clock, 0-60 for minutes Recognise and understand that there are different styles of Converting clocks, Telling time e.g. analogue and digital and different types of timers units of time Be able to count in 5s Units of time Be able to round appropriately Know that there are Supports 24 hours in the a day, development 60 minutes in of an hour skills and in effective time 60 seconds in a minute management. Time, Have an understanding of ¼, ½ and ¾ turn calculations Concept Telling the including of time time Analogue Telling the time more andcomplex digitaldurations Time/speed/ distance Time management Duration of time Using appropriate units of time Calendars

136 Time Concept of time Analogue and digital Understand the position of and relationship between the hour and minutes hands. Familiarisation with the position of the hands and the vocabulary of half past and quarter to/past. Understanding the link between analogue and the 24 Recording hour digital andclock. displaying Previous knowledge and understanding Recognise different types of displays which indicate time Know that an analogue clock has an hour Converting hand and a minute hand Telling the time Be able to count on and back units of time Understand Units of time on a standard analogue clock the main increments are in 5s Understand that am is before midday Understand Supports the that development is after midday of skills in effective time Have an understanding of ¼, ½, ¾ in fractions and are able to relate this management. to quarter past, half past and quarter to Time, calculations Telling the Time/speed/ including time Analogue distance Telling the time more andcomplex digitaldurations Time management Duration of time Using appropriate units of time Calendars

137 Time Concept of time Duration of time Recording and Why displaying it important? Understanding duration of time helps to plan and organise events and activities effectively. Converting Understanding the duration of time introduces start and finish units times of time and leads to being Units able of time to work out how long events last. The ability to calculate the length of time taken is essential for planning and organising events in daily life. Using timetables helps to develop mental agility in relation to Time, time calculations and develops calculations Telling the skills in estimation and in rounding. time Duration of time including more complex durations Timing of tasks Simple timetables Time/speed/ distance Time management Duration of time Estimating duration Using appropriate units of time Calendars

138 Time Concept of time Duration of time Recording and Duration of time Why displaying it important? Understanding duration of time helps to plan and organise The length of time between the start and finish point. events and activities effectively. Converting Understanding the duration Previous knowledge of time and introduces understanding start and finish units times of time and leads to Know that there being Units are able 60 of minutes time to work in an out hour, how 120 long events last. The ability to minutes in two calculate hours and the so on length of time taken is essential for planning An awareness and of quantity organising events in daily life. Using timetables helps to Know and be able to respond to the instructions develop mental agility in relation to Time, time calculations and start and stop/beginning and end develops calculations Telling the skills in estimation and in rounding. Be able to count on and back Time/speed/ including time distance more complex durations Duration of time Timing of tasks Simple timetables Time management Duration of time Estimating duration Using appropriate units of time Calendars

139 Time Concept of time Duration of time Recording and displaying Timing of tasks Why it important? Understanding Linking the chosen duration unit of of time time to helps the most to appropriate plan and organise timing events device. and Degree activities of accuracy effectively. is dependent Converting Understanding the situation. the duration of time introduces start and finish units times of time and leads to being Units Previous able of time to knowledge work out and how understanding long events last. The ability to calculate Have the an understanding length of time of place taken value is essential for planning Have an awareness of different units of time and organising events in daily life. Using timetables helps to Recognise different tools for measuring, e.g. stopwatch, develop wrist mental watch, agility clocks, calendars in relation to Time, time calculations and develops calculations Telling Recognise the skills different in estimation displays, and e.g. in analogue, rounding. digital time Duration of time including more complex durations Timing of tasks Simple timetables Time/speed/ distance Time management Duration of time Estimating duration Using appropriate units of time Calendars

140 Time Concept of time Duration of time Simple timetables Recording and Why displaying it important? Timetables and schedules provide information including start and finish times for journeys. They Understanding duration of time helps to plan and organise can be used to plan events and demonstrate the events and activities effectively. importance Converting Understanding of 24 hour the time. duration of time introduces start and finish units times of time and leads to being Units able of time to work out how long Previous events knowledge last. The and ability understanding to calculate the length of time taken Have is experience essential of for displays, planning e.g. seasons of the year and organising events in daily life. Have Using an understanding timetables of helps place to value Can calculate simple time durations develop mental agility in relation to Time, time calculations and Recognise different displays, e.g. analogue, digital, develops calculations Telling the skills in estimation and 12 in hour, rounding. 24 hour time Time/speed/ including time distance more complex durations Duration of time Timing of tasks Simple timetables Time management Duration of time Estimating duration Using appropriate units of time Calendars

141 Time Duration of time Recording and Why displaying it important? Estimating duration Understanding duration of time helps to plan and organise events and activities effectively. Converting Understanding the duration The ability to estimate of time how long introduces an event start took or and will finish take, units times of time and leads to using non-standard or standard units of time. Developing being Units able of time to work out how long events last. The ability to a sense of how long a task will take, by using familiar benchmarks. calculate the length of time taken is essential for planning and organising events in daily life. Using timetables helps to Previous knowledge develop and understanding mental agility in relation to Time, time calculations and Know and understand develops the units calculations Concept Telling the skills of in time, estimation e.g. seconds, and in rounding. minutes, hours, days Time/speed/ including of time Understand the cyclical time nature of time distance more complex Be able to count on and back (in steps of 1 or more) Duration of time Timing of tasks durations Have experience of how long something takes within familiar Simple timetables contexts, e.g. interval/playtime compared to lunchtime Duration of time Estimating duration Using appropriate units of time Time management Calendars

142 Time Recording and displaying Concept of time Converting Calendars units of time Units of time Use of calendars to organise daily routines, events and activities. Time, calculations Telling the Time/speed/ including time distance Calendars more complex durations Time management Duration of time Using appropriate units of time Calendars

143 Time Calendars Calendars are a structured representation of the months of the year. They reinforce the order of and number of days in the months of the year and can be used to illustrate the irregularity of number patterns in the months. Calendars Recording can also be andused to calculate elapsed time. displaying Previous knowledge and understanding Have experience of displays, e.g. seasons of the year Be able to count on Converting Calendars and back Know the days of the week, months of the year units of time Know the ordinal number Units of of the time months, e.g. January 1st month Understand the cyclical Why nature is it important? of time Know important events Use in of learners calendars own to lives, organise e.g. birthdays daily routines, events and Select the most appropriate activities. duration to count in, e.g. seconds, Time, minutes, hours, days or years calculations Concept Telling the including of time time Calendars more complex durations Time/speed/ distance Time management Duration of time Using appropriate units of time Calendars

144 Time Recording and displaying Converting units of time Units of time Converting units of time Concept of time Converting between units of time is necessary when identifying and carrying out time calculations. Time, calculations Telling the including time Converting units more complex of time durations Time/speed/ distance Time management Duration of time Using appropriate units of time Calendars

145 Time Converting units of time Knowledge that Recording there are 60 and seconds in a minute, 60 minutes in an hour displaying and 24 hours in a day are essential when estimating or calculating lengths of time. Concept of time Previous knowledge and understanding Converting Converting units of time Know and understand the relationships between units the of time different units Units of time, of time e.g. 60 seconds in a minute, 60 minutes in Why an hour is it important? Understand Converting values of time, between e.g. that seconds units of are time is necessary when smaller than minutes and years are longer than identifying and carrying out time calculations. months Time, calculations Telling the including time Converting units more complex of time durations Time/speed/ distance Time management Duration of time Using appropriate units of time Calendars

146 Time Concept of time Recording and displaying Time calculations including more complex durations Converting units of time Using Units information of time from a variety of sources to plan and schedule events and activities, including journeys, for personal lives and for work and leisure is an important life skill. Calculating journey times is an introduction Time, to establishing the relationship between calculations time, speed and Telling distance the and sets the foundation Time/speed/ including for more complex time calculations and estimation. distance more complex durations Time management Time Duration calculations including more of time complex durations Calendars and timetables Using appropriate units of time Journey times Calendars

147 Time Concept of time Recording and displaying Time calculations including more complex durations Time calculations including more complex durations Converting Using the four operations accurately to do calculations units in of time relation to time, using Time Units the calculations of most time efficient including method and more unit. complex durations Extracting and using specific information from a variety Previous knowledge of sources. and understanding Using this information to plan and schedule Be able to tell the time events and activities, including journeys, Time, for personal lives Be able to apply the four operations Be able to convert and for work and leisure. Calculating calculations journey times is an Telling times into thea common unit, e.g. 2hrs and Time/speed/ 90 mins = 2 hours introduction and including time 1.5 hours to establishing the relationship between time, distance Have an understanding speed and of decimal distance fractions and sets the more foundation complex for more complex Have an understanding calculations of place and value estimation. durations Time management Time Duration calculations including more of time complex durations Calendars and timetables Using appropriate units of time Journey times Calendars

148 Time Concept of time Recording and displaying Calendars and timetables Time calculations including more complex durations Converting Why Identifying is it important? and then using specific information in order to calculate durations of journeys or units events. of time Time Units calculations of time including more complex durations Extracting Previous and knowledge using specific and understanding information from a variety of sources. Understand Using that this timetables information and calendars to plan and can both schedule be used to events represent and activities, time durations including journeys, Time, for personal lives and for Can work identify and information leisure. Calculating from a table calculations journey of data times is an Telling Can the use simple timetables and calendars Time/speed/ introduction including time to establishing the relationship between time, Understand the difference between 12 hour and 24 hour distance speed notation and distance and sets the more foundation complex for more complex calculations and estimation. durations Be able to count and back in a variety of units Time management Time Duration calculations including more of time complex durations Calendars and timetables Using appropriate units of time Journey times Calendars

149 Time Concept of time Recording and Journey times Time displaying calculations including more complex durations Using the start and finish times to calculate how long a journey will last. Converting Previous units knowledge of time and understanding Time Units calculations of time including more Be able complex to tell the durations time Extracting and using specific Be information able to identify from 12 a and variety 24 hour notation of sources. Using this information Can convert to plan between and schedule 12 and 24 hour notation as events and activities, including appropriate journeys, Time, for personal lives and for work and leisure. Calculating Know and calculations journey be able to times use the is four an operations Telling the Have an understanding of decimal Time/speed/ fractions introduction including time to establishing the relationship between time, Understand the relationship between distance the units of time speed and distance and sets the more foundation complex Be able to convert for times more into complex a common unit, e.g. 2hrs calculations and estimation. and 90 durations mins = 2 hours and 1.5 hours Time management Time Duration calculations including more of time complex durations Calendars and timetables Using appropriate units of time Journey times Calendars

150 Time Recording and displaying Concept of time Using appropriate units of time Converting units of time Why Units is of it time important? Understanding that using appropriate units of time helps when selecting the most appropriate form to calculate and Time, express the answer, dependent on the context. Telling the time Using appropriate units of time calculations including more complex durations Time/speed/ distance Time management Duration of time Using appropriate units of time Calendars

151 Time Concept of time Using appropriate units of time Being able to select Recording and use and the most appropriate and efficient unit of time displaying for the situation and context. Previous knowledge and understanding Know the units Using of timeappropriate units Converting of time Understand values of time, e.g. that seconds are units of time smaller than minutes Why Units is of and it time years are longer than months important? Understand Understanding the differences and that relationships using appropriate units of time helps between units when of time selecting the most appropriate form to calculate and Know how to convert between the different units of Time, express the answer, dependent on context. time Telling the time Using appropriate units of time calculations including more complex durations Time/speed/ distance Time management Duration of time Using appropriate units of time Calendars

152 Time Concept of time Recording and displaying Time/speed/distance Converting It is important in some aspects units of travel of time and leisure to be able Units of time to estimate time taken, speed and distance travelled. More accurate time, speed and distance calculations are required for a range of real life contexts. Time, calculations Telling the Estimation Time/speed/ including Time/speed/ time relation to distance distance more distance/ complex Calculations speed/time durations Time management Duration of time Graphs Using appropriate units of time Calendars

153 Time Concept of time Time/speed/distance Recording and Using the standard formula to calculate the unknown displaying value when given the other two. Time/ speed/ distance Previous knowledge and understanding Converting Know units of time Know units It of is speed, important e.g. mph, in km/h some aspects units of travel of time and leisure to be able Units of time Know units to of distance estimate time taken, speed and distance travelled. More Know and understand inverse operations accurate time, speed and distance calculations are required Have experience of exploring a range of approaches for to calculating a range of speed, real distance life contexts. or time Time, calculations Telling the Estimation Time/speed/ Time/speed/ including time relation to distance distance more distance/ complex Calculations speed/time durations Time management Duration of time Graphs Using appropriate units of time Calendars

154 Time Concept of time Estimation in relation to distance/ speed/time Estimations are used in daily situations to determine Recording and either an approximate arrival time, speed or distance displaying for a journey. Time/ speed/ distance Previous knowledge and understanding Why is it important? Have experience of estimating Converting appropriately It is important Have in experience some aspects of rounding units of travel of time and leisure to be able Units of time to estimate Know time and taken, understand speed the and relationship distance travelled. between More speed, distance and time, and how this relates to the accurate time, speed and distance calculations are required units of measure for a range Apply of real the life four contexts. operations in Time, calculations calculations Telling the Estimation Time/speed/ Time/speed/ including time relation to distance distance more distance/ complex Calculations speed/time durations Time management Duration of time Graphs Using appropriate units of time Calendars

155 Time Concept of time Recording and displaying Time/speed/distance Calculations Calculations are required for specific more formal situations, e.g. areas of employment where this is a necessary part of daily business. Formula can be used to calculate one quantity given the other two. Previous Converting knowledge and understanding It is important in some aspects units of Be travel able of time to and use leisure the four to operations be able Units of time Understand the inverse relationships between the to estimate time taken, speed and distance travelled. More four operations accurate time, speed and distance calculations are required Have experience of using the speed distance time for a range of real life contexts. formula Time, calculations Telling the Estimation Time/speed/ Time/speed/ including time relation to distance distance more distance/ complex Calculations speed/time durations Time management Duration of time Graphs Using appropriate units of time Calendars

156 Time Recording and displaying Time/speed/distance Graphs Converting units of time Time distance graphs It can is important Units be of used time to investigate in some aspects the relationships of travel and leisure to be able between distance, speed to estimate and time. time Used taken, to describe speed the and features distance travelled. More of a journey. accurate time, speed and distance calculations are required for a range of real life contexts. Previous knowledge and understanding Time, calculations Concept Apply knowledge of graphs Telling (link the to data and analysis) Estimation Time/speed/ including of time Be able to interpret simple Time/ time graphs speed/ relation to distance Understand that a line graph distance shows a continuous measure more distance/ complex Calculations Can estimate appropriately speed/ time durations Time management Duration of time Graphs Using appropriate units of time Calendars

157 Time Concept of time Recording and displaying Time management Converting units of time Units of time Time management is an essential skill for life, learning and work. Time management is important in business in terms of meeting deadlines for submitting projects and in life for Time, coordinating leisure activities. calculations Telling the including time more complex durations Time management Time/speed/ distance Time management Duration of time Using appropriate units of time Calendars

158 Time Concept of time Time management Planning for different real-life situations. Flexible planning is taken into account when any Recording adjustments and are required. Responsive planning is necessary in order displaying to address any unexpected events or changes. Time management Previous knowledge and understanding Converting Be able to use a range Why of timetables is it important? in a variety of contexts units of time Be able to tell the time Units from of different time displays Be able to calculate Time durations management is an essential skill for life, learning and Have an understanding work. of the Time different management types of calendars is important and be in business in terms able to use them effectively of meeting deadlines for submitting projects and in life for Understand the appropriateness Time, coordinating of leisure rounding activities. in relation to time Have experience of scheduling Telling the tasks within a given time time Time management calculations including more complex durations Time/speed/ distance Time management Duration of time Using appropriate units of time Calendars

159 Measurement Concept of area Convert units Awareness of size and amount Comparison of size and amount Non-standard units Standard units Formula and interrelationships Tolerance in measurement Concept of volume Calculations involving measurement

160 Measurement Awareness of size and amount Awareness of size and amount Comparison of size and amount An understanding Concept of how measurements can be taken and applied of area in everyday contexts in an important Convert life skill. Developing an awareness of size and amount promotes units an understanding of spacial awareness and develops the specific vocabulary needed to make comparisons. Non-standard Standard units units Awareness of size and amount Concept of volume Calculations involving measurement Formula and interrelationships Tolerance in measurement

161 Measurement Awareness of size and amount Awareness of size and amount Awareness of size and amount Use appropriate vocabulary to describe the features of shapes and objects, linking to size and amount. Use the language of opposites An understanding Concept comparisons, of how particularly measurements can be taken within practical and situations, applied of to area in develop everyday understanding contexts of in an important Convert life skill. these concepts Developing and how they an can awareness be applied. of size and amount promotes units an understanding of spacial awareness and develops the specific Previous knowledge and understanding Comparison vocabulary needed to make comparisons. In play, can group or Non-standard segregate items by own criteria Standard of size and units units amount Awareness of size and amount Concept of volume Calculations involving measurement Formula and interrelationships Tolerance in measurement

162 Measurement Comparison of size and amount Concept The ability of to area compare size and amount leads to a deeper understanding of relationships between measurements Convert and units how these can be applied to a range of situations and contexts. Awareness of size and amount Comparison of size and amount Non-standard units Comparison of size and amount Concept of volume Standard units Ordering Conservation of size, weight and volume Calculations involving measurement Formula and interrelationships Tolerance in measurement

163 Measurement Awareness of size and amount Comparison of size and amount Use appropriate vocabulary to describe the features of shapes and objects, linking to size and amount. Concept Previous knowledge The ability and of understanding to area compare size and amount leads to a deeper Can talk about understanding objects shapes of relationships in own words between measurements Convert and and has a basic awareness of the vocabulary of units how these can be applied to a range of situations and contexts. comparison, e.g. taller, smaller, less, more Comparison of size and amount Comparison of size and amount Non-standard units Comparison of size and amount Concept of volume Standard units Ordering Conservation of size, weight and volume Calculations involving measurement Formula and interrelationships Tolerance in measurement

164 Measurement Ordering Awareness of size and amount Comparison of size and amount Comparison Develop vocabulary of size associated and amount with comparison and order objects according to set criteria and for different purposes. Concept The ability of Previous to area compare knowledge size and amount understanding leads to a deeper understanding of relationships between measurements Convert Can describe objects and shapes using own languageand units how these can Through be applied play, can to show a range ability of situations to sort and and order contexts. items by own criteria Non-standard units Comparison of size and amount Concept of volume Standard units Ordering Conservation of size, weight and volume Calculations involving measurement Formula and interrelationships Tolerance in measurement

165 Measurement Awareness of size and amount Comparison of size and amount Comparison of size and amount Previous knowledge and understanding Can compare and contrast objects and shapes to Concept identify common properties The ability of to area compare size and amount Can group leads objects to a and deeper shapes with identical understanding of relationships between properties measurements together Convert and units how these can be applied to a range Can of compare situations and order and contexts. objects according to set criteria Non-standard units Comparison of size and amount Concept of volume Conservation of size, weight and volume Recognise that shapes and objects that look different can have equal length, weight or volume. Standard units Ordering Conservation of size, weight and volume Calculations involving measurement Formula and interrelationships Tolerance in measurement

166 Measurement Non-standard units Awareness of size and amount Comparison of size and amount Concept Measuring of area and estimating with non-standard units develops understanding of why standard units are necessary Convert and help units to provide an estimation of size. This leads to developing an understanding of the concept of standard units. Non-standard Standard units units Non-standard units Concept of volume Calculations involving measurement Formula and interrelationships Tolerance in measurement

167 Measurement Awareness of size and amount Non-standard units Non-standard units Non-standard Why measurements is it important? Concept can be used to develop the concept that Measuring measure of area and estimate estimating of surface with area non-standard units develops can be described understanding terms of numerical of why values. standard units are necessary Convert and help units to provide an estimation of size. This leads to developing an understanding of the concept of standard units. Previous knowledge and understanding Comparison Can apply counting skills Non-standard of size and units amount Non-standard units Concept of volume Standard units Calculations involving measurement Formula and interrelationships Tolerance in measurement

168 Measurement Concept of area The ability to compare size and amount leads to a deeper understanding Concept of relationships between measurements and of area how these can be applied to a range of situations Convert and contexts. units Awareness of size and amount Comparison of size and amount Concept of area Non-standard units Understanding area Standard units Estimating area Formula and interrelationships Tolerance in measurement Units of area Concept of volume Calculations involving measurement

169 Measurement Concept of area Develop an understanding of the concept of area through practical Concept activities, investigation of areaand discussion. This is related to geometric concept of enclosed area. Previous knowledge The ability and Concept understanding to compare size and amount leads to a deeper Through play, understanding have experience of of relationships investigating and between measurements and of area comparing different how these objects can and be the applied amount to of a space range of situations Convert and contexts. they cover units Awareness of size and amount Comparison of size and amount Concept of area Non-standard units Understanding area Standard units Estimating area Formula and interrelationships Tolerance in measurement Units of area Concept of volume Calculations involving measurement

170 Measurement Understanding area Area is used to describe the size of any surface. This includes the surface within any given 2D shape. The conservation of area is knowing that when any surface is split into smaller parts then the total area of the parts is equal to the original surface area. Concept of area Why Previous is it important? knowledge and understanding Can describe area as the amount of space covered by an object The ability Understand to compare that the size amount and of amount space taken leads up by to a 2D deeper object understanding Concept is known as of area relationships between measurements and of area how these Understand can be that applied objects to can a look range different of situations but have Convert and equal contexts. areas units Awareness of size and amount Comparison of size and amount Concept of area Non-standard units Understanding area Standard units Estimating area Formula and interrelationships Tolerance in measurement Units of area Concept of volume Calculations involving measurement

171 Measurement Concept of area Estimating area Use non-standard units to build an understanding of estimating the area of a surface. Then select the most appropriate standard unit for the context. Previous knowledge and understanding Have an awareness of vocabulary of comparison Understand that an estimated value is not exact The ability to compare size Can and use amount knowledge leads of sizes to a of deeper common objects to compare size, understanding Concept of relationships e.g. is between bigger than, measurements smaller than and of area how these can be applied to Understand a range area of situations is the size Convert of and any contexts. surface, including the space within any 2D shape units Awareness of size and amount Comparison of size and amount Concept of area Non-standard units Understanding area Standard units Estimating area Formula and interrelationships Tolerance in measurement Units of area Concept of volume Calculations involving measurement

172 Measurement Units of area Awareness of size and amount Conventions for describing Concept and recording of area experiential measurements of area are introduced when it is recognised that there is a need for a standard unit of area Why and initially is it important? in context to build from nonstandard to standard. The ability to compare size and amount leads to a deeper Concept Previous knowledge understanding of relationships between measurements and of area Have experience of talking how these about can and be recording applied area to using a range a variety of situations Convert and contexts. of non-standard units, e.g. hands, cubes, sticks units Have explored a range of measuring instruments, e.g. cubes, sticks, jugs, buckets Comparison Can use non-standard units Concept Non-standard accurately of areawhen measuring Understanding Standard a length area Estimating area of size and Can apply counting skills units units amount Units of area Concept of volume Calculations involving measurement Formula and interrelationships Tolerance in measurement

173 Measurement Concept of volume Volume links with spatial awareness and impacts on a variety of objects encountered Concept daily. The skills required to solve problems of area relating to volume are skills needed for learning, Convert life and work. units Awareness of size and amount Comparison of size and amount Concept of volume Non-standard units Unit of volume Standard units Estimating volume Formula and interrelationships Tolerance in measurement Capacity Concept of volume Mass Calculations involving measurement

174 Concept of volume Volume is the measure of space taken up by a 3D object. The conservation of volume is knowing that when any object is split Measurement into smaller parts then the total volume of the parts is equal to the original volume. Concept of volume Previous knowledge and understanding Through play, have experience of investigating the amount different objects and Why containers is it important? can hold Explore objects with same volume but different dimensions to Volume links with spatial awareness and impacts on a variety of develop awareness of conservation objects encountered Concept of volume Can give examples of objects/containers where daily. volume The skills could required to solve problems of area be measured in relation relating to real-life, to volume e.g. lunch are skills box, water needed for learning, Convert life and work. bottle, sand pit units Awareness of size and amount Comparison of size and amount Concept of volume Non-standard units Unit of volume Standard units Estimating volume Formula and interrelationships Tolerance in measurement Capacity Concept of volume Mass Calculations involving measurement

175 Measurement Unit of volume Conventions for describing and recording measurements of volume should be introduced when appropriate and initially in context. Previous knowledge and understanding Concept Understand of that volume the amount of space taken up by a 3D object is known as volume Why Understand is it important? that objects can look different but have equal volume Have experience of talking about and recording volume using a variety Volume links with spatial awareness and impacts on a variety of of non-standard objects encountered Concept units, e.g. bean bags, handfuls of sand Can use daily. The skills required to solve problems of non-standard area units accurately to measure and record a range of relating volumeto volume are skills needed for learning, Convert life and work. Can apply counting skills units Awareness of size and amount Comparison of size and amount Concept of volume Non-standard units Unit of volume Standard units Estimating volume Formula and interrelationships Tolerance in measurement Capacity Concept of volume Mass Calculations involving measurement

176 Measurement Concept of volume Estimating volume The ability to estimate volume is built on an understanding of how to estimate other properties of shapes, e.g. length, breadth, depth, area. Previous knowledge and understanding Understand and use vocabulary of comparison Understand that an estimated value is not exact Volume links with spatial Can awareness use knowledge and of impacts volume of on common a variety objects/containers of to compare objects encountered Concept daily. size, The e.g. It skills has less required space than to solve this bucket problems of area relating to volume are skills Apply needed knowledge for of learning, length and Convert life area and to provide work. an estimation of size Be able to estimate properties of 2D shapes, e.g. length, breadth and area units Awareness of size and amount Comparison of size and amount Concept of volume Non-standard units Unit of volume Standard units Estimating volume Formula and interrelationships Tolerance in measurement Capacity Concept of volume Mass Calculations involving measurement

177 Measurement Concept of volume Capacity Volume links with spatial awareness and impacts on a variety of Concept objects encountered daily. The skills required to solve problems of area Spatial awareness relating of 3D objects to volume and the are amount skills needed they for learning, Convert life and work. can contain. Interior volume of an object. units Awareness of size and amount Previous knowledge and understanding Comparison Understand that Concept the Non-standard amount of volume of space taken up Standard by a of 3D size object andis known as volume units units amount Unit of volume Estimating volume Formula and interrelationships Tolerance in measurement Capacity Concept of volume Mass Calculations involving measurement

178 Measurement Concept of volume Volume links Mass with spatial awareness and impacts on a variety of objects encountered Concept daily. The skills required to solve problems of area relating to A volume large body are of skills matter needed with no for definite learning, shape. Convert life and work. The amount of matter in an object. units Awareness of size and amount Comparison of size and amount Previous knowledge and understanding Non-standard Understand and Unit use Standard of the volume vocabulary of volume and units capacity units Concept of volume Estimating volume Formula and interrelationships Tolerance in measurement Capacity Concept of volume Mass Calculations involving measurement

179 Measurement Standard units Using standard units ensures a universal system of measurement Concept which helps us to interpret, communicate and of area calculate measurements. Convert units Awareness of size and amount Comparison of size and amount Standard units Non-standard units Measure using standard units Standard units Inter-relationships between units of measurement Formula and interrelationships Tolerance in measurement Link between concept and formula of area Concept of volume Calculations involving measurement

180 Standard units Standard units are the universal system of measurement. Measurement Previous knowledge and understanding Have experience of talking about and recording measurement using a variety of non-standard Standard units, e.g. hands, units cubes, sticks, handfuls of sand Can estimate and use non-standard units accurately when measuring and recording Can apply counting skills Have experienced standard Using units standard of measure units in ensures their own a universal environment system of measurement Concept even if they do not understand the meaning, which e.g. helps 2litre us bottle to interpret, of Cola, communicate and of area 25g packet of crisps calculate measurements. Convert units Awareness of size and amount Comparison of size and amount Standard units Non-standard units Measure using standard units Standard units Inter-relationships between units of measurement Formula and interrelationships Tolerance in measurement Link between concept and formula of area Concept of volume Calculations involving measurement

181 Measurement Measure using standard units Use of a wide range of measuring instruments to accurately measure length, weight and volume. Awareness of a variety of types of scales should include analogue and digital and the most effective and efficient measuring instruments to be used. Previous knowledge and understanding Standard Through play, units have an experience of a wide range of measuring instruments Why Understand is it important? that agreed unit of measure is essential Be aware of common standard units and the appropriate use Using Understand standard that units different ensures measurements a universal are system required of for different measurement types of Concept objects/shapes which helps us to interpret, communicate and of area calculate Can select measurements. an appropriate unit of measure, e.g. strides Convert to measure the length of a classroom, cubes to measure the length of units a pen Awareness of size and amount Comparison of size and amount Standard units Non-standard units Measure using standard units Standard units Inter-relationships between units of measurement Formula and interrelationships Tolerance in measurement Link between concept and formula of area Concept of volume Calculations involving measurement

182 Measurement Standard units Inter-relationships between units of measurement Understanding the relationship between units of measure e.g. 10mm=1cm, 100cm=1m. Previous knowledge and understanding Can describe measurements using a range of units as Using standard units ensures appropriate, a universal e.g. system mm, cm, of m, km, g, ml measurement Concept which helps us Understands to interpret, that communicate the metric system and is structured in of area calculate measurements. multiples and powers Convert of 10 Have an understanding units of decimals and place value Awareness of size and amount Comparison of size and amount Standard units Non-standard units Measure using standard units Standard units Inter-relationships between units of measurement Formula and interrelationships Tolerance in measurement Link between concept and formula of area Concept of volume Calculations involving measurement

183 Measurement Awareness of size and amount Link between concept and formula of area More efficient ways Standard of calculating surface unitsarea. Methodology should not detract from the concept of area. Previous knowledge and understanding Using standard units ensures a universal system of Understand the concept of measurement Concept area Be able to calculate the area which helps us to interpret, communicate and of of area common shapes using a range of methods, e.g. calculate cover with measurements. cubes then count, counting Convert squares units Understand that areas of common shapes can be calculated using a standard process Comparison Measure using Can apply multiplication Standard Non-standard division units facts (inverse Standard of size and standard operations) units to whole numbers, fractions units and decimal fractions units amount Link between concept and formula of area Concept of volume Inter-relationships between units of measurement Calculations involving measurement Formula and interrelationships Tolerance in measurement

184 Measurement Convert units Awareness of size and amount Comparison of size and amount Concept Ability to of convert area between units enables the most efficient and appropriate unit or measurement to be used. Convert units It underpins the rules and concepts in many areas, e.g. science, engineering and technology. Non-standard Standard units units Convert units Concept of volume Selecting appropriate units Calculations involving measurement Formula and interrelationships Tolerance in measurement

185 Measurement Awareness of size and amount Convert units The metric system is the internationally agreed system of units. Knowledge and Convert understanding units of the inter-relationship between different units. Knowledge of appropriate prefixes and understanding the language Why is of it measurement important? and notation. Concept Previous knowledge Ability and understanding to of convert area between units enable the most efficient and appropriate unit or measurement to be used. Convert Can apply multiplication and division facts (inverse operations) It to whole numbers, units underpins fractions and the decimal rules fractions and concepts in many areas e.g. science, Understand the relationship engineering between and technology. the units within the metric Comparison system Non-standard Standard of size and units units amount Convert units Concept of volume Selecting appropriate units Calculations involving measurement Formula and interrelationships Tolerance in measurement

186 Measurement Awareness of size and amount Comparison of size and amount Selecting appropriate units Use the most appropriate unit of measurement in relation to individual contexts. The most appropriate unit of measurement is used to carry out a calculation. Convert units Previous knowledge and understanding Understand the relationship between the unit of measure and the measuring instrument, e.g. cm ruler, m metre stick Understand Conceptthat different objects require different units of Ability measure to of convert area between units enable the most efficient and appropriate Be able to describe unit or common measurement uses for the to different be used. Convert units It of units underpins measure the rules and concepts in many areas e.g. science, Understand that changing the unit of measure impacts on the engineering and technology. numerical value of the measure Non-standard units Convert unit Concept of volume Standard units Selecting appropriate units Calculations involving measurement Formula and interrelationships Tolerance in measurement

187 Measurement Calculations involving measurements Awareness of size and amount Comparison of size and amount Why is it Concept important? Calculations of area involving perimeter, area and volume Convert are needed in real life contexts and enable us to work out accurate units amounts. Non-standard units Calculations involving measurements Concept of volume Standard units Select the most appropriate calculation dependent on the situation Calculations involving measurement Formula and interrelationships Tolerance in measurement

188 Calculations involving measurements Measurement Carrying out calculations using the four operations involving perimeter, area and volume. Using whole numbers, fractions, decimal fractions or percentages according to context. Awareness of size and amount Previous knowledge and understanding Understand the terms Calculations perimeter, area involving and volume measurements Can apply the four operations to whole numbers, fractions, decimal fractions Why or percentages is it Concept important? Select the appropriate unit of measure Calculations of area Can convert between standard units involving perimeter, area and volume Convert are needed Understand that using real a common life contexts standard and unit enable across us all to work out accurate units dimensions can simplify amounts. a calculation, e.g. l = 2m b = 90cm l = 200cm b = 90cm Comparison of size and amount Non-standard units Calculations involving measurements Concept of volume Standard units Select the most appropriate calculation dependent on the situation Calculations involving measurement Formula and interrelationships Tolerance in measurement

189 Measurement Awareness of size and amount Comparison of size and amount Being able to apply the right calculation to fit the situation or context. Selecting the appropriate Calculations calculation, involving perimeter, measurements area, or volume taking account of the dimensional aspect of the situation or context. Why is it Concept important? Calculations of area Previous knowledge and understanding involving perimeter, area and volume Convert are needed Select the appropriate unit of measure in real life contexts Can apply and enable the four us operations to work to out problems accurate unitsinvolving amounts. measure Non-standard units Calculations involving measurements Concept of volume Select the most appropriate calculation dependent on the situation Standard units Select the most appropriate calculation dependent on the situation Calculations involving measurement Formula and interrelationships Tolerance in measurement

190 Measurement Formula and inter-relationships Awareness of size and amount Comparison of size and amount Concept Formula is of used areato simplify the process of calculations and to calculate an unknown variable. Awareness of Convert the interrelationship between different formulae supports units further calculations to be made, e.g. diameter=2 x radius C=πD or C=2π r Non-standard units Formula Concept of volume Standard units Inter-relationship Calculations involving measurement Formula and interrelationships Tolerance in measurement

191 Measurement Awareness of size and amount Formula Specific formula are used to carry out calculations involving measurement. These provide a method for accurately and efficiently calculating perimeter area and volume. Use knowledge of the formula to be able to undertake a number of related calculations associated with length, breadth, height, area and volume. Understand the interconnectivity between the variances in the formula. Formula and inter-relationships Previous knowledge and understanding Can apply the four operations to Concept problems involving measure Understand that a common Formula strategy is of used area can to be simplify applied to the the process same of calculations and shape but with different to calculate dimensions, a e.g. an unknown the same formula variable. can Awareness be Convert of the interrelationship applied to rectangles of all sizes between different formula and supports unitsfurther Be able to describe dimensions of shapes using length, breadth, calculations to be made e,g, diameter=x radius C=πD or C=2π r height etc. Comparison Non-standard Standard of size and units units amount Formula Concept of volume Inter-relationship Calculations involving measurement Formula and interrelationships Tolerance in measurement

192 Measurement Awareness of size and amount Comparison of size and amount Inter-relationships Understand the links between perimeter and area. Being able to work backwards and forwards when calculating measurements. Knowledge and understanding of Formula and inter-relationships relationships between dimensions and how to manipulate formula dependent on the context. Concept Formula Previous is of used knowledge area to simplify and the understanding process of calculations and to calculate Can a apply an unknown common formula variable. to calculate Awareness perimeter/ Convert of the interrelationship between different formula and supports unitsfurther Can apply the four operations to problems involving area/volume of common shapes calculations measure to be made e,g, diameter=x radius C=πD or C=2π r Non-standard Standard units units Formula Concept of volume Inter-relationship Calculations involving measurement Formula and interrelationships Tolerance in measurement

193 Measurement Tolerance in measurement Awareness of size and amount Comparison of size and amount Concept Relates to of area acceptable margins of error when measuring, estimating or calculating measurements. Understanding Convert of units tolerance in measurement is appreciation of accuracy when making calculation. Non-standard Standard units units Tolerance in measurement Concept of volume Calculations involving measurement Formula and interrelationships Tolerance in measurement

194 Measurement Awareness of size and amount To understand Why margins is it Concept of important? error are acceptable in different contexts Relates and the to of impact area acceptable this could margins have. of error when measuring, estimating or calculating measurements. Understanding Convert of Previous knowledge units tolerance and in understanding measurement is appreciation of accuracy when Describe when exact measurements could be making calculation. difficult to calculate Non-standard Standard units units Comparison of size and amount Tolerance in measurement Tolerance in measurement Tolerance in measurement Concept of volume Calculations involving measurement Formula and interrelationships Tolerance in measurement

195 Data and analysis Collect and organise Concept of data analysis Display and communicate Drawing conclusions Interrogate

196 Data and analysis Concept of data analysis Collect and organise Data and analysis is an essential aspect of everyday life. The ability to read and analyse data is an important life skill. Concept of data analysis Concept of data analysis Display and communicate Drawing conclusions Interrogate

197 Data and Concept of data analysis Using data to make informed choices and decisions. Exploring data to make sense of the world around us. Concept of data analysis Previous knowledge and understanding Understand the need to organise objects and/or information Collect and Awareness of different Why displays is it of important? data, and the use organise of these to make choices in everyday Data situations and analysis is an essential aspect of everyday life. It is Awareness of appropriate the ability vocabulary to use to talk a range about of and information organise presented in various data by their own criteria forms. Awareness of the existence of information in different forms Concept of data analysis Concept of data analysis Display and communicate Drawing conclusions Interrogate

198 Data and analysis Collect and organise Collect and organise Collecting and organising data and information supports decision making relevant to the context. Concept of data analysis Collect and organise Display and communicate Matching, sorting and comparing Drawing conclusions Gathering and organising Interrogate

199 Collect and organise Data and analysis Gathering information from a variety of sources and organising it in a way that suits the audience. Previous knowledge and understanding Awareness of the existence of various sources of information, e.g. Collect and organise self-registration, giving and receiving party invitations Collect and Awareness of being able to gather information by appropriate means Why it important? organise Awareness of the need to organise information Awareness of appropriate Collecting vocabulary and to organising collect data data and begin and to information supports organise it decision making relevant to the context. Concept of data analysis Collect and organise Display and communicate Matching, sorting and comparing Drawing conclusions Gathering and organising Interrogate

200 Data and analysis Matching, sorting and comparing Matching objects which have the same characteristics. As criteria increases then this become sorting, e.g. matching more than two objects. Sorting involves separating objects into groups according to their similarities or differences. Progression is made when moving from comparing individual items to comparing groups. This becomes increasingly sophisticated as learners progress their understanding. MAIN MENU Previous knowledge and understanding In play, have experience of matching, sorting and comparing using own criteria Collect and organise Have an understanding of characteristics Collect andthat they are being asked to match, sort and compare with, e.g. organise size, colour Understand that objects (and data) have different characteristics (colour, size, Collecting etc.) and organising data and information supports Recognise decision these making characteristics, relevant to and the be context. able to differentiate objects based on these Concept of data analysis Collect and organise Display and communicate Matching, sorting and comparing Drawing conclusions Gathering and organising Interrogate

201 Data and analysis Gathering and organising A range of information and data can be collected from a variety of appropriate sources and for many purposes. This is organised into an appropriate form; table, chart or diagram to support interrogation and analysis. Data can be organised into groups depending on the context. Previous knowledge and understanding Collect and organise Know that data must be sourced Collect and Understand that, to make sense of data, one must organise it organise Have had experience of organising techniques, e.g sorting, matching, comparing Collecting and organising data and information supports Understand that organisation of the data is preparation for decision making relevant to further the context. communication Concept of data analysis Collect and organise Display and communicate Matching, sorting and comparing Drawing conclusions Gathering and organising Interrogate

202 Data and analysis Display and communicate Collect and organise Accuracy in displaying and communicating data is important to ensure it is clear and easily understood by the audience. Display and communicate Concept of data analysis Display and communicate Types of display Communicating findings Drawing conclusions Interrogate

203 Display and communicate Sharing information in a variety of forms that can be Data and analysis understood by the intended audience. Previous knowledge and understanding Demonstrate knowledge of appropriate organising techniques Know how to design a survey appropriate to level, e.g. question(s), Display organising and response(s) communicate Collect and Understand that the purpose of displaying data organise communication Have had experience of different types of chart/ graph of appropriate To share complexity information to the and learner s findings level in a logical form. Display and communicate Concept of data analysis Display and communicate Types of display Communicating Drawing findings conclusions Interrogate

204 Data and analysis Types of display The choice of how to display information will vary and should be appropriate for the context and the intended audience. Progression from simple bar graphs and picture charts to venn diagrams and pie charts. Display and communicate Collect and Previous knowledge organise and understanding Why is it important? Awareness that there are different types of displays Understand that the purpose of displaying data To share information and findings in a logical form. graphically is to ease communication Display and communicate Concept of data analysis Display and communicate Types of display Communicating Drawing findings conclusions Interrogate

205 Data and analysis Communicating findings Presenting the findings and conclusions from the collation of information and data. Previous knowledge and understanding Know how to construct diagrams/charts Know how to interpret diagrams/charts Know how to select the most appropriate display method to Display and communicate Collect fit a given and purpose/data set organise Understand how to compare data displays Understand and recognise that data collecting has a purpose To share information and findings Use appropriate in a logical vocabulary form. to describe displays and comparisons e.g. more than, most Display and communicate Concept of data analysis Display and communicate Types of display Communicating Drawing findings conclusions Interrogate

206 Data and analysis Interrogate Collect and organise In real life situations information is provided in a variety of ways. To interrogate the information enables choices and decisions to be made. Concept of data analysis Interrogate Display and communicate Critical analysis of data Drawing conclusions Interrogate

207 Interrogate Data and analysis Simple interrogation of data is reading and extracting key information from tables, charts, graphs etc. This enables decisions around the validity and reliability of the data, e.g. in relation to sample size. Interrogate Previous knowledge and understanding Know where to find data in relevant displays, e.g. Collect timetable, and bar chart, pictograph organise Understand and interpret In real life information situations from information displays a is level provided in a variety of appropriate to the ways. learner To interrogate the information enables choices and When considering decisions the data, have to be an made. awareness of reliability and validity, e.g. what is the sample size? Concept of data analysis Interrogate Display and communicate Critical analysis of data Drawing conclusions Interrogate

208 Data and analysis Critical analysis of data Critical analysis is an indepth scrutiny of data which could include looking at trends, correlations and relationships between data. Interrogate Previous knowledge and understanding Knowledge and understanding Collect and of different comparison techniques organise In real life Demonstrate situations ability information to compare is data provided sets in in context, a variety and with of ways. To purpose, interrogate e.g. back the to back information stem and enables leaf diagram choices and decisions Understand to be made. and interpret various graphs and charts, e.g. pie charts, line graphs, scatter graphs Concept of data analysis Interrogate Display and communicate Critical analysis of data Drawing conclusions Interrogate

209 Data and analysis Drawing conclusions Collect and Knowing how to draw conclusions organise from data helps make informed choices. Drawing conclusions Concept of data analysis Statistical calculations Reliability and validity Display and communicate Bias and sample size Drawing conclusions Interrogate

210 Drawing conclusions Using the information presented in different forms and its source Data and analysis to draw conclusions which could affect decision making. Previous knowledge and understanding Knowledge and understanding of the most appropriate graphical representation Drawing for data conclusions (line graphs, pie charts etc.) Knowledge and understanding of spread of data/account for outliers Collect and Demonstrate ability to compare data sets in context, Drawing conclusions from organise and with purpose data to help make informed choices. Drawing conclusions Concept of data analysis Statistical calculations Reliability and validity Display and communicate Bias and sample size Drawing conclusions Interrogate

211 Data and analysis Reliability and validity Reliability is the credibility of the source as well as the collation of the data. Reliability is the repeatability of a particular set of findings e.g. how accurate would the information be in a second identical information gathering activity? Reliability is a necessary ingredient for determining the overall validity of an investigation or survey and enhancing the strength of the results. MAIN MENU Previous knowledge and understanding Know how to obtain information from real life sources Demonstrate Drawing an conclusions awareness that not all information is equally reliable Understand different types of average and how these can be misleading due to the Why existence it important? of outliers Collect and Be able to use calculations to interpret Drawing conclusions from organise data Demonstrate knowledge of how to data make to predictions help make based informed on the choices. data supplied Drawing conclusions Concept of data analysis Statistical calculations Reliability and validity Display and communicate Bias and sample size Drawing conclusions Interrogate

212 Data and analysis Bias and sample size Bias is who or what is included in the intended sample. A biased sample can result in a non-valid data set. The size of the group can have an impact on the validity of the survey. Previous knowledge and understanding Awareness of word bias Drawing conclusions Know how to design and interpret surveys Know how to display data Know Collect how and to draw conclusions Awareness Drawing conclusions from organiseof sample size data to help make informed choices. Understand reliability of data Drawing conclusions Concept of data analysis Statistical calculations Reliability and validity Display and communicate Bias and sample size Drawing conclusions Interrogate

213 Data and analysis Statistical calculations Statistical calculations support the evaluation and interpretation of data and draw conclusions from data. Drawing conclusions Previous knowledge and understanding Has experienced Why working is it with important? fractions, decimal Collect fractions and and percentages Drawing a range conclusions of contexts from organise data to help make informed choices. Knowledge and understanding of a range of strategies to carry out calculations Apply knowledge and understanding Drawing of integers, Reliability e.g. Bias and temperature conclusions and validity sample size Understanding of what averages are intended to represent Concept of data analysis Statistical Display and communicate Drawing conclusions calculations Interrogate

214 Ideas of chance and uncertainty Simple choice and decision making Predicting and describing likelihood Choice and decision making based on likelihood Probability Applying knowledge of probability

215 Ideas of chance and uncertainty Simple choice and decision making Simple choice and decision making Using everyday language to identify outcomes of familiar events supports the development Choice and of critical thinking skills. Predicting This enables and discussion around choices and consideration of decision describing alternative options when making choices and decisions. Probability making based likelihood on likelihood Simple choice and decision making Applying knowledge of probability

216 Ideas of chance and uncertainty Simple choice and decision making Simple choice and decision making Simple choice and decision making Describing the possible outcomes using everyday language, e.g. will happen, won t happen, always, never, sometimes. Using everyday language to identify outcomes of familiar events supports the development Choice and of critical thinking skills. Predicting This enables and discussion around choices and consideration of decision describing alternative options when making choices and decisions. Probability making based likelihood on likelihood Previous knowledge and understanding Understand that you can make choices Simple choice and decision making Applying knowledge of probability

217 Ideas of chance and uncertainty Predicting and describing likelihood Simple choice and decision making Predicting and describing the likelihood of events occurring can help develop the ability Choice to make and informed choices and Predicting mathematical and thinking. decision describing Probability making based likelihood on likelihood Predicting and describing likelihood Language of chance Scale Applying knowledge of probability

218 Ideas of chance and uncertainty Simple choice and decision making Predicting and describing likelihood Predicting and describing likelihood Using information to determine possible outcomes. Previous knowledge and understanding Know and understand Predicting appropriate and describing vocabulary the for likelihood simple of events occurring choice and decision can help making develop the ability Choice to make and informed choices and Have an awareness Predicting mathematical of and reasonableness thinking. of an outcome decision Be able to make describing simple choices and decisions Probability making based likelihood on likelihood Predicting and describing likelihood Language of chance Scale Applying knowledge of probability

219 Ideas of chance and uncertainty Language of chance Simple choice and decision making Being able to classify outcomes using appropriate language, e.g. likely, certain. Predicting and describing likelihood Previous knowledge and understanding Know and understand appropriate vocabulary of chance Predicting Be and able describing to make and the justify likelihood simple choices of events and occurring can help develop decisionsthe ability Choice to make and informed choices and Predicting mathematical and Verbally thinking. justify reasons decision for outcomes using describing appropriate vocabulary Probability making based likelihood on likelihood Predicting and describing likelihood Language of chance Scale Applying knowledge of probability

220 Ideas of chance and uncertainty Simple choice and decision making Predicting and describing What is likelihood it? Predicting and describing the likelihood of events occurring can help develop the ability Choice to An make awareness and informed of scale choices and Predicting mathematical and thinking. decision describing Probability making based likelihood on likelihood Predicting and describing likelihood Scale Knowledge of the numerical scale to describe probability 0-1. Previous knowledge and understanding Understand the concepts of certainty and impossibility Awareness the vocabulary of chance and uncertainty Language of chance Scale Applying knowledge of probability

221 Ideas of chance and uncertainty Choice and decision making based on likelihood Simple choice and decision making Choice and Predicting Developing and an understanding of how likely an event is to decision describing happen will support the decision making process. Probability making based likelihood on likelihood Choice and decision making based on likelihood Conducting chance experiments Order the chance of specified outcomes Applying knowledge of probability

222 Ideas of chance and uncertainty Simple choice and decision making Choice and decision making based on likelihood Likelihood is the probable chance of an event occurring and using this information to make informed choices. Choice and decision making based on likelihood Previous knowledge and understanding Know and understand appropriate vocabulary for likelihood, e.g. impossible, possible, certain Understand their predictions of outcomes based on past experiences Have an awareness that you can predict probability based on described likelihood of past events Choice and Predicting Developing and an understanding of how likely an event is to decision describing happen will support the decision making process. Probability making based likelihood on likelihood Choice and decision making based on likelihood Conducting chance experiments Order the chance of specified outcomes Applying knowledge of probability

223 Conducting chance experiments Ideas of chance and uncertainty Practical experiments to support understanding of possible outcomes and the likelihood of event occurring. Simple choice and decision making Previous knowledge and understanding Know and understand appropriate vocabulary for likelihood, e.g. impossible, possible, certain Choice and decision making based on likelihood Understand how to predict probability based on described likelihood of past events Know how to explain possible outcomes in the context of probability Awareness of desired outcome(s), e.g. picking a red counter from a bag of red, blue and green Choice and Predicting Understand Developing and certainty an understanding impossibility of how likely an event is to decision describing happen will support the decision making process. Probability making based likelihood on likelihood Choice and decision making Conducting chance experiments Order the chance of specified outcomes Applying knowledge of probability

224 Order the chance of specified outcomes Ideas of chance and uncertainty Use the numerical value to order events from most likely to least likely. Simple choice and decision making Choice and decision making based on likelihood Choice and Predicting Developing and an understanding percentages of how likely an event is to decision describing happen will support the decision making process. Probability making based likelihood on likelihood Choice and decision making Previous knowledge and understanding Know the scale between 0-1 Know that probability can be represented by a numerical scale from 0 to 1 inclusive, using the appropriate language, e.g. possible, certain, evens Demonstrate ability to order probabilities of particular events, appropriate to level using appropriate language, e.g possible Know and understand place value with especially decimal fractions Know the interrelationship between fractions, decimal fractions and Conducting chance experiments Order the chance of specified outcomes Applying knowledge of probability

225 Ideas of chance and uncertainty Probability Simple choice and decision making Calculating theoretical probability helps build an understanding of the consequences of events and likelihood of an event occurring. Choice and Predicting and decision describing Probability making Assigning based Interpreting likelihood Probability numerical values probability on likelihood Applying knowledge of probability Notation

226 Ideas of chance and uncertainty Simple choice and decision making Probability The likelihood of an event occurring. Many events cannot be predicted with total certainty. Previous knowledge and understanding Know and understand Probability appropriate vocabulary for probability, e.g. impossible, possible, certain Know that probability can be represented by a numerical scale from 0 to 1 inclusive Understand the concepts Calculating of mathematical theoretical certainty probability and helps build an impossibility understanding of the consequences of events and likelihood Be able to describe a simple outcome s probability by placing it on of an event occurring. the scale, with divisions appropriate to level Choice and Predicting and decision describing Probability making Assigning based Interpreting likelihood Probability numerical values probability on likelihood Applying knowledge of probability Notation

227 Ideas of chance and uncertainty Previous knowledge and understanding Simple choice and decision making Assigning numerical values A probability scale is used to numerically represent the probability of an event occurring. The numerical representation can be in the form of fractions, decimal fractions or percentages within a scale of 0-1 or 0-100%. The probability of any possible mutually exclusive event happening is 1, i.e. certain. Know that probability can be represented by a numerical scale from 0 to 1 inclusive Be able to describe Probability a simple outcome s probability by placing it on the scale, with divisions appropriate to level Know how to construct a numerical representation of probability Know and understand appropriate vocabulary for probability, e.g. mutually exclusive Relate vocabulary to the probability scale fluently Understand and be able to use fractional notation Know and understand place value especially decimal fractions Know and understand the interrelationship between fractions, decimal fractions and percentages Calculating theoretical probability helps build an understanding of the consequences of events and likelihood of an event occurring. Choice and Predicting and decision describing Probability making Assigning based Interpreting likelihood Probability numerical values probability on likelihood MAIN MENU Applying knowledge of probability Notation

228 Ideas of chance and uncertainty event happening to inform decision making. Simple choice and decision making Probability Interpreting probability Using the numerical representation to determine the likelihood of the Previous knowledge and understanding Know that probability can be represented by a numerical scale from 0 to 1 inclusive Calculating theoretical scale, probability with divisions helps appropriate build an to level understanding of the consequences of events and likelihood of an event occurring. predict Choice future and outcomes Predicting and decision describing Probability making Assigning based Interpreting likelihood Probability numerical values probability on likelihood Be able to describe a simple outcome s probability by placing it on the Know how to construct a numerical representation of probability Awareness that the numerical representation of an outcome, can Applying knowledge of probability Notation

229 Ideas of chance and uncertainty Notation Simple choice and decision making Probability A method of expressing the probability of an event occurring using a mathematical statement. Calculating theoretical probability helps build an understanding of the consequences of events and likelihood Previous knowledge and understanding Know that probability can be represented by a numerical scale from 0 to 1 inclusiveof an event occurring. Know how to construct a numerical representation of probability Know how to order Predicting probabilities and based on numerical scale 0-1 Understand place value describing especially decimal fractions Know and understand likelihood the Probability interrelationship between fractions, decimal fractions and percentages Choice and decision making Assigning based numerical values on likelihood Probability Interpreting probability Applying knowledge of probability Notation

230 Ideas of chance and uncertainty Applying knowledge of probability Simple choice and decision making Understanding and being able to quantify risks helps us to Choice and Predicting make more and informed decisions. decision describing Probability making based likelihood on likelihood Applying knowledge of probability Formula Applying knowledge of probability

231 Applying knowledge of probability The ability to assess risk involves considering all the possible outcomes and planning for them. This would include understanding of chance experiments involving repeated trials often with the use of technology. Ideas of chance and uncertainty Previous knowledge and understanding Know and understand how to use numerical representations of probability Know how to give the probability of an event happening or not occurring Demonstrate awareness of how influencing the possible outcomes affects the probability of the desired outcome Know the difference between theoretical and experimental probability, e.g. you CAN toss a coin 3 times and get 3 heads. Simple choice and decision making Applying knowledge of probability Awareness of the concept of risk, and how this affects real life, e.g. insurance Understand chance and experiments Understand sample size and its relationship to reliability and validity Understanding and being able to quantify risks helps us to Choice and Predicting make more and informed decisions. decision describing Probability making based likelihood on likelihood Applying knowledge of probability Formula Applying knowledge of probability

232 Formula Ideas of chance and uncertainty Is used to calculate the probability of an event occurring. Simple choice and decision making Previous knowledge and understanding Know that probability can be represented by a numerical scale from 0 to 1 inclusive Be able to describe a simple outcome s probability by placing it on the scale, Applying with divisions knowledge appropriate to of level Know how to construct a numerical representation of probability Know Why is and it understand important? appropriate vocabulary for probability, e.g. mutually exclusive Understanding and being able to quantify risks helps us to Relate vocabulary to the probability Choice scale and fluently Predicting Understand make more and sample informed size and decisions. its decision relationship to reliability and validity describing Probability making based likelihood on likelihood Applying knowledge of probability Formula Applying knowledge of probability

233 Expressions and equations Simple algebraic equations Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and symbols Evaluate algebraic expressions Equations Formulae Factors of algebraic expressions Simplifying algebraic terms Solution Sets

234 Expressions and equations pathway showing milestones Initial algebraic thinking Simple Developing early algebraic thinking will lay the foundations algebraic for learners to be more equations successful in achieving the associated key milestones for the progression pathway in algebra. Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and Evaluate algebraic symbols Initial algebraic expressions thinking Equations Formulae Factors of algebraic expressions Simplifying algebraic terms Solution Sets

235 Expressions and equations pathway Initial algebraic thinking showing milestones Initial algebraic thinking Initial algebraic thinking is understanding the order of numbers, their place on the number line and how they can be combined. This is an essential step to developing algebraic Why capabilities. is it important? Simple Previous knowledge and understanding algebraic Basic number bonds equations The concept of the number line algebra. The order of numbers on a number line Developing early algebraic thinking will lay the foundations for learners to be more successful in achieving the associated key milestones for the progression pathway in Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and Evaluate algebraic symbols Initial algebraic expressions thinking Equations Formulae Factors of algebraic expressions Simplifying algebraic terms Solution Sets

236 Expressions and equations pathway showing milestones Mathematical operators Simple algebraic equations Being able to use and interpret mathematical symbols is a necessary skill in developing an understanding of algebra. Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and Mathematical symbols operators Evaluate algebraic Equality expressions and balance Inequality Equationsand imbalance Formulae Greater than/ less than Factors of algebraic expressions Simplifying algebraic terms Solution Sets

237 Expressions and equations pathway showing Mathematical operators milestones Mathematical operators Symbols are part of the universal language of mathematics. Being able to use and interpret mathematical symbols is a necessary skill in developing an understanding of algebra. Simple The four operators +,,, are the first set of algebraic symbols that learners usually become familiar with. equations These symbols allow mathematical statements to be expressed in as short and concise a way as possible. Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and Mathematical symbols operators Evaluate algebraic Equality expressions and balance Inequality Equationsand imbalance Formulae Greater than/ less than Factors of algebraic expressions Simplifying algebraic terms Solution Sets

238 Expressions and equations pathway showing milestones Mathematical operators Why is it Equality important? and balance Being able to use and interpret mathematical symbols is a necessary skill in developing an understanding of algebra. Simple The equal sign indicates algebraic that one quantity is the same as another. Visualising the equations equals sign (=) as a balance point is very useful as algebraic operations progress and extend to more challenging equations. Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and Mathematical symbols operators Evaluate algebraic Equality expressions and balance Inequality Equationsand imbalance Formulae Greater than/ less than Factors of algebraic expressions Simplifying algebraic terms Solution Sets

239 Expressions and equations pathway showing milestones Mathematical operators Being able to use and interpret mathematical symbols is a necessary skill in developing an understanding of algebra. Simple algebraic Inequality and imbalance equations A symbol for is not equal to ( ) is required when quantities on either side do not have the same value. Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and Mathematical symbols operators Evaluate algebraic Equality expressions and balance Inequality Equationsand imbalance Formulae Greater than/ less than Factors of algebraic expressions Simplifying algebraic terms Solution Sets

240 Expressions and equations pathway showing milestones Initial algebraic thinking Mathematical operators Mathematical operators Being able to use and interpret mathematical symbols is a necessary skill in developing an understanding of algebra. Pictures and Mathematical symbols operators Simple algebraic equations Evaluate algebraic Equality expressions and balance Greater than/less than Symbols to represent greater than (>), less than (<), greater than or equal to ( ) and less than or equal to ( ) are also part of the language of algebra. Previous knowledge and understanding Recognising the four operations Confidence with number bonds The order of numbers on the number line Inequality Equationsand imbalance Formulae Greater than/ less than Factors of algebraic expressions Mathematical Modelling Simplifying algebraic terms Solution Sets

241 Expressions and equations pathway showing milestones Pictures and symbols Understanding that numbers, and operators, can be replaced by pictures or symbols Simple is fundamental to all algebraic thinking. Introducing algebraic the concept of finding the unknown equations quantity, or operator, is an essential step in developing the ability to work with expressions and solve equations. Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and Evaluate algebraic symbols Pictures and expressions Abstract symbols Thinking Equations Formulae Factors of algebraic expressions Simplifying algebraic terms Solution Sets

242 Expressions and equations pathway showing What is milestones it? Initial algebraic thinking A picture or symbol that replaces a certain number, or operator, in one equation or expression can have a completely different value in Why another is it equation important? expression. A picture or symbol can represent a number or operator but not necessarily the same number all the time. The understanding of variability is important in algebra. Simple algebraic equations Previous knowledge and understanding The concept of greater than and less than when relating to the number line Mathematical operators Pictures and symbols Pictures and symbols Understanding that numbers, and operators, can be replaced by pictures or symbols is fundamental to all algebraic thinking. Introducing the concept of finding the unknown quantity, or operator, is an essential step in developing the ability to work with expressions and solve equations. Pictures and Evaluate algebraic symbols Pictures and Equations expressions Abstract symbols Thinking Formulae Factors of algebraic expressions Mathematical Modelling Simplifying algebraic terms Solution Sets

243 Expressions and equations pathway showing milestones Pictures and symbols Understanding that numbers, and operators, can be replaced by pictures or symbols is fundamental to all algebraic thinking. Introducing the concept of finding the unknown quantity, or operator, is an essential step in developing the ability to work with expressions and solve equations. Simple Abstract algebraic Thinking equations Abstract thinking is about thinking logically without the use of concrete material or visual representations. Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and Evaluate algebraic symbols Pictures and expressions Abstract symbols Thinking Equations Formulae Factors of algebraic expressions Simplifying algebraic terms Solution Sets

244 Expressions and equations pathway showing milestones Simple algebraic equations Moving from pictures or symbols to letters paves the way for solving algebraic Simple equations and evaluating algebraic expressions. This also algebraic helps develop an understanding of equations variables and constants. Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and Evaluate algebraic Developing Equations symbols Simple algebraic expressions approaches to equations solving equations Formulae Factors of algebraic expressions Simplifying algebraic terms Solution Sets

245 Expressions and equations pathway showing milestones Initial algebraic thinking Simple algebraic equations Simple algebraic variables equations and (variables constants. to a power are not included) that have one variable or one letter have one correct solution, e.g. 4 + x = 9. Mathematical operators Simple algebraic equations Moving from pictures or symbols to letters paves the way Simple algebraic for solving equations algebraic equations and evaluating algebraic expressions. This also helps develop an understanding of Pictures and Evaluate algebraic Developing Equations symbols Simple algebraic expressions approaches to equations solving equations Simplifying algebraic terms Formulae Factors of algebraic expressions Mathematical Modelling Solution Sets

246 Expressions and equations pathway showing milestones Developing approaches to solving equations Simple algebraic equations A sound knowledge of number facts will support the ability to solve simple algebraic equations. Learners may use their knowledge of inverse operations to find solutions when the equations become progressively more challenging. Simple Previous knowledge algebraic and understanding Using pictures equations to represent numbers Number bond problems involving pictures or symbols The significance of the = sign and its link to balance Moving from pictures or symbols to letters paves the way for solving algebraic equations and evaluating algebraic expressions. This also helps develop an understanding of variables and constants. Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and Evaluate algebraic Developing Equations symbols Simple algebraic expressions approaches to equations solving equations Formulae Factors of algebraic expressions Simplifying algebraic terms Solution Sets

247 Expressions and equations pathway showing milestones Simplifying algebraic terms Many problems involve a number of algebraic terms, some of which have common Simple variables. Being able to simplify this combination of algebraic terms makes solving the problem equations considerably less challenging. Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and Evaluate algebraic symbols Simplifying algebraic expressions terms Equations Formulae Factors of algebraic expressions Simplifying algebraic terms Solution Sets

248 Expressions and equations pathway showing Simplifying milestones algebraic terms Simplifying algebraic terms The simplification of like terms, or collecting like terms, is the process of writing a combination of different algebraic terms in as compact a way as possible. Simple Previous knowledge and understanding algebraic Familiarity with algebraic conventions, equations e.g. a + a = 2a and 1a is always written as a The properties of basic geometric shapes for context Many problems involve a number of algebraic terms, some of which have common variables. Being able to simplify this combination of terms makes solving the problem considerably less challenging. Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and Evaluate algebraic symbols Simplifying algebraic expressions terms Equations Formulae Factors of algebraic expressions Simplifying algebraic terms Solution Sets

249 Expressions and equations pathway showing milestones Evaluate algebraic expressions Substituting given values into algebraic expressions and consequently obtaining Simple a value for the expression is important in mathematical algebraic modeling. Understanding that equations the values to be substituted into the expressions can change allows different problems to be solved. Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and Evaluate algebraic symbols Evaluate algebraic Equations expressions Substitution expressions Formulae Variables Factors of algebraic expressions Simplifying algebraic terms Solution Sets

250 Expressions and equations pathway showing milestones Evaluate algebraic expressions Substituting given values into algebraic expressions and Evaluate algebraic consequently expressions obtaining a value for the expression is important in mathematical modeling. Understanding that the values to be substituted into the expressions can change allows different problems to be solved. Simple algebraic equations Evaluating is performing the calculations which are implied in the expression to find the value of an algebraic expression. Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and Evaluate algebraic symbols Evaluate algebraic Equations expressions Substitution expressions Formulae Variables Factors of algebraic expressions Simplifying algebraic terms Solution Sets

251 Expressions and equations pathway showing milestones Evaluate algebraic expressions Substitution Substituting given values into algebraic expressions and consequently obtaining a value for the expression is important in mathematical modeling. Understanding that the values to be substituted into the expressions can change allows different problems to be solved. Substitution Simple is replacing a letter in an algebraic expression with a numerical algebraic value. Different letters can be assigned different numerical equations values, unless they are constants such as Pi (π). If a letter appears more than once in an expression, the same numerical value is assigned each time. Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and Evaluate algebraic symbols Evaluate algebraic Equations expressions Substitution expressions Formulae Variables Factors of algebraic expressions Simplifying algebraic terms Solution Sets

252 Expressions and equations pathway showing milestones Evaluate algebraic expressions Variables A variable quantity, as its name suggests, can change in value. Substituting given values into algebraic In algebra, expressions letters can be and assigned a number. consequently obtaining Simple a value for the expression is important in mathematical algebraic modeling. Previous Understanding knowledge understanding that equations the values to be substituted into the Familiarity expressions with algebraic can change convention, e.g. 3c = 3 c = c + c + c allows different problems to be solved. Simplifying groups of like terms Using the four operations Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and Evaluate algebraic symbols Evaluate algebraic Equations expressions Substitution expressions Formulae Variables Factors of algebraic expressions Simplifying algebraic terms Solution Sets

253 Expressions and equations pathway showing milestones Equations Translating a real problem from words into a simple equation demonstrates Simple the importance and relevance of mathematics. Being algebraic able to form equations from equations written, pictorial or spoken information is fundamental to mathematical modelling. Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and symbols Equations Evaluate Forming algebraic simple equations Equations expressions from statements and problems Formulae Solving equations Factors of algebraic expressions Simplifying algebraic terms Solution Sets

254 Expressions and equations pathway showing milestones Equations Initial algebraic thinking Equations Simple algebraic equations Equations use letters, numbers, signs and symbols and allow given situations or mathematical conditions to be modelling. expressed in the most concise way possible. Mathematical operators Translating a real problem from words into a simple equation demonstrates the importance and relevance of mathematics. Being able to form equations from written, pictorial or spoken information is fundamental to Pictures and symbols Equations Evaluate Forming algebraic simple equations Equations expressions from statements and problems Simplifying algebraic terms Formulae Solving equations Factors of algebraic expressions Mathematical Modelling Solution Sets

255 Expressions and equations pathway showing milestones Equations Forming simple equations from statements and problems Letters are assigned to each variable and appropriate mathematical signs are used to imply the correct calculation. Simple equations Simple will normally have one variable and one solution. Familiarity algebraic with integers and fractions allows scope for forming equations that may not have whole number solutions. The facts and properties of geometric shapes can be used to form simple equations. Translating a real problem from words into a simple equation demonstrates the importance and relevance of mathematics. Being able to form equations from written, pictorial or spoken information is fundamental to mathematical modelling. Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and symbols Equations Evaluate Forming algebraic simple equations Equations expressions from statements and problems Formulae Solving equations Factors of algebraic expressions Simplifying algebraic terms Solution Sets

256 Expressions and equations pathway Solving equations showing milestones Equations Translating a real problem from words into a simple equation demonstrates Simple the importance of individual and values. relevance of mathematics. Being algebraic able to form equations from equations written, pictorial or spoken information is fundamental to mathematical modelling. An equals symbol (=) and language such as solve would indicate that a numerical value has to be found. An equation can be solved using different procedures. Solutions to equations can be found algebraically or graphically. Solving an equation or inequation can result in a unique solution (one answer), an interval of values or a choice Previous knowledge and understanding Solving simple equations The properties of geometric shapes for context Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and symbols Equations Evaluate Forming algebraic simple equations Equations expressions from statements and problems Formulae Solving equations Factors of algebraic expressions Simplifying algebraic terms Solution Sets

257 Expressions and equations pathway showing milestones Formulae Being able to use formulae is essential in many areas of the curriculum and beyond. Simple Being able to construct a formula supports the type algebraic of problem solving skills needed in many equations occupations in the modern world. Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and symbols Formulae Evaluate algebraic Equations expressions Creating formulae and generating solutions Formulae Factors of algebraic expressions Simplifying algebraic terms Solution Sets

258 Expressions and equations pathway showing milestones Formulae Formulae Being able to use formulae is essential in many areas of the curriculum and beyond. Being able to construct a formula supports the type of problem solving skills needed in many Formulae show the proven relationship Simple between quantities using letters, signs and symbols and algebraic describe the calculations needed to evaluate any given quantity. equations Some formulae can have constants occupations involved as well in as the letters modern for each world. variable. Formulae can involve a combination of constants and letters. Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and symbols Formulae Evaluate algebraic Equations expressions Creating formulae and generating solutions Formulae Factors of algebraic expressions Simplifying algebraic terms Solution Sets

259 Expressions and equations pathway different quantities and obtaining a rule that links these showing milestones Formulae Creating formulae and generating solutions Formulae are created by comparing the relationship between quantities. Solutions can be found from the calculations involved in using formulae. Formulae are a mechanism for producing different output values dependent on the values substituted in the first place. Simple formulae are ideal for comparing changes in output with changes in input. Being able to use formulae is essential in many areas of the curriculum and beyond. Being able to construct a formula supports the type of problem solving skills needed in many occupations in the modern world. Previous knowledge Simple and understanding Letters can algebraic represent quantities, e.g. P can represent perimeter equations (important reminder: if the perimeter was 20cm then P would represent 20 and Pcm would be 20cm) Algebraic conventions, e.g. abc means a b c, a x a = a 2 Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and symbols Formulae Evaluate algebraic Equations expressions Creating formulae and generating solutions Formulae Factors of algebraic expressions Simplifying algebraic terms Solution Sets

260 Expressions and equations pathway showing milestones Factors of algebraic expressions Simple algebraic equations The ability to factorise algebraic expressions enables more complex equations to be solved in an efficient manner. Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and Evaluate algebraic symbols Factors of algebraic Equations expressions Recognising common expressions factors Understanding Formulae the distributive law Factors of algebraic expressions Simplifying algebraic terms Solution Sets

261 Expressions and equations pathway showing milestones Factors of algebraic expressions Factors of algebraic expressions Simple algebraic This development builds on the previous equations work and now involves common algebraic factors as well as numerical factors and the use of brackets to represent the factorised terms. The ability to factorise algebraic expressions enables more complex equations to be solved in an efficient manner. Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and Evaluate algebraic symbols Factors of algebraic Equations expressions Recognising common expressions factors Understanding Formulae the distributive law Factors of algebraic expressions Simplifying algebraic terms Solution Sets

262 Expressions and equations pathway showing milestones Factors Recognising of algebraic common expressions factors Simple When comparing algebraic the factors of two or more terms, being able to list factors equations that are common, is important. The concept of a highest common factor is critical to factorising fully an expression. The ability to factorise algebraic expressions enables more complex equations to be solved in an efficient manner. Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and Evaluate algebraic symbols Factors of algebraic Equations expressions Recognising common expressions factors Understanding Formulae the distributive law Factors of algebraic expressions Simplifying algebraic terms Solution Sets

263 Expressions and equations pathway Understanding the distributive law showing milestones Factors of algebraic expressions Simple algebraic equations The distributive law highlights a basic mathematical process and its equivalent inverse process. Multiplying the sum of two numbers by a third number is the same as multiplying the two numbers individually by the third number first and then finding the sum of the two new numbers formed. a (b + c) = ab + ac Previous knowledge and understanding The factors of a number Listing common factors for two or more numbers The ability to factorise algebraic expressions enables more complex equations to be solved in an efficient manner. Recognising the highest common factor Algebraic convention, e.g. 6a = 3 x 2a Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and Evaluate algebraic symbols Factors of algebraic Equations expressions Recognising common expressions factors Understanding Formulae the distributive law Factors of algebraic expressions Simplifying algebraic terms Solution Sets

264 Expressions and equations pathway showing milestones Mathematical modelling Many problems in manufacturing, engineering, technology and science require Simple the skills involved in mathematical modelling. This ability algebraic to construct, interpret and solve equations equations or inequations that represent a real life, or theoretical, situation are fundamental to the process. Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and Evaluate algebraic symbols Mathematical Equations expressions Solving inequalities modelling Formulae Factors of algebraic expressions Simplifying algebraic terms Solution Sets

265 Expressions and equations pathway showing milestones Mathematical modelling Initial algebraic thinking Mathematical modelling is a skill that involves translating a complex problem into the most concise algebraic form. It is the ability to read and interpret a Simple problem, to express the information appropriately as an equation, algebraic inequation, equations inequality or formula, to solve it and to be able to communicate the answer using the context of the original information. Mathematical operators Mathematical modelling Many problems in manufacturing, engineering, technology and science require the skills involved in mathematical modelling. This ability to construct, interpret and solve equations or inequations that represent a real life, or theoretical, situation are fundamental to the process. Pictures and Evaluate algebraic symbols Mathematical Equations expressions Solving inequalities modelling Formulae Factors of algebraic expressions Mathematical Modelling Simplifying algebraic terms Solution Sets

266 Solving inequalities Expressions and equations pathway either greater than sign, greater than or equal to sign, less showing milestones Solving inequalities is the idea of a set of possible solutions. An inequality does not have an equality sign but instead uses than sign or less than or equal to sign. The same concepts and skills used to solve equations can help to solve inequalities. It is important to stress that attention should be paid to the conditions that are applied to the inequality as this will impact on what is permitted in the solution set. Mathematical modelling e.g. x 5, where x is a single digit whole number Many problems in manufacturing, engineering, technology and science require the skills involved in mathematical modelling. This ability to construct, interpret and solve equations or inequations that represent a real life, or theoretical, situation are fundamental to the process. Previous knowledge Simple and understanding Changing algebraic words and diagrams into algebraic form The properties equations of geometric shapes for context Angle classifications, e.g. complementary and supplementary angles Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and Evaluate algebraic symbols Mathematical Equations expressions Solving inequalities modelling Formulae Factors of algebraic expressions Simplifying algebraic terms Solution Sets

267 Expressions and equations pathway showing milestones Solution sets Simple algebraic equations Many mathematical problems can have more than one solution. The ability to list all possible solutions is essential in mathematical problems of this type. Mathematical Modelling Initial algebraic thinking Mathematical operators Pictures and Evaluate algebraic symbols Solution sets expressions Equations Formulae Factors of algebraic expressions Simplifying algebraic terms Solution Sets

268 Expressions and equations pathway showing milestones Initial algebraic thinking A solution set is a set of numbers that lists all possible solutions to a given mathematical problem. In many cases the solution lies within defined mathematical sets. E.g. Whole numbers Solution {0, 1, 2, 3, }, sets Natural numbers (1, 2, 3,.}, Integers {.., -2, -1, 0, 1, 2,.} and Real numbers {all points on an infinitely Simple Why is long it important? number line (e.g. fractions, decimal fractions, roots, π, )} algebraic equations Previous knowledge and understanding Equations, inequations and formulae Mathematical operators Solution sets Many mathematical problems can have more than one solution. The ability to list all possible solutions is essential in mathematical problems of this type. Pictures and Evaluate algebraic symbols Solution sets expressions Equations Formulae Factors of algebraic expressions Mathematical Modelling Simplifying algebraic terms Solution Sets

269 Angles, symmetry and transformation Angles Angle relationships Bearings Positional language Directions and turnings Scale Enlargement and reduction Similarity Understanding symmetry Symmetry Grid references Coordinate system Transformations

270 Angles, symmetry and transformation Angles Positional language Angle relationships Bearings Positional language The use of positional language is one of the first steps in understanding spatial awareness. Directions and turnings Scale Enlargement and reduction Similarity Positional language Understanding symmetry Symmetry Grid references Coordinate system Transformations

271 Angles, symmetry and transformation Positional language Angle Angles Positional language relationships Understanding the position of something in relation to something else and using language such as in front of, behind, Positional above, below. Directions language and turnings Previous knowledge understanding understanding spatial awareness. Vocabulary of position through personal experience. Enlargement and Scale reduction The use of positional language is one of the first steps in Positional language Bearings Similarity Understanding symmetry Symmetry Grid references Coordinate system Transformations

272 Angles, symmetry and transformation Angles Directions & turnings Angle relationships Bearings Positional language Being able to follow and give directions is a necessary life skill that allows local areas to be efficiently navigated. It also develops basic map reading skills. Directions and turnings Directions & turnings Scale Cardinal compass points Enlargement and reduction Similarity Understanding symmetry Symmetry Grid references Coordinate system Transformations

273 Angles, symmetry and transformation Directions & turnings Angles Directions & turnings Angle relationships Positional A description Directions of Why personal is it locations, important? following and giving language directions using and turnings language such as forwards, backwards, left, right, clockwise, anti-clockwise as well as North, South, East and West. develops basic map reading skills. Enlargement and Scale reduction Bearings Being able to follow and give directions is a necessary life skill that allows local areas to be efficiently navigated. It also Directions & turnings Cardinal compass points Similarity Understanding symmetry Symmetry Grid references Coordinate system Transformations

274 Angles, symmetry and transformation Positional language Angle Cardinal Angles compass points Bearings Directions & turnings relationships Understanding that the points of the compass can be used to Directions describe and give directions. and Being turnings able to follow and give directions is a necessary life skill that Previous allows local knowledge areas and to be understanding efficiently navigated. It also Understand and follow instructions develops basic map reading skills. Enlargement and Scale Similarity reduction Directions & turnings Cardinal compass points Understanding symmetry Symmetry Grid references Coordinate system Transformations

275 Angles, symmetry and transformation Angles Angles Angle relationships Bearings Positional language Directions and turnings A knowledge of angles is required for the understanding of position and geometrical properties of shapes. Scale Enlargement and reduction Similarity Angles Classifying angles Measuring Angles Drawing Angles Compass points and angles Understanding symmetry Symmetry Grid references Coordinate system Transformations

276 Angles, symmetry and transformation Angles Angles An angle measures amount of turning. Understanding the relationship between the vocabulary of direction and the associated angle, Positional e.g. ¼ turn = 90º. Directions language and turnings Previous knowledge and understanding Vocabulary associated with position: to the right of etc. Angles A knowledge of angles is required for the understanding of position and geometrical properties of shapes. Angles Classifying angles Scale Measuring Angles Angle relationships Enlargement and reduction Bearings Similarity Drawing Angles Compass points and angles Understanding symmetry Symmetry Grid references Coordinate system Transformations

277 Angles, symmetry and transformation Angles Angles Angle relationships Bearings Why is it Classifying important? angles A knowledge of angles is required for the understanding of position and geometrical properties of shapes. Positional Directions language and turnings Angles can be classified depending on their size, e.g. acute is less than 90º. Enlargement and Scale reduction Angles Classifying angles Measuring Angles Similarity Drawing Angles Compass points and angles Understanding symmetry Symmetry Grid references Coordinate system Transformations

278 Angles, symmetry and transformation Angles Angles Angle relationships Bearings Measuring Angles Positional Directions A language knowledge of angles and turnings is required What for is it? the understanding of position and geometrical properties of shapes. Angles Angles are measured in degrees ( ) using a protractor. Classifying angles Scale Measuring Angles Enlargement and reduction Similarity Drawing Angles Compass points and angles Understanding symmetry Symmetry Grid references Coordinate system Transformations

279 Angles, symmetry and transformation Angles Angles Angle relationships Bearings Drawing Angles Positional Directions A language knowledge of angles and turnings is required for the understanding of position and geometrical properties of shapes. Angles Classifying angles Scale Making use of ruler and protractor to accurately measure and draw a given angle. Enlargement and Similarity reduction Measuring Angles Drawing Angles Compass points and angles Understanding symmetry Symmetry Grid references Coordinate system Transformations

280 Angles, symmetry and transformation Angles Angles Angle relationships Bearings Positional Directions A language knowledge of angles and turnings is required for the understanding of position and geometrical properties of shapes. Angles Classifying angles Scale Measuring Angles Enlargement and reduction Compass points and angles Investigate the angle between two compass points. Similarity Drawing Angles Compass points and angles Understanding symmetry Symmetry Grid references Coordinate system Transformations

281 Angles, symmetry and transformation Angle Relationships Angles Angle relationships Bearings Positional language Directions An understanding turnings of the angle relationships in 2D diagrams allows for the calculation of missing angles. Angle Relationships Scale Naming angles Enlargement and reduction Angles in geometric shapes and intersecting lines Similarity Angles and circles Understanding symmetry Symmetry Grid references Coordinate system Transformations

282 Angles, symmetry and transformation Angle Relationships Angles Angle relationships Bearings Angle Relationships An understanding of the angle relationships in 2D diagrams allows for the calculation of missing angles. Positional Directions What language is it? and turnings Knowledge of the sum of the angles in 2D shapes. Angle Relationships Scale Naming angles Understanding symmetry Enlargement and reduction Angles in geometric shapes and intersecting lines Similarity Angles and circles Symmetry Grid references Coordinate system Transformations

283 Angles, symmetry and transformation Naming angles Positional language Angles are named using three letters. These are written at the vertex and at the ends of the two arms that form the angle. The vertex is always the middle of the three letters. Angle Angles This angle is made from two arms, AB and relationships BD, with vertex at B. <DBA or <ABD D Directions and turnings A Angle Relationships An understanding of the angle relationships in 2D diagrams allows for the calculation of missing angles. Angle Relationships B Scale Naming angles Enlargement and reduction Angles in geometric shapes and intersecting lines Bearings Similarity Angles and circles Understanding symmetry Symmetry Grid references Coordinate system Transformations

284 Angles, symmetry and What transformation is it? Positional language Angle Relationships Directions An understanding turnings of the angle relationships in 2D diagrams allows for the calculation of missing angles. Angle Relationships Angles in geometric shapes and intersecting lines Knowledge of the sum of the angles in 2D shapes. The conditions for complementary (add up to 90º) and supplementary (add up to 180º) angles. The occurrence of corresponding and alternate angles in parallel lines. Angle Angles The occurrence Bearings relationships of vertically opposite angles. (F, Z and X angles) Scale Naming angles Enlargement and reduction Angles in geometric shapes and intersecting lines Similarity Angles and circles Understanding symmetry Symmetry Grid references Coordinate system Transformations

285 Angles, symmetry and transformation Positional language Angle Relationships Angles Directions An understanding turnings of the angle relationships in 2D diagrams allows for the calculation of missing angles. Angle Relationships Scale Naming angles Angles and circles A tangent is a straight line that touches the diameter of a circle at one point only. If a radius is also drawn to this point then Angle the resulting angle between radius and tangent is right-angled Bearings relationships and so the tangent is perpendicular to the radius at the point of contact. Understand that a triangle formed using the endpoints of the diameter of a circle and the third point rests on the circumference of the circle will always be right-angled. Previous knowledge and understanding The meaning of perpendicular Enlargement and Similarity reduction Angles in geometric shapes and Angles and circles intersecting lines Understanding symmetry Symmetry Grid references Coordinate system Transformations

286 Angles, symmetry and transformation Bearings Angles Angle relationships Bearings Positional language Understanding bearings is essential for the daily safety of millions when travelling on planes or ships at sea. Directions and turnings Scale Enlargement and reduction Similarity Bearings Understanding symmetry Symmetry Grid references Coordinate system Transformations

287 Angles, symmetry and transformation Bearings Understanding the convention used when describing a bearing. Being able to link all standard compass points with their associated bearings. Being able to construct accurate scale Angle drawings for journeys involving distances Angles and bearings. relationships Bearings Previous knowledge and understanding Positional Scale drawing Directions language Points on and a compass turnings Measuring angles Complimentary and supplementary angles Understanding bearings is essential for the daily safety of millions when travelling on planes or ships at sea. Bearings Scale Enlargement and reduction Bearings Similarity Understanding symmetry Symmetry Grid references Coordinate system Transformations

288 Angles, symmetry and transformation Scale Angles Angle relationships Bearings Positional language Scale is essential for regularly encountered contexts such as maps, plans and modelling. Directions and turnings Scale Enlargement and reduction Similarity Scale Understanding symmetry Symmetry Grid references Coordinate system Transformations

289 Angles, symmetry and transformation Scale Understanding scale factors and using them to solve problems Angle that relate to similar objects, shapes, Angles maps and plans. Choose Scale relationships an appropriate scale to draw journeys where all actual information is given. Positional Directions Previous knowledge and understanding language and turnings Ratio Measuring and drawing angles Scale Enlargement and reduction Bearings Scale is essential for regularly encountered context such as maps, plans and modelling. Scale Similarity Understanding symmetry Symmetry Grid references Coordinate system Transformations

290 Angles, symmetry and transformation Positional language Enlargement and Reduction Directions and turnings Angles Scale Angle relationships Enlargement and reduction Bearings Enlargement of molecular structures assists with investigations into cells and supports medical advancements. Reduced scale models are commonly used in wind tunnels to determine wind resistance etc. Enlargement and reduction Similarity Understanding symmetry Symmetry Grid references Coordinate system Transformations

291 Angles, symmetry and transformation Angle Enlargement Angles and Reduction relationships Positional Being able to Directions enlarge and reduce a given diagram or model by a language scale factor, understanding turnings the application of scale factor to all lengths. Understand that there is conservation of angles within reduction and enlargement. determine wind resistance Enlargement and Scale etc. reduction Bearings Enlargement and reduction Enlargement of molecular structures assists with investigations into cells and supports medical advancements. Reduced scale models are commonly used in wind tunnels to Enlargement and reduction Similarity Understanding symmetry Symmetry Grid references Coordinate system Transformations

292 Angles, symmetry and transformation Positional language Similarity Directions and turnings Angles Scale Angle relationships Enlargement and reduction Bearings Appreciating that two objects which are similar will share key properties, underpins the practice of modelling. This allows wind tunnels, wave tanks etc. to be used on scaled down models knowing results obtained will mirror real-life outcomes. Similarity Similarity Understanding symmetry Symmetry Grid references Coordinate system Transformations

293 Similarity Angles, symmetry and transformation Being able to calculate and use a scale factor that connects two similar figures. Understand that problems involving the area of similar figures requires the scale factor to be squared. Possible extension: problems that compare Similarity the volumes Angle Angles of two similar objects require the scale factor to be cubed. relationships Previous knowledge and understanding Positional Ratio Directions language Scale factors and turnings Solving basic scale problems Squaring and cubing fractions Scale Similarity Enlargement and reduction Bearings Appreciating that two objects which are similar will share key properties, underpins the practice of modelling. This allows wind tunnels, wave tanks etc. to be used on scaled down models knowing results obtained will mirror real-life outcomes. Similarity Understanding symmetry Symmetry Grid references Coordinate system Transformations

294 Angles, symmetry and transformation Angle Understanding Anglesymmetry relationships Bearings Positional language Interpreting and drawing symmetrical patterns, shapes and pictures develops an understanding of the relationship between reflection and symmetry. Directions and turnings Understanding symmetry Scale Enlargement and reduction Similarity Understanding symmetry Symmetry Grid references Coordinate system Transformations

295 Angles, symmetry and transformation Understanding symmetry Angle Understanding symmetry Angles relationships Exposure to constructing Why is it symmetrical important? patterns, shapes and Positional pictures to help Directions develop an elementary understanding of language symmetry. Exploring and turnings mirror symmetry and recognising that size, shape and distances from the centre line are preserved in between reflection and symmetry. symmetry. Enlargement and Scale reduction Interpreting and drawing symmetrical patterns, shapes and pictures develops an understanding of the relationship Understanding symmetry Bearings Similarity Understanding symmetry Symmetry Grid references Coordinate system Transformations

296 Angles, symmetry and transformation Positional language Symmetry Directions and turnings Angles Scale Angle relationships Enlargement and reduction Bearings Investigating symmetrical patterns and designs enhances an understanding and appreciation of the natural world and art. It is also fundamental to developing skills associated with geometrical reasoning. Similarity Symmetry Line symmetry Rotational symmetry Understanding symmetry Symmetry Grid references Coordinate system Transformations

297 Angles, symmetry and transformation Symmetry Symmetry Angles Angle relationships Positional Directions language and turnings Recognising that symmetrical patterns have proportion and balance. geometrical reasoning. Enlargement and Scale reduction Bearings Investigating symmetrical patterns and designs enhances an understanding and appreciation of the natural world and art. It is also fundamental to developing skills associated with Similarity Symmetry Line symmetry Rotational symmetry Understanding symmetry Symmetry Grid references Coordinate system Transformations

298 Angles, symmetry and transformation Positional language Symmetry Directions and turnings Angles Line symmetry Scale Angle relationships Enlargement and reduction Bearings Why is it What important? is it? Investigating congruent symmetrical parts, each patterns of which and is the designs mirror enhances image of the an understanding other. The and line of appreciation symmetry can of be the horizontal, natural world vertical and or art. It is also inclined. fundamental to developing skills associated with geometrical reasoning. Recognising that a line of symmetry divides a shape into two Similarity Symmetry Line symmetry Rotational symmetry Understanding symmetry Symmetry Grid references Coordinate system Transformations

299 Angles, symmetry and transformation Positional language Symmetry Directions and turnings Angles Scale Rotational symmetry Angle Bearings What relationships is it? A shape has rotational symmetry if it can be rotated through an angle to fit exactly on to its original outline. The order of rotational symmetry is the number of times a shape can be rotated and fit exactly on top of its original position within a complete turn. The centre of symmetry is the fixed point about which the shape is rotated. Enlargement and Similarity reduction Investigating symmetrical patterns and designs enhances an understanding and appreciation of the natural world and art. It is also fundamental to developing skills associated with geometrical reasoning. Symmetry Line symmetry Rotational symmetry Understanding symmetry Symmetry Grid references Coordinate system Transformations

300 Angles, symmetry and transformation Grid References Angles Angle relationships Bearings Positional language Understanding how different grids operate is essential when locating seats on planes or trains, participating in games such as battleships or locating buildings in cities, such as New York. Directions and turnings Scale Enlargement and reduction Similarity Grid References Understanding symmetry Symmetry Grid references Coordinate system Transformations

301 Angles, symmetry and transformation Grid References Angles Angle relationships Bearings Grid References Understanding how different grids operate is essential when locating seats on planes or trains, participating in games such as battleships or locating buildings in cities, such as New York. Positional Directions language Using grids and to help turnings identify position relative to a scale in the horizontal and vertical directions on a page or screen. The scale can use letters or numbers or a combination of Enlargement both. and Scale reduction Grid References Similarity Understanding symmetry Symmetry Grid references Coordinate system Transformations

302 Angles, symmetry and transformation Co-ordinate Angles system Angle relationships Bearings Positional language Co-ordinate grids provide the foundation for describing a unique point and are essential for graphing and transforming geometrical shapes. Directions and turnings Scale Enlargement and reduction Similarity Co-ordinate system Understanding symmetry Symmetry Grid references Coordinate system Transformations

303 Angles, symmetry and transformation Co-ordinate system Labeling and numbering axes. Emphasise the numbering of lines and not spaces in-between. Be able to plot points and Angle give the co-ordinates Co-ordinate of a group of points. Angles system Be able to extend relationships a one quadrant grid to one with four quadrants. Positional Previous knowledge Directions and understanding language Understanding turnings grids Know the numbers on the number line Understand negative geometrical numbers shapes. Scale Enlargement and reduction Bearings Co-ordinate grids provide the foundation for describing a unique point and are essential for graphing and transforming Co-ordinate system Similarity Understanding symmetry Symmetry Grid references Coordinate system Transformations

304 Angles, symmetry and transformation Transformations Angles Angle relationships Bearings Positional language Directions and turnings Transformation of points and 2D shapes is key to integrating all previous geometrical skills and knowledge. Scale Enlargement and reduction Similarity Transformations Understanding symmetry Symmetry Grid references Coordinate system Transformations

305 Angles, symmetry and transformation Transformations Angles Angle relationships Positional Carry out transformations Directions on 2D shapes and points within a language four quadrant and grid turnings all previous involving reflection geometrical and skills translation. and knowledge. The rotation of points and 2D shapes should be considered as a possible extension Enlargement and Scale reduction Bearings Transformations Transformation of points and 2D shapes is key to integrating Transformations Similarity Understanding symmetry Symmetry Grid references Coordinate system Transformations

306 Multiples, factors and primes Multiples and factors Common multiples and factors Prime numbers

307 Multiples, factors and primes Multiples and Factors Understanding of multiples and factors is essential to support work in fractions. A clear understanding of the links within the multiplication tables and Common the use of inverse processes are Multiples essential. and multiples and factors factors Multiples and Factors Prime numbers

308 Multiples, factors and primes Multiple and factors A multiple can be found in the multiplication tables eg the multiples of 7 are Multiples 14, 21, The and multiples Factors are never ending. The factors of a number are any numbers that divide exactly into a larger number. Understanding of multiples and factors is essential to support work in fractions. A clear understanding of the links within the multiplication tables and Common the use of inverse processes are Multiples essential. and multiples and factors factors Previous knowledge and understanding Multiplication tables Division with or without a remainder Multiples and Factors Prime numbers

309 Multiples, factors and primes Common multiples and factors Common multiples and factors help and support learners when working with fractions and algebraic manipulations. Common multiples and factors Multiples and factors Common multiples and factors Lowest common multiple Prime numbers Highest common factor

310 Multiples, factors and primes Common multiples and factors Common multiples Why is and it important? factors Common multiples and factors help and support learners A common multiple when is working a number with that is fractions a multiple and of two algebraic or manipulations. more numbers. If numbers share one or more factors, then Common they are Multiples called the common and factors of those numbers. multiples and factors factors Common multiples and factors Lowest common multiple Prime numbers Highest common factor

311 Multiples, factors and primes Common multiples and factors Lowest common multiple Common multiples and factors help and support learners when working with fractions and algebraic manipulations. which two or more numbers have in common. Common multiples and factors Multiples and factors Common multiples and factors The lowest common multiple (LCM) is the lowest multiple Lowest common multiple Prime numbers Highest common factor

312 Multiples, factors and primes Common multiples and factors Highest common factor Common multiples and factors help What and is support it? learners when working with fractions and algebraic manipulations. Common multiples and factors Multiples and factors Common multiples and factors The largest common factor of two or more numbers is called the highest common factor (HCF). Lowest common multiple Prime numbers Highest common factor

313 Multiples, factors and primes Prime numbers Prime numbers are the building blocks of the number system. The link with factors will establish that every whole number greater than 1 is either prime or is a product of prime numbers. This is the Fundamental Theorem of Arithmetic. Prime numbers are used to encrypt information through communication networks Common utilised by mobile phones and the Multiples internet. and Prime multiples and factors numbers factors Prime numbers

314 Multiples, factors and primes Prime numbers Prime Numbers Prime numbers are the building blocks of the number system. The link with factors will establish that every whole number Prime numbers have only two distinct factors. Prime numbers greater than one is either prime or is a product of prime are whole numbers greater than 1. A prime number can only be divided by itself numbers. and 1 to This give is a the whole Fundamental number solution. Theorem of Arithmetic. Prime numbers are used to encrypt information through Previous knowledge communication and understanding networks Common utilised by mobile phones and the Being Multiples able to internet. list all and the factors of a number Prime multiples and factors numbers factors Prime numbers

315 Patterns and relationships Number patterns Patterns Formulae Creating graphical representations Gradient Equations of straight lines Number sequences

316 Patterns and relationships Patterns Number patterns Recognising and using patterns is an essential building block for algebraic thinking and understanding numbers. Patterns Patterns Formulae Creating graphical representations Gradient Equations of straight lines Number sequences

317 Patterns and relationships Patterns A pattern is a repetitive sequence of events, shapes or numbers which can be continued. Patterns Previous knowledge and understanding Personal experiences of looking for patterns in the environment Vocabulary of next, before, after Number Knowledge of colour and simple shapes patterns Able to count in order Recognising and using patterns is an essential building block for algebraic thinking and understanding numbers. Patterns Patterns Formulae Creating graphical representations Gradient Equations of straight lines Number sequences

318 Patterns and relationships Number Patterns Recognising and using number patterns is an essential building block for algebraic thinking, algebraic sequencing, generating formulae and graphical representation. Number patterns Patterns Number patternformulae Creating Exploring number graphical patterns representations Gradient Equations of straight lines Number sequences

319 Patterns and relationships Number pattern A number pattern is a set of numbers that is governed by a rule which makes the pattern predictable, e.g. odds and evens, times tables etc. Number Patterns Previous knowledge and understanding Know odd and even numbers Able to add, subtract, multiply and divide Number Multiples patterns Recognising and using number patterns is an essential building block for algebraic thinking, algebraic sequencing, generating formulae and graphical representation. Patterns Number patternformulae Creating Exploring number graphical patterns representations Gradient Equations of straight lines Number sequences

320 Patterns and relationships Number Patterns Exploring number patterns Recognising What and is using it? number patterns is an essential building block for algebraic Explore and thinking, extend prominent algebraic number sequencing, patterns, generating such as formulae and square, graphical triangular representation. and Fibonacci numbers. Number patterns Patterns Number patternformulae Creating Exploring number graphical patterns representations Gradient Equations of straight lines Number sequences

321 Patterns and relationships Number sequences Understanding number sequences allows us to generate algebraic formulae either pictorially, orally or using algebraic notation Number patterns Patterns Number sequences Formulae Creating Modelling graphical representations Gradient Equations of straight lines Number sequences

322 Patterns and relationships Number sequences A number sequence has a rule, which can be used to find the value of each term. It is important to understand and explain the rule associated Number with a number sequences and use the rule to predict any number in the sequence. This is usually developed pictorially, orally or using algebraic notation. Understanding number sequences allows us to generate algebraic formulae either pictorially, orally or using algebraic notation Previous knowledge and understanding Number Able to spot and continue number patterns patterns Confidence in using the 4 operations Patterns Number sequences Formulae Creating Modelling graphical representations Gradient Equations of straight lines Number sequences

323 Patterns and relationships Number Modelling sequences Generating a number sequence illustrated by a physical or pictorial pattern and determining the equation that the Understanding number sequences allows us to generate Number sequence represents. The formula is used to determine patterns algebraic formulae information either about pictorially, the items at orally any position or using the algebraic sequence to notation make evaluations and solve problems. Patterns Number sequences Formulae Creating Modelling graphical representations Gradient Equations of straight lines Number sequences

324 Patterns and relationships Formulae Formulae are fundamental in developing mathematical modelling and underpin all graphical representation. Number patterns Patterns Formulae Formulae Generating Creating a set of outputs using graphical a formula representations Determining a formula from Gradient a table of values Equations of straight lines Number sequences

325 Patterns Formulae and relationships A formula is a special type of equation that shows the relationship between different variables. Using a formula is the most efficient way of solving problems that compare different Formulae sets of variables. e.g. Area of rectangle = length x breadth, Volume of a cuboid = l x b x h Formulae are fundamental in developing mathematical modelling and underpin all graphical representation. Previous knowledge Number and understanding Knowing the patterns convention of algebra, e.g. ab means a x b, a 2 means a x a Patterns Formulae Formulae Generating Creating a set of outputs using graphical a formula representations Determining a formula from Gradient a table of values Equations of straight lines Number sequences

326 Patterns and relationships Formulae Generating a set of outputs using a formula Formulae are fundamental in developing mathematical modelling and underpin all graphical representation. Number patterns Use a given set of inputs to generate a set of outputs. This combination of inputs and outputs allows for graphical representations to be developed. Patterns Formulae Formulae Generating Creating a set of outputs using graphical a formula representations Determining a formula from Gradient a table of values Equations of straight lines Number sequences

327 Patterns and relationships Formulae Determining a formula from a table of values Formulae are fundamental in developing mathematical modelling and underpin all graphical representation. Number patterns Being able to construct a formula is a fundamental algebraic process and permits the expansion of any input/output. Patterns Formulae Formulae Generating Creating a set of outputs using graphical a formula representations Determining a formula from Gradient a table of values Equations of straight lines Number sequences

328 Patterns and relationships Creating graphical representations Patterns Creating graphical representations is the most efficient way of representing the comparison between two variables and presenting it in a visual form. It helps develop the fundamental skills of interpolation and extrapolation. Number patterns Number sequences Formulae Creating graphical representations Creating graphical Determining representations a general formula Gradient Equations of straight lines

329 Patterns and relationships Patterns Creating graphical representations Creating graphical representations It is the most efficient Why is method it important? of comparing two related variables, in a visual way. Creating graphical representations is the most efficient way of representing the comparison between two variables and presenting it in a visual form. It helps develop the fundamental skills of interpolation and extrapolation. Number Previous knowledge patterns and understanding Plotting points Constructing appropriate formulae Number sequences Formulae Creating graphical representations Creating graphical Determining representations a general formula Gradient Equations of straight lines

330 Patterns and relationships Creating graphical representations Patterns Why is it Determining important? a general formula Creating graphical representations is the most efficient way of representing The ability the to comparison generate a formula between for two a given variables sequence and of presenting it in a visual form. It helps develop the fundamental without having to calculate all previous numbers skills of interpolation and extrapolation. Number patterns Number sequences numbers allows any number in the sequence to be determined Formulae Creating graphical representations Creating graphical Determining representations a general formula Gradient Equations of straight lines

331 Patterns and relationships Gradient Patterns Through the ability of allocating a numerical value to a slope, it allows limits to be placed for design and safety considerations, e.g. a mobility ramp access to buildings, slopes of roofs, incline of roads. Number patterns Number sequences Gradient Formulae Creating graphical representations Gradient Equations of straight lines

332 Gradient Patterns and relationships The rate at which vertical height changes with respect to horizontal distance covered, numerically represented as a fraction, decimal fraction or percentage. The gradient can be found by inspection of co-ordinate diagrams or the gradient formula. Understand that a straight line that rises from left to right has a positive gradient and a straight line that falls from Gradient left to right has a negative gradient. It should be understood that a horizontal line has a gradient of zero whereas the gradient of a vertical line is undefined. Through the ability of allocating a numerical value to a slope, it allows limits to be placed for design and safety considerations e.g. a mobility ramp access to buildings, slopes of roofs, incline Number Previous knowledge patterns and understanding Be able to calculate the change between two values Be able to plot given points of roads. Creating Patterns Formulae graphical Gradient representations Gradient Equations of straight lines Number sequences

333 Patterns and relationships Equations of straight lines Patterns Understanding equations of straight lines enables comparisons to be made using graphical representations and allows for informed decisions. Familiarisation with linear equations enables more complicated equations to be investigated. Number patterns Number sequences Equations of straight lines Formulae Creating graphical Locus representations Gradient Equations of straight lines

334 Patterns and relationships Patterns Equations of straight lines A form of the equation of the straight line is y = mx + c. Graphically, m represents Equations the gradient of straight and c represents lines the point where the line intercepts the y-axis (y-intercept). Horizontal and vertical lines are special cases of y = mx + c Understanding equations of straight lines enables comparisons to be made using graphical representations and allows for informed decisions. Familiarisation with linear equations enables more complicated equations to be investigated. Previous knowledge and understanding Number Be able to calculate the gradient between 2 points patterns Understand the vocabulary of intercept on the x-axis and y-axis Number sequences Equations of straight lines Formulae Creating graphical Locus representations Gradient Equations of straight lines

335 Patterns and relationships Equations of straight lines Patterns Locus Understanding What equations is it? of straight lines enables comparisons to be made using graphical representations and allows for informed decisions. Familiarisation with linear equations enables more complicated equations to be investigated. Number patterns Number sequences Determining a few points from the equation of a straight line allows us to join these points and therefore identify the locus of all points that conform to the formula. Creating Formulae graphical Equations of Locus representations straight lines Gradient Equations of straight lines

336 Powers and roots Powers Scientific Notation Roots

337 Powers and roots Powers Powers enable large numbers to be expressed more concisely. Powers Scientific notation Roots Powers

338 Powers Understanding that the shorthand notation for repeated multiplication can be expressed in power notation. Powers and roots Possible extension work could include: Fractions to whole number powers Negative numbers to whole numbers powers, e.g. (-2) 3 = -8 Negative powers, for example, 4-2 = 1/16 The concept of a zero power, e.g. 5 0 = 1 Introducing the laws of indices Powers Previous knowledge and understanding Knowledge of square numbers, noting the link to area The concept of repeatedly multiplying the same number, e.g = 8 3 = 512, noting the link to volume Knowledge of place value and multiplication by 10 Powers enable large numbers to be expressed more concisely. Powers Powers Scientific notation Roots

339 Powers and roots Scientific Notation Scientific notation enables large and small numbers to be written in a shorter form. Problems involving multiplication and division of large or small numbers become more manageable through the use of scientific notation. It also allows very large or very small Scientific numbers to be displayed on Powers Roots calculator screens when they notation would otherwise overflow. Scientific Notation Calculations involving scientific notation

340 Powers and roots Scientific Notation Scientific notation enables large and small numbers to be Scientific Notation written in a shorter form. Problems involving multiplication and division of large or small numbers become more Scientific notation manageable is a standardised through method the use of writing of scientific notation. It also numbers in the allows form a very 10 large or very small Scientific numbers to be displayed on Powers n Where 1 a <10 and n is an Roots calculator screens when they notation would otherwise overflow. integer. Scientific Notation Calculations involving scientific notation

341 Powers and roots Scientific Notation Calculations involving scientific notation Undertake calculations with numbers written in scientific Scientific notation enables large and small numbers to be notation. written in a shorter form. Problems involving multiplication and division Previous of large knowledge or small and numbers understanding become more manageable Place through valuethe use of scientific notation. It also allows very large Multiplying or very by small powers Scientific numbers of 10 to be displayed on Powers Roots calculator screens Dividing when by powers they notation of would 10 otherwise overflow. Scientific Notation Calculations involving scientific notation

342 Powers and roots Roots Roots are an essential tool when performing calculations and develop the understanding of the inverse operation of powers. Scientific Powers notation Roots Roots Square roots Cube roots Higher roots

343 Powers and roots Roots Roots Roots are the inverse process of powers. Previous knowledge and understanding The concept of powers The concept of inverse operations Roots are an essential tool when performing calculations and develop the understanding of the inverse operation of powers. Scientific Powers notation Roots Roots Square roots Cube roots Higher roots

344 Powers and roots Roots Square roots Finding the square root is the inverse process of squaring a number. The square root of all positive numbers has two solutions, one negative and one positive. Square roots can be evaluated mentally within the commonly known multiplication tables. Roots are an essential tool when performing calculations and develop the Previous understanding knowledge and of the understanding inverse operation of powers. Knowledge of square numbers Scientific Powers notation Roots Roots Square roots Cube roots Higher roots

345 Powers and roots Roots Cube roots Finding the cube root is the inverse process of cubing a number. Roots are an essential tool when performing calculations and develop the understanding of the inverse operation of powers. Scientific Powers notation Previous knowledge and understanding Knowledge of trial and improvement as a strategy, e.g. 64, student could try , Roots Roots Square roots Cube roots Higher roots

346 Powers and roots Roots Roots are an essential tool when performing calculations and develop the understanding of the inverse operation of powers. Scientific Powers notation Higher roots Higher roots work in the same way as cube roots and common roots can be evaluated within the commonly known multiplication tables. Previous knowledge and understanding Knowledge of trial and improvement as a strategy Use of a calculator Roots Roots Square roots Cube roots Higher roots

347 Properties of 2D shapes and 3D objects Nets of 3D objects Awareness of 2D shapes and 3D objects Properties of 2D shapes and 3D objects Using 2D shapes and 3D objects Accurate drawing of 2D shapes Formulae and inter-relationships within triangles Circles Representation of 2D shapes and 3D objects

348 Properties of 2D shapes and 3D objects Awareness of 2D shapes and 3D objects Awareness of 2D shapes and 3D objects Properties of 2D shapes and 3D objects Using 2D shapes and 3D objects Nets of 3D objects It links personal experiences and observations with a more structured way of investigating 2D shapes and 3D objects. Awareness of 2D shapes and 3D objects Representation 2D shapesof 2D shapes and 3D objects Accurate drawing of 2D shapes 3D objects Formulae and Inter-relationships within triangles Circles

349 Properties of 2D shapes and 3D objects Awareness of 2D shapes and 3D objects Awareness of 2D shapes and 3D objects Awareness of 2D shapes and 3D objects Nets of 3D Awareness of 2D Why shapes is it and important? 3D objects is the informal objects and experiential aspect of learning. It involves naming and identifying shapes and objects in the world beyond the classroom Properties or of 2D play setting. Using 2D shapes shapes and 3D and 3D objects objects It links personal experiences and observations with a more structured way of investigating 2D shapes and 3D objects. Awareness of 2D shapes and 3D objects Representation 2D shapesof 2D shapes and 3D objects Accurate drawing of 2D shapes 3D objects Formulae and Inter-relationships within triangles Circles

350 Properties of 2D shapes and 3D objects Awareness of 2D shapes and 3D objects Awareness of 2D shapes and 3D objects Properties of 2D shapes and 3D objects Nets of 3D objects 2D shapes It links personal experiences and observations with a more structured way of investigating 2D shapes and 3D objects. Using 2D 2D shapes shapes have only two dimensions Accurate and are drawing flat. and 3D objects of 2D shapes Awareness of 2D shapes and 3D objects Representation 2D shapesof 2D shapes and 3D objects 3D objects Formulae and Inter-relationships within triangles Circles

351 Properties of 2D shapes and 3D objects Awareness of 2D shapes and 3D objects Properties of 2D shapes and 3D objects Awareness of 2D shapes and 3D objects Using 2D shapes and 3D objects Nets of 3D objects Previous knowledge and understanding Experience of outdoor learning Observational skills Basic vocabulary Formulae and Accurate drawing Inter-relationships of 2D shapes within triangles It links personal experiences and observations with a more structured way of investigating 2D shapes and 3D objects. Awareness of 2D shapes and 3D objects Representation 2D shapesof 2D shapes and 3D objects 3D objects 3D objects have three dimensions. The sides, or faces, of many 3D objects are made up of 2D shapes. 3D objects can be stacked or rolled and items can be put inside some 3D objects. They can also be combined to make models. 3D objects Circles

352 Properties of 2D shapes and 3D objects Properties of 2D shapes and 3D objects Awareness of 2D shapes and 3D objects Properties of 2D shapes and 3D objects Understanding the properties of 2D shapes and 3D objects enables more sophisticated Nets identification of 3D and sorting by their objects features. An understanding of the properties of 2D shapes and 3D objects will enable learners to appreciate how they fit together and how they are used in everyday life. Using 2D shapes and 3D objects Properties of 2D shape and 3D objects Representation Tiling of 2D shapes and 3D objects Accurate drawing of 2D shapes Formulae and Inter-relationships within triangles Circles

353 Properties of 2D shapes and 3D objects Awareness of 2D shapes and 3D objects Properties of 2D shapes and 3D objects Properties of 2D shape and 3D objects Knowing the properties Why is it of important? 2D shapes and 3D objects develops a problem solving approach to solving many geometric problems. Nets of 3D objects Previous knowledge and understanding Name 2D shapes and 3D objects Properties Recognise of 2D shapes and 3D objects in the environment Using 2D shapes shapes and 3D and 3D objects objects Properties of 2D Representation Tiling of shape and 3D objects 2D shapes and 3D objects Understanding the properties of 2D shapes and 3D objects enables more sophisticated identification and sorting by their features. An understanding of the properties of 2D shapes and 3D objects will enable learners to appreciate how they fit together and how they are used in everyday life. Accurate drawing of 2D shapes Formulae and Inter-relationships within triangles Circles

354 Properties of 2D shapes and 3D objects Properties of 2D shapes and 3D objects Awareness of 2D shapes and 3D objects Properties of 2D shapes and 3D objects Tiling Understanding the properties of 2D shapes and 3D objects enables more sophisticated identification and sorting by their features. An understanding of the properties of 2D shapes and 3D objects Previous will knowledge enable learners and understanding to appreciate how they fit together and Understanding how they are how used shapes in everyday fit together life. Determining which Nets 2D shapes of 3D are suitable for tiling is a key step in extending geometrical objects knowledge of 2D shapes. Using 2D shapes and 3D objects Properties of 2D shape and 3D objects Representation Tiling of 2D shapes and 3D objects Accurate drawing of 2D shapes Formulae and Inter-relationships within triangles Circles

355 Properties of 2D shapes and 3D objects Using 2D shapes and 3D objects Awareness of 2D shapes and 3D objects Properties of 2D shapes and 3D objects Understanding why certain shapes and objects are more suited to specific areas of use helps Nets link of the 3D main properties of the objects shapes and objects with the key requirements of their usage. This has major implications in product design and efficient use of resources. Using 2D shapes and 3D objects Using 2D shapes and 3D objects Properties of Representation of triangles 2D shapes and 3D objects Accurate drawing of 2D shapes Formulae and Inter-relationships within triangles Circles

356 Properties of 2D shapes and 3D objects Using 2D shapes and 3D objects Awareness of 2D shapes and 3D objects Using 2D shapes Why and is it 3D important? objects Understanding why certain shapes and objects are more suited to specific areas of use helps link the main properties of the shapes and objects with the key requirements of their usage. This has major implications in product design and efficient use Determining when and where triangles are used Nets in of the 3D construction of buildings links the properties of objects triangles with the strength of triangular frames. Understanding why cuboids are more commonly used in packaging than spheres recognises Properties that the ability of 2D of to stack resources. Using objects 2D shapes is crucial in the retail business. Accurate drawing shapes and 3D and 3D objects of 2D shapes objects Using 2D shapes and 3D objects Properties of Representation of triangles 2D shapes and 3D objects Formulae and Inter-relationships within triangles Circles

357 Properties of 2D shapes and 3D objects Using 2D shapes and 3D objects Awareness of 2D shapes and 3D objects Properties of 2D shapes and 3D objects Understanding why certain shapes and objects are more suited Properties of triangles to specific areas of use helps link the main properties of the shapes and objects with the key requirements of their usage. This has major implications in product design and efficient use of resources. Nets of 3D objects The ability to classify triangles as acute, obtuse, equilateral, isosceles, right-angled and scalene develops the ability to match properties with agreed definitions. Accurate drawing of 2D shapes Using 2D shapes and 3D objects Using 2D shapes and 3D objects Properties of Representation of triangles 2D shapes and 3D objects Formulae and Inter-relationships within triangles Circles

358 Properties of 2D shapes and 3D objects Nets of 3D Objects Develops the spacial awareness that allows a 3D object to be unpacked to form a combination Nets of 3D of 2D surfaces. This has objects important applications in the packaging industry. Awareness of 2D shapes and 3D objects Properties of 2D shapes and 3D objects Using 2D shapes and 3D objects Accurate drawing of 2D shapes Formulae and Inter-relationships within triangles Circles Nets of 3D Objects Representation of 2D shapes and 3D objects

359 Properties of 2D shapes and 3D objects Awareness of 2D shapes and 3D objects Nets of 3D objects Nets of 3D Objects A net is the 2D representation of an unpacked 3D object. The lengths and angles in the 3D object are conserved within the net. Nets of 3D objects Previous knowledge and understanding Properties of 2D shapes Properties of 2D Understanding edges, Using faces 2D and shapes vertices shapes and 3D and 3D objects objects Develops the spacial awareness that allows a 3D object to be unpacked to form a combination of 2D surfaces. This has important applications in the packaging industry. Accurate drawing of 2D shapes Formulae and Inter-relationships within triangles Circles Nets of 3D Objects Representation of 2D shapes and 3D objects

360 Properties of 2D shapes and 3D objects Representation of 2D shapes and 3D objects Awareness of 2D shapes and 3D objects Properties of 2D shapes and 3D objects Nets of 3D This develops spacial awareness objects and promotes the concepts of equal lengths and angles when they are distorted in the 2D representations. Using 2D shapes and 3D objects Representation of 2D shapes and 3D objects Representation of 2D shapes and 3D objects Accurate drawing of 2D shapes Formulae and Inter-relationships within triangles Circles

361 Properties of 2D shapes and 3D objects Awareness of 2D shapes and 3D objects Representation of 2D shapes and 3D objects Representation of 2D shapes and 3D objects Using sketches, isometric paper or computer packages to draw 3D objects on a Why 2D plane. is it important? Nets of 3D Previous knowledge and understanding objects Familiarity with the properties of 3D objects Properties of representations. 2D shapes Properties of 2D Experience of perspective Using 2D in art shapes (drawing) Accurate drawing shapes and 3D and 3D objects of 2D shapes objects This develops spacial awareness and promotes the concepts of equal lengths and angles when they are distorted in the 2D Representation of 2D shapes and 3D objects Representation of 2D shapes and 3D objects Formulae and Inter-relationships within triangles Circles

362 Properties of 2D shapes and 3D objects Accurate drawing of 2D shapes Drawing accurately develops dexterity, reading scales and the ability to follow instructions. Nets of It 3Dis an essential life skill in objects architecture and many areas of the construction industry. Awareness of 2D shapes and 3D objects Properties of 2D shapes and 3D objects Using 2D shapes and 3D objects Accurate drawing of 2D shapes Drawing triangles and Representation of quadrilaterals 2D shapes and 3D objects Accurate drawing of 2D shapes Regular and irregular polygons Formulae and Inter-relationships within triangles Circles

363 Properties of 2D shapes and 3D objects Awareness of 2D shapes and 3D objects Accurate drawing of 2D shapes Accurate drawing of 2D shapes This requires the scaling of the lengths and the conservation of the angles. Drawing accurately develops dexterity, reading scales and following instructions. It is an Nets essential of 3D life skill in architecture objects and many areas of the construction industry. Previous knowledge and understanding Measure lengths accurately Know how to name angles Properties of 2D Measure angles accurately Using 2D shapes shapes and 3D and 3D objects objects Accurate drawing of 2D shapes Drawing triangles and Representation of quadrilaterals 2D shapes and 3D objects Accurate drawing of 2D shapes Regular and irregular polygons Formulae and Inter-relationships within triangles Circles

364 Properties of 2D shapes and 3D objects Awareness of 2D shapes and 3D objects Properties of 2D shapes and 3D objects Accurate drawing of 2D shapes Drawing triangles and quadrilaterals Drawing a range of triangles with different properties. Drawing a range of quadrilaterals with different properties and investigating how the Nets diagonals of 3D intersect. objects Previous knowledge and understanding Able to use relevant instruments Formulae and Using 2D Able shapes to measure accurately Accurate drawing Inter-relationships and 3D objects of 2D shapes within triangles Accurate drawing of Drawing triangles and Regular and irregular Representation of 2D shapes quadrilaterals polygons 2D shapes and 3D objects Drawing accurately develops dexterity, reading scales and following instructions. It is an essential life skill in architecture and many areas of the construction industry. Circles

365 Properties of 2D shapes and 3D objects Awareness of 2D shapes and 3D objects Properties of 2D shapes and 3D objects Accurate drawing of 2D shapes Using 2D shapes and 3D objects Understanding the difference between regular and irregular polygons. Demonstrating the properties of regular polygons to draw accurate representations. Understand that all polygons Nets of can 3D be constructed through a summation of triangles. objects Previous knowledge and understanding Understand the term regular when describing 2D shapes Accurately measure angles Formulae and Accurate drawing Inter-relationships Circles of 2D shapes within triangles Drawing accurately develops dexterity, reading scales and following instructions. It is an essential life skill in architecture and many areas of the construction industry. Accurate drawing of 2D shapes Drawing triangles and Representation of quadrilaterals 2D shapes and 3D objects Regular and irregular polygons Regular and irregular polygons

366 Properties of 2D shapes and 3D objects Formulae and inter-relationships within triangles Awareness of 2D shapes and 3D objects Properties of 2D shapes and 3D objects Nets of 3D This milestone develops the objects mathematical concepts associated with Pythagoras Theorem and trigonometry. These concepts are fundamental, as much of the mathematics encountered after this will be built upon these foundations. Using 2D shapes and 3D objects Formulae and inter-relationships within triangles Accurate drawing of 2D shapes Pythagoras theorem Representation and Converse of of 2D shapes Pythagoras and 3D objects Trigonometry within right-angled triangles Formulae and Inter-relationships within triangles Circles

367 Properties of 2D shapes and 3D objects Awareness of 2D shapes and 3D objects Formulae and inter-relationships within triangles Formulae and inter-relationships Through investigating within the triangles lengths of sides in right-angled triangles the theorem and converse of Pythagoras are developed. Building Why on is similar it important? triangles and investigating ratios of different pairs of sides leads to right-angled Nets trigonometry. of 3D objects Previous knowledge and understanding Name and identify different triangles Properties of 2D Know the properties after this Using of will different 2D be shapes built types upon of triangles these foundations. Accurate drawing shapes and 3D and 3D objects of 2D shapes objects Formulae and interrelationships within Representation and Converse of of Pythagoras theorem triangles 2D shapes Pythagoras and 3D objects This milestone develops the mathematical concepts associated with Pythagoras Theorem and trigonometry. These concepts are fundamental, as much of the mathematics encountered Trigonometry within right-angled triangles Formulae and Inter-relationships within triangles Circles

368 Properties of 2D shapes and 3D objects Awareness of 2D shapes and 3D objects Properties of 2D shapes and 3D objects Formulae and inter-relationships within triangles Applying Pythagoras Theorem enables the length of one side of a right-angled triangle to be calculated, given the lengths of the other two sides. The converse can also be used to establish if a triangle is right-angled. Nets of 3D Previous knowledge objects and understanding Algebra Number processes/operations Using 2D Know shapes and understand square and Accurate square root drawing and 3D objects of 2D shapes Pythagoras theorem Trigonometry within Representation and Converse of of right-angled triangles 2D shapes Pythagoras and 3D objects This milestone develops the mathematical concepts associated with Pythagoras Theorem and trigonometry. These concepts are fundamental, as much of the mathematics encountered after this will be built upon these foundations. Formulae and interrelationships within triangles Pythagoras theorem and Converse of Pythagoras Formulae and Inter-relationships within triangles Circles

369 Properties of 2D shapes and 3D objects Awareness of 2D shapes and 3D objects Properties of 2D shapes and 3D objects Formulae and inter-relationships within triangles This milestone develops the mathematical concepts associated with Pythagoras Theorem and trigonometry. These concepts are fundamental, as much of the mathematics encountered after this will be built upon these foundations. Using 2D shapes and 3D objects Formulae and interrelationships within triangles Trigonometry within right-angled triangles Enables the length of a side to be calculated, given the length of another side and the size of either of the acute angles. It also enables the calculation of an angle, given the length of any two of the triangle s sides. Previous knowledge and understanding Algebraic manipulation Number processes/operations Similar triangles Nets of Possible 3D Extension objects Although this building block concentrates on trigonometry within right-angled triangles, students can be encouraged to investigate trigonometry within all triangles. This naturally leads on Formulae and Accurate to problems drawing involving the sine and cosine rule. Inter-relationships Circles of 2D shapes within triangles Pythagoras theorem Trigonometry within Representation and Converse of of right-angled triangles 2D shapes Pythagoras and 3D objects

370 Properties of 2D shapes and 3D objects Circles Awareness of 2D shapes and 3D objects Properties of 2D shapes and 3D objects The circle is a commonly used shape that occurs both in nature and everyday life. Its importance is based on the fact that a circle encloses the maximum Nets area of 3D for a given perimeter. The circle, despite being one of the objects simplest shapes, has numerous geometric properties. An understanding of these properties, and associated formulae, provides a foundation for further learning in geometry. Using 2D shapes and 3D objects Circles Circumference Representation of and arcs 2D shapes and 3D objects Accurate drawing of 2D shapes Area and sectors Formulae and Inter-relationships within triangles Circles

371 Properties of 2D shapes and 3D objects Circles Awareness of 2D shapes and 3D objects Circles The circle is a commonly used shape that occurs both in nature and everyday life. Its importance is based on the fact that a circle encloses the maximum area for a given perimeter. The circle, despite being one of the simplest shapes, has numerous geometric properties. An understanding of these properties, and associated formulae, provides a foundation for further Circle calculations are interrelated. Given any one of radius, diameter, circumference or area all the others can be calculated. Nets of 3D objects Previous knowledge and understanding Vocabulary: radius, diameter, circumference and area Properties Know the of relationship 2D Using 2D shapes shapes and 3D learning between geometry. a radius and a diameter and 3D objects objects Circumference Circles Representation of and arcs 2D shapes and 3D objects Accurate drawing of 2D shapes Area and sectors Formulae and Inter-relationships within triangles Circles

372 Properties of 2D shapes and 3D objects Circles Awareness of 2D shapes and 3D objects Properties of 2D shapes and 3D objects The circle is a commonly used shape that occurs both in nature and everyday life. Its importance is based on the fact that a circle encloses Circumference the maximum and area arcsfor a given perimeter. The circle, despite being one of the simplest shapes, has numerous geometric properties. An understanding of these properties, and associated formulae, provides a foundation for further learning in geometry. Nets of 3D objects Investigate the significance of π and establish the formula connecting the radius, diameter and circumference of a circle. Investigate arc lengths. Formulae and Using 2D shapes Accurate drawing Inter-relationships and 3D objects of 2D shapes within triangles Circles Circumference Representation of and arcs 2D shapes and 3D objects Area and sectors Circles

373 Properties of 2D shapes and 3D objects Circles Awareness of 2D shapes and 3D objects Properties of 2D shapes and 3D objects The circle is a commonly used shape that occurs both in nature and everyday life. Its importance is based on the fact that a circle encloses the maximum area Area for a and given sectors perimeter. The circle, despite being one of the simplest shapes, has numerous geometric properties. An understanding of these properties, and associated formulae, provides a foundation for further learning in geometry. Using 2D shapes and 3D objects Circles Nets of 3D objects Investigate the significance of π and establish the formula connecting the radius, diameter and area of a circle. Investigate the area of sectors of circles. Formulae and Accurate drawing Inter-relationships of 2D shapes within triangles Circumference Representation of Area and sectors and arcs 2D shapes and 3D objects Circles

374 Mathematics its impact on the world past, present and future Numbers through history Famous mathematicians Mathematics in the environment Uses of mathematics Careers and mathematics in the workplace

375 Mathematics its impact on the world past, present and future Mathematics in the environment It is important that learners recognise mathematics in their environment Numbers as it provides the foundations for exploring the use of mathematics through in their everyday lives. history Famous mathematicians Mathematics in the environment Mathematics in the environment Uses of mathematics Careers and mathematics in the workplace

376 Mathematics its impact on the world past, present and future Mathematics in the environment Mathematics in the environment Mathematics It in is the important environment that learners recognise mathematics in their environment Numbers as it provides the foundations for exploring the This is the awareness use of of mathematics the through vast amount in their of mathematics everyday and lives. mathematical information in history the environment which provides information to help with real-life, everyday situations. It also reinforces the concept of mathematics being relevant and important to future learning. Mathematics in the environment Uses of mathematics Famous mathematicians Careers and mathematics in the workplace

377 Mathematics its impact on the world past, present and future Numbers through history It is important learners know the origins of their own number system Numbers through exploring those from the past to understand through how they have evolved, changed and improved. It also highlights history the multi-cultural nature of mathematical development and how other great civilisations contribute. Famous mathematicians Mathematics in the environment Numbers through history Decimal number system Uses of mathematics Careers and mathematics in the workplace

378 Mathematics its impact on the world past, present and future Mathematics in the environment Numbers through history It is important learners know the origins of their own number system Numbers through exploring those from the past to Numbers through understand history through how they have evolved, changed and improved. It also highlights history the multi-cultural nature of mathematical Number systems development from around the and world how have other evolved great over civilisations contribute. time and become more efficient. This includes number systems used in the computer age, such as binary. Numbers through history Decimal number system Uses of mathematics Famous mathematicians Careers and mathematics in the workplace

379 Mathematics its impact on the world past, present and future Mathematics in the environment Numbers through history It is important learners know the origins of their own number system Numbers Decimal through number exploring systemthose from the past to understand What through how is they it? have evolved, changed and improved. It also highlights history the multi-cultural nature of mathematical development and how other great civilisations contribute. Based on 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). It is the place of the digit(s) which makes the difference to the value of the number, both in whole numbers and decimal fractions. Zero is important as a placeholder. Numbers through history Decimal number system Uses of mathematics Famous mathematicians Careers and mathematics in the workplace