Mathematics Medium Term Plan Year 5

Transcription

1 Mathematics Medium Term Plan Year 5 strategiesthe strategies embedded in the activities are easily adaptable and can be integrated into your classroom routines. They have been gathered from a range of sources including real lessons, past questions, children s work and other classroom practice. Strategies include: Spot the mistake / Which is correct? True or false? What comes next? Do, then explain Make up an example / Write more statements / Create a question / Another and another Possible answers / Other possibilities What do you notice? Continue the pattern Missing numbers / Missing symbols / Missing information/connected calculations Working backwards / Use the inverse / Undoing / Unpicking Hard and easy questions What else do you know? / Use a fact Fact families Convince me / Prove it / Generalising / Explain thinking Make an estimate / Size of an answer Always, sometimes, never Making links / Application Can you find? What s the same, what s different? Odd one out Complete the pattern / Continue the pattern Another and another Ordering Testing conditions The answer is Visualising

2 Autumn Spring Summer Number and Place Value The Big Idea Large numbers of six digits are named in a pattern of three: hundreds of thousands, tens of thousands, ones of thousands, mirroring hundreds, tens and ones. It is helpful to relate large numbers to real-world contexts, for example the number of people that a local sports arena can hold. read, write, order and compare numbers to at least and determine the value of each digit compare and order numbers up to A1 compare and order numbers to A2 What can we say about ? Using all of the digits from 0 to 9, write down a 10- digit number. What is the largest number you can write? What is the smallest number you can write? Write down the number that is one less than the largest number. Write down the number that is one more than the smallest number. Captain Conjecture says, Using the digits 0 to 9 we can write any number, no matter how large or small. Do you agree? Explain your reasoning. Do, then explain If you wrote these numbers in order starting with the smallest, which number would be third? Explain how you ordered the numbers. Do, then explain Show the value of the digit 5 in these numbers? Explain how you know. Make up an example Give further examples Create six digit numbers where the digit sum is five and the thousands digit is two. Eg What is the largest/smallest number? count forwards or backwards in steps of powers of 10 for any given number up to count forwards or backwards in 10s, 100s and 1000s, from any number up to A2 count forwards or backwards in 10s, 100s, 1000s, s from any number up to A3

3 Explore 1 million: Write 1 million in digits. Write down the number that is 1 more than 1 million. Write down the number that is 10 more than 1 million. Write down the number that is 100 more than 1 million. Explore 1 million: How large would a stadium need to be to hold one million people? How much would a million grains of rice weigh? Spot the mistake: ,187000,197000, What is wrong with this sequence of numbers? True or False? When I count in 10 s I will say the number 10100? What comes next? = = = interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero count forwards and backwards with positive and negative whole numbers through zero A1 interpret negative numbers in context A1 The temperature at 6 a.m. was recorded each day for one week. The temperature at 6 a.m. was recorded each day for one week. What was the coldest morning? What was the warmest morning? What is the difference in temperature between Monday and Tuesday? Place the recorded temperatures in order from smallest to largest. What is the difference in temperature between the coldest day and the warmest day? At what time of year do you think these temperatures were recorded? Do you think it might have snowed during the week? Explain your reasoning. round any number up to to the nearest 10, 100, 1000, and round any number up to to the nearest 10, 100, round any number up to to the nearest 1000 or A1 10, 100, 1000, and A2 In June 2014 the population of the UK was In June 2014 the population of the UK was Possible answers

4 approximately Round this number to the nearest million. approximately What is the current approximate population of the UK? Is this number larger or smaller than ? How accurate is this figure in terms of the number of people in the UK at this moment? A number rounded to the nearest thousand is What is the largest possible number it could be? What do you notice? Round to the nearest Round it to the nearest What do you notice? Can you suggest other numbers like this? solve number problems and practical problems that involve all of the above solve number problems and practical problems using the mental skills in this unit A1/A3 solve number problems and practical problems using the mental skills in this unit A1/A3 read Roman numerals to 1000 (M) and recognise years written in Roman numerals read Roman numerals to 200 (1-CC) A1 read Roman numerals to 500 (1-D) A2 read Roman numerals to 1000 (1-M) A3 recognise years written in Roman Numerals A3

5 Mathematics Medium Term Plan Year 5 Autumn Spring Summer Addition and subtraction: The Big Ideas Before starting any calculation is it helpful to think about whether or not you are confident that you can do it mentally. For example, may be done mentally, but may require paper and pencil. Carrying out an equivalent calculation might be easier than carrying out the given calculation. For example is equivalent to (constant difference). add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction) add and subtract whole numbers with more than 4 digits, including formal written methods (columnar addition and subtraction) C1/C3 Set out and solve these calculations using a column method. True or False? add and subtract whole numbers with more than 4 digits, including formal written methods (columnar addition and subtraction) C1/C3 Convince me = 6 24 What numbers go in the boxes? What different answers are there? Convince me Explain your reasoning. Using this number statement, = write three more pairs of equivalent calculations. Pupils should not calculate the answer to these questions but should look at the structure and relationships between the numbers. add and subtract numbers mentally with increasingly large numbers add and subtract small multiples of 100 and a 1000 with a 4 digit number mentally (e.g ) A1 Write four number facts that this bar diagram shows. add and subtract multiples of 100 and a 1000 with a 4 digit number mentally (e.g ) A2 Use this number sentence to write down three more pairs of decimal numbers that sum to 3: = 3 add and subtract numbers mentally with increasingly large numbers (e.g ) A3 True or false? Are these number sentences true or false? = 6.57

6 = 8.3 Give your reasons. Hard and easy questions Which questions are easy / hard? = = = = Explain why you think the hard questions are hard? Captain Conjecture says, When working with whole numbers, if you add two 2-digit numbers together the answer cannot be a 4-digit number. Do you agree? Explain your reasoning. Captain Conjecture says, If you keep subtracting 3 from 397 you will eventually reach 0. Do you agree? Explain your reasoning. use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy C1/C2/C3 use rounding to help me estimate my mental calculations A2/A3 use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy C1/C2/C3 use rounding to help me estimate my mental calculations A2/A3 use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy C1/C2/C3 Making an estimate Which of these number sentences have the

7 answer that is between 0.5 and Always, sometimes, never Is it always, sometimes or never true that the sum of four even numbers is divisible by 4. solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why C1 The table shows the cost of train tickets from different cities. What is the total cost for a return journey to York for one adult and two children? How much more does it cost for two adults to make a single journey to Hull than to Leeds? Sam and Tom have between them. If Sam has 6 20 more than Tom, how much does Tom have? The bar model can help children solve these type of problems, please visit ncetm.org for further information on how to build understanding = = Tom has 30 80

8 Mathematics Medium Term Plan Year 5 Autumn Spring Summer Multiplication and division: The Big Ideas Pupils have a firm understanding of what multiplication and division mean and have a range of strategies for dealing with large numbers, including both mental and standard written methods. They see the idea of factors, multiples and prime numbers as connected and not separate ideas to learn. They recognise how to use their skills of multiplying and dividing in new problem solving situations. Fractions and division are connected ideas: = 36/18 = 2; 18/36 = 1/2.Factors and multiples are connected ideas: 48 is a multiple of 6 and 6 is a factor of 48. identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers know how to find multiples and factors of a number A2 use and understand the terms factor and multiple C2 Captain Conjecture says, Factors come in pairs so all numbers have an even number of factors. Do you agree? Explain your reasoning. know how to find factor pairs of a number and common factors of two numbers A3 Always, sometimes, never? Is it always, sometimes or never true that multiplying a number always makes it bigger Is it always, sometimes or never true that when you multiply a whole number by 9, the sum of its digits is also a multiple of 9 Count forwards or backwards in steps of powers of 10 for any given number up to Missing numbers 6 x 0.9 = x x 0.04 = x

9 Which numbers could be written in the boxes? Making links Apples weigh about 170 g each. How many apples would you expect to get in a 2 kg bag? know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers know and can use the vocabulary of prime numbers, use and understand the term prime number C2 prime factors and composite (non-prime numbers) C1 Always, sometimes, never? Is it always, sometimes or never true that prime numbers are odd. establish whether a number up to 100 is prime and recall prime numbers up to 19 establish whether a number up to 100 is prime and recall prime numbers up to 19 C1 multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers multiply numbers up to 4 digits by a one-digit number using a formal written method C1 multiply numbers up to 3 digits by a two-digit number using the formal written method of long multiplication for two-digit numbers C2 Prove It multiply numbers up to 4 digits by a one- or twodigit number using a formal written method, including long multiplication for two-digit numbers C3 What goes in the missing box? = = = 321 r x 1 = 13243

10 Prove it. multiply and divide numbers mentally drawing upon known facts multiply and divide numbers mentally drawing upon multiply and divide numbers mentally drawing upon known facts A1/ A2 /A3 known facts A1/ A2 /A3 use multiplication and division as inverses C1/C2/C3 use multiplication and division as inverses C1/C2/C3 Fill in the missing numbers: Fill in the missing numbers: multiply and divide numbers mentally drawing upon known facts A1/ A2 /A3 use multiplication and division as inverses C1/C2/C3 begin to write laws algebraically (e.g. distributive law as a(b + c) = ab + ac C3 Use a fact 3 x 75 = 225 Use this fact to work out = = To multiply by 25 you multiply by 100 and then divide by 4. Use this strategy to solve 48 x x x 25 divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context divide numbers up to 2 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context C1 divide numbers up to 3 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context C2 Prove It divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context C3 What goes in the missing box?

11 = = = 321 r x 1 = Prove it. multiply and divide whole numbers and those involving decimals by 10, 100 and 1000 multiply and divide whole numbers and those involving decimals by 10, 100 and 1000 C1/C2 multiply and divide whole numbers and those involving decimals by 10, 100 and 1000 C1/C2 Making links multiply and divide whole numbers and those involving decimals by 10, 100 and 1000 C1/C2 7 x 8 = 56 How can you use this fact to solve these calculations? 0.7 x 0.8 = = recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³) use and understand the terms square and cube numbers C2 recognise and use square numbers and cube numbers C2 use the notation for squared (²) & cubes (³) C2 Always, sometimes, never? Is it always, sometimes or never true that a square number has an even number of factors.

12 solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes solve problems involving mental multiplication and division by splitting them into their factors A2 solve problems involving multiplication and division where larger numbers are used by decomposing them into their factors C2 A 50 cm length of wood is cut into 4 cm pieces. How many 4 cm pieces are cut and how much wood is left over? A 1 m piece of ribbon is cut into equal pieces and a piece measuring 4 cm remains. What might the lengths of the equal parts be? In how many different ways can the ribbon be cut into equal pieces? Fill in the blanks to represent the problem as division: Fill in the blanks to represent the problem as multiplication: Fill in the missing numbers in this multiplication pyramid. Put the numbers 1, 2, 3 and 4 in the bottom row of this multiplication pyramid in any order you like. What different numbers can you get on the top of the number pyramid? How can you make the largest number? Explain your reasoning.

13 Sally s book is 92 pages long. If she reads seven pages each day, how long will she take to finish her book? A 5p coin has a thickness of 1 7 mm. Ahmed makes a tower of 5p coins worth 50p. Write down the calculation you would use to find the height of the tower. solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign C1/C3 solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign C1/C3 solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates solve problems involving multiplications and division, including scaling by simple fractions and problems involving simple rates C2 Estimating, checking Use the inverse Use the inverse to check if the following calculations are correct:

14 4321 x 12 = = 4563 Size of an answer The product of a two digit and three digit number is approximately What could the numbers be?

15 Mathematics Medium Term Plan Year 5 Autumn Spring Summer Fractions (including decimals and percentages): The Big Idea Representations that may appear different sometimes have similar underlying ideas. For example 1/4, 0 25 and 25% are used in different contexts but are all connected to the same idea. compare and order fractions whose denominators are all multiples of the same number count in thousandths D1 count forwards in simple fractions D1 compare fractions with the same denominator and multiples of the same number D1 Make each number sentence correct using =, > or <. know how to count in thousandths in both decimals & fractions D2 count backwards in simple fractions D2 order fractions whose denominators are multiples of the same number D2 Write down two fractions where the denominator of one is a multiple of the denominator of the other. Which is the larger fraction? Explain your reasoning. count in thousandths and know how to write them as both decimals and fractions D3 count forwards and backwards in simple fractions D3 compare and order fractions whose denominators are multiples of the same number D3 Spot the mistake 0.088, 0.089, 1.0 What comes next? 1.173, 1.183, Mark and label on this number line where you estimate that 3/4 and 3/8 are positioned. Russell says 3/8 > 3/4 because 8 > 4. Do you agree? Explain your reasoning. Give an example of a fraction that is more than three quarters. Now another example that no one else will think of. Explain how you know the fraction is more than three quarters. Imran put these fractions in order starting with the smallest. Are they in the correct order? Two fifths, three tenths, four twentieths How do you know? identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths identify, name and write equivalent fractions of a identify, name and write equivalent fractions of a

16 given fraction, represented visually D1 Choose numbers for each numerator to make this number sentence true. Which is closer to 1? Explain how you know. given fraction, represented visually, including tenths and hundredths D3 Odd one out. Which is the odd one out in each of these collections of 4 fractions 6/10 3/5 18/20 9/15 30/100 3/10 6/20 3/9 Why? What do you notice? Find 30/100 of 200 Find 3/10 of 200 What do you notice? Can you write any other similar statements? recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [for example, + = = 1] convert from an improper fraction to a mixed number D1 recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [for example, 2/5 + 4/5 = 6/5 = 11/5] D1/D2 Chiz and Caroline each had two sandwiches of the same size. Chiz ate 1 1 /2 of his sandwiches. Caroline ate 5/4 of her sandwiches. Draw diagrams to show how much Chiz and Caroline each ate. Who ate more? How much more? convert from an improper fraction to a mixed number and vice versa D2 recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [for example, 2/5 + 4/5 = 6/5 = 11/5] D1/D2 Chiz and Caroline each had two sandwiches of the same size. Chiz ate 1 1/4 of his sandwiches. Caroline ate 5/4 of her sandwiches. Fred said Caroline ate more because 5 is the biggest number. Tammy said Chiz ate more because she ate a whole sandwich. Explain why Fred and Tammy are both wrong. recognise mixed numbers and improper fractions and convert from an improper fraction to a mixed number and vice versa and represent these numbers on a number line D3 What do you notice? ¾ and ¼ = 4/4 = 1 4/4 and ¼ = 5/4 = 1 ¼ 5/4 and ¼ = 6/4 = 1 ½ Continue the pattern up to the total of 2. Can you make up a similar pattern for subtraction? The answer is 1 2/5, what is the question add and subtract fractions with the same denominator and denominators that are multiples of the same number mentally add tenths and one-digits whole numbers and tenths D1 add fractions with the same denominator and mentally subtract tenths and one-digits whole numbers and tenths D2 add and subtract fractions with the same mentally add and subtract tenths and one-digit whole numbers and tenths D3 add and subtract fractions with the same

17 multiples of the same number D1 denominator and multiples of the same number D2 denominator and multiples of the same number simplifying my answer or giving it as a mixed number D3 Each bar of toffee is the same. On Monday, Sam ate the amount of toffee shown shaded in A. On Tuesday, Sam ate the amount of toffee shown shaded in B. How much more, as a fraction of a bar of toffee, did Sam eat on Tuesday? Each bar of toffee is the same. On Monday, Sam ate the amount of toffee shown shaded in A. On Tuesday, Sam ate the amount of toffee shown shaded in B. What do you notice? ¾ and ¼ = 4/4 = 1 4/4 and ¼ = 5/4 = 1 ¼ 5/4 and ¼ = 6/4 = 1 ½ Continue the pattern up to the total of 2. Can you make up a similar pattern for subtraction? Using the numbers 5 and 6 only once, make this sum have the smallest possible answer: Sam says he ate 7/8 of a bar of toffee. Jo says Sam ate 7/16 of the toffee. Explain why Sam and Jo are both correct. Using the numbers 3, 4, 5 and 6 only once, make this sum have the smallest possible answer: multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams multiply proper fractions by whole numbers, supported by materials and diagrams D1 make the connection between finding a fraction of and multiplying by a fraction D1/D3 Graham is serving pizzas at a party. Each person is given 3/4 of a pizza. Graham has six pizzas. How many people can he serve? Draw on the pizzas to show your thinking. multiply mixed numbers by whole numbers, supported by materials and diagrams D2 Graham is serving pizzas at a party. Each person is given 3/4 of a pizza. Fill in the table below to show how many pizzas he must buy for each number of guests. multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams D3 make the connection between finding a fraction of and multiplying by a fraction D1/D3 solve problems involving finding fractions of amounts and write remainders as a fraction D3 Continue the pattern ¼ x 3 = ¼ x 4 =

18 Write your answer as a multiplication sentence. ¼ x 5 = Continue the pattern for five more number sentences. How many steps will it take to get to 3? When will he have pizza left over? read and write decimal numbers as fractions [for example, 0.71 = ] read and write decimal numbers as fractions A1 say, read and write decimal fractions and related tenths accurately D1 say, read and write decimal fractions and related tenths, and hundredths accurately D2 read and write decimal numbers as fractions [for example, 0.71 = 71/100] D2/D3 5/3 of 24 = 40 Write a similar sentence where the answer is 56. The answer is 2 ¼, what is the question Give your top tips for multiplying fractions. Complete the pattern ?? 100?? 100?? 100 say, read and write decimal fractions and related tenths, hundredths and thousandths accurately D3 read and write decimal numbers as fractions [for example, 0.71 = 71/100] D2/D ?????? recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents recognise the value of tenths and hundredths and give decimal equivalents A2 Complete the table. What do you notice? One tenth of 41 One hundredth of 41 One thousandth of 41 Another and another Write a fraction with a denominator of one hundred which has a value of more than 0.75? and another, and another, recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents A3

19 Continue the pattern What do you notice? = = = 0.1 Continue the pattern for the next five number sentences. Complete the pattern ?? 100?? 100?? ?????? round decimals with two decimal places to the nearest whole number and to one decimal place round decimals with two decimal places to the nearest whole number A2 Complete the table. Do, then explain Another and another Write a fraction with a denominator of one hundred which has a value of more than 0.75? and another, and another, round decimals with two decimal places to the nearest whole number and to one decimal place A3 Circle each decimal which when rounded to one decimal place is Explain your reasoning read, write, order and compare numbers with up to three decimal places compare and order numbers with the same number of compare and order numbers with up to 2 decimal Top tips Explain how to round decimal numbers to one decimal place? Also see rounding in place value compare and order numbers with up to 3 decimal

20 decimal places up to 2 decimal places A1/B1 places A2/B2 places A3/B3 Missing symbol Put the correct symbol < or > in each box What needs tobe added to 3.63 to give 3.13? What needs to be added to to give 4.1? solve problems involving number up to three decimal places add decimals, including a mix of whole numbers and decimals, decimals with different numbers of decimals places D1 add and subtract decimals, including a mix of whole numbers and decimals, decimals with different numbers of decimals places and complements of 1 (e.g = 1) D2 solve problems and puzzles involving numbers up to three decimal places, check my answers for reasonableness and round where appropriate D2/D3 True or false? 0.1 of a kilometre is 1m. 0.2 of 2 kilometres is 2m. 0.3 of 3 Kilometres is 3m 0.25 of 3m is 500cm. solve problems and puzzles involving numbers up to three decimal places, check my answers for reasonableness and round where appropriate D2/D3 2/5 of 2 is 20p recognise the per cent symbol (%) and understand that per cent relates to number of parts per hundred, and write percentages as a fraction with denominator 100, and as a decimal know a percentage is a proportion of a quantity D1 understand that fractions, decimals and percentage are all different ways of expressing proportions D1/D2/D3 represent the per cent symbol (%) & understand that per cent relates to number of parts per hundred D1 know a percentage is an operator D2 understand that fractions, decimals and percentage are all different ways of expressing proportions D1/D2/D3 represent the per cent symbol (%) & understand that per cent relates to number of parts per hundred & write percentages as a fraction with denominator know a percentage is a proportion of a quantity as well as an operator D3 understand that fractions, decimals and percentage are all different ways of expressing proportions D1/D2/D3 represent the per cent symbol (%) & understand that per cent relates to number of parts per hundred &

21 Krysia wanted to buy a coat that cost 80. She saw the coat on sale in one shop at 1/5 off. She saw the same coat on sale in another shop at 25% off. Which shop has the coat at a cheaper price? Explain your reasoning. Express the yellow section of the grid in hundredths, tenths, as a decimal and as a percentage of the whole grid. Do the same for the red section. hundred D2 make connections between percentages, fractions and decimals (e.g. 100% represents a whole quantity and 1% is 1/100, 50% is 50/100, 25% is 25/100) and relate this to fractions of D2 Jack and Jill each go out shopping. Jack spends 1/4 of his money. Jill spends 20% of her money. Frank says Jack spent more because 1/4 is greater than 20%. Alice says you cannot tell who spent more. Who do you agree with, Frank or Alice? Explain why. Suggest another way to colour the grid to show clearly each fraction that is shaded. What fraction of the grid is shaded in total? How many different ways can you express the fraction of the grid that is shaded? write percentages as a fraction with denominator hundred and as a decimal fraction D3 make connections between percentages, fractions and decimals D3 Ordering Put these numbers in the correct order, starting with the largest. 7/10, 0.73, 7/100, % Explain your thinking Which is more: 20% of 200 or 25% of 180? Explain your reasoning. solve problems which require knowing percentage and decimal equivalents of,,,, and those fractions with a denominator of a multiple of 10 or 25 solve problems which require knowing percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and those fractions with a denominator of a multiple of 10 or 25 D2/D3 solve problems which require knowing percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and those fractions with a denominator of a multiple of 10 or 25 D2/D3

22 Multiply and divide numbers by 10, 100, 1000 Undoing I divide a number by 100 and the answer is 0.33 What number did I start with? Another and another Write down a number with two decimal places which when multiplied by 100 gives an answer between 33 and and another, and another,

23 Mathematics Medium Term Plan Year 5 Autumn Spring Summer Measurement The Big Ideas The relationship between area and perimeter is not a simple one. Increasing or decreasing area does not necessarily mean the perimeter increases or decreases respectively, or vice versa. Area is measured in square units. For rectangles, measuring the length and breadth is a shortcut to finding out how many squares would fit into each of these dimensions. convert between different units of metric measure (for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre) convert between different units of metric measure (e.g. kilometre and metre; centimetre and metre; centimetre and millimetre) E1 Complete this: Which has the greater mass? 1/5 kg or 1/10 kg Explain why. use my knowledge of place value and multiplication and division to convert between standard units E2/E3 convert between different units of metric measure (e.g. kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram) E2 True or false? 1 5 kg g = 2 1 kg g 32 cm m = 150 cm 0 13 m 3/4 l l = half of 1 6 l Explain your reasoning. use my knowledge of place value and multiplication and division to convert between standard units E2/E3 convert between different units of metric measure (e.g. kilometre & metre; centimetre & metre; centimetre & millimetre; gram & kilogram; litre & millilitre E3 The answer is. 0.3km What is the question? understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints know the names of metric units and some common imperial units E1 know the names of metric units and common imperial units E2 understand equivalence between metric units and common imperial units such as inches, pounds and pints E2 A litre of water is approximately a pint and three quarters. know the names of metric units and an increasing number of common imperial units E3 understand and can use equivalence between metric units and common imperial units such as inches, pounds and pints E3

24 How many pints are equivalent to 2 litres of water? Using the approximation, when will the number of litres and the equivalent number of pints be whole numbers? measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres E1 Here is a picture of a square drawn on cm2 paper. Here is a picture of a square drawn on cm2 paper. [Algebra] Undoing Draw another rectangle with the same perimeter as this square. Do the two rectangles have the same area? Is this always, sometimes or never true of other pairs of rectangles with the same perimeter? Explain your reasoning. How many other rectangles are there with the same perimeter as the square, where the sides are a whole number of cm? Show your workings. The perimeter of a rectangular garden is between 40 and 50 metres. What could the dimensions of the garden be? Testing conditions Shape A is a rectangle that is 4m long and 3m wide. Shape B is a square with sides 3m. The rectangles and squares are put together side by side to make a path which has perimeter between 20 and 30 m. For example Can you draw some other arrangements where the perimeter is between 20 and 30 metres? calculate and compare the area of rectangles (including squares), and including using standard units, square centimetres (cm²) and square metres (m²) and estimate the area of irregular shapes calculate and compare the area of squares and rectangles and related composite shapes including using standard units, square centimetres (cm²) and square metres (m²) and estimate the area of irregular shapes E2 Top Tips Put these amounts in order starting with the largest cm m 2

25 13 m 2 Explain your thinking Always, sometimes, never When you cut off a piece of a shape you reduce its area and perimeter. See also Geometry Properties of Shape estimate volume [for example, using 1 cm³ blocks to build cuboids (including cubes)] and capacity [for example, using water] estimate volume (e.g. using 1 cm³ blocks to build cubes and cuboids) and capacity (e.g. using water) E3 Other possibilities (links with geometry, shape and space) A cuboid is made up of 36 smaller cubes. solve problems involving converting between units of time use all four operation in problems involving time including conversions (e.g. days to weeks, leaving the answers as weeks and days) E1 solve problems involving converting between units of time E1/E2 solve problems involving converting between units of time E1/E2 use coordinates and scales to solve problems involving interpreting time graphs E2 If the cuboid has the length of two of its sides the same what could the dimensions be? Convince me Undoing A school play ends at 6.45pm. The play lasted 2 hours and 35 minutes. What time did it start? Working backwards Put these lengths of time in order starting with the longest time. 105 minutes 1 hour 51 minutes 6360 seconds What do you notice?what do you notice?

26 1 minute = 60 seconds 60 minutes = seconds Fill in the missing number of seconds down some more time facts like this. use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling use all four operation in problems involving money, including conversions E1 The weight of a football is 400 g. How much do five footballs weigh in kilograms? solve problems using the relations of perimeter and area to find unknown lengths. Missing length questions such as these can be expressed algebraically 4 + 2b = 20 for a rectangle of sides 2cm and b cm and perimeter 20cm E2 A football weighs 0 4 kg. Three footballs weigh the same as eight cricket balls. How many grams does a cricket ball weigh? use all four operations to solve problems involving measures (e.g. length, mass, volume, money) using decimal notation including scaling E3 Write more statements Mr Smith needs to fill buckets of water. A large bucket holds 6 litres and a small bucket holds 4 litres. If a jug holds 250 ml and a bottle holds 500 ml suggest some ways of using the jug and bottle to fill the buckets. Joe and Kate are using two metre sticks to measure the height of the climbing frame. Their measurements are shown in the diagram. How tall is the climbing frame? A 1 2 m ribbon and a 90 cm ribbon are joined by overlapping the ends and gluing them together. The total length of ribbon needs to be 195 cm long. How much should the two pieces overlap? A box weighs 1 3 kg. A box and two tins weigh 1 6 Here are some tins and boxes on two different

27 kg. How much does one tin weigh in grams? scales. How many grams does a tin weigh? How many grams does the box weigh? Hamsa has some juice in a jug and he pours it into a different jug. Draw the level of the juice in the jug on the right.

28 Mathematics Medium Term Plan Year 5 Autumn Spring Summer Properties of shapes: During this year, pupils increase the range of 2-D and 3-D shapes that they are familiar with. With 3-D shapes they think about the faces as well as the number of vertices and through considering nets think about the 2-D shapes that define the 3-D shapes. Pupils learn about a range of angle facts and use them to describe certain shapes and derive facts about them. Regular shapes have to have all sides and all angles the same. Although non-square rectangles have four equal angles, the fact that they do not have four equal sides means that they are not regular. Some properties of shapes are dependent upon other properties. For example, a rectangle has opposite sides equal because it has four right angles. A rectangle is defined as a quadrilateral with four right angles. It does not have to be defined as a quadrilateral with four right angles and two pairs of equal sides. identify 3-D shapes, including cubes and other cuboids, from 2-D representations identify 3-D shapes, including cubes and other cuboids, from 2-D representations B1/B3 What shapes do you make when these 2-D representations (nets) are cut out and folded up to make 3-D shapes? Draw the 2-D representation (net) that will make this cuboid when cut out and folded up. identify 3-D shapes, including cubes and other cuboids, from 2-D representations B1/B3 What s the same, what s different? What is the same and what is different about the net of a cube and the net of a cuboid?

29 Visualising I look at a large cube which is made up of smaller cubes. If the larger cube is made up of between 50 and 200 smaller cubes what might it look like? know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles know angles are measured in degrees B1/B2 know angles are measured in degrees B1/B2 estimate acute, obtuse and reflex angles B1/B2 estimate acute, obtuse and reflex angles B1/B2 Convince me estimate and compare acute, obtuse and reflex angles B3 What is the angle between the hands of a clock at four o clock? At what other times is the angle between the hands the same? Convince me draw given angles, and measure them in degrees ( ) draw given angles and measure them in degrees ( ) B1 Other possibilities Here is one angle of an isosceles triangle. You will

30 need to measure the angle accurately. What could the other angles of the triangle be? Are there any other possibilities? identify: angles at a point and one whole turn (total 360 ) identify angles at a point and one whole turn (total 360 ) B1/B2 identify angles at a point and one whole turn (total 360 ) B1/B2 The circle is divided into quarters by the two diameter lines and four angles A, B, C and D are marked. Are the statements below true or false? Angle C is the smallest angle. Angle D is the largest angle. All the angles are the same size. Angle B is a right angle. Angle B is an obtuse angle. Explain your reasoning. In the questions, below all of Harry s movement is in a clockwise direction. If Harry is facing North and turns through 180 degrees, in which direction will he be facing? If Harry is facing South and turns through 180 degrees, in which direction will he be facing? What do you notice? If Harry is facing North and wants to face SW how many degrees must he turn? From this position how many degrees must he travel through to face North again? identify: angles at a point on a straight line and a turn (total 180 ) identify angles at a point on a straight line and 1/2 a turn (total 180 ) B2/B3 identify angles at a point on a straight line and 1/2 a turn (total 180 ) B2/B3 identify: other multiples of 90 identify other multiples of 90 B3

31 use angle sum facts and other properties to make deductions about missing angles and relate these to missing number problems B3 use the properties of rectangles to deduce related facts and find missing lengths and angles use the properties of rectangles to deduce related facts and find missing lengths B1/B2 use the term diagonal and make conjectures about the angles formed by diagonals and sides, and other properties of quadrilaterals, for example using dynamic geometry ICT tools B1/B2 use the properties of rectangles to deduce related facts and find missing lengths B1/B2 use the term diagonal and make conjectures about the angles formed by diagonals and sides, and other properties of quadrilaterals, for example using dynamic geometry ICT tools B1/B2 draw lines with a ruler to the nearest millimetre B2 use conventional marking for parallel lines and right angles B3 [Algebra] Connected Calculations The number sentence below represents the angles in degrees of an isosceles triangle. A + B + C = 180 degrees A and B are equal and are multiples of 5. Give an example of what the 3 angles could be. Write down 3 more examples Other possibilities A rectangular field has a perimeter between 14 and 20 metres. What could its dimensions be? distinguish between regular and irregular polygons based on reasoning about equal sides and angles distinguish between regular and irregular polygons based on reasoning about equal sides and angles B2/B3 distinguish between regular and irregular polygons based on reasoning about equal sides and angles B2/B3 Identify the regular and irregular quadrilaterals. Which of these statements are correct? A square is a rectangle. A rectangle is a square. A rectangle is a parallelogram. A rhombus is a parallelogram. Always, sometimes, never Is it always, sometimes or never true that the number of lines of reflective symmetry in a regular polygon is equal to the number of its sides n.

32 Pupils should recognise that a square is the only regular quadrilateral and there are two within this set. Explain your reasoning.

33 Mathematics Medium Term Plan Year 5 Autumn Spring Summer Position and direction identify, describe and represent the position of a shape following a reflection or translation, using the appropriate language, and know that the shape has not changed identify, describe and represent the position of a shape following a translation, using the appropriate language and know that the shape has not changed B1 identify, describe and represent the position of a shape following a reflection using the appropriate language and know that the shape has not changed B2 recognise and use reflection and translation in a variety of diagrams, including continuing to use a 2-D grid and coordinates in the first quadrant. Reflection should be in lines that are parallel to the axes B3 Working backwards A square is translated 3 squares down and one square to the right. Three of the coordinates of the translated square are: (3, 6) (8, 11) (8, 6) What are the co-ordinates of the original square? Mathematics Medium Term Plan Year 5 Autumn Spring Summer Statistics The Big Ideas Different representations highlight different aspects of data. It is important to be able to answer questions about data using inference and deduction, not just direct retrieval. solve comparison, sum and difference problems using information presented in a line graph solve comparison, sum and difference problems using information presented in a line graph E2/E3 solve comparison, sum and difference problems using information presented in a line graph E2/E3

34 Use the line graph to answer the following questions: Approximately how much does the average child grow between the ages of 1 and 2? Do they grow more between the ages of 1 and 2 or 7 and 8? Use the line graph to answer the following questions: From the graph can you predict the approximate height of an average 10 year old? Explain how. Consider what might be the similarities and differences between this graph and a graph of the average height of teenagers. complete, read and interpret information in tables, including timetables read and interpret information in tables, including complete information in tables, including timetables timetables E1/E3 E1/E2 complete information in tables, including timetables E1/E2 read and interpret information in tables, including timetables E1/E3 begin to decide which representations of data are most appropriate and why E3

35 True or false? (Looking at a train time table) If I want to get to Exeter by 4 o clock this afternoon, I will need to get to Taunton station before midday. Use the bus timetable to answer the following questions: On the 6:50 bus how long does it take to get from Highway Rd to Westland Rd? Can you travel to Long Rd on the 8:45 bus? Which journey between Rain Rd and Kingswell Rd takes the longest time, the bus that leaves Rain Rd at 7:25 or the bus that leaves Rain Rd at 7:41? Explain your reasoning. Use the bus timetable to answer the following questions: If you needed to travel from Coldcot Rd and arrive at Kingswell Rd by 8:20, which would be the best bus to catch? Explain why. Is this true or false? Convince me. Make up your own true/false statement about a journey using the timetable. What s the same, what s different? Pupils identify similarities and differences between different representations and explain them to each other Which journey takes the longest time? Create a questions Pupils ask (and answer) questions about different statistical representations using key vocabulary relevant to the objectives. (see above) Deleted: