Number and Place Value Read, write, order and compare numbers up to 10,000,000 and determine the value of each digit

Transcription

1 Exemplification Year 6 End of year Number and Place Value Read, write, order and compare numbers up to 10,000,000 and determine the value of each digit Can order a set of mixed numbers, with support for larger, and/or more complex numbers (including decimals) eg Read, write & order numbers above 1 million using place value prompts, manipulatives Can order and compare a range of numbers using different representations and explain their thinking. Children should be able to determine the steps used in different scales, and so complete activities such as; Can demonstrate understanding of large numbers and decimals, and communicate their thinking to solve. Do, then explain Show the value of the digit 6 in these numbers? Explain how you know. True or false? In all of the numbers below, the digit 6 is worth more than 6 hundredths Is this true or false? Change some numbers so that it is true. complex/broader and non-routine Can use knowledge of numbers flexibly and creatively to solve related E.g:Make up an example Create some seven digit numbers where the digit sum is six and the tens of thousands digit is two. E.g What is the largest/smallest number? Do, then explain Find out the populations in five countries. Order the populations starting with the largest. Explain how you ordered the countries and their populations. What needs to be added to to give 7? What needs to be added to to give 5? Circle the two decimals which are closest in value to each other Round any whole number to a required degree of accuracy Can round any whole number using a given number line eg to round 1dp integers to the whole number using a tenths number line Can round a 6 digit number or more, to any required degree of accuracy, and explain their thinking eg choose appropriate resources such as blank number lines round to nearest ten, hundred, thousand, ten thousand, hundred thousand & million. Can solve simple which require answers to be rounded to specified degrees of accuracy eg Two numbers each with one decimal places round to 23.0 to a whole integer. What could the numbers be? Find more than one solution. eg Shopping bills: , & Tom rounds each bill to nearest 10 & adds them up. What is the total amount that Tom gets? Can solve more complex/broader and non-routine which require answers to be rounded to specified degrees of accuracy eg Two numbers each with two decimal places round to 23.1 to one decimal place. The total of the numbers is What could the numbers be? How many possibilities are there, how do you know you have found them all? What do you notice? Give an example of a six digit number which rounds to the same number when rounded to the nearest and Use negative numbers in context, and calculate intervals Can use negative numbers in context, and calculate intervals across 0, with Can use negative numbers in context, and calculate intervals across 0, Can use negative numbers to solve Megan makes a sequence of numbers starting with 100. She subtracts 45 each time ?? Can use negative examples to solve more complex across a broad range of situations.

2 across 0 support eg to order +ve & - ve numbers on a number line The temperature inside an aeroplane is 20 C. The temperature outside the aeroplane is 30 C. What is the difference between these temperatures? Write the next 2 numbers in the sequence. Circle two numbers which have a difference of complex/broader and non-routine Q1. Here is a square on coordinate axes. The temperature in York is 4 C. Rome is 7 degrees colder than York. What is the temperature in Rome? C is the centre of the square. Find the coordinates of P and Q. eg Megan makes a sequence of numbers starting with 100. She subtracts 45 each time ?? Write the next 2 numbers in the sequence. Write the nth term in the sequence. Would [ -95] be in the sequence, explain your answer. Solve number and practical that involve all of the above Can solve simple number and practical that involve all of the above. See above examples Solve number and practical that involve all of the above. See above examples Solve number and practical that involve all of the above. See above examples Solve number and practical that involve all of the above. See above examples

3 Addition, Subtraction, Multiplication and Division Multiply multidigit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication Can multiply multi digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication, using concrete apparatus & visual representations Can multiply multi digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication,, with an increasing degree of confidence, explaining their method x 47 = Can multiply multi digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication apply to simple contexts / eg Sam wants to collect 4000 football stickers. She buys 273 packets of football stickers. Each pack contains 13 stickers, how many more packs of stickers does she need? complex/broader and non-routine Can apply formal written methods for long multiplication accurately in a range of contexts. eg Using the digits 3,4,5,6,7,8 arrange into a 4 digit by 2 digit multiplication, so that you have the largest product / smallest / largest prime etc Explain your answer. eg Give a formal written long multiplication algorithm with numbers missing, work out the missing digits. e.g 243 x 53 = Divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context (see progressions in calculations document) Can divide numbers up to 4 digits by a twodigit whole number using the formal written method of long division, and interpret remainders as whole number remainders, using concrete apparatus & visual representations eg = Can divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context eg = Can apply this to simple, considering which remainder would be most appropriate. eg There are 67g of rice in one portion. How many portions are there in a 3kg bag of rice? eg A factory boxes 4900 eggs a day. They are packed into groups of 16. How many full boxes will this be and what fraction of the last box is left empty? Can apply formal written methods for long division accurately in a range of contexts. eg Give a formal written long division algorithm with numbers missing, work out the missing digits. eg A coach can hold 53 children and 6 adults. Rosewood primary school are going on a school outing. There are 12 classes of 30 pupils, each requiring 1 teacher and 4 other adults as well as 25 office staff. How many coaches will be required? eg Create a division problem where the remainder will be equivalent to 1/3? Divide numbers up to 4 digits by a two-digit number using the formal Can divide numbers up to 4 digits by a twodigit whole number using the formal written method of Can divide numbers up to 4 digits by a two-digit whole number using the formal written method of short division, and interpret remainders as appropriate for the context Can apply this to simple, considering which remainder would be most appropriate. 22?3 7 = 321 r 6 Can apply formal written methods for short division accurately in a range of contexts. Is it always, sometimes, or never true that when you square an even number the answer is always divisible by 4?

4 written method of short division where appropriate, interpreting remainders according to the context short division, and interpret remainders using concrete apparatus and visual representations A car can hold 5 people. How many cars would be needed to take a class full of 30 pupils and 6 adults to the local museum? PROVE IT! How many boxes of 40 matches can be filled from 2688 matches? complex/broader and non-routine Can you find the smallest number that can be added to or subtracted from 87.6 to make it exactly divisible by 8/7/18? Perform mental calculations, including with mixed operations and large numbers Can do with support, extra time or, manipulatives. Can do, within a reasonable time. Liam thinks of a number. He divides it by 9 and then adds 25 to the result. His answer is 36 Can do, applied to a range of problem solving situations. Ben thinks of a number. He adds half of the number to a quarter of the number. The result is 60. What was the number Ben first thought of? Can do, applied to a range of complex problem solving situations. Chen chooses a prime number. He multiplies it by 10 and then rounds it to the nearest hundred. His answer is 400. What number did Liam start with? Write all the possible prime numbers Chen could have chosen. Evidence for mastery level will be found within other strands. Identify common factors, common multiples and prime numbers Can identify factors, multiples and prime numbers with support. Support given with multiplication squares/ counters Can identify common factors, common multiples and prime numbers. Circle all the numbers that are common multiples of 4 and 6. Can identify common factors, common multiples and prime numbers and explain reasoning. Samuel says that his number ending in zero is a multiple of 5 and a multiple of 2. Is he correct? Explain your answer. Can identify common factors, common multiples and prime numbers and explain reasoning over a range of context. The factors of 11 sum to 12. Write the other numbers whose factors sum to 12.

5 /numicon etc Check a number is a prime number by using counters to identify one array. His number is between 15 and 30 what could his number be? complex/broader and non-routine P stands for a multiple of 3. Q stands for a different multiple of 3 Show that 10 is not a prime number by using counters. Tick ( ) each statement according to whether it is always true, sometimes true or never true. always true sometimes true The sum of P and Q is a multiple of 6 The difference between P and Q is a multiple of 3 The product of P and Q is a multiple of 9 Use their knowledge of the order of operations to carry out calculations involving the 4 operations Can understand the order of operations affects the answer. Can work out calculations with support. BODMAS Can use their knowledge of the order of operations to carry out calculations. Calculate ( ) - (6.65 2) Write in the missing numbers = ( ) = Can use their knowledge of the order of operations to solve. 14 x = 70 Put the brackets in to make this number sentence correct. 2 calculations involving brackets and ask the chn to decide which is greater than/ less than (using correct symbols) Can use their knowledge of the order of operations to solve complex with further mathematical symbols. Put brackets into this expression to make it correct = ² = Solve addition and subtraction multi-step in Can use a range of practical resources to approach a given multi step problem in familiar Can solve addition and subtraction multi-step in a range of contexts. Can solve multi step using formal written methods accurately and clearly. Explain their methods. Can create and solve multi step involving addition and subtraction using formal written methods accurately and explain their methods to use and why. E.g

6 contexts, deciding which operations and methods to use and why contexts with accessible numbers. Hats cost 2, suncream cost 1 and towels cost 8. Tom needs to buy 2 hats and a bottle of a suncream. How much change will he get from 20? Hats cost 3.50, suncream cost 1.99 and towels cost Tom needs to buy 2 hats and a bottle of a suncream. How much change will he get from 20? A shop sells food for birds for 1.35 for 8.95 a bag a bag each Lara has 10 to spend on peanuts. How many bags of peanuts can she get for 10? Amir has 20. He wants to buy a bird-feeder and 4 bags of bird seed. How much more money does he need? complex/broader and non-routine Provide chn with a range of prices for a fair ground and ask the chn to create their own multi-step. Solve involving addition, subtraction, multiplication and division Using diennes and visual support. Can use a range of practical resources to approach a given problem in familiar contexts involving the four operations using accessible numbers. Can solve involving addition, subtraction, multiplication and division across a range of contexts. e.g Harry gets 5 a week from his mother and 2 from his grandparents. He is trying to save for a new bike costing 480. How many weeks will he need to save to reach this target? Can solve more complex involving addition, subtraction, multiplication and division, explaining methods. Can solve more complex involving addition, subtraction, multiplication and division, in a methodical / systematic way, explaining methods. Emily has 5 to spend on peaches. She decides to buy only small peaches or only large peaches. How many more small peaches than large peaches can she buy for 5? Small peaches 15p Large peaches 25p This fence has three posts, equally spaced. Each post is 15 centimetres wide. The length of the fence is 153 centimetres. Calculate the length of one gap between two posts. NB This will involve elements from other strands, eg FDP NB This will involve elements from other strands, eg FDP

7 Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy I can round numbers and use this to estimate answers with support. Apply as appropriate to other stands of maths. Fractions (including decimals and percentages) I can round numbers and use this to estimate answers to an appropriate degree of accuracy. Apply as appropriate to other stands of maths. I can use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy to solve. See embedded in all strands of maths. Circle the number that is the best estimate to is it or 1.9? complex/broader and non-routine I can use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy to solve. See mastery in all strands of maths. Use common factors to simplify fractions; use common multiples to express fractions in the same denomination Can recognise equivalent fractions and identify the lowest common denominator to simplify fractions. to understand the relationship between division/ multiplication and fractions. Use of manipulatives, fraction walls, visual cues. Creating own fraction cards/walls. Simplify a range of fractions. Can use common factors to simplify fractions; use common multiples to express fractions in the same denomination. Fraction given, chn to find as many equivalent fractions as they can. Order these fractions from smallest to largest (changing to have the same denominator) 2/5 1/6 3/10 1/2 Can use common factors to simplify fractions; use common multiples to express fractions in the same denomination with confidence. Odd one out. Which is the odd one out in each of these collections of 4 fraction s¾ 9/12 26/36 18/24 4/20 1/5 6/25 6/30 Why? What do you notice? 8/5 of 25 = 40 5/4 of 16 = 20 7/6 of Can you write similar statements? Use common factors to simplify fractions; use common multiples to express fractions in the same denomination and explain your answer. 9/36 +? = 2 ¾ (Can also be used in addition and subtraction of fractions) Here are some number cards Use two of the cards to make a fraction that is less than 3/5? How much less than one is your answer? (Evidence for mastery level will be found in other fraction strands)

8 complex/broader and non-routine Compare and order fractions, including fractions >1 Can compare and order fractions 1 with manipulatives and/or support. Draw one line to join two fractions which have the same value. Can compare & order fractions, including fractions 1,. Draw one line to join two fractions which have the same value. Can compare & order fractions including fractions 1, confidently & within a range of situations. Which is larger: 9/27 or 14/35? Explain how you know? Write these numbers in order, starting with the smallest. Can compare & order fractions including fractions 1, confidently & within a broad / complex range of situations. Write a fraction which is greater than 0.7 and less than Write a decimal which is greater than less than. and Anna says is greater than. smallest Explain why Anna is correct. Write these in order of size, starting with the smallest % (Evidence for mastery level will be found in other fraction strands) smallest

9 Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions Can add and subtract simple fractions with different denominators and mixed numbers. eg 3/8 of a class are boys, how many are girls? Can add and subtract fractions with different denominators and mixed numbers, making good use of equivalent fractions. 6/7 + 1 ¾ + 2 ½ = Can add and subtract fractions with different denominators and mixed numbers, confidently making use of equivalent fractions, in different situations. complex/broader and non-routine Can add and subtract fractions with different denominators and mixed numbers, confidently making use of equivalent fractions, in complex situations Write two fractions, each greater than 0 and less than 1, which have a difference of eg 4/5 + 3/10 = = = The diagram shows part of a number line. Two of the fractions are not complete. Write the missing numerator in each box Multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, 1/4 1/2 = 1/8] Can multiply simple pairs of proper fractions writing the answer in its simplest form, with support and manipulatives. Can multiply simple pairs of proper fractions writing the answer in its simplest form,. Can multiply simple pairs of proper fractions writing the answer in its simplest form,, applied to different situation. Can multiply simple pairs of proper fractions writing the answer in its simplest form,, applied to a wider range of situations. (Evidence for mastery level will be found in other fraction strands)

10 Divide proper fractions by whole numbers [for example, 1/3 2 =1/6] Can divide simple proper fractions by simple whole numbers with support. Sam had ½ a banana to share between himself and his brother. What fraction of the banana would each boy receive? ¼ 3 = Can divide proper fractions by whole numbers. Tom had ½ a bar of chocolate to share between 4 friends. What fraction of the bar would each friend receive? 7/8 6 = Can divide proper fractions by whole numbers confidently in different situations. What number is exactly halfway between 2 = and complex/broader and non-routine Can divide proper fractions by whole numbers in complex situations. In this circle, each shaded part is of the area of the circle. The two white parts have equal areas. What fraction of the circle is one of the white areas? Associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 3/8] Can associate simple fractions with division & can calculate decimal fractional equivalences with support. Write these numbers in order, starting with the smallest / /10 Can associate a range of fractions with division & can calculate decimal fractional equivalences. eg eg Match each decimal number to its equivalent fraction. One has been done for you. Can associate a range of fractions with division & can calculate decimal fractional equivalences, in order to solve various. Write a decimal which is greater than and less than. Circle the two fractions that are equivalent to 0.6: 6/10, 1/60, 60/100, 1/6 Can associate a range of fractions with division & can calculate decimal fractional equivalences, in order to solve more complex. = Find a fraction that is equal in value to

11 complex/broader and non-routine Identify the value of each digit in numbers given to 3 decimal places and multiply and divide numbers by 10, 100 and 1,000 giving answers up to 3 decimal places Can identify the value of each digit to 3dp in familiar contexts and can x and by 10, 100, 100 with support. columns. Write these prices in order, starting with the smallest. 72p, 2.70, 0.27, 7.20, 2.07 Can identify the value of each digit to 3dp in different contexts, inc. abstract, and can x and by 10, 100, 100, with answers up to 3dp.. Circle all the numbers that are greater than 0.6: 0.5, 0.8, 0.23, 0.09, = Can identify the value of each digit to 3dp in different contexts and can x and by 10, 100, 100, giving answers up to 3dp. Write in the missing numbers. One is done for you. Can identify the value of each digit to 3dp in different contexts and can x and by 10, 100, 100, giving answers up to 3dp, in order to solve more complex. This is part of a number line. Write in the missing numbers =

12 Multiply onedigit numbers with up to 2 decimal places by whole numbers Can multiply 1 digit numbers with up to 2dp, by whole numbers, with support / use of manipulatives. 5 x 3.42 = Can multiply 1 digit numbers, up to 2dp, by whole numbers,. Can multiply 1 digit numbers with up to 2dp, by whole numbers, confidently, in different situations. How much less than 1000 is ? Write in the missing numbers. complex/broader and non-routine Can multiply 1 digit numbers with up to 2dp, by whole numbers, confidently, in more complex situations. (Evidence for mastery level will be found in other fraction strands) Use written division methods in cases where the answer has up to 2 decimal places Can use written division methods with answers up to 2dp, with support = Can use written division methods with answers up to 2dp, ? 21.7 = 37.5 Can use written division methods with answers up to 2dp, in a range of situations. Here are five calculations. A B C D E Can use written division methods with answers up to 2dp in more complex situations = Write the letter of the calculation that has the greatest answer. Write in the missing numbers. Write the letter of the calculation that has an answer closest to 11. Write in the missing numbers x 6 = 25 x? (Evidence for mastery level will be found in other fraction strands) Ratio and Proportion Solve involving the relative sizes of 2 quantities where missing values can be found by using integer multiplication and division facts Can model the structure with support using concrete or pictorial representation E.g. Harry has four times as many Can use the structure of the relationship to solve in a given context E.g. Harry has four times as many sweets as Ella. Ella has 20 sweets. How many does Harry have? Ella 20 Can decide how to solve a problem involving the relative sizes of two quantities efficiently E.g. Here is a recipe for pasta sauce. 300 g tomatoes 120 g onions Understands and can use the structure behind such to work flexibly and efficiently E.g. In a flower bed, a gardener plants 3 red bulbs for every 4 white bulbs. How many red and white bulbs might she plant? If she has 100 white bulbs, how many red bulbs does she need to buy? If she has 75 red bulbs, how many white bulbs does she

13 Solve involving the calculation of percentages [for example, of measures and such as 15% of 360] and the use of percentages for comparison sweets as Ella. Ella Harry Can solve using key percentages 1%, 10%, 25%, 50% e.g Would you rather walk 10% of 500m or 25% of 300m? Harry Can solve involving the calculation of percentages and using comparison Would you rather have 15% of 260 or 30% of g mushrooms Sam makes the pasta sauce using 900 g of tomatoes. What weight of onions should he use? What weight of mushrooms? Can solve involving the calculation of percentages and using comparison and explain reasoning people visited a theme park in one year. 15% visited in April and 40% in August. How many visited in the rest of the year? complex/broader and non-routine need to buy? If she wants to plant 140 bulbs altogether, how many of each colour should she buy? Purple paint is made from red and blue paint in the ratio of 3:5. To make 40 litres of purple paint how much would I need of each colour? Explain your thinking. Can solve more complex involving the calculation of percentages and using comparison and explain reasoning Solve involving similar shapes where the scale factor is known or can be found Can solve simple single step with support Here is a drawing of a model car. Can solve simple scaling using given information Find the missing length when 3 out of 4 sides are provided. Can solve multi-step Here are some picture frame sizes. Can manipulate given information This photograph shows three Russian dolls. The height of the model is 2.8

14 centimetres. complex/broader and non-routine The height of the real car is 50 times the height of the model. What is the height of the real car? Give your answer in metres. For each frame, the length is twice the height, subtract 4. What is the length of a frame which has a height of 36cm? A new frame has its length twice its height. It is made with 126cm of wood. The real-life height of the largest Russian doll is 13.5 cm. Solve involving unequal sharing and grouping using knowledge of fractions and multiples Can solve simple with support and manipulatives Together, Joe and Del have 20 stickers, but Joe has 4 more than Del. How many do they each have? Can solve multi-step Kate, Lynn and Sam received a total of 85 for their hard work. Kate received 8 more than Sam but 6 less than Lynn. How much did they each receive? There are 25 children in the lunch queue, including Nik. Nik says What is the length of this frame? Can use reasoning skills to choose correct operation to solve multi-step Tom, Dick and Harry share out a bag of 59 sweets so that Dick ends up with twice as much as Harry but 4 less than Tom. How many sweets do they each end up with? What is the real-life height of the smallest Russian doll? Can interpret ratios and use this information to solve Children were asked to choose between a safari park and a zoo for the school trip. They had a vote. The result was a ratio of 10:3 in favour of going to a safari park. 130 children voted in favour of going to a safari park. How many children voted in favour of going to the zoo? There are twice as many children in front of me as there are behind me. How many children are in front of Nik?

15 Algebra Use simple formulae Can use simple formulae with support Solve for q. q 52 = 9 q = Can use simple formulae. E.g. What is the value of 4x + 7 when x = 5? Can use simple formulae with confidence. E.g. j and k stand for two numbers. Double j equals half of k. Write numbers to complete the sentence below. When j is then k is complex/broader and non-routine Can use formulae and explain your answer. E.g. Look at these equations. a = 2b b = 3c Which equation below is also true? Put a ring round the correct one. b = 2a a = 2b + 3c a = 5c a = 6ca + b = 5 Generate and describe linear number sequences to generate linear number sequences. E.g. What is the next number in this pattern? Rule: multiply by 2, then add 2 2, 6, 14, 30,... Can generate and describe linear number sequences in word. E.g. A new cookbook is becoming popular. The local bookstore ordered 1 copy in May, 2 copies in June, 4 copies in July, 8 copies in August, and 16 copies in September. If this pattern continues, how many copies will the bookstore order in October? Can generate and describe linear number sequences. E.g. Here is a sequence of patterns made from squares and circles. Can generate, describe and explain linear number sequences. E.g. Here is a sequence of shapes made from squares and circles. The sequence continues in the same way. Calculate how many squares there will be in the pattern which has 25 circles. The sequence continues in the same way. The formula for the number of circles (c) n shape number (n) is c = 3n 1 Use the formula to work out the shape number which has 104 circles. Show your working. Write the formula for the number of squares (s) in shape number (n). S =... Express missing number Can solve missing number and am beginning to express them algebraically. Can express missing number algebraically. E.g. n stands for a whole number. Can express missing number algebraically when solving. E.g. There are n counters in Alfie s bag. Can express missing number algebraically and explain answers. E.g. The box below shows all the possible values for x.

16 algebraically E.g. n stands for a number. n + 7 = 13 What is the value of n + 10? 2n is greater than 30 5n is less than 100 Write all the numbers that n stands for. Alfie puts 3 more counters in the bag. Write an expression for the number of counters that are in the bag now. complex/broader and non-routine x is a whole number. 40 < x < 45 x could be 41, 42, 43 or 44 Write all the possible values for k. (b) Megan has two boxes. There are m counters in each box. She puts all her counters together in a pile, then removes 5 of them. Write an expression for the number of counters that are in the pile now. k is a whole number. 29 < 2k < 35 k could be Write all the possible values for w. w is a whole number. 18 < 3w + 1 < 24 w could be Find pairs of numbers that satisfy an equation with 2 unknowns to find pairs of numbers that satisfy an equation with 2 unknowns. E.g. Here is an equation. m 2n = 10 When n = 20 what is the value of m? m =... When m = 20 what is the value of n? n =... Can find pairs of numbers that satisfy an equation with 2 unknowns. E.g. Write the missing numbers so that 2a + 5b = 30. One is done for you. 2a + 5b = 30 when a = 0 and b = _6_ 2a + 5b = 30 when a = 5 and b = 2a + 5b = 30 when a = 15 and b = Can find pairs of numbers that satisfy an equation with 2 or more unknowns. E.g. Here are three equations. a + b + c = 30 a + b = 24 b + c = 14 What are the values of a, b and c? Can find pairs of numbers that satisfy an equation with more than 2 unknowns. E.g. A, B and C stand for three different numbers. The mean of A and B is 40 The mean of B and C is 35 A + B + C = 100 Calculate the values of A, B and C. Enumerate possibilities of combinations of 2 variables Can find possibilities of combinations of 2 variables with support. E.g. Ben has 2 types of coin in his pocket. He has 4 coins of one type and 2 coins of another type. Can find possibilities of combinations of 2 variables. E.g. 2x + y = 20 when x = 6 y = when y = 2 x = Can find possibilities of combinations of 2 variables and use to solve. E.g. "The red ribbon is 10 centimetres longer than the blue ribbon." Complete the table to show how the length of the red ribbon, r, depends on the length of the blue ribbon, b. Function: r = b + 10 Can find possibilities of combinations of 2 variables with increasingly difficult calculations E.g. "There are 14 elastic bands in each box and 8 elastic bands on the counter." Complete the table to show how the number of elastic bands, r, depends on the number of boxes, b. Function: r = 14b + 8

17 complex/broader and non-routine b r b r Altogether he has 1. What two types of coins does he have? Ben has and 2 coins coins. Measurement Solve involving the calculation and conversion of units of measure, using decimal notation up to 3 decimal places where appropriate Can do with support and/or more familiar forms of measure, or using manipulatives such as number lines. Kate has a piece of ribbon one metre long. She cuts off 30 centimetres. How many centimetres of ribbon are left? Can do with a range of measures. Here are 2 measuring jugs. Which jug contains the most water? Tick A or B. How much more does it contain? Can solve involving the calculation and conversion of units of measure, using decimal notation up to 3 decimal places where appropriate in a range of situations, knowing confidently which conversions to carry out. Chen and Megan each have a parcel. Chen s parcel weighs 1 ½ kg. Megan s parcel weighs 1.2 kg. How many more grams does Chen s parcel weigh then Megan s? A packet contains 1.5 kilograms of guinea pig food. Can solve involving the calculation and conversion of units of measure, using decimal notation up to 3 decimal places where appropriate in a range of more complex situations. (Evidence for mastery level will be found in other fraction strands) Remi feeds her guinea pig 30 grams of food each day.

18 Use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to 3 decimal places Can do with simpler measurements with support or practically. Write these times in order, starting with the shortest: 24 days 1 month 10 weeks 48 hours Can do with a range of measurements, and without practical apparatus. Megan wants to fill a bucket with water. A bucket holds 5 litres. A jug holds 500ml. How many jugs of water does Megan need to fill an empty bucket? These are all times on the same morning. A 7:56 am B quarter to eight Can convert a wider range of measures and apply skills to problem solving situations. Here are five letters on a scale. Match each letter to one of the capacities in the list below: 1200ml 1.7 l 1 ¼ l 1560 ml 1.07 l complex/broader and non-routine Can convert a wide range of measures, expressing each in an appropriate format, and applying these skills to a complex range of problem solving situations. How many days old will the baby be when she has lived for one million seconds? Every second, 300cm 3 of water comes out of a tap into a cuboid tank. Not actual size C six minutes to eight D half past seven Write the letters for the times in order, starting with the earliest. The base of the tank is 40cm by 40cm. The height is 12cm. How many seconds does it take to fill the tank? Convert between miles and kilometres Can do with support and the use of conversion graphs. Can do. Here are 4 distances. Write them in order starting with the shortest. 10 miles 20km 6 miles 10 km (Evidence for embedded level will be found in other areas, when skills are applied to problem solving situations. ) (Evidence for embedded level will be found in other areas, when skills are applied to more complex problem solving situations.)

19 Recognise that shapes with the same areas can have different perimeters and vice versa Can recognise that shapes with the same areas can have different perimeters & vice versa, with support & manipulatives. Carry out an investigation between areas & perimeters and note findings with support. Can recognise that shapes with the same areas can have different perimeters & vice versa,. investigate a wider range of perimeters & areas of shapes and draw conclusions. Can confidently recognise that all shapes with the same areas can have different perimeters & vice versa and can explain / illustrate why. complex/broader and non-routine Can recognise that all regular & irregular shapes with the same areas can have different perimeters & vice versa and can explain / illustrate why confidently. Recognise when it is possible to use formulae for area and volume of shapes Can do with guidance towards which formula is appropriate. A square has a length of side of 6. What is the area of the square? Can do and apply to areas and volumes of a range of shapes. This cuboid is made from centimetre cubes. Can do applied to a variety of situations and shapes. Can do applied to a wide variety of situations and shapes. Calculate the volume of this triangular prism. It is 4 centimetres by 3 centimetres by 2 centimetres. What is the volume of the cuboid? Another cuboid is made from centimetre cubes. It has a volume of 30 cubic centimetres. What could the length,

20 height and width be? complex/broader and non-routine Length = Height = Width = Calculate the area of parallelograms and triangles Can calculate areas of parallelograms and triangles with support / manipulatives eg shapes to rearrange. This is a centimetre grid. Draw 3 more lines to make a parallelogram with an area of 10cm 2 Can calculate the areas of parallelograms and different triangles. Here are some shapes drawn on a grid. Can do and apply to a range of problem solving situations. This is a centimetre grid. Draw 3 more lines to make a parallelogram with an area of 10cm 2 Can do and apply to a wider range of more complex problem solving situations. The diagram shows a shaded triangle inside a rectangle. (cm grid with diagonal short end of rectangles given.) Write the letters of the two shapes that are equal in area. What is the area of the shaded triangle? Calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm³) and cubic metres (m³), and extending to other units, mm³ & km³ Can find volumes practically and can calculate simple volumes of cubes and cuboids using a given formula. Find the volume of a cube measuring 4cm by 4cm by 4cm. Use cubes to make the larger cube or use length x width x depth to calculate the volume. Can do with knowledge of the appropriate formula and with a range of measurements. Be able to extend to some other units: mm³ or km³. Investigate how the volumes of cubes change as the length one each side increases by 1. Start at 1m by 1m by 1m and calculate the volumes up to a cube, length of side 10m. Can do, estimating volumes in a wider range of situations, being able to justify calculations by drawing on prior knowledge of volume. Calculate the volume of your classroom and use this to estimate the volume of the school hall. Give your answer in m³ and cm³. Can do, estimating volumes in a wider range of situations, wide a wider range of units, being able to justify calculations by drawing on prior knowledge of volume. Bert the Beetle lives in a cube shape house that has length of side 3cm. Justify and estimate how many houses Anthony could fit in your school hall.

21 Properties of Shape Draw 2-D shapes using given dimensions and angles Can draw 2D shapes using given dimensions and angles with support. Can you draw a triangle with one side measuring 6cm and one of the angles measuring 40 degrees? Can accurately draw 2D shapes and explain mathematical thinking where necessary. Can solve involving drawing 2D shapes What is the length of one side of the square in the circle? Can you draw the shapes, sing the cards to help you: complex/broader and non-routine Can solve complex and explain their mathematical thinking based on given dimensions and angles. Sorting activities that require knowledge of 2D shapes and Drawing them with accuracy. Recognise, describe and build simple 3- D shapes, including making nets Can recognise and build simple 3D shapes and make nets practically with support. Can you make a net of a cube? Can recognise 3D shapes, including their nets. Can solve more complex involving 3D shapes and their nets. Can solve complex involving drawing and building 3D shapes and explain mathematical reasoning. Can you find a cuboid amongst these 3D shapes?

22 How many faces/vertices/ edges does a cuboid have? What shape are the faces? complex/broader and non-routine

23 Compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons Can compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons with support. Compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons. Can classify geometric shapes based on their properties and sizes and find unknown angles. complex/broader and non-routine Can solve complex involving angles within a polygon Calculate the missing angle in the triangle

24 Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius Can illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius with support. Can illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius. Can use prior knowledge of parts of a circle to label and draw parts of a circle involving radius, diameter and circumference. complex/broader and non-routine Can solve complex involving parts of a circle. Label more complex parts of a circle(level 6) Extend chns mathematical knowledge to Pi: Recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles Can recognise with support angles at a point, on a straight line or vertically opposite using written addition and subtraction methods to support understanding. Provide children with prompt cards to support understanding Can use prior knowledge of angles at a point, on a straight line and vertically opposite to solve. On a clock face, how many degrees are between 12 and 1? Knowing there are 360 degrees around a point, what would the remaining angle be and how many degrees is it? Can recognise angles where they meet at a point, on a straight line, or are vertically opposite and find missing angles. What is the angle between the hands of a clock at four o clock? Can solve complex involving angles.

25 complex/broader and non-routine Position and Direction Describe positions on the full coordinate grid (all 4 quadrants) Can describe positions on the full coordinate grid (all 4 quadrants) with support Using a coordinate grid with all four quadrants, what are the coordinates for A, B and C? Can describe positions on the full coordinate grid (all 4 quadrants) with visible grid and numbered axis. Using a coordinate grid with all four quadrants, what are the coordinates for A, B and C? Can describe positions on the full coordinate grid (all 4 quadrants) with selected coordinates given. Here is a shaded square on x and y axes. Can describe more complex positions on the full coordinate grid (all 4 quadrants) with selected coordinates given Here is a square on coordinate axes. Battleships game

26 complex/broader and non-routine For each of these points, put a tick ( ) to show if it is inside the square or outside the square. C is the centre of the square. Find the coordinates of P and Q. (50, -70) (60.-30) (-10,50) (-30,-50) Draw and translate simple shapes on the coordinate plane, and reflect them in the axes Can draw and translate simple shapes on the coordinate plane, and reflect them in the axes horizontally or vertically, with support. Can draw and translate simple shapes on the coordinate plane, and reflect them in the axes horizontally or vertically. Can draw and translate shapes on the coordinate plane, and reflect them in the axes horizontally, vertically and diagonally. Can draw and translate complex shapes on the coordinate plane, and reflect them in the axes horizontally, vertically and diagonally. Can work backwards given the translated shape and work out where the original shape was. The diagram shows the triangle ABC and the line y = x. Reflect a square across x-axis. Draw the triangle PQR which is the reflection of the triangle ABC in the line y = x. Reflect a rectangle across the y-axis.

27 Statistics complex/broader and non-routine Interpret and construct pie charts and line graphs and use these to solve Can interpret pie charts using halves, quarters and wholes and lines graphs with scales set with intervals of 2, 5 and 10. Can construct pie charts (halves, quarters) and line graphs with support Can interpret pie charts and lines graphs. Can construct simple pie charts and line graphs. Questions involving one pie chart and children need to interpret information to answer simple. Can interpret pie charts and lines graphs to compare data. Can construct pie charts and line graphs from collected data. e.g Megan asked children from two different schools, How do you travel to school? Here are her results. Foxwood School 80 children Can interpret pie charts and lines graphs to compare data. Can construct pie charts and line graphs from collected data. Can solve more complex and explain reasoning. e.g Alfie did a survey to find which soup was most popular. The choices were: tomato Questions involving one pie chart and children to interpret information involving halves and quarters. Midtown School 240 children chicken mushroom A quarter of the children chose chicken soup. Calculate and interpret the mean as an average Can do with support, with simpler integers Can do within a range of situations. Find the mean of these spelling test scores. Megan says, The number of children walking to Foxwood School is more than the number walking to Midtown School. Is she correct? Circle Yes or No. Can do in a wider range of situations and be able to compare to other average measures (eg median). Find the mean of these long jump lengths. Mark the mean line on the graph. Four times as many children chose tomato soup as chose mushroom soup. Alfie makes a pie chart to show this information. What angle should he use for the children who chose tomato soup? Make up your own true or false statement using the pie chart / line graph. Convince me that you are right. (Evidence for mastery level will be found in other areas of maths.)