I can work out how much I have left from 20p when I buy a toy

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1 Year 1 Block D: calculating, measuring and understanding shape progression map 2 weeks 10 lessons Framework objectives, children s learning outcomes and examples of assessment for learning questions in blue. Speaking & listening Y1 Block D Unit 1 Y1 Block D Unit 2 Y1 Block D Unit 3 Retell stories, ordering events using story language I can tell the robot step by step how to go around the chair and back to me I can tell the story of Goldilocks and the three bears What happens first? And next? What happens at the end of your story? These cards tell a story of how some children built a snowman. Put the cards in order. Experiment with and build new stores of words to communicate in different contexts I can use words that describe position and direction Michelle and Solomon are going to take the register to the school office. Give them instructions to tell them how to get there. Use words like forwards, left, right... Experiment with and build new stores of words to communicate in different contexts I can retell a story that I have heard The pictures on the cards tell the story that you heard on the tape. Put the cards in time order. What do you think happens next? Money Counting Calculating Recognising coins Word problems Solve problems involving counting, adding, subtracting, doubling or halving in the context of numbers, measures or money, for example, to 'pay' and 'give change' I can use counting to solve problems involving measures Count reliably at least 20 objects, recognising that when rearranged the number of objects stays the same; estimate a number of objects that can be checked by counting I can find out how long a room is by counting the paces I take to cross it Children count, compare, add and subtract in contexts involving measures or money. This helps them to transfer their calculation skills from the context of number and apply them to the measures, and vice versa. When they are working with money, children initially use only 1p coins or only 1 coins to 'pay' in the classroom shop, counting out coins for an object that they want to buy. They buy a number of 2p stamps using 2p coins. Slowly, they understand that a 2p coin has the same value as two 1p coins, and that a 2 coin has the same value as two 1 coins. They begin to read and write prices such as 8p or 4, responding to instructions such as: Tell me how much you think this toy boat costs. Watch while I write how much it is. This toy car costs 9 pence. Find a price label to match how much. These activities can be demonstrated on an interactive whiteboard to a large group. They can also be linked to counting in twos to 10 and back again to zero, and to hops of 2 on a number line. Assessment focus: Ma2, Solving numerical problems Look out for children interpreting the language used to describe a problem and recognising when counting could be used to solve it. For example, look for children counting coins of one value to solve problems such as, How many 2p coins do you need to pay for this sheet of 2p stickers?, Which coins from the purse would you use to pay the right amount for the apple? or How much money is there altogether in the bag of 1 coins? Look for children recognising what they need to do to solve problems that involve both addition and subtraction How did you find out which of these two objects was the lighter, shorter, held the least amount...? I am giving each of you six paper strips. Find two strips in your set which are the same length. Show them to me. Now find a strip in your set which is longer than this one. What is each of these coins worth? In how many different ways can you make 10p using only 2p and 1p coins? Guess how many cubes are in the jar. Now check by counting. Why did you think it was that number of cubes? How many cubes will balance the parcel on the scales? How many glasses will fill the jug? How many jumbo bricks do you need to make a tower that is as tall as you are? Solve problems involving counting, adding, subtracting, doubling or halving in the context of numbers, measures or money, for example to 'pay' and 'give change' I can add up and take away when I measure Relate addition to counting on; recognise that addition can be done in any order; use practical and informal written methods to support the addition of a one-digit number or a multiple of ten to a one-digit or two-digit number I can buy two toys and work out how much they cost altogether Understand subtraction as 'take away' and find a 'difference' by counting up; use practical and informal written methods to support the subtraction of a one-digit number from a one-digit or two-digit number and a multiple of ten from a twodigit number I can work out how much I have left from 20p when I buy a toy Children continue to work with money. They distinguish coins by sorting them and start to understand their value. They begin to recognise that some coins have a greater value than others, and will buy more: for example, 2p is worth more than 1p; 5p is worth more than 2p; 2 is worth more than 1. They play money games and collect 1p or 2p coins to the value of 10p and begin to count up 'how much this is altogether'. They extend their activities in the classroom shop, paying for items that cost 1p, 3p, 5p, 7p or 9p using only 2p coins, and receiving the appropriate amount of change in 1p coins. They use coins to help them to respond to questions such as: Michael had 5. He spent 3. How much did he have left? Rosie had a 10p coin. She spent 3p. How much change did she get? How much altogether is 1p and 2p and 5p? Sunita spent 5p and 6p on toffees. What did she pay altogether? Chews cost 2p each. How much do three chews cost? An apple costs 12p. Which two coins would pay for it? Which three coins make 11p? How else could you make 11p? James paid 13p for chews. What coins could he use? What if he paid 17p? Assessment focus: Ma2, Solving numerical problems Look for evidence of children solving problems that involve money. Look for children who can find the total of sets of 1p or 1 coins and those children who can find the total value of a small set of mixed coins, for example, 1p, 2p and 5p coins. Look for children who use coins to work out the change from 10p when they pay various amounts. When paying larger amounts such as 15p look for the coins children choose to pay and their strategies for checking the total. Which of these: containers holds the most water? ribbons is the longest? packages is the heaviest? How do you know? How could you check? Look at the five paper strips. Put all your five strips in order, from longest to shortest. Now put your longest strip on its own on the table. Find two strips which, put together, are the same length as your longest strip. Show me how to find half of this strip of paper. How do you know it is exactly half? How did you work out how much they cost altogether? Does it cost more if I buy them in a different order? Make up a question using the words 'sum of' and tell me how to do it. Tell me some addition questions that have 20p as an answer. How did you work out how much you had left? Make up a 'take away' question and show me how to do it. Tell me some subtraction questions that have 10p as an answer. Solve problems involving counting, adding, subtracting, doubling or halving in the context of numbers, measures or money, for example to 'pay' and 'give change' I can find out which of three objects is the heaviest by using the scales I can work out which coins to use to pay the exact price for something I can work out what something costs when it is half price Relate addition to counting on; recognise that addition can be done in any order; use practical and informal written methods to support the addition of a one-digit number or a multiple of ten to a one-digit or two-digit number I can work out how many 10p badges I can buy for 1 Understand subtraction as 'take away' and find a 'difference' by counting up; use practical and informal written methods to support the subtraction of a one-digit number from a one-digit or two-digit number and a multiple of ten from a two-digit number I can count up to find how much I have left from 50p when I buy an object Children continue to work with money and understand the value of all coins. They exchange 20p and 50p coins for smaller coins in different ways. They count up 'how much altogether' there is in a purse containing several 2p coins, or several 5p coins or several 10p coins, linking the counting to counting in twos, fives and tens. They then count up how much there is in a pursewith a few mixed coins. They learn that when they are counting up coins it is usually easier to start with the largest coin or coins, and finish with the smallest. They link this to putting the larger number first when adding. Children extend their activities in the classroom shop, paying exactly for items costing less than 50p using 10p, 5p, 2p and 1p coins. They then pay for an item costing, say, 17p by rounding up to 20p and paying that amount. They work out the change that they expect to get from the shopkeeper. They use coins to help them to respond to questions such as: Fatima paid 57p for a yogurt. What coins could she use? Carole has 30p. She spends 25p. How much does she have left? Robert had a 50p coin. He spent 3p. How much change did he get? How much altogether is 5p and 10p and 10p? Ahmed spent 14p and 9p on apples. What did he pay altogether? Lollipops cost 5p each. How much do six lollipops cost? An orange costs 17p. Which three coins would pay for it? Which three coins make 32p? How else could you make 32p? Assessment focus: Ma2, Solving numerical problems Look for evidence of children choosing to use coins to help them solve problems involving money. Look out for children who choose to represent problems using just 1p coins and for those who are able to select and use larger denominations. Look for children who can use their knowledge of counting in twos, fives or tens to work out the value of a number of coins of one type. At the shop, all packets of crisps cost the same. Hannah buys two packets. She pays 40 pence. How much does one packet cost? In how many different ways can you make 30p using only silver coins? Put this box on one side of the balance (scales). Find two other boxes that together balance this one. [Point to the box on the balance.] Tell me when both sides balance. Use the balance (scales) to find out which of these three boxes is heaviest, which is the lightest, and which is in between. [Use statements like: The taller the container, the more water it holds. The larger the package, the heavier it is.] Do you agree? Can you find an example that shows that the statement is wrong? What if the badges cost 5p? How many could you buy for 1? Tell me how you worked it out. Tell me some addition questions that have 80p as an answer. Make up a question that uses the word total and tell me how to do it. How will you check your change? Build me two towers that have a difference of four cubes in their heights. Tell me some subtraction questions that have 50p as an answer. Make up a question that uses the words difference between and tell me how to do it.

2 Year 1 Block D: calculating, measuring and understanding shape progression map 2 weeks 10 lessons Framework objectives, children s learning outcomes and examples of assessment for learning questions in blue. Y1 Block D Unit 1 Y1 Block D Unit 2 Y1 Block D Unit 3 Measures Time Estimate, measure, weigh and compare objects, choosing and using suitable uniform non-standard or standard units and measuring instruments (for example, a lever balance, metre stick or measuring jug) I can guess how many cubes will balance a parcel I can use a metre stick to measure how far it is across the hall Children continue to make direct comparison of the length, weight or capacity of two objects without any counting. They begin to use uniform non-standard units to estimate and then measure length, using objects such as cubes or art straws that are all the same size. They select an egg cup to measure the capacity of a small jug, and a larger jug to measure the capacity of a bucket, recognising that it would not be appropriate to measure the capacity of the bucket using the egg cup. They weigh on the scales parcels that have been carefully prepared by the teacher to match an equivalent number of identical bricks or weights, estimating first how many bricks will balance the parcel. Assessment focus: Ma1, Problem solving Look for children engaging purposefully with practical mathematical activities and who explain what they are doing and what they want to find out. Look out for children who begin to select the mathematics they need to use in some activities. For example, in order to answer a question that involves the comparison of two lengths that cannot be placed together for direct comparison, such as, Are the tables in our classroom as long as the ones in the corridor?, look for children who suggest using string, linking cubes or other material. Where do you start to measure the length of the carpet? Ann measured the height of these two dolls in blocks. How many blocks taller is the large doll? Use vocabulary related to time; order days of the week and months; read the time to the hour and half hour I know the days of the week and can say them in order I can remember the order of a favourite story Children continue to develop the concept of time in terms of time passing and sequencing events in familiar story or day-to-day routines. They use terms such as morning, afternoon and evening, yesterday and tomorrow. They learn to order the days of the week and learn that weekend days are Saturday and Sunday. They listen to stories and rhymes about time, such as The Very Hungry Caterpillar or The Bad-Tempered Ladybird by Eric Carle, Monster Monday by Susanna Gretz or Hard Boiled Legs by Michael Rosen and Quentin Blake. They count how many times they can clap in a steady rhythm while a child writes their name on the board, and discuss who took more time and who took less time. They count regular beats on a drum while children pace across a room or cut out a square of paper. They estimate whether they can pack the bricks away while someone counts to 20. Estimate, measure, weigh and compare objects, choosing and using suitable uniform non-standard or standard units and measuring instruments (for example, a lever balance, metre stick or measuring jug) I can guess how many jugs of water I will put into the bowl to fill it I can use the red weights to balance a parcel Children continue to use and apply their calculation skills to solve problems involving measures. For example, they solve problems such as: One bottle of water will fill 10 cups. How many cups will two bottles fill? Which is heavier: the large roll of cotton wool or the small tin of tomatoes? Estimate how many art straws will fit across this table. How many of the long paintbrushes will fit across the table? They order small sets of objects according to their weight, capacity, length, height or width. At first they use direct comparisons to order the objects. They then use uniform non-standard units to match each object and count the number of units. Look for evidence of children measuring by direct comparison, for example when they compare two objects using a balance or pour water from one container to another to find out which holds more. When using direct comparison look for the strategies children use when they compare three or more objects, for example, look for children who balance pairs of objects to find the heavier object of each pair and then reason about which must be the heaviest of the three. Look for children who are beginning to use uniform non-standard or standard units. For example, look for children balancing each object with a number of cubes or a number of weights of the same size and using the numbers to order the objects by weight. Similarly, look for children ordering containers by counting how many cups of water it takes to fill each. They record each count in a table and work out which of the set of objects is longest or shortest, heaviest or lightest, and so on. These activities involve children in making decisions about the accuracy of the measure; for example: The shelf is 6 and a bit exercise books long. Is it nearer to 6 or 7 exercise books? They discuss questions such as: If the book is 24 cubes long, will it also be 24 counters long? Assessment focus: Ma1, Communicating Look for evidence of the language children use when they describe and discuss numbers and the measurements they make. Look for children who compare numbers and measurements and are beginning to use comparative language such as more/fewer than, longer, longest, holds more/less than, holds most and heavier or heaviest. Is this stick longer or shorter than this straw? How do you know? Is the red parcel heavier than this other one? How do you know? Does this container hold more than this other one? How do you know? Which of these three containers holds the most water? How do you know? How could you check? Which of these objects are sensible to use for measuring? Why? What sort of measuring could you use them for? Would it be fair to measure with...? Why or why not? Estimate how many art straws will fit across this table. How many of the long paintbrushes will fit across the table? Why do you think that there will be fewer paintbrushes? Use vocabulary related to time; order days of the week and months; read the time to the hour and half hour I know that it is 3 o'clock when the big hand points to the 12 and the small hand points to the 3 This unit continues to develop the concept of time. Children use the language of clock time in rhymes such as Hickory Dickory Dock or stories such as Mr Wolf's Week by Colin Hawkins. They being to know key times of the day such as assembly at 9 o'clock, going home at 3 o'clock and bed time at 8 o'clock. They read and record the time to the hour on a clock with hands and use the clock hands to respond to questions such as: It's 5 o'clock. What time will it be in two hours' time? What time was it three hours ago? Mum cooked a cake. She put it in the oven at 8 o'clock. She took it out at 10 o'clock. How long was the cake in the oven? Look for evidence of children s understanding of time. Look for children who can put familiar daily events into order and describe the sequence. Look out for children who are able to read the time from an analogue clock on the hour and those who are Estimate, measure, weigh and compare objects, choosing and using suitable uniform non-standard or standard units and measuring instruments (e.g. a lever balance, metre stick or measuring jug) I can estimate how many straws I need to measure this table I can find out how many kilogram weights I need to balance the big bag of potatoes Children continue to solve problems involving measurements. They begin to understand the relationship between the size of the unit and the number of units needed for the measurement. They predict whether they will need more counters or more matchboxes to measure the length of a book. They fill a container such as a watering can with jugs of water and then beakers of water. They discover, say, that the watering can holds 4 jugs but 20 beakers, so fewer are needed of the larger unit and more are needed of the smaller unit. Children begin to use standard units such as a metre stick to estimate, measure and compare how far they can throw a bean bag, recording distances to the nearest metre. They use a litre jug to fill three different large bowls or buckets, estimating first. They use their calculation skills to respond to questions such as: The telegraph pole is 7 metres tall. The tree is 11 metres tall. How much taller is the tree? Tom bought 18 litres of lemonade for a party. Children at the party drank 15 litres of lemonade. How many litres were left? As children measure lengths that cannot be compared by direct comparison, look for evidence of them choosing appropriate materials and units for the task. As they gain confidence using standard units, look out for children who can make sensible estimates. For example, look for children who recognise when a length is about a metre, or when a container might hold about a litre. What did you know that helped you to estimate? Before you measure, what are the important things to remember about measuring? Five children used cubes to balance one of their shoes. This table shows the number of cubes they needed. Whose shoe is heaviest? Whose shoe is two cubes lighter than Gareth's shoe? Use vocabulary related to time; order days of the week and months; read the time to the hour and half hour I know that the big hand points to the 6 when it is half past the hour I can say the months of the year in order Children continue to develop the concept of time. They order the months of the year and make a 12-page classroom 'calendar' with pictures of each month, writing significant events underneath, such as Divali, Pancake Day or Midsummer's Day, or the dates of their birthdays. They read time to the hour and half hour on a clock with hands and recognise half past the hour in day-to-day routines. They use time lines or clocks to help them to respond to questions such as: It's half past seven. What time will it be in four hours' time? What time was it two hours ago? John went to the park at 9 o'clock. He left at half past eleven. How long was he at the park? Assessment focus: Ma1, Problem solving and Communicating Look out for children who can choose and use a clock or a time line independently to help them solve time problems. Look for evidence of children knowing and using the order of everyday events. Look out for children using the correct mathematical vocabulary when

3 Year 1 Block D: calculating, measuring and understanding shape progression map 2 weeks 10 lessons Framework objectives, children s learning outcomes and examples of assessment for learning questions in blue. Time (continued) Y1 Block D Unit 1 Y1 Block D Unit 2 Y1 Block D Unit 3 Look out for children who know the order of activities that take place at the start, middle or end of the school day and can say what happens before or just after these activities. Look for evidence of children who are using the vocabulary of time themselves, including the days of the week. What day is it today? So what will tomorrow be? Which are the weekend days? Which days are we at school? Look at these pictures. Point to a picture which shows something that you think happened in the morning. Point to a picture which shows something that you think happened in the afternoon. Point to a picture which shows something that you think happened in the evening. beginning to read it at the half hour. Turn the hands of this clock so that it shows four o'clock. Who took the shortest time to...? working with time; for example, using the names of days of the week in the correct order and terms such as first, second, before, after, hour, day and week. Starting at 12, which number is halfway around the clock face? What month is your birthday? Is it in the summer? Which month comes after March? At what time of the year do the leaves fall off the trees? Sam's school starts at 9 o'clock. Sam went to the dentist and got to school half an hour late. Draw the time Sam got to school on the clock. Imagine a clock with hands on the wall in front of you. The long hand is pointing to the 6. The small hand is pointing between 8 and 9. What time is it? Position, direction and movement Visualise and use everyday language to describe the position of objects and direction and distance when moving them, for example, when placing or moving objects on a game board I can describe where something is using words like 'next to', 'in front of', 'underneath', 'on top of'... Children use everyday language to describe position, direction or movement. For example, they place objects above, below, to the right of and to the left of other objects on a magnetic board or interactive whiteboard. They follow instructions to put play-people in a scene. In PE, they follow instructions to roll or slide, or to make whole and half-turns on the spot. They turn to the left and they turn to the right. Who is sitting next to you? Put the pencil pot in front of/behind the tray of crayons. Stand in front of the board. Stand in front of, behind, beside, or opposite a partner. Stand between two other children. Show me your left hand. Tell me something in the classroom that is higher than, lower than, above, below, between, beside, next to, in the middle of, at the edge of, or in the corner of the... We can't see the hall, but what is next to the piano? What is below the big window? Visualise the position of objects and use everyday language to describe both the position and the direction and distance when moving them, for example, when placing or moving objects on a game board I can tell my partner where to place their cubes to make the same shape as mine I can follow instructions to make the same shape as my partner Identify objects that turn about a point (for example, scissors) or about a line (for example, a door); recognise and make whole, half and quarter-turns I know how to turn right and to turn left Children continue to develop the use of everyday language to describe position, direction and movement, capitalising on opportunities in classroom games and in PE, for example, playing 'Simon says...' or 'Follow my leader'. They describe where objects are in a picture or on a playing board, or how things are stored on shelves or in a cupboard. Make a model using six interlocking cubes. Tell me how to build a model the same as yours. Take a green cube. Put a second green cube on top of it. Put a yellow cube to the right of the top green cube. Put a red cube behind the yellow cube. Now show me your models. Are they all the same? Here is a birthday card that I have cut up into interesting shapes. I have shuffled the shapes on the table. Give me instructions so that I can put the card together. Visualise and use everyday language to describe the position of objects and direction and distance when moving them, for example when placing or moving objects on a game board I know how to program the robot to move around the skittles Identify objects that turn about a point (e.g. scissors) or about a line (e.g. a door); recognise and make whole, half and quarter-turns I can turn myself through a number of whole and half-turns I can tell you some objects that turn, such as windmill sails or a water tap Children continue to use everyday language to describe position, direction and movement. For example, they follow and give instructions to make whole, half and quarterturns to the left or right. They describe the route through a simple maze. They program a simple floor robot to follow a route that is marked on the floor, using previous moves and 'trial and improvement' to estimate how many 'robot steps' are needed. Assessment focus: Ma3, Properties of position and movement Look out for children using directional language. As they give instructions to another child, look for evidence of children using half-turn and quarter-turn as their units and knowing that they need to use right or left to complete the instruction. How did you decide which way the robot should turn? How did you decide how many steps the robot needed to move to reach...? Look at this map. Start at the bottom. Point to the second house on the left. Which of these shapes will roll in a straight line? Which will roll in a curved line? Follow my instructions to get through the maze. Move forwards, turn left, go straight on, turn the corner... The big hand of the clock is pointing to the 3. What number will it point to when it has made half a turn? If you face the door and make half a turn, what can you then see? Look at the map. Go to Start. Follow this route from there. Go to the end of Park Street. Turn left. Go to the fourth house

4 Year 2 Block D: calculating, measuring and understanding shape progression map 2 weeks 10 lessons Framework objectives, children s learning outcomes and examples of assessment for learning questions in blue. Speaking & listening Counting Mental calculations + / - Word problems Y2 Block D Unit 1 Y2 Block D Unit 2 Y2 Block D Unit 3 Listen to others in class, ask relevant questions and follow instruction Listen to others in class, ask relevant questions and follow instructions Listen to others in class, ask relevant questions and follow instructions I can listen to others and ask them questions about their work I can listen to others and ask them questions about their work I can listen to others and ask them questions about their work Listen while these children explain how they tackled a problem. What questions would Listen while these children explain how they tackled a problem. What questions would Listen while these children explain how they tackled a problem. What questions would you like to ask them? you like to ask them? you like to ask them? Children continue to count in ones, twos, fives and tens. They use these skills to help them to tot up a mixed set of 10p, 5p, 2p and 1p coins. They learn to count up the 10p coins first, then the 5p coins, then the 2p coins and finally the 1p coins. Assessment focus: Ma1, Problem solving Look for evidence of children selecting the mathematics to use in some classroom activities. Look for children who represent a problem using objects such as coins, pictures and numbers so that they can understand the problem more clearly and decide how to solve it. Look for children independently making connections between similar situations, for example to find the total of five 2p coins, relating this to counting in twos, doubling five or the multiplication fact, 5 2. Add or subtract mentally a one-digit number or a multiple of 10 to or from any twodigit number; use practical and informal written methods to add and subtract twodigit numbers I can add and subtract some numbers in my head Children use mental strategies to add or subtract one-digit numbers to or from twodigit numbers, bridging through a multiple of 10 where appropriate. They first practise adding on a number to reach the next multiple of 10; for example, they find the missing number in 47 + = 50. They use a 100-square to add or subtract a multiple of 10 to or from any two-digit number by counting on or back in tens. They begin to make use of number facts to partition the number being added or subtracted; for example, to add 7 to 56, they add on 4 to make 60, then another 3 to make 63. Look at the number line. It shows the sum that Fred did. Which of these sums did Fred do? = = = = 14 What is ? What number facts might you use to help you work this out? What do you need to add to 34 to get to the next multiple of 10? How might you partition 8 to help you? Find the answer for each of these. Explain how you worked out your answers = = 72 8 = Find the missing number = 35 Solve problems involving addition, subtraction, multiplication or division in contexts of numbers, measures or pounds and pence I can decide what calculation to do to solve a problem They transfer their calculation skills from the context of number and apply them to measures and money, and vice versa. They use their new skills to count on from zero in steps of 3 or 4. Assessment focus: Ma2, Solving numerical problems Look for evidence of children interpreting a range of oral and written language used to present problems and who can decide whether a problem involves addition or subtraction. In the context of money and measures, look for children solving problems involving counting in ones, twos, fives and/or tens, addition or subtraction, and where the problem is about taking away or finding a difference. Look for children making sense of their answers in the context of the problem. Look for children creating problems or stories to go with a given calculation. Children apply their calculation skills to solving word problems involving money and Add or subtract mentally a one-digit number or a multiple of 10 to or from any twodigit number; use practical and informal written methods to add and subtract twodigit numbers I can add and subtract some numbers in my head I can add and subtract bigger numbers using practical equipment or written notes to help me Children add or subtract multiples of 10, find the sum or difference of one- and two-digit numbers and use doubling and halving in the context of money or measures. They answer questions such as: A plant is 48 cm tall. It grows another 30 cm. How tall is it now? There are 18 pencils in a pack. How many pencils are there in two packs? Children find differences in practical situations. For example: How much longer/shorter than the red ribbon is the blue ribbon? Cut a strip of paper to show the difference. How much lighter than half a kilogram is each of these objects just a bit lighter, a lot lighter, or about the same? How could we check? What is ? How did you work this out? Find the answer for each of these = = = Explain how you worked out your answers. Solve problems involving addition, subtraction, multiplication or division in contexts of numbers, measures or pounds and pence I can decide what calculation to do to solve a problem Using money, children know that 1 is equal to 100p. They answer problems involving finding change and know that this is linked to subtraction. For example: I want to buy a toy costing 1. I have saved 70p so far. How much more money do I need? Children use a range of calculation strategies to solve one- and two-step problems involving money and measures. For example: A piece of string is 50 cm long. I cut off two pieces each 15 cm long. What length of string is left? They use informal recording, pictures and diagrams where appropriate to support calculation. They work in small groups to discuss problems and ways of solving them and agree on what mathematics is needed. Choose three of these numbers: 14, 15, 16, 17. Add them up. What different totals can Children continue to count along number lines in twos, fives and tens. They estimate positions of numbers on a number line where only multiples of 2, 5 or 10 are marked. They develop this understanding to read a range of scales, giving their answers to the nearest division. They discuss their answers and explain their thinking. Add or subtract mentally a one-digit number or a multiple of 10 to or from any twodigit number; use practical and informal written methods to add and subtract twodigit numbers I can add and subtract two-digit numbers using practical equipment or written notes to help me Children add or subtract mentally a one-digit number or a multiple of 10 to or from any two-digit number. They use informal jottings, number lines, number grids and practical equipment to add and subtract two-digit numbers. Children use their knowledge of number facts to respond quickly to questions such as: How many 5p coins do you need to make 35p? A cheese string is 12 cm long. I bite off and eat 4 cm. How long is the cheese string now? The yellow ribbon is 15 cm long. The green ribbon is twice as long. How long is the green ribbon? I put the yellow and green ribbons end to end. How far do they reach? They explain what calculation they did and why. Assessment opportunity: Ma2, Mental methods Look for evidence of the range of number facts children know and the different mental strategies that they use. Look for children who recall doubles to and other doubles that they use often, for example, double 50p is 100p or 1. Notice if children count in twos, fives and tens or are beginning to use mental recall of facts from the 2, 5 and 10 multiplication tables. What is ? What number facts might you use to help you to work this out? How many do you need to add to 34 to get to the next multiple of 10? How might you partition 8 to help you? Show me how you could work out the answer to What about 72 12? Can you work out your answer in a different way? Which way do you find most helpful? Why? Find the missing number: = 58 Solve problems involving addition, subtraction, multiplication or division in contexts of numbers, measures or pounds and pence I can decide which calculations are needed to solve a two-step word problem Children solve word problems involving money and measures. They use practical resources where helpful, recording their work using jottings, pictures, number lines or number sentences. For example: I rolled a toy car 47 cm. I pushed it another 39 cm. How far did the car travel? Patrick has 46p. Someone gave him another 56p. How much money does he have now? Four friends picked a total of 12 kg of strawberries. They each picked the same amount of strawberries. How many kilograms of strawberries did each of the friends pick? A baker bought six bags of flour. Each bag weighed 3 kg. How many kilograms of flour did the baker buy? Children discuss the difficulty of the problems that they are given. They respond to

5 Year 2 Block D: calculating, measuring and understanding shape progression map 2 weeks 10 lessons Framework objectives, children s learning outcomes and examples of assessment for learning questions in blue. Word problems (continued) Practical Measures and reading scales. Length, mass and capacity. Y2 Block D Unit 1 Y2 Block D Unit 2 Y2 Block D Unit 3 measures. For example: I have 72p in my purse. I add another 5p. How much do I have now? Sam's shoe is 25 cm long. His father's shoe is 31 cm long. How much longer is his father's shoe? 23 children are on the bus. 8 more children get on. How many children are on the bus now? Mary buys a notebook for 37p. What coins could she use to pay for it? Children decide on the calculation(s) needed to solve the problem, justify their decisions and check their answers. Solve these problems. What calculations are needed? How did you decide? Mina and Ben play a game. Mina scores 70 points. Ben scores 42 points. How many more points does Mina score than Ben? I think of a number then halve it. The answer is 9. What was my number? Rosie spent 48p. Suzy spent 36p more than Rosie. How much did Suzy spend? How much money is in the hand? Read the numbered divisions on a scale, and interpret the divisions between them (e.g. on a scale from 0 to 25 with intervals of 1 shown but only the divisions 0, 5, 10, 15 and 20 numbered); use a ruler to draw and measure lines to the nearest centimetre I can read numbers on a scale Children undertake practical Estimate, compare and measure lengths, weights and capacities, choosing and using standard units (m, cm, kg, litre) and suitable measuring instruments I can use a metre rule to mark out 1 metre I can measure out a litre of water Carry out measurement activities, estimating first. For example, they use a balance to find how many pencils or counters weigh the same as a 100 g weight. They use a measuring jug to measure a litre of water to find out how many yogurt pots could be filled from a litre of water. They add 10 g weights to a balance scale, and see that 10 of the weights balance a 100 g weight. Children position numbers on a number line or scale numbered in 2s, 5s or 10s. They read a measurement to the nearest centimetre on a metre stick numbered in 10cm intervals or a ruler numbered in 5 cm intervals, using the numbered divisions as reference points. Look for children who suggest appropriate tools to measure different lengths or heights, to weigh objects, to find how much a container holds or to find out how long an event lasts, for example how long it takes to run around the playground. Look for evidence of children s developing knowledge of units of measurement. Look for children beginning to match appropriate units to a measurement. For example, look for children selecting which unit, from a list of centimetres, metres, seconds, years, grams and litres, they would use to measure how old a child is, how long the corridor is, how much the watering can holds, etc. Point to 65cm on a metre stick marked in centimetres and numbered in tens.] What measurement is this? [Point to half a litre on a 1 litre measuring jug.] What measurement is this? Measure these two lines. How much longer is line A than line B? Suggest things that: you make? Using coins if necessary, show me how to find the total of 29p and 36p. Solve these problems. What calculations are needed? How did you decide? These beads weigh 2 kg. What would a quarter of them weigh? Susan bought three chocolate bars at 15p each. How much change from 50p did she get? Joe has three 20p and two 15p stamps. What values can he make using one or more of the stamps? How many different ways can you find to pay 50p using only silver coins? A week has 7 days. How many weeks are there in 35 days? Estimate, compare and measure lengths, weights and capacities, choosing and using standard units (m, cm, kg, litre) and suitable measuring instruments I can estimate length in centimetres I can estimate length in metres I can decide whether it is better to use centimetres or metres for measuring different lengths Read the numbered divisions on a scale and interpret the divisions between them (e.g. on a scale from 0 to 25 with intervals of 1 shown but only the divisions 0, 5, 10, 15 and 20 numbered); use a ruler to draw and measure lines to the nearest centimetre I can use a ruler or metre rule to measure how long something is I can read numbers on a scale and can work out the numbers between them Children continue to estimate and measure length. For example, they estimate approximately how far you can step in one stride, then measure, giving the distance as just more than/just less than/about a number of centimetres. They use metre sticks to measure distances up to 10 metres and a measuring tape to measure longer distances, in metres. They begin to estimate in metres. For example, they work in pairs to estimate, and then measure, the distance from the classroom to the hall. They agree where to start and finish, how to record the distance and then decide how close their estimate was. They suggest lengths that you could measure using centimetres and lengths to measure in metres. Children read a scale to the nearest division. They use a ruler to draw lines and measure to the nearest centimetre. They create their own tape measure, marked every 10 cm, and use it to measure longer objects to the nearest 10 cm. As they measure length, mass and capacity, look for evidence of children s knowledge of units. Look for children who suggest objects that are shorter than, about the same length as, or longer than one metre. Look for evidence of how children record longer lengths. For example, look for children recording 125 cm and those who use mixed units to record 1 metre 25 centimetres. How long is a line 3 cm longer than this [4 cm] line? Use a ruler. How long do you think this crayon is? Tell me what you do to help you estimate. Use this 10 cm strip to estimate the width of your table. Now use the tape measure to measure it. How close were you? Point out something that you think is about two metres away from you. Ten metres away? Find something that is about 50 cm long. Think of something that would be better measured in metres rather than centimetres. Explain why. Choose a word from the box to finish each sentence. questions such as: Which did you find easy/difficult? Why? They evaluate the usefulness of the strategy they chose, for example: Was the number line helpful? How did the number line help you? Ellen has a 5 note. She spends Draw a ring around each coin she gets in her change. Write the two missing amounts in this sequence. The same amount is added each time Look at these [two-step] problems. Tell me what calculations you will do. Show me how to do those calculations. There are 38 bean bags. Kerry takes 15 and Paul takes 11. How many are left? There are 60 sweets in a bag. 20 sweets are red. 16 sweets are yellow. The rest are green. How many sweets are green? Make up a story that would mean that you need to work out 2 9 then add 16. Estimate, compare and measure lengths, weights and capacities, choosing and using standard units (m, cm, kg, litre) and suitable measuring instruments I know that a metre is 100 centimetres long I know that a kilogram is 1000 grams I know that a litre is 1000 millilitres Read the numbered divisions on a scale, and interpret the divisions between them (e.g. on a scale from 0 to 25 with intervals of 1 shown but only the divisions 0, 5, 10, 15 and 20 numbered); use a ruler to draw and measure lines to the nearest centimetre I can read scales marked in 2s, 5s and 10s I can measure and draw lines to the nearest centimetre Children solve practical problems involving measures. For example, they make a paper scale showing cupfuls, to stick on a bottle, and use this to find the number of cups that different containers will hold or fill. They progress to using 100 ml measures for the scale. By counting in hundreds, they establish that 1000 ml of water is needed to fill up to 1 litre. They explain why 1000 ml is the same as 1 litre by making use of the scale; they point to each division as they count up in 100s of millilitres to reach 1 litre. They combine their knowledge of number facts and place value to answer questions such as: There is 600 ml of water in a container. I pour out 100 ml. How many millilitres of water are left in the container? Children pour 1 litre of water into various bottles and containers. They use what they have learned to estimate where half a litre will reach. They check how close their estimate was. Assessment opportunity: Ma3, Measures As they use rulers, mechanical bathroom scales and measuring cylinders, look for children who read scales with increments of 2, 5, 10 or 100. Look for evidence of children beginning to measure to the nearest half-unit, for example recording 3 1 /2 cups as the amount a container holds or reading to the nearest 50 ml on a scale in increments of 100 ml. Children recognise that 1 metre is a measurement of length, 1 litre is a measurement of capacity and 1 kilogram is a measurement of weight. They suggest suitable units and measuring instruments to measure, for example, the capacity of a watering can or the height of the door. Children continue to count along number lines in twos, fives and tens. They estimate positions of numbers on a number line where only multiples of 2, 5 or 10 are marked. They develop this understanding to read a range of scales, giving their answers to the nearest division. They discuss their answers and explain their thinking. Assessment opportunity: Ma1, Problem solving and communicating As children read scales to solve practical measuring problems, look for evidence that they make connections, for example, between reading scales and counting in steps of a

6 Year 2 Block D: calculating, measuring and understanding shape progression map 2 weeks 10 lessons Framework objectives, children s learning outcomes and examples of assessment for learning questions in blue. Practical Measures and reading scales. Length, mass and capacity. (continued) Y2 Block D Unit 1 Y2 Block D Unit 2 Y2 Block D Unit 3 are longer than 1 m; are shorter than 10 cm; are lighter than 1 kg; hold more than 1 litre Show me where the 2 metre mark is on the tape measure. And the 3 metre mark? How could you mark out 2 metres using a metre stick? How could you find out how much water this bucket will hold? If you have a half-kilogram weight, how could you use it to weigh out a kilogram of sand to go in this bucket? I can measure the length of the classroom in... I can measure the capacity of a bucket in... If this scale continued, what other numbers would be marked? Here is a ruler [marked in centimetres] and here are some lines [measuring for example 8 cm, 15 cm]. Tell me how you would measure the lines using the ruler. How heavy is Peter? regular size or positioning numbers on a number line. Look for evidence of children discussing their work, using appropriate mathematical language such as long, longer and longest Draw a line that is twice as long as this [5cm] line. Use a ruler. About how long do you think this line is? How could you measure it? Tell me two lengths that make 1 metre. Another two lengths? Tell me two weights that make 1 kilogram. Another two weights? Look at the mug I am holding. Which of these amounts is the estimate of the capacity of the mug? 1 metre 1 litre 1 centimetre 1 /4 kilogram 1 /4 litre Look at the number line. The arrow points to 50. Draw an arrow to show where the number 125 belongs. Some children rolled toy cars down a slope. How far did the blue car roll? How much further did the green car roll than the red car? Estimate how far the yellow car rolled. This scale shows the weight of a letter. How much does the letter weigh? Tell me some important tips when you measure the length of something, using a measuring tape or ruler. How do you work out the numbers not shown on a scale? Time Use units of time (seconds, minutes, hours, days) and know the relationships between them; read the time to the quarter hour; identify time intervals, including those that cross the hour I can estimate how long an activity might take, then check using a timer I can tell the time when it is something o'clock or half past the hour Children become familiar with minutes and seconds. They estimate and time how long activities take. For example, they estimate how many times in 1 minute they can walk across the hall or jump on the spot, then use a minute timer to check. They count each second as a second hand moves round a clock, then use what they have learned to count how many seconds it takes a friend to write their name or put on their shoes. They count how many seconds it takes for the sand to run through a 1-minute timer to discover that 1 minute is the same as 60 seconds. They consolidate reading the time to the hour and half hour on a clock with hands. What takes about 10 seconds? 1 minute? 1 hour? Look at these pictures of different events. [Point to a picture.] How long would this activity take? Use this seconds timer. Time me while I walk across the room and back again. How long did I take? How many minutes are there in 1 hour? It is half past 4. How many minutes have passed since 4 o'clock? What is the time on this clock? What time was it 2 hours ago? Use units of time (seconds, minutes, hours, days) and know the relationships between them; read the time to the quarter hour; identify time intervals, including those that cross the hour I know that one hour is the same as 60 minutes I can tell the time when it is quarter past, half past or quarter to the hour I know that a quarter past three is the same time as three fifteen Children recognise that as the minute hand of a clock turns through a quarter turn this represents a quarter of an hour. They use this to tell the time to the quarter hour. They know that one hour is the same as 60 minutes, that a quarter of 60 (found by halving and halving again) is 15, and that a quarter past 3 is also said as three fifteen. They look at a digital clock and read the time 3:15. Look for evidence of children reading the time on an analogue clock at the hour and halfhour. Look for children who also read the time at quarter to and quarter past different hours of the day. Look for evidence of children knowing the times of regular daily events and recognising them on both analogue and digital clock displays. How many minutes are there in one hour? Reading takes 20 minutes, and playing takes 40 minutes. Think of some more pairs of activities to make up one hour. Turn the hands of this clock so that it shows a quarter past 4. What time will it show in half an hour's time? Who took the shortest time to...? Anya went into the library at a quarter to eleven and came out at a quarter past twelve. How long was she in the library? Jane left home at ten fifteen. It took her half an hour to get to the seaside. At what time did Jane get to the seaside? The bus left at 9 o'clock to go to the zoo. It arrived 1 hour and 15 minutes later. Draw a ring around the time it got to the zoo. 09:15 11:15 09:30 10:45 10:15 Use units of time (seconds, minutes, hours, days) and know the relationships between them; read the time to the quarter hour; identify time intervals, including those that cross the hour I know that there are 24 hours in a day I can use a clock face to help me to count in steps of 5 minutes Children read time to the quarter hour on analogue and digital clocks. They know that there are 24 hours in a day. They know what they are doing at key times in the day, and find time intervals. For example, they find how long they have been out at play, using a clock face to help them to count in steps of 5 minutes. They use the time line or clock face to explain how they work out time intervals, pointing to appropriate divisions to support their explanation. Roughly, how long does it take you to walk home? To sleep each night? To count to 50? To grow 5cm taller? Bethany says she sleeps for 19 hours every night. Can that be right? How do we know? How do you use a clock face to help you to work out how many minutes there are between a quarter past 2 and a quarter to 3? Two clocks show the same time. Which are they? I went for a walk at 4 o'clock. My walk took me 45 minutes. Draw on these clocks what time it was when I ended my walk. Mark got into the pool at 4:30. He was in the pool for 45 minutes. At what time did he get out? Jane left home at ten fifteen. It took her half an hour to get to the seaside. At what time did Jane get to the seaside?

7 Year 2 Block D: calculating, measuring and understanding shape progression map 2 weeks 10 lessons Framework objectives, children s learning outcomes and examples of assessment for learning questions in blue. Y2 Block D Unit 1 Y2 Block D Unit 2 Y2 Block D Unit 3 Position and movement Follow and give instructions involving position, direction and movement I can make a floor robot follow a path marked out on the floor I can estimate the number of robot steps that the robot must take to reach the traffic cone Children follow and give instructions involving position and movement. For example, they give instructions for a partner to follow a maze drawn on squared paper or describe how to get to an object that is hidden in the classroom. They evaluate the accuracy of their instructions and adjust them accordingly. The tick is in square B5. Follow my instructions. Draw a cross in square D2. Draw a circle in square E4. Draw a triangle in square A5. Now tell me where to put a cross, a circle and a triangle. Recognise and use whole, half and quarter turns, both clockwise and anticlockwise; know that a right angle represents a quarter turn In PE I can turn on the spot through whole, half or quarter turns, either clockwise or anticlockwise Follow and give instructions involving position, direction and movement I can follow and give instructions to mark a position on a grid Children give instructions involving position, direction and movement, including those that involve turn. For example, they give instructions to a simple floor robot to follow a route marked out on the floor. They use whole, half and quarter turns and recognise that a quarter turn produces a right angle. Assessment focus: Ma3, Properties of position and movement As they provide instructions to move around objects and on to a given destination, look for children who recognise that turns, as well as straight-line movements, have size and direction Assessment focus: Ma1, Reasoning Look for evidence of children reasoning about position and movement. For example, as they instruct a programmable toy to move along a given route, look for children who enter one instruction at a time and those children who combine several instructions before they press go Turn this picture half a turn clockwise. Now turn the picture a quarter turn anticlockwise. How can we get it back to where it started from? Is there any other way? Look at this picture. Close your eyes while I turn it. Now open your eyes. What did I do? Are you sure? How could you check? How could you make the robot come back to its starting point? What instructions would you give? The robot went too far/hasn't gone far enough. What do we need to change in our instructions? Roughly, how many centimetres is one robot step? How can we find out? Recognise and use whole, half and quarter-turns, both clockwise and anticlockwise; know that a right angle represents a quarter turn I know that a quarter turn makes a right angle I can point out right angles in the classroom Children recognise whole, half and quarter-turns. They continue to describe turns and to give and follow instructions to turn. For example, they give instructions to a friend to follow a route around the playground. They make and draw half and quarter turns from the same starting point using, for example, two geo-strips. Use these geo-strips to show me what a right angle looks like. Assessment opportunity: Ma3, Measures Look for evidence of children choosing suitable materials and units for measuring in different situations. Look for children measuring length, capacity and time, using units that provide a sufficient degree of accuracy to solve a problem. Look out for children who make a connection between quarter turns and right angles in shapes. Point out some right angles in the classroom. For those we can reach, how could we check? Which of these shapes has a right angle?

8 Year 3 Block D: calculating, measuring and understanding shape progression map 2 weeks 10 lessons Framework objectives, children s learning outcomes and examples of assessment for learning questions in blue. Speaking & listening Y3 Block D Unit 1 Y3 Block D Unit 2 Y3 Block D Unit 3 Explain a process or present information, ensuring items are clearly sequenced, Explain a process or present information, ensuring items are clearly sequenced, relevant details are included and accounts ended effectively relevant details are included and accounts ended effectively I can give and follow instructions to make turns I can understand instructions to follow a route Work in pairs to agree instructions for walking from our classroom to the hall. Write down your instructions then swap them with another pair. Try out their instructions. Give them feedback on how clear their instructions were. Which words were helpful? Were any of the instructions difficult to follow? Make a compass with a card arrow and a split pin. Label it north, south, east and west. Write instructions such as: Start with the arrow facing north. Turn it three right angles clockwise. Decide which direction the arrow will end up facing. Swap instructions with someone else. Compare your results. Did you agree where the arrow would end up? If not, what error did you make? Explain a process or present information, ensuring items are clearly sequenced, relevant details are included and accounts ended effectively I can explain the steps involved in answering a problem. I make sure that the answer I give makes sense You have to explain how you solved this problem to your group. Record your method on a whiteboard. Practise what you will say. Make sure that you explain every step in order. What is the answer to the problem? Can you say this in a sentence? Using calculation strategies to solve word problems, money and measures. Solve one-step and two-step problems involving numbers, money or measures, including time, choosing and carrying out appropriate calculations I can work out what calculations to do to solve a word problem that involves measurements Add or subtract mentally combinations of one-digit and two-digit numbers I can add or subtract a one-digit number to or from a two-digit number I can add or subtract a multiple of 10 to or from a two-digit number Children use the range of calculation strategies that they know to answer problems in the context of measures. They use their knowledge of number bonds to add or subtract a one-digit number to or from a two-digit number, bridging over a multiple of 10 where appropriate. They add and subtract multiples of 10 and 100. They find one-half and one-quarter of amounts. They use these strategies to solve problems involving money and measures, such as: Ella buys a 6p lolly. She pays with a 50p piece. How much change does she get? A sunflower is 67 cm tall at the start of the week. It grows 8 cm over the week. How tall is it at the end of the week? How much orange juice is left in a 500-ml bottle after 200 ml is poured out? Carla has used one-quarter of her crayon. It was 20cm long. How long is it now? Children check that the answer to a problem sounds reasonable in the context of the problem. Represent the information in a puzzle or problem using numbers, images or diagrams; use these to find a solution and present it in context, where appropriate using.p notation or units of measure I can draw a picture, make jottings or write calculations to help me answer a problem Add or subtract mentally combinations of one-digit and two-digit numbers I can add or subtract two 2-digit numbers I know how to find the difference between two 2-digit numbers Develop and use written methods to record, support or explain addition and subtraction of two-digit and three-digit numbers I can record how I work out an addition or subtraction calculation showing each step Use practical and informal written methods to multiply and divide two-digit numbers (e.g. 13 3, 50 4); round remainders up or down, depending on the context I can multiply a 'teen' number by a one-digit number I can divide a two-digit number by a one-digit number Children consolidate their calculation strategies in all four operations through solving one- and two-step problems involving measures. They represent the information in a problem using diagrams or calculations. They explain their method and record their working clearly, showing the steps involved. They use their understanding of operations and their inverses to check answers. Solve one-step and two-step problems involving numbers, money or measures, including time, choosing and carrying out appropriate calculations I can explain how I found the answer to a word problem that involves measurements Use knowledge of number operations and corresponding inverses, including doubling and halving, to estimate and check calculations I can check whether the answer to a calculation is correct Develop and use written methods to record, support or explain addition and subtraction of two-digit and three-digit numbers I write down my method to add or subtract two-digit or three-digit numbers Use practical and informal written methods to multiply and divide two-digit numbers (e.g. 13 3, 50 4); round remainders up or down, depending on the context I can multiply and divide a two-digit number by a one-digit number Children use a range of calculation strategies to solve problems involving money and measures. They respond to oral or written questions, identifying appropriate calculations to solve the problem. They use a range of mental, mental-with-jottings and paper-and-pencil methods to record their working. They explain their method, ensuring that all stages are included, and state the answer in the context of the original problem. Children check the results of calculations by repeating addition in a different order, using an inverse operation or using an equivalent calculation. Assessment focus: Ma1, Communicating Look for children who can explain their thinking by referring to what they have recorded when they talk about their findings. Look for children using mathematical language, for example, to describe the methods and strategies they used. What is the first calculation you will do to solve this problem? What does this answer tell you? What will you do next? Look at this problem. Ella buys a 6p lolly. She pays with a 50p piece. How much change does she get? Which calculation will you do to solve this problem? How did you choose the correct calculation? What unit is the answer in? Look at this problem. Explain how to work it out. Wilf has 68p in his money bank. He adds another 5p. How much is in his money bank Children develop greater understanding of the term difference through problems such as: Amy weighs 35 kg and Carl weighs 52 kg. What is the difference in their weights? Two snakes are 56 cm and 83 cm long. What is the difference in their lengths? Children understand that finding the difference between two measurements is the same as asking: How much bigger is one than the other? They recognise that one way to find this is to count up from the smaller to the larger amount. They record their working using informal methods such as number lines. Assessment focus: Ma2, Operations and relationships between them As they solve problems that involve finding a difference, look for children who explain the problem as: How many more to make and those who understand that subtraction can Assessment opportunity: Ma2, Operations and relationships between them Look for evidence of children using inverse operations to check their results, for example using an addition calculation to check their answer to a subtraction question or using multiplication facts to derive related division facts. Look for children who are developing their understanding of the role of =, the equals sign and can solve balancing questions such as 56 = Children recognise when a problem involves multiplication or division. They understand that multiplication and division are inverses and use this to check answers. Children recognise that where a problem involves division the answer may involve a remainder and that they need to consider the context to decide whether to round the answer up or down. They use practical and informal written methods to solve problems involving two-digit numbers such as: Will balances a pear with three 50 g and three 20 g weights. How much does the pear weigh?

9 Year 3 Block D: calculating, measuring and understanding shape progression map 2 weeks 10 lessons Framework objectives, children s learning outcomes and examples of assessment for learning questions in blue. Using calculation strategies to solve word problems, money and measures. (continued) Y3 Block D Unit 1 Y3 Block D Unit 2 Y3 Block D Unit 3 now? be used. For example, look for children finding the difference between lengths such as What is the missing number? What calculation is represented on the number line? 37 cm and 74 cm by locating them on a metre stick and counting on from the smaller number. Sam adds a 50-g weight to scales containing 45 g. What is the weight on the scales Look for children who represent the problem as 37 + = 74 and those who represent it using =. What did you write down to help you answer this problem? Look at this problem. Two snakes are 56 cm and 83 cm long. What is the difference in their lengths? Draw a picture that will help you to solve the problem. What part of your picture shows the difference? Becky has three 1 coins and four 1p coins in her purse. Write down the amount of money she has altogether. A 95 g orange is placed in some balance scales. There is 35 g in the other pan. How much needs to be added to the 35 g so that the scales balance? How did you work this out? The difference between the heights of two children is 37 cm. What could their heights be? Are your suggestions reasonable? Roughly how old do you think the children would be? Find the different totals you can make by adding pairs of these numbers: Choose two calculations in which you used a different strategy to find the total. Explain why you chose different strategies. Find the total cost of a book costing 2.50 and a comic costing 99p. Jot down your method, showing each step. Bill records these steps to work out a calculation: = = 218 What calculation did he work out? A square pool has sides 12 m long. If you walked around the edge of it, how far would you walk? What calculation did you do? How did you work it out? Altogether the four sides of a square picture frame are 60 cm long. How long is each side? What calculation did you do? How did you work it out? What two multiplication facts could you use to work out 13 3? Jake has 2. He wants to buy seven packets of crisps. They cost 31p each. Does he have enough money? A songbook is 3 cm wide. How many copies of the songbook can be placed on a 65 cm shelf? Assessment opportunity: Ma2, Solving numerical problems As they solve a range of word problems, including some that involve two steps, look for evidence of children identifying and using relevant information. Look for children who choose appropriate operations to use and complete all of the necessary calculations. Where problems involve division and remainders, look for evidence of children making sensible decisions about rounding up or down. Children round measures in appropriate contexts to answer problems such as: Roughly how many chairs will fit across the back wall of the classroom if each chair is 45cm wide and the back wall of the classroom is 8 1 /2 metres wide? They use rounding to give approximate answers to problems where they choose to use a written method. For example, when finding the total of 6.78 and 2.84, children recognise that 6.78 is less than 7 and 2.84 is less than 3, so they expect the answer to be a little less than 10. Children appreciate the importance of the units when they solve measures problems. For example, to solve the problem: Wesley is 86 cm tall and Rob is 1 m 14 cm tall. How much taller is Rob than Wesley? They realise that they need to convert 1 m 14 cm to 114 cm. Look at this problem. Ella buys one toy costing 35p and another costing 48p. She pays with a 5 note. How much change does she get? What two calculations do you need to do to answer this problem? What does the answer to the first calculation tell you? Make up a word problem that would lead to the calculation 8 4. How do you recognise that this problem involves multiplication? Tracey works out that 92cm 48cm = 56cm. How could you check whether her answer is right? I think of a number, double it and then take away 2. I get the answer 6. What was my number? How did you find it? Will the answer to be closer to 8, 9 or 10? I spend 6.78 and 2.84 on shopping. Work out how much I have spent altogether. Explain each step of your calculation. Work out Decide how to record your working. An egg weighs about 50 g. Roughly, how much do 6 eggs weigh? Jot down how you worked this out. What is 20 4? What is 6 4? What is 26 4? What is the remainder when 35 is divided by 3? 35 crayons are shared fairly into three pots. How many crayons are in each pot? How did you decide on your answer? How many 5-minute cartoons can I watch in 20 minutes? What division calculation matches this problem? What multiplication fact can help you to find the answer? Charlie starts with the number 20. He multiplies it by 6 then divides the answer by 6. What number does he get? How do you know? Solve puzzles Solve puzzles such as: Two packets of sweets together cost 90p. One costs double the other. How much does the more expensive packet cost? In my purse I have 1 coins, 10p coins and 1p coins. Find all the possible amounts I can make by choosing three of these coins. Assessment focus: Ma1, Communicating As they solve problems that involve finding how many ways look for evidence of children checking that each result is different from those already recorded. Look for evidence of children comparing their results to a partner s to check for results they have

10 Year 3 Block D: calculating, measuring and understanding shape progression map 2 weeks 10 lessons Framework objectives, children s learning outcomes and examples of assessment for learning questions in blue. Y3 Block D Unit 1 Y3 Block D Unit 2 Y3 Block D Unit 3 not yet found. Look for children using an organised approach to checking. For example, when finding all possible amounts that can be made using three coins from a collection of 1p, 10p and 1 coins, children might check they have all results using just one type of coin, using just two types of coin and using one of each. Measures Find unit fractions of numbers and quantities (e.g. 1 /2, 1 /3, 1 /4, and 1 /6 of 12 litres) I can find 1 1 /2 or 1 /4 of a measurement Know the relationships between kilometres and metres, metres and centimetres, kilograms and grams, litres and millilitres; choose and use appropriate units to estimate, measure and record measurements I know how many grams are the same as 1 kg I can estimate whether an object is lighter than a 100 g weight Read, to the nearest division and half-division, scales that are numbered or partially numbered; use the information to measure and draw to a suitable degree of accuracy I can read scales to the nearest division or half-division Children know the relationships between standard units of measure; for example, they know that 1 kg is the same as 1000 g. Children increase their experience of measures through practical activities such as finding objects that weigh about 1 kg or weighing and comparing 100 g of various materials. Children suggest suitable units and measuring equipment to estimate or measure length, mass or capacity. They explain why they think an estimate is reasonable, for example, by comparing an estimated weight with a known one such as a 1-kg bag of sugar. Children relate their experience of number lines to reading scales. They use a numbered interval to calculate the value of each division on a scale and check that they are right by counting along the divisions. They use these skills to read a scale to the nearest marked division or half-division when they are measuring, for example weighing ingredients for a recipe or ordering three objects by weighing them. Look for evidence that children know which measuring equipment to select to measure mass and can read a simple scale. Look for children who make reasonable estimates and adjust them in light of their experience. For example, if they estimate the weight of a book and then compare this to a 100-g weight, look for children who can check and adjust their estimate appropriately. What calculation would you do to find 1 /4 of 12 litres? One-half of 32p is 16p. What is one-quarter of 32p? This line is 6 cm long. Use a ruler to divide it into quarters. Find 1 /4 of 6 cm. A sack of rice weighs 5 kg. How many grams is this? Find unit fractions of numbers and quantities (e.g. 1 /2, 1 /3, 1 /4 and 1 /6 of 12 litres) I can use division to find 1 /2, 1 /3, 1 /4, 1 /5 and 1 /6 of a measurement Know the relationships between kilometres and metres, metres and centimetres, kilograms and grams, litres and millilitres; choose and use appropriate units to estimate, measure and record measurements I know how many cm make 1 metre and how many metres make 1 km I can decide whether a length would be measured in centimetres, metres or kilometres Children know the relationship between standard units of length, mass and capacity. They know, for example, that 1 km is 1000 m and that 1 m is 100 cm. They use the relationship 1 m = 100 cm to work out that 2 m = 200 cm and 3 m = 300 cm. They recognise that the number of centimetres is the number of metres multiplied by 100. Children suggest suitable units and measuring equipment to estimate or measure length, mass or capacity. For example, they suggest lengths that would be measured in centimetres, metres or kilometres. They use a ruler to measure or draw lines accurately to the nearest half-centimetre; for example, they use a ruler and setsquare to draw a square with sides of 12 cm and then discuss how long the lines are altogether. Milly has a 100 ml bottle of medicine. She takes one fifth of the medicine each day. How many days does she take the medicine for? How much medicine does she take each day? What calculation did you do to work this out? John has a 120 g bar of chocolate. He cuts it into six equal pieces. How much does each piece weigh? What fraction of the bar is this? A bench is 2 metres and 40 centimetres long. How many centimetres is this? Explain how you worked this out. How many 100 m runs would you need to do to run a total of 1 km? What calculation did you do to work this out? Suggest an object whose length would be measured in metres. What about centimetres? And millimetres? Match the measurement to the appropriate unit: the amount of water in a cup kg the length of a road ml the weight of a dog km Read, to the nearest division and half-division, scales that are numbered or partially numbered; use the information to measure and draw to a suitable degree of accuracy I can say what one division on a scale is worth I can read a scale to the nearest division or half-division Children read numbered and partially numbered scales to the nearest division and halfdivision, for example using the ITP Measuring cylinder. Assessment opportunity: Ma3, Measures As their practical experience of measuring broadens, look for evidence of how children use their knowledge of units to interpret different scales. As children use metric units, look for children who know that 1 metre = 100 centimetres, or that 1 litre = 1000 millilitres, and use this to interpret scales and work out what each division represents. Look for children who calculate time durations independently, referring to an analogue clock face and using intervals of 5 minutes. Look out for children who are as consistently accurate with examples where start and finish times bridge the hour as they are with examples within an hour. They apply their skills when they solve practical measuring problems. For example, they pour 100 ml of water into three differently shaped bottles, using this to estimate the capacities when the bottles are full, and then checking how close their estimates were by measuring. Assessment opportunity: Ma1, Problem solving Look for evidence of children making choices about how to solve problems involving measurement. Look out for them choosing measuring equipment and units that are appropriate to the task and the degree of accuracy that is needed. What is each division on this measuring jug worth? How did you work this out? How much water is in the jug? Compare the weight of this book with this bag of sugar and with this 100-g weight. Suggest an estimate for the weight of the book. Which is a newborn baby more likely to weigh? A 30 g B 3 kg C 30 kg Draw where the dial would go for a weight of 45 g. How do you know?

11 Year 3 Block D: calculating, measuring and understanding shape progression map 2 weeks 10 lessons Framework objectives, children s learning outcomes and examples of assessment for learning questions in blue. Y3 Block D Unit 1 Y3 Block D Unit 2 Y3 Block D Unit 3 What measurement is shown on these scales? Explain how you worked this out. What is each division on this scale worth? How did you work this out? How could you check that you are right? Time - Reading time - calculating time intervals Read the time on a 12-hour digital clock and to the nearest 5 minutes on an analogue clock; calculate time intervals and find start or end times for a given time interval I can tell the time to the nearest 5 minutes I can find how long an activity takes if I know when it starts and when it ends Read the time on a 12-hour digital clock and to the nearest 5 minutes on an analogue clock; calculate time intervals and find start or end times for a given time interval I can tell the time to the nearest 5 minutes I can work out the start or end time for an activity Children know the relationships between seconds, minutes, hours and days. They read the time on a 12-hour digital clock and on an analogue clock to the nearest 5 minutes. They use counting strategies to work out simple time differences. For example, to find the length of Joy's journey to school if she leaves home at 8:40 and arrives at school at 9:05, children count on in 5-minute intervals, using a clock face. Alternatively, they may use the fact that there are 60 minutes in an hour to bridge over the hour, recording their working, using informal recording such as a timeline. Children remember that 1 hour is 60 minutes when they solve time problems, such as finding a start or end time for a given interval. For example, to find what time the school play will end if it starts at half past 7 and runs for 50 minutes, children first count on 30 minutes from half past 7 to bridge to 8 o clock; this leaves 20 minutes, so the play will end at 20 minutes past 8. They choose to draw a time line to record this. Children explain their choice of method to others and discuss alternative strategies. How would a digital clock show the time twenty minutes to six? The car journey to work takes Rob 20 minutes. He needs to be at work at 9 o clock. Move the hands on this clock face to show the time that he should leave. Ben's clock says 7:50 when he gets up. Place the hands on this clock to show this time. How long is it between the times shown on these two clocks? Show me how you worked this out. Position, direction and movement including angles Read and record the vocabulary of position, direction and movement, using the four compass directions to describe movement about a grid I can describe the position of a square on a grid I can use the compass points (north, south, east and west) to describe a direction Children use, read and record the vocabulary associated with position, direction and movement. They describe and find the position of a square on a grid with the rows and columns labelled; for example, they play Battleships. They secretly create a simple picture by colouring squares on the grid then describe to their partner how to create an identical picture. They use compass points and other directional language to follow and describe a route, for example, around a maze or grid marked out on the playground. They interpret and describe both the direction of travel and the distance for each section of the route. Assessment focus: Ma3, Properties of position and movement Look for the types of instructions children give, for example, distinguishing between straight and turning movements and using instructions such as forward, back, left, right, clockwise, anticlockwise. Look for children giving instructions about how far to move or turn, for example, using a number of paces, quarter-turn, half-turn or 90. Read and record the vocabulary of position, direction and movement, using the four compass directions to describe movement about a grid I can follow and give instructions to make turns Use a set-square to draw right angles and to identify right angles in 2-D shapes; compare angles with a right angle; recognise that a straight line is equivalent to two right angles I can identify right angles in shapes and use a set-square to check Children understand that angle is a measure of turn. They follow and give directions, for example, in PE, including instructions to turn right or left through quarter- and halfturns. They appreciate that two quarter-turns are equivalent to a half-turn. They recognise that when you turn through a half-turn you end up facing in the opposite direction. They learn that a quarter-turn is equal to a turn of 90 degrees when, for example, programming a floor robot to follow a marked route. Through looking at the route, they appreciate that a quarter-turn is also equivalent to a right angle. Children use compass points to explore, for example, how many right angles are needed to turn clockwise from east to west. If you stand facing north, then make a half turn, what direction would you be facing? Give instructions to draw the route below. Use the direction words: north, south, east and west. Give the exact length of each line. Route from left to right with line and start and finish and a compass guide showing Use a set-square to draw right angles and to identify right angles in 2-D shapes; compare angles with a right angle; recognise that a straight line is equivalent to two right angles I can test whether an angle is equal to, bigger than or smaller than a right angle Children continue to develop their understanding of angle. For example, they use geostrips or strips of card joined by a split pin to create an angle-maker and use it to show angles that are less than, more than or approximately equal to a right angle. They use a set-square to compare given angles (for example, the angles in a 2-D shape) with a right angle. They place two right angles together and realise that they form a straight line. Assessment opportunity: Ma3, Measures Look for evidence of children making the connection between turning through quarterturns and making right angles and realising that there are four right angles in a complete turn, for example. Look for children who know that there are 360 in a complete turn. Paula says that angle A is smaller than angle B. Is she right? Explain your answer. A: A small picture of a right angle; B: a large image of a right angle Place a set of shapes in the correct place in this table.

12 Year 3 Block D: calculating, measuring and understanding shape progression map 2 weeks 10 lessons Framework objectives, children s learning outcomes and examples of assessment for learning questions in blue. Y3 Block D Unit 1 Y3 Block D Unit 2 Y3 Block D Unit 3 Which square lies halfway between squares A3 and E3? direction north A table for sorting shapes into all right angles, some right angles and no right angles Use a set-square and a ruler to draw a square with sides of 12 cm. Move a counter from square B4 to E2. Describe each move you make using the words north, south, east or west. How many right angles are there in this pentagon? How could you check? Image showing pentagon shape Symmetry Children understand that shapes can be reflected by considering, for example, the reflections of objects in water or by using the reflection tool in an ICT program. They predict where the image of a shape will be when it is reflected in a mirror line along one of its sides and check by placing a mirror on the line of symmetry or by using ICT. Draw and complete shapes with reflective symmetry; draw the reflection of a shape in a mirror line along one side I can reflect a shape in one of its sides Draw the reflection of this shape in the mirror line. Image showing mirror line reflection A letter d is reflected in its straight side. Its reflection is a different letter. Which one? Year 4 Block D: calculating, measuring and understanding shape progression map 2 weeks 10 lessons Framework objectives, children s learning outcomes and examples of assessment for learning questions in blue. Speaking & listening Written calculations +/- x/ Y4 Block D Unit 1 Y4 Block D Unit 2 Y4 Block D Unit 3 Listen to a speaker and take notes on the talk I can listen to someone else speak and write down important bits of information that will help me with my task Maria is going to describe how she worked out a time interval using a number line. Make some notes so that you can do it in the same way. Listen carefully while I explain how to read a number from this scale. Make a note of what to do. Add or subtract mentally pairs of two-digit whole numbers (e.g , 91 35) I can use mental addition and subtraction to help me solve problems Why do , and all give the same answer? What strategies would you use to work out the answers to these calculations: , 81 36? Could you use a different method? How could you check that your answer is correct? Take different roles in groups and use the language appropriate to them, including roles of leader, reporter, scribe and mentor I can play the role of... in group work I can work as a member of a group to decide how to measure and record capacity Discuss in your group how to find out which of these six containers holds the most water. I would like... to be the group leader, to take notes and... to draw any diagrams that you need. Tell me about the contribution you made to the group work. Refine and use efficient written methods to add and subtract two-digit and three-digit whole numbers and.p I can add and subtract a two-digit and a three-digit number using an efficient written method Derive and recall multiplication facts up to 10 10, the corresponding division facts and multiples of numbers to 10 up to the tenth multiple I know my tables to Develop and use written methods to record, support and explain multiplication and division of two-digit numbers by a one-digit number, including division with remainders (e.g. 15 9, 98 6) I can record how to multiply and divide a two-digit number by a one-digit number Children continue to develop and refine written methods to multiply and divide a two-digit number by a one-digit number and efficient written methods to add and subtract two-digit and three-digit whole numbers. Children who confidently explain how an expanded method works move on to a more compact method of recording. Assessment focus: Ma2, Written methods Look for evidence of those calculations for which children choose to use a written method. Look for the range of written methods they use and their awareness of efficient methods for different types of number. As they subtract three-digit numbers, for example, look for evidence of children recognising that an empty number line method can be efficient for finding differences between numbers that are both close to a multiple of 100. Mary drove 58 km to Andover. She then drove 238 km to Cambridge. How far did Mary drive altogether? Show me the calculations that you did to solve these problems. Is there a more efficient way to do them? Look at these number sentences. What number goes in the box? How do you know? 7 = 35 9 = 72 What numbers are missing? = 36 If 7 9 = 63, what is 63 7? What other facts do you know? If I multiply a number by 8 and then divide the answer by 8, what happens? One length of the swimming pool is 25 metres. Jane swims 5 lengths of the pool. How far does Jane swim altogether? Kiz swims 225 metres in the pool. How many lengths does he swim? Explain how you solved these problems. Could you have done them differently? Take different roles in groups and use the language appropriate to them, including roles of leader, reporter, scribe and mentor I can play the role of... in group work I can work as a member of a group to plan a bus timetable Discuss in your group how to plan a bus timetable from school to the town centre. I would like... to be the group leader,... to take notes and... to draw any table that you need. Tell me about the contribution you made to the group work. Refine and use efficient written methods to add and subtract two-digit and three-digit whole numbers and.p I can use written methods to add and subtract measurements made in our classroom What tips would you give to someone to help them with column addition/subtraction? Which of these are correct? What has this person done wrong? How could you help them to put it right? Word problems Solve one-step and two-step problems involving numbers, money or measures, Solve one-step and two-step problems involving numbers, money or measures, Solve one-step and two-step problems involving numbers, money or measures,

13 Year 4 Block D: calculating, measuring and understanding shape progression map 2 weeks 10 lessons Framework objectives, children s learning outcomes and examples of assessment for learning questions in blue. Measures U1 Mass U2 Length, U3 Capacity, Y4 Block D Unit 1 Y4 Block D Unit 2 Y4 Block D Unit 3 including time; choose and carry out appropriate calculations, using calculator methods where appropriate I can work out how to solve problems with one or two steps I can solve problems using measurements I can choose what calculation to work out and I can decide whether a calculator will help me Children continue to add and subtract mentally pairs of two-digit whole numbers. They use their mental skills to solve problems such as: Two shelves are 75 cm and 87 cm long. What is their total length? What is the difference between their lengths? I need to weigh 150 g of flour. So far I've poured in 68 g. How much more do I need to add? Assessment focus: Ma2, Solving numerical problems Look for children who solve a range of problems in the context of measures. As they add and subtract numbers mentally, on paper or with apparatus, look for evidence of them recalling addition and subtraction facts to 10 and 20 and using these to help solve problems involving larger numbers. Identify children who can calculate complements to 60 when solving problems involving hours and minutes, or complements to 100 for problems with centimetres and metres, for example. Look for evidence of children using relationships between units, for example, using the number of minutes in an hour, centimetres in a metre, grams in a kilogram and millilitres in a litre. These are the prices of coconuts and bananas. Josh buys one coconut and half a kilogram of bananas. How much does he spend altogether? Explain what you did to get your answer. How did you know what operation(s) to use? Could you have done it in a different way? Did you use a calculator? Why/why not? Choose and use standard metric units and their abbreviations when estimating, measuring and recording length, weight and capacity; know the meaning of 'kilo', 'centi' and 'milli' and, where appropriate, use decimal notation to record measurements (e.g. 1.3 m or 0.6 kg) I can estimate and measure a weight I know the relationships between units of weight I can write a mass in kilograms using a decimal point Interpret intervals and divisions on partially numbered scales and record readings accurately, where appropriate to the nearest tenth of a unit I can use kitchen scales or a bathroom scale to measure a weight I can read a weight in kilograms and grams from a scale marked in kg Children learn the relationships between familiar units of measurement. They learn that kilo means one thousand to help them remember that there are 1000 grams in 1 kilogram and 1000 metres in 1 kilometre. They respond to questions such as: A bag of flour weighs 2 kg. How many grams is this? They suggest suitable units to measure length, weight and capacity; for example, they suggest a metric unit to measure the length of their book, the weight of a baby, the capacity of a mug. They suggest things that you would measure in specific units such as kilometres, metres, litres, kilograms. Practical activities help children to increase their accuracy of measurement and estimation. For example, they take a bag of counters and estimate what they think is half, putting these into another bag. They then weigh both bags to see how close they were. They calculate the difference, in grams. When weighing, they choose appropriate instruments, recognising that different weighing scales are used to weigh different objects. They look at the numbering on scales and the number of intervals between the numbers. They calculate the value of each interval and learn to count on from the last numbered interval in order to take a reading. They gain extra practice using the ITP Measuring scales. including time; choose and carry out appropriate calculations, using calculator methods where appropriate I can work out how to solve problems with one or two steps I can solve problems involving measures and time I can choose what calculation to work out and I can decide whether a calculator will help me Children draw on their calculation strategies to solve one- and two-step word problems, including those involving money and measures. They use rounding to estimate the solution, choose an appropriate method of calculation (mental, mental with jottings, written method) and then check to see whether their answer seems sensible. They throw a beanbag three times and find the difference between the lengths of their longest and shortest throws. After measuring their height, they work out how much taller they would have to grow to be the same height as their teacher. They solve problems such as: Dad bought three tins of paint at 5.68 each. How much change does he get from 20? A family sets off to drive 524 miles. After 267 miles, how much further do they still have to go? Assessment focus: Ma2, Mental methods Look for evidence of the calculations children choose to perform using a mental method. Look for children recalling addition facts to 10 and using these, with place value, to add multiples of 10. Look for evidence of children adding other two-digit numbers mentally. Look for evidence of the multiplication facts children know without counting through the multiples and the division facts they derive. Look for children using multiplication facts and place value to perform calculations such as 40 8 mentally. A piece of rope 204 cm long is cut into 4 equal pieces. Which of these gives the length of each piece in centimetres? A , B , C , D How did you know whether to add, subtract, multiply or divide? What clues did you look for in the problem? What are the important things to remember when you solve a word problem? Look at this problem: Jenny can walk 103 metres in 1 minute. How far can she walk in 2 minutes? Explain what you should do to get your answer. Show me how to record any calculations you need to do to solve the problem. Choose and use standard metric units and their abbreviations when estimating, measuring and recording length, weight and capacity; know the meaning of kilo, centi and milli and, where appropriate, use decimal notation to record measurements (e.g m or 0.6 kg) I can estimate and measure a length using metres, centimetres or millimetres I know the relationships between metres, centimetres and millimetres Use decimal notation for tenths and hundredths and partition decimals; relate the notation to money and measurement; position one-place and two-place decimals on a number line I can write lengths such as 5 metres and 62 centimetres, using decimal points Interpret intervals and divisions on partially numbered scales and record readings accurately, where appropriate to the nearest tenth of a unit I can use a measuring tape, metre stick or ruler to measure a length accurately Children learn the meaning of kilo (one thousand), centi (one hundredth) and milli (one thousandth) to help remember the relationships between kilometres, metres, centimetres and millimetres. They multiply and divide numbers by 10 and 100 and use this to convert metres into centimetres or centimetres into millimetres, completing tables such as: Item Length in metres Length in cm Metre stick 1 m 100cm Height of door 2 m Length of room 9 m and responding to questions such as: How many metres are in 8 km? How many millimetres are in 8 cm? Children choose and use appropriate units to measure length, realising that different units are needed for different distances. They suggest lengths that would be measured in km, m, cm and mm. They undertake practical activities to increase their accuracy in estimating lengths, choosing appropriate units and measuring instruments and reading the including time; choose and carry out appropriate calculations, using calculator methods where appropriate I can choose what calculation to work out and I can decide whether a calculator will help me I can work out how to solve problems with one or two steps I can solve problems involving measures and time Children use their calculation strategies to solve one- and two-step problems involving measures. They decide whether to use mental, mental with jottings, written methods or a calculator to find the answer. For example: Tins of dog food cost 42p. They are put into packs of 10. How much does one pack of dog food cost? 10 packs? A can of soup holds 400 ml. How much do 5 cans hold? Each serving is 200 ml. How many cans would I need for servings for 15 people? I spent 4.63, 3.72 and 86p. How much did I spend altogether? A string is 6.5 metres long. I cut off 70 cm pieces to tie up some balloons. How many pieces can I cut from the string? A jug holds 2 litres. A glass holds 250 ml. How many glasses will the jug fill? Dean saves the same amount of money each month. He saves in a year. How much money does he save each month? Assessment focus: Ma2, Written methods As they solve problems involving money and measurements, look for evidence of the written methods that children choose to use. Look out for children who can add and subtract decimals in this context and can use units and record amounts such as 7.4 cm or 1.05 m when answering the problem. When they solve problems, children use their understanding of the relationships between units to convert measurements to the same unit. It takes Chris 4 minutes to wash a window. He wants to know how many minutes it will take him to wash 8 windows at this rate. He should: A multiply 4 8 B divide 8 by 4 C subtract 4 from 8 D. add 8 and 4 How did you know which of these to choose? Maria has half a litre of orange juice. She fills some glasses by pouring 100ml of orange juice into each of them. How many glasses does Maria fill? What calculation did you do? Did you use a calculator? Why or why not? Did you have to do anything to your answer to make it fit with the problem? Tell me what you did. Choose and use standard metric units and their abbreviations when estimating, measuring and recording length, weight and capacity; know the meaning of kilo, centi and milli and, where appropriate, use decimal notation to record measurements (e.g m or 0.6 kg) I can estimate and measure a capacity I know the relationship between litres and millilitres I can write a capacity in litres, using a decimal point Interpret intervals and divisions on partially numbered scales and record readings accurately, where appropriate, to the nearest tenth of a unit I can read the scale on a measuring cylinder or measuring jug Use decimal notation for tenths and hundredths and partition decimals; relate the notation to money and measurement; position one-place and two-place decimals on a number line I can order decimals on a number line Children use the meaning of milli (one thousandth) to help remember the relationship between litres and millilitres. In practical work, they choose and use appropriate units to estimate and measure capacity. They make statements such as: This container will hold about half as many small cubes as this one, or This small bottle holds about 25 ml teaspoons of water. They take on different roles to read and record measurements. They estimate, measure and compare the capacity of different containers, reading a range of partly numbered scales to the nearest division. They get extra practice using the ITP Measuring cylinder.

14 Year 4 Block D: calculating, measuring and understanding shape progression map 2 weeks 10 lessons Framework objectives, children s learning outcomes and examples of assessment for learning questions in blue. Measures U1 Mass U2 Length, U3 Capacity (continued) Y4 Block D Unit 1 Y4 Block D Unit 2 Y4 Block D Unit 3 measurement from a scale. For example, they measure how far they can throw a beanbag, or the growth of a plant over time. Estimate the height of the door. The width of your table. Tick ( ) the correct box. The length of a banana is about... 2 cm 20 cm 200 cm 2000 cm What unit would you use to measure the length of the River Thames? The length of a drinking straw? Look at these cards. They have lengths in kilometres, metres, centimetres or millimetres m, 2 km, 3 cm, 1 /2 m, 4.5 m, 40 cm, 5 cm, 400 mm Put the cards in order from the smallest to the largest. How did you order the cards? Why did you put this measurement here? Were any of the measurements hard to order? Why? Can you tell me another way to say or write 2 km? What about 4 m? And 5 cm? Assessment focus: Ma1, Problem solving Look for children who suggest their own approaches and overcome difficulties as they investigate situations and solve problems. For example, identify children who, given a balance scale, two 20 gram masses and two 50 gram masses, look for ways to make balls of modelling material that weigh any multiple of 10 grams up to 100 grams. Look for evidence of children overcoming the difficulty of making a ball that weighs, for example, 10 grams, 60 grams or 80 grams. Estimate the weight of this bag of potatoes. And of this tin of beans. Which units would you use to measure the weight of an egg? A centimetres B millilitres C grams D kilograms Which is heavier: 2900 g or 3 kg? Explain how you know. Can you tell me another way to say or write 8 kilograms? What about 250 grams? Look at these cards. They have weights in kilograms or grams. 5 kg, 500 g, 1 /4 kg, 1.5 kg, 750 g Put the cards in order from the lightest to the heaviest. How did you order the cards? Why did you put this measurement here? Were any of the measurements hard to order? Why? Which would you prefer: 3 /4 kg of gold or 700 g of gold? Why? Emily is making a cake. She puts flour on the scales. She then adds sugar to the flour. How much sugar does she add? Children record lengths, using decimal notation, for example, recording 5 m 62 cm as 5.62 m, or 1 m 60 cm as 1.6 m. They identify the whole-number, tenths and hundredths parts of numbers presented in decimal notation and relate the whole number, tenths and hundredths parts to metres and centimetres in length. Children use a ruler to measure and draw lines to the nearest millimetre. They get extra practice using the ITP Ruler. Children make measurements of lengths and heights in centimetres and millimetres and practise estimating before measuring. They make comparisons and calculate differences and totals. Assessment focus: Ma1, Problem solving Look for evidence of children applying their knowledge and understanding of measures to solve practical problems. Look for children choosing the measuring instruments to use so that they can measure to an appropriate degree of accuracy. For example, they might decide that whole metres are accurate enough to check if a carpet is long enough for the corridor, but millimetres are needed to check if a letter is small enough to send using the cheapest first class stamp. Tell me what the digit 4 represents in each of these amounts: 4.3 litres, 0.4 litre. Which is larger: 300 ml or 0.25 litre? How do you know? What is 0.1 litre in millilitres? Estimate the capacity of this bucket. Of this egg cup. Tick the correct box. A can of drink holds about litre 3 litres 30 litres 300 litres What unit would you use to measure the capacity of a washing-up bowl? Of a can or a tea-cup? Can you tell me another way to say or write 3 litres? What about 500 millilitres? Which would you prefer, 3 /4 of a litre or 650 ml of lemonade? Why? Look at these cards. They have capacities in litres or millilitres. 2 litres, 20 ml, 1 /2 litre, 1.5 litre, 700 ml Put the cards in order from the smallest to the largest. How did you order the cards? Why did you put this measurement here? Were any of the measurements hard to order? Why? This jug has water in it. I am going to pour 150 millilitres of water out of the jug. How much water will be left in the jug? Measures Perimeter & area Draw rectangles and measure and calculate their perimeters; find the area of rectilinear shapes drawn on a square grid by counting squares I can draw a rectangle and work out its perimeter They measure the edges of a rectangle and then combine these measurements. They realise that by doing this they are calculating its perimeter. Given the perimeter of a rectangle they investigate what the lengths of its sides could be. They work out the perimeter of irregular shapes drawn on a centimetre square grid, e.g. using the ITP Area. Assessment focus: Ma1, Communicating As they find the perimeter of irregular shapes, look for children who develop an organised approach. Look out for children who annotate diagrams and record their work so that they can check whether they have added the lengths of all sides when calculating the perimeter. The perimeter of a square is 28 cm. What is the length of one side? Use centimetre squared paper to draw different rectangles with a perimeter of 28 cm. Draw different rectangles with an area of 12 cm 2. Explain to someone else how to measure the length of a line that is between 4 cm and 5 cm long. Measure accurately the length of the diagonal of this square. Give your answer in centimetres. Draw rectangles and measure and calculate their perimeters; find the area of rectilinear shapes drawn on a square grid by counting squares I can find the area of shapes by counting squares Children find the areas of rectilinear shapes by counting squares. For example, they draw irregular shapes on centimetre square grids, and compare their areas and perimeters. They compare the perimeter and area of squares and rectangles by measuring the lengths of the sides to the nearest centimetre and calculating the area, using a calculator where appropriate. Look for evidence of children beginning to understand perimeter as a measure of length, which might be recorded in centimetres, and area as a measure of surface, recorded in squares. The perimeter of a rectangle is 24 cm. What could its area be? Draw a rectangle with an area of 28 cm 2. Is there more than one way of doing this?

15 Year 4 Block D: calculating, measuring and understanding shape progression map 2 weeks 10 lessons Framework objectives, children s learning outcomes and examples of assessment for learning questions in blue. Y4 Block D Unit 1 Y4 Block D Unit 2 Y4 Block D Unit 3 Leon s grid has two shaded shapes. Leon says: Shape A has a larger area than shape B. Explain how he could have worked this out. Time - Reading time - Calculation time intervals Position, Direction and Movement angles, Read time to the nearest minute; use am, pm and 12-hour clock notation; choose units of time to measure time intervals; calculate time intervals from clocks and timetables I can tell the time to the minute on a clock with hands I can write down a time using am and pm I can work out how long it takes to do something if I know the start and end times Children revise the relationship between hours, minutes and seconds. They read the time to the nearest minute on a 12-hour digital clock and on an analogue clock. They practise making number pairs with a total of 60 and then discuss, for example, that 4:37, 37 minutes past 4 and 23 minutes to 5 are equivalent. They record time, using am or pm notation. They recognise what they might typically be doing at certain times and can make a time line to show their day. They use counting strategies and a number line or time line to work out time differences, remembering there are 60 minutes in an hour when they bridge over the hour. For example, they solve problems such as: The cake went in the oven at 1:35. It cooked for 40 minutes. What time did it come out? by calculating that it is 25 minutes until 2:00; this leaves another 15 minutes, so the cake would come out at 2:15. Children also find information in timetables and calculate time intervals. For example, they use a TV guide to find out when programmes begin and end and work out how long different programmes last. How long do you spend at school each day? How long do you play computer games each day? How long have you lived in your house? How long is it until your next birthday? What are the most suitable units of time to use to answer these questions? Could you give the answer using a different unit of time? What time is it on the clock on the wall? What time will it be 50 minutes from now? The time is 2:00 pm. What time was it three hours ago? Recognise horizontal and vertical lines; use the eight compass points to describe direction; describe and identify the position of a square on a grid of squares I know when a line is horizontal or vertical I can describe the position of a square on a grid of squares Children use the vocabulary associated with position, direction and movement. They recognise when lines are horizontal and vertical and identify simple examples in the environment, for example, that the edge of the table is horizontal. They know that rows on a grid are described as horizontal and columns as vertical, and can describe the position of a square on a grid with the rows and columns labelled. Using a grid they shade in some squares to make a shape with a given number of sides, e.g. an octagon. They sit back to back with a partner and use the labels of the rows and columns to describe the position of the squares they have shaded. Their partner listens to the speaker, making notes on their own grid to replicate the shape. Assessment focus: Ma3, Properties of position and movement As they use grid references to define the position of a square on a grid, look for children who remember the mathematical convention of giving the horizontal reference first. As they describe movements around a grid, listen for children who accurately use vocabulary such as: row, column, horizontal, vertical, left, right, north, south, west and east. Know that angles are measured in degrees and that one whole turn is 360 ; compare and order angles less than 180 I know that angles are measured in degrees I know that a whole turn is 360 degrees or four right angles Recognise horizontal and vertical lines; use the eight compass points to describe direction; describe and identify the position of a square on a grid of squares I can use the eight compass points I can give directions, follow directions and say how good someone else's directions are Children understand that angle is a measure of turn. They follow and give directions that include turning through whole, half and quarter-turns. They know that a quarter-turn is equivalent to 90 degrees and a whole turn is 360 degrees or four right angles. They recognise angles that are smaller than and larger than a right angle and start to order angles. They recognise which of two angles is greater and place in order a set of angles, each less than 180 degrees. Children give directions, using the eight compass directions N, S, E, W, NE, NW, SE and SW. They look at weather forecasts to track changes in wind direction. They investigate the different routes from A to B, using only the directions northwest and north-east and record their results systematically in a table. Children take different roles in groups of three, taking turns to give directions, to follow directions and to observe, commenting on how accurately directions were given and followed. For example: Face SE and turn clockwise 180 degrees/two right angles. Which direction are you now facing? Read time to the nearest minute; use am, pm and 12-hour clock notation; choose units of time to measure time intervals; calculate time intervals from clocks and timetables I can solve time problems where I have to work out start and finish times I can use a timetable Children solve problems involving units of time, explaining and recording how the problem was solved. For example: Raiza got into the pool at 2:26 pm. She swam until 3 o'clock. For how long did she swim? They count on to find the difference between two given times, using a number line or time line where appropriate. Children work in groups to find information in timetables and calculate time intervals. For example, they use a class timetable to find out how much time they spend on mathematics during a day or week, and they look at simple bus or train timetables to see how long a journey takes. Look for evidence of children s understanding of units of time and the relationships between them. As they gain more experience of calculating time differences, look for children who independently calculate differences that bridge the hour. Look out for children who apply mental methods to solving time problems, for example, using intervals of 5 minutes on an analogue clock face or knowing pairs of numbers that total 60 minutes. Estimate how long your favourite TV programme lasts. Use a television guide to work out how close your estimation was. It takes 35 minutes to walk from home to school. I need to be there by 8:55 am. What time do I need to leave home? How much does it cost to hire a rowing boat for three hours? Boat hire Motor boats 1.50 for 15 minutes Rowing boats 2.50 for 1 hour Sasha pays 3.00 to hire a motor boat. She goes out at 3:20 pm. By what time must she return? Explain how you solved this problem. Could you have done it in a different way? Know that angles are measured in degrees and that one whole turn is 360 ; compare and order angles less than 180 I know if an angle is smaller than 180 I can put a set of angles in order, from smallest to largest I can estimate in degrees the size of an angle less than a right angle Children continue to develop their understanding of angle. They recognise when an angle is less than 180. They use a 45 or 60 set-square to draw and measure angles of 90, 60, 45 and 30. They compare the size of angles, for example, estimating whether an angle is greater than 60, between 60 and 30, or less than 30. They use their set-squares to check. Look at these six angles. Which is the smallest angle? One of the angles is a right angle. Which is a right angle? One of the angles is an obtuse angle. Which is an obtuse angle?

16 Year 4 Block D: calculating, measuring and understanding shape progression map 2 weeks 10 lessons Framework objectives, children s learning outcomes and examples of assessment for learning questions in blue. Y4 Block D Unit 1 Y4 Block D Unit 2 Y4 Block D Unit 3 Lisa places a counter on square D4. She moves it 2 squares east and 3 squares south. Write the position of the square she moves it to. Look for evidence of children s understanding of turns and angles and for children using quarter and half-turn when giving instructions. Look for children who recognise that a quarter-turn is the same as turning through one right angle. Look for children who begin to use the knowledge that there are 360 in a whole turn to work out how many degrees in a half-turn or a right angle. Tell me an angle that is bigger than one right angle and smaller than two right angles. Two of these angles are the same size. Put rings around the two angles that are the same size. Draw an angle that is bigger than a right angle. Kelly is facing north. She turns clockwise through 3 right angles. Which direction is she facing now? Aled is facing north-west. He turns clockwise through 2 right angles. Which direction is he facing now? Year 5 Block D: calculating, measuring and understanding shape progression map 2 weeks 10 lessons Framework objectives, children s learning outcomes and examples of assessment for learning questions in blue. Speaking & listening Y5 Block D Unit 1 Y5 Block D Unit 2 Y5 Block D Unit 3 Plan and manage a group task over time by using different levels of planning Understand the process of decision making Understand different ways to take the lead and support others in a group I can plan and manage my time to work on an extended group task I can explain why I decided to use a particular method to solve a problem I can lead a group and make sure that tasks are shared fairly I can make an overall plan of the tasks to be done and a detailed plan for each task with I can describe what was special about the problem that prompted my decision I can support others in a group by helping them with their tasks when I have finished their tasks when I have finished mine Why did you decide to use a mental/written/calculator method for this calculation? mine I want you to measure the perimeter of the playground as accurately as you can. Work in Why did you decide to change all the units to metres rather than centimetres? I want you to plan an itinerary for a journey around the world. You will have one week to a group. Draw a plan of the playground and write the measurements on it. Then work out Why did you decide to use the scales rather than the balance? do your research and make your plans. Start by deciding on your roles in the group and the area of the playground. Plan your work carefully. You will have 2 hours during the what tasks you need to carry out. week to do it.

17 Year 5 Block D: calculating, measuring and understanding shape progression map 2 weeks 10 lessons Framework objectives, children s learning outcomes and examples of assessment for learning questions in blue. X / 10, 100, 1000 Calculation Written methods Word problems Y5 Block D Unit 1 Y5 Block D Unit 2 Y5 Block D Unit 3 Use understanding of place value to multiply and divide whole numbers and Use understanding of place value to multiply and divide whole numbers and decimals by 10, 100 or 1000 I can multiply and divide whole numbers by 10, 100, 1000 decimals by 10, 100 or 1000 Children multiply and divide whole numbers by 10, 100 and They answer I can multiply and divide whole numbers by 10, 100 and 1000 questions like: Children extend their knowledge of multiplication and division by 10, 100 and 1000 to How many times bigger than 60 is 6000? How many times smaller than 5000 is 5? include decimal numbers. They use this knowledge to convert units of mass; for What did I multiply 6 by to get 600? What did I divide 7500 by to get 75? example, they convert grams to kilograms and vice versa. They work out mentally They see the effect of these operations. They combine this knowledge with their conversions such as: knowledge of relationships between units of measurement to convert units of length. How many grams are there in 3.6 kilograms? They respond to questions such as: How many centimetres are there in 7 metres? How How many kilograms is 4200 grams? many metres are there in 8 kilometres? How many centimetres is 50 millimetres? How many kilometres is metres? Assessment focus: Ma2, Numbers and the number system Assessment focus: Ma2, Numbers and the number system Look out for children who use understanding of place value to explain the effect of Look for evidence of children s understanding of place value. Look out for children who multiplying a number by 10 or by 100. Look for children who understand the effect of understand what each digit represents in numbers with up to five digits. Look for children dividing by 10 or by 100, including examples that give rise to decimal answers. Look for who use place value to multiply and divide whole numbers by 10 or 100 as they solve children who can multiply and divide by 1000 and who can apply this when converting problems involving metric measure. Look for children who are beginning to multiply and between grams and kilograms, and between millilitres and litres divide by 1000 with consistent accuracy. Look for children who pose similar problems for Tell me a quick way of multiplying a number by 10. By 100. a partner to solve and who know whether their responses are correct. Tell me a quick way of dividing a number by 10. By 100. Tell me a quick way of multiplying a number by 10. By 100. Explain what happens to the digits when you multiply or divide a whole number by Tell me a quick way of dividing a number by 10. By 100. What do you notice about the digits in your answer? Explain what happens to the digits when you multiply or divide a whole number by How many times larger than 60 is 600? What do you notice about the digits in your answer? How many times larger than 60 is 600? Solve one-step and two-step problems involving whole numbers and decimals and all four operations, choosing and using appropriate calculation strategies, including calculator use I can identify the steps I need to take to solve problems I can decide whether to do a calculation using mental methods, written methods or a calculator Use a calculator to solve problems, including those involving decimals or fractions (e.g. to find 3 /4 of 150 g); interpret the display correctly in the context of measurement Use efficient written methods to add and subtract whole numbers and decimals with up to two places I can add and subtract whole numbers and decimal numbers with two places in columns Refine and use efficient written methods to multiply and divide HTU U, TU TU, U.t U and HTU U I can use an efficient method to multiply HTU by U and TU by TU Children use efficient written methods to add and subtract whole numbers (with up to five digits) and numbers with up to two decimal places. They refine their multiplication methods to multiply TU U and HTU U They multiply, for example, by relating this to 56 7 and dividing the answer by 10. Children extend their knowledge of division to short division of HTU by U, by repeated subtraction of multiples of the divisor (taking away chunks), aiming to subtract as few chunks as necessary Answer: 137 What tips would you give to someone to help with column addition of decimal numbers? What about subtraction? Show me your method for solving these problems: Three parcels weigh 785 g, 55 g and 0.25 kg. How much do they weigh altogether? I had 0.6 kg of sugar. I have 247 g left after I make a cake. How much sugar did I use? How would you solve these problems? I have 9 parcels each weighing 346 g. How much do they weigh altogether? 72 boxes of dog food weigh 38 kg each. How much do they weigh altogether? Solve one-step and two-step problems involving whole numbers and decimals and all four operations, choosing and using appropriate calculation strategies, including calculator use I can decide what calculations to do to solve a problem and how to do them (mental methods, jottings, written methods, calculator) Use knowledge of rounding, place value, number facts and inverse operations to estimate and check calculations I can use rounding to estimate and check calculations Use a calculator to solve problems, including those involving decimals or fractions (e.g. to Use efficient written methods to add and subtract whole numbers and decimals with up to two places I can add and subtract whole numbers and decimals with up to two places in columns Refine and use efficient written methods to multiply and divide HTU U, TU TU, U.t U and HTU U I can use efficient methods to multiply U.t by U and divide HTU by U I can recognise when to round up or down, depending on the problem Show me your method for solving these problems: Max jumped 2.35 metres on his second try at the long jump. This was 68 centimetres longer than on his first try. How far in metres did he jump on his first try? Nasreen made some fruit punch. She poured 2.4 litres of water, 1.35 litres of pineapple juice and 780 ml of mango juice into a large bowl. How much fruit punch did she make? Did you make any estimates? Explain how you worked out the answers. Show me your method for solving these problems: I fill 6 jugs with water. Each jug holds 2.3 litres. How much water do I have altogether? 5 boxes of chocolates weigh 645 g. How much does each box of chocolates weigh? What is the total mass of 235 screws each weighing 6 grams? What estimates did you make? Explain how you worked out the answers. Solve one-step and two-step problems involving whole numbers and decimals and all four operations, choosing and using appropriate calculation strategies, including calculator use I can use the most efficient method of solving a problem, including using a calculator Use knowledge of rounding, place value, number facts and inverse operations to estimate and check calculations I can use rounding of whole numbers and decimals to estimate and check calculations I can round numbers to the nearest whole unit

18 Year 5 Block D: calculating, measuring and understanding shape progression map 2 weeks 10 lessons Framework objectives, children s learning outcomes and examples of assessment for learning questions in blue. Measures including perimeter and area Measures including perimeter and area Y5 Block D Unit 1 Y5 Block D Unit 2 Y5 Block D Unit 3 I can use a calculator to solve problems that involve decimal measurements Children continue to develop their problem-solving skills in the context of measurement, focusing on length and time, including using a calendar. They solve reallife problems involving one or two steps and any of the four operations. They interpret the wording, then decide the best way to solve a problem, which calculations to do and how to do them: mentally, with jottings, using an efficient written method or using a calculator. They learn to change any units to the same unit before they calculate. They estimate and check their answers. find 3 /4 of 150 g); interpret the display correctly in the context of measurement I can use a calculator to solve weight problems involving decimal numbers What information did you use to solve the problem? How did you decide what calculations to do? Solve a problem such as: Three prize pigs weigh 850 kg altogether. The heaviest pig is 378 kg. The lightest pig is half the mass of the heaviest pig. How heavy is the middle-sized pig? How did you work out your answer? The perimeter of a regular pentagon is 285 cm. What is the length of each side? Explain your method. The perimeter of a square field is 1300 m. It has a hedge along one side. How much fencing does the farmer have to buy to fence the other three sides? A relay team has 5 members. They run a race that is 28 km long. Each member of the team runs the same distance. How far does each team member run? Read, choose, use and record standard metric units to estimate and measure length, weight and capacity to a suitable degree of accuracy (e.g. the nearest centimetre); convert larger to smaller units using decimals to one place (e.g. change 2.6 kg to 2600 g) I can choose appropriate units to measure length and distance I can read metre sticks, tape measures and rulers marked in cm and mm accurately I can make sensible estimates of length in everyday contexts I know how many millimetres there are in a centimetre or metre, and how many metres there are in a kilometre Interpret a reading that lies between two unnumbered divisions on a scale I can interpret a reading between two unnumbered divisions on a ruler, tape measure or metre stick Draw and measure lines to the nearest millimetre; measure and calculate the perimeter of regular and irregular polygons; use the formula for the area of a rectangle to calculate the rectangle's area I can draw and measure lines to the nearest millimetre I can measure the sides of polygons and add them to find the perimeter Children work in small groups to measure lengths and distances, using tape measures, metre sticks and rulers to a suitable degree of accuracy, for example, to the nearest metre, centimetre or millimetre. They read unnumbered divisions on measuring scales, for example, on a ruler marked in millimetres and numbered every centimetre. They estimate the length, height and width of everyday objects, explaining how they made their estimates and discussing the benchmarks they have used; where possible, they then measure to see how accurate their estimates were. They measure the sides of regular and irregular polygons and calculate the perimeter, either by totalling the sides or, for regular polygons, multiplying the length of one side. Children use their knowledge of parallel and perpendicular lines and of measurement to construct squares, rectangles and right-angled triangles, using a set-square and Children continue to develop their problem-solving skills in the context of measurement, focusing on mass. They continue to solve real-life problems involving one or two steps and any of the four operations. They recognise that they may need to change the units of measurement to the same unit in problems such as: A horse eats 560 g of feed from a 2 kg bag. How much of the feed is left? Children refine their written methods of calculation to make them efficient. They decide the best way to solve a problem and explain why they chose, say, a written method rather than a mental method. They use their knowledge of number facts, place value, inverse operations and rounding to make estimates and check calculations. Children use calculation methods when they solve word problems involving mass to give meaning to their work, such as: Two parcels together weigh 2.4 kg. One parcel weighs 1.68 kg. What is the mass of the other parcel? Mary posts seven identical parcels. Each parcel weighs 3.2 kg. What is the total mass of the parcels? The answer is 15.4 kg. What was the question? Solve these problems: A spoonful is 5 ml. How many spoonfuls can you get from a bottle that holds one quarter of a litre? A tin of baked beans weighs 400 grams. How many grams less than 1 kilogram is this? Did you have to change any of the information to help you solve the problem, e.g. convert units of measurement? Did you need to use the calculator to solve the problem? What key sequence did you use? Roughly, what will the answer to this calculation be? How did you arrive at that estimate? Do you expect your answer to be greater or less than your estimate? Why? How do you know that this calculation is probably right? Could you check it a different way? This answer is wrong. How can I tell? Find two different ways to check the accuracy of this answer. What key presses would you make on a calculator to work out ? Explain how to use your calculator to solve these problems. What key sequences will you use? I use 1375 g of sugar to make 5 cakes. How much sugar do I need for 1 cake? For 3 cakes? There are 75 g of rice in a portion. How many portions are there in a 3 kg bag of rice? How will you check your answers to the problems? Read, choose, use and record standard metric units to estimate and measure length, weight and capacity to a suitable degree of accuracy (e.g. the nearest centimetre); convert larger to smaller units using decimals to one place (e.g. change 2.6 kg to 2600 g) I can choose and use a suitable metric unit to estimate and measure weight I can use benchmarks to help me to estimate weight I know how many grams there are in a kilogram Interpret a reading that lies between two unnumbered divisions on a scale I can work out the reading between two unnumbered divisions on kitchen and bathroom scales Draw and measure lines to the nearest millimetre; measure and calculate the perimeter of regular and irregular polygons; use the formula for the area of a rectangle to calculate the rectangle's area I can explain the difference between perimeter and area I can solve problems involving calculating a perimeter or area When they measure weight, children use a range of weighing scales, kitchen scales, bathroom scales. They weigh to a suitable degree of accuracy, depending on the object, for example, to the nearest 100 g or to the nearest 1 g. They read scales with some unnumbered divisions, for example kitchen scales with divisions of 10 g numbered every 100 g, or bathroom scales with divisions of 1 kg numbered every 10 kg. They estimate the masses of everyday objects, say how they made their estimates and then measure to see how accurate their estimates were. They investigate the cost of sending different parcels by first-class post, researching postage costs on the Post Office website. Look for evidence of children who can explain what the terms area and perimeter mean and who can use the associated notation, for example, cm and cm 2, consistently and Use a calculator to solve problems, including those involving decimals or fractions (e.g. to find 3 /4 of 150 g); interpret the display correctly in the context of measurement I can use a calculator to solve a measurement problem and interpret the display correctly Children continue to develop their problem-solving skills in the context of measurement. They now focus on capacity, and on using the 24-hour clock to measure time. They continue to solve real-life problems involving one or two steps and any of the four operations. They use efficient written methods for all four operations and are able to explain the methods they have used. They change the units of measurement to the same unit before doing any calculations. They estimate their answers and check them by using an alternative calculation method. They interpret their answers in the context of the problem. For example, they recognise when to round up or down after a division in problems such as: 256 children attend a summer camp. They sleep in tents that hold 7 children. How many tents are needed? [round up] A farmer's chickens lay 152 eggs. How many boxes of 6 eggs can he fill? [round down] Assessment opportunity: Ma1, Communicating Look for evidence of children who work in an organised and systematic way and who present their work clearly, so that they can check their results. Look for children who consider and record the appropriate units, when presenting answers to problems involving capacity and time, and who make use of appropriate vocabulary when describing their solutions. Write instructions for a friend to solve the problem. What estimates did you make before you worked out the calculations? How did you check your answer? Could you have checked it in a different way? How? Write another problem using the information in this problem Round these measurements to the nearest whole unit: 4275 ml 3.25 kg 5.85 km What is the approximate perimeter and area of this rectangle? About how heavy are 8 boxes of apples weighing 5.6 kg each? About how many 185 ml glasses of water can you pour from a 2 litre bottle? Show me how you used your calculator to solve these problems: I use 2.4 kg of apples to make 4 pies. How many grams of apples are there in each pie? What mass of apples would I need to make 3 pies? A piece of wood is 3.25 m long. I use all the wood to make five shelves of equal length. How long is each shelf in metres? In centimetres? What key sequence did you use? Read, choose, use and record standard metric units to estimate and measure length, weight and capacity to a suitable degree of accuracy (e.g. the nearest centimetre); convert larger to smaller units using decimals to one place (e.g. change 2.6 kg to 2600 g) I can choose and use the correct metric unit to estimate and measure capacity I can use benchmark objects to help me to estimate capacity I know how many millilitres there are in a litre Interpret a reading that lies between two unnumbered divisions on a scale. I can interpret a reading between two unnumbered divisions on a scale on measuring cylinders and jugs I can read accurately the number of millilitres in a litre jug Draw and measure lines to the nearest millimetre; measure and calculate the perimeter of regular and irregular polygons; use the formula for the area of a rectangle to calculate the rectangle's area I can find the area of a rectangle using the formula length width I know that area is measured in cm2 When they estimate and measure capacity, children compare the sizes of containers, using a benchmark such as a 1 litre bottle or jug. They put a range of containers in order of capacity, from smallest to largest, estimate the capacity to the nearest 100 ml and then measure the capacity to see how accurate their estimates were. They solve problems such as: How many cups of water do you think it would take to fill this jug? How many teaspoons of water can I put in this coffee cup? Children read scales, such as measuring cylinders with divisions of 10 ml numbered every 100 ml, or with divisions of 25 ml numbered every 100 ml. Children reflect on the units that they are familiar with. They suggest suitable units to

19 Year 5 Block D: calculating, measuring and understanding shape progression map 2 weeks 10 lessons Framework objectives, children s learning outcomes and examples of assessment for learning questions in blue. (continued) Y5 Block D Unit 1 Y5 Block D Unit 2 Y5 Block D Unit 3 ruler. They measure a dimension such as a diagonal of a rectangle or the hypotenuse of a right-angled triangle for their teacher to check the accuracy of their drawings. How tall is the tree at the top of the playground? How do I write 6 metres 4 centimetres as a decimal? Tell me an example of something you would measure in kilometres. What about metres? Centimetres? Millimetres? What unit of measurement would you use for: the length of fencing to go around the playground? the distance around your head? a 'fun run' to raise money for charity? the width of a pin head? Is the height of the classroom about 3 m, 6 m or 12 m? Is the length of this crayon about 5 mm, 55 mm or 555 mm? What is the distance between the two arrows? How many of these cherries weigh between 85 g and 90 g? Draw these lines accurately using a 300 mm ruler marked in cm: 5.2 cm 0.7 cm 83 mm 7 mm Measure the sides of these polygons in centimetres and millimetres. What is the perimeter of each shape in centimetres? In millimetres? Solve these problems: What is the perimeter of: a regular octagon with sides of 25 mm? An equilateral triangle with sides of 8.7 cm? A square has a perimeter of 64 cm. How long is each side? A rectangle has a perimeter of 72 m. The shortest side is 9 m long. What is the length of the longest side? Explain how you worked them out. accurately. Look for children who find an area by counting squares and for those who can begin to express the formula for the area of a rectangle as number of squares in a row times number of rows. Assessment focus: Ma1, Problem solving Look for children selecting appropriate equipment and units to measure in a range of contexts. Look out for children estimating and then measuring with an appropriate degree of accuracy. When measuring the mass of a bag of apples, they might decide that measuring to the nearest 25 g is sufficiently accurate, whereas measuring to the nearest kilogram would be more appropriate for the mass of a child. Children construct shapes that have parallel or perpendicular sides. For example, they draw a right-angled triangle where they are given the lengths of the two shorter sides. They then measure the third side to the nearest millimetre. They draw a rectangle with a perimeter of 28 cm and a longest side of 8 cm. They measure the length of the diagonal, again to the nearest millimetre. How do I write 6 kilograms 400 grams as a decimal number? What about 9 kilograms 50 grams? Tell me an example of something you would measure in kilograms. What about grams? What unit of measurement would you use for: weighing a tomato? weighing yourself? Circle one amount each time to make these sentences correct. The distance from London to Manchester is about: 320 cm 320 m 320 km A tea cup is likely to hold about: 15 ml 150 ml 150 l A hen's egg is likely to weigh about: 6 g 60 g 600 g What is the total mass of the apples on the scales? A piece of cheese has a mass of 350 grams. Mark an arrow on the scale to show the reading for 350 g. measure, say, the area of the school hall, the amount of liquid in a tablespoon or the mass of a baby. Children consolidate their understanding of perimeter and area, appreciating the difference between the two. They solve problems such as: Create different T-shapes that have an area of 26 cm 2. Do they all have the same perimeter? Find as many rectangles as you can with whole-number sides and an area of 36 cm 2. Which has the smallest perimeter? A picture frame is created from a narrow length of wood 60 cm long. Suggest some possible measurements for the frame. Work out the area inside each frame. A rectangle drawn on a centimetre coordinate grid has three vertices at (1, 5), (1, 3) and (5, 3). Complete the rectangle and find its perimeter and area. A rectangular mirror has a perimeter of 1.7 m. It is 50 cm long. Work out its area. Assessment opportunity: Ma3, Measures Look for children using the terns area and perimeter accurately and consistently. Look out for children which know they can multiply the number of squares in a row by the number of rows to begin calculating area, rather than counting all of the squares individually. Look for children beginning to divide T-shapes into rectangles to calculate their areas. Assessment opportunity: Ma2, Written Methods Look for evidence of children using efficient written methods when appropriate to add and subtract the decimal numbers that arise in their measurements, for example, when they find the perimeter of a shape of find differences in length. Look for children who can multiply a number such as 3.7 by a single digit, for example, when they work out the perimeter of a regular shape. Children construct shapes that have parallel or perpendicular sides. For example, they draw a right-angled triangle where they are given the lengths of the two shorter sides. They then measure the third side to the nearest millimetre. They draw a rectangle with a perimeter of 28 cm and a longest side of 8 cm. They measure the length of the diagonal, again to the nearest millimetre. What unit of measurement would you use to measure the amount of water in: a drinking glass? a teaspoon? a bath? Kate's glass holds a quarter of a litre when it is full. She fills it nearly to the top with juice. Tick the approximate amount of juice she puts in the glass. 4 millilitres 20 millilitres 120 millilitres 220 millilitres 420 millilitres 50 millilitres of water are poured out from this container. How much water is left in the container? Measure accurately the longest side of this shape. Give your answer in millimetres. 180 ml of water are added to the water in this container. Draw a line to show the new level of the water in the container. What tips would you give someone who wanted to measure a line in millimetres? Solve these problems: What is the area of a rectangle measuring 34 cm by 29 cm? The area of a rectangle is of 132 m 2. The shortest side is 4 m long. What is the length of the longest side? Explain how you worked out your answers. Tell me a rule for working out the area of a rectangle. The area of a rectangle is 24 cm 2. What are the lengths of the sides? Are there other possible answers? Tell me something that has an area of approximately 30 m 2. What did you use to help you? Estimate the area of the front cover of this exercise book. How did you go about doing that? Time - 24 hour clock - time Read timetables and time using 24-hour clock notation; use a calendar to calculate time intervals I can use a calendar to work out how many days and weeks it is to my birthday I can change am or pm times to 24-hour clock times, and vice versa Read timetables and time using 24-hour clock notation; use a calendar to calculate time intervals. I can solve problems, using a timetable written in 24-hour clock notation They solve more problems involving time, including using the 24-hour clock. They record

20 Year 5 Block D: calculating, measuring and understanding shape progression map 2 weeks 10 lessons Framework objectives, children s learning outcomes and examples of assessment for learning questions in blue. intervals Y5 Block D Unit 1 Y5 Block D Unit 2 Y5 Block D Unit 3 Children use 24-hour clock times. They recognise the difference between am times their work, using jottings such as time lines to support their calculations. They interpret from midnight to before noon and pm times from noon to before midnight, and they train and bus timetables, flights of long-distance planes, and TV schedules like the one convert these to 24-hour clock times. They complete a simple conversion table, such as: below. Children rehearse how many days there are in each month. They understand how a calendar is organised and understand the significance of a leap year. They use a BBC 1 ITV 1 calendar to work out the day of the week for a particular date, or the time interval seven o'clock in the evening quarter to 10 in the morning Midnight 17 minutes past 4 in the afternoon between one date and another, for example, how long they have to wait for their birthday or how many days it has been since they last had their pocket money. Given part of a calendar for a month they can say whether a given date will fall on a particular day. Assessment focus: Ma2, Solving numerical problems Look for evidence of children solving problems with and without a calculator. Look for children making sense of the context of the problem, recognising the information that is relevant and the calculations they need to do. Look for children who recognise the calculations they need to perform in order to solve time duration problems. For example, look for children who are aware of the mixed units of hours and minutes, particularly if they decide to use a calculator to help them solve a problem such as finding the time an event takes if it starts at 5:15 pm and ends at 7:49 pm. Here is the calendar for August :00 7:00 pm 14:20 22:15 7:00 pm: Doctor Who 6:45 pm: X Factor 7:40 pm: Strictly Come Dancing 8:00 pm: The Bill 8:50 pm: News and Weather 8:45 pm: X Factor Results 9:15 pm: Film Special 9:05 pm: News and Weather 11:05 pm: Match of the Day 9:35 pm: Movie Special 12:20 am: Live Music Special 11:15 pm: Sport Round-up 1:10 am: Open University 12:20 am: Planet Earth They answer questions such as: How long does Dr Who last? If I turn over to ITV 1 at the end of Dr Who, what programme is on? I switch the TV on at 8:00 pm. What programme is on BBC 1? I switch on the TV at 10:25 pm. How long do I have to wait for Match of the Day? Planet Earth lasts 45 minutes. At what time does it finish? Which is longer: Film Special on BBC 1 or Movie Special on ITV 1? Here is part of a train timetable. Simon's birthday is on August 20th. In 1998 he had a party on the Sunday after his birthday. What was the date of his party? Tina's birthday is on September 9th. On what day of the week was her birthday in 1998? What time will this clock show in 20 minutes? How long does the first train from Edinburgh take to travel to Inverness? Ellen is at Glasgow station at 1:30 pm. She wants to travel to Perth. She catches the next train. At what time will she arrive in Perth? How would quarter past four in the afternoon be shown on a 24-hour digital clock? A plane takes off on Tuesday at 22:47. It lands on Wednesday at 07:05. How long in hours and minutes is the flight? Here is part of a train timetable. Which is the fastest train from Birmingham New Street to Reading? You have to arrive at Oxford at 2:00pm. Which train would you catch from Coventry? Position and movement Coordinates Read and plot coordinates in the first quadrant; recognise parallel and perpendicular lines in grids and shapes; use a set-square and ruler to draw shapes with perpendicular or parallel sides Read and plot coordinates in the first quadrant; recognise parallel and perpendicular lines in grids and shapes; use a set-square and ruler to draw shapes with perpendicular or parallel sides Read and plot coordinates in the first quadrant; recognise parallel and perpendicular lines in grids and shapes; use a set-square and ruler to draw shapes with perpendicular or parallel sides

21 Year 5 Block D: calculating, measuring and understanding shape progression map 2 weeks 10 lessons Framework objectives, children s learning outcomes and examples of assessment for learning questions in blue. Reflection/ symmetry Y5 Block D Unit 1 Y5 Block D Unit 2 Y5 Block D Unit 3 I can read and plot coordinates to make shapes I can recognise parallel and perpendicular lines in shapes and in the environment I can use a set-square and ruler to draw shapes with parallel and perpendicular sides Children read and plot coordinates in the first quadrant. They explain why the point Give an example of parallel lines in everyday life. How can you recognise them? What Complete patterns with up to two lines of symmetry; draw the position of a shape after a (4, 1) is not the same as (1, 4). Given some of the vertices of squares or rectangles, they about perpendicular lines? reflection or translation plot the missing points, recognising that there may be more than one solution to the Points A (3, 4) and B (3, 7) are joined by a straight line. Plot the coordinates of two points I can complete a pattern with one or two lines of symmetry problem. For example: if (6, 5) and (8, 5) are two vertices of a square, they find all three C and D so that line CD is parallel to AB. I can draw where a shape will be after it has been reflected or translated possibilities for the pair of missing vertices. Now plot two points E and F so that line EF is perpendicular to AB. Children develop their ideas of reflection and symmetry to complete patterns and Assessment focus: Ma1, Reasoning reflect and translate shapes. They reflect shapes in a mirror line where not all the sides Look for evidence of children using pattern to formulate rules or generalisations. When of the shape are parallel or perpendicular to the mirror line. They translate shapes in they solve calendar problems, look for children recognising sequences of numbers that directions parallel to the axes of a coordinate grid, giving the coordinates of the new increase in steps of 7, as they determine the dates of consecutive Wednesdays in a position. month, for example. When they work with coordinates in the first quadrant, look for Assessment opportunity: Ma3, Properties of position and movement children who recognise that, for all the points in a vertical line, the first number in the Look for evidence of children reflecting shapes in a mirror line presented at 45. Look for coordinate pair is the same. Look for evidence of children reasoning about coordinates children beginning to use the distance of each vertex of a shape from the mirror to reflect and the properties of shapes as they solve problems involving the coordinates of missing it more accurately. vertices. How would you check if two lines are parallel? How would you check that two lines are Here is a shaded square. perpendicular? On plain paper, use a ruler and set-square to construct: a square with sides 56 mm a rectangle with length 6.3 cm, width 4.9 cm Construct a right-angled triangle with the two shorter sides measuring 3.5 cm and 4.2 cm. What is the length of the third side? The heavy lines are lines of symmetry. Complete the pattern. Write the coordinates for point A and point C. Three of the four corners of a square are (3, 10), (5, 12) and (7, 10). Work out the coordinates of the fourth corner. (8, 10) and (10, 8) are two vertices of a right-angled triangle. What are the coordinates of the third vertex? Are there any other possibilities? This triangle is translated two squares to the left. Draw the triangle in its new position. The shaded triangle is a reflection of the white triangle in the mirror line. Write the coordinates of point A and point B. Position and movement angles Estimate, draw and measure acute and obtuse angles, using an angle measurer or protractor to a suitable degree of accuracy; calculate angles in a straight line I can estimate and measure angles less than 180 I can recognise acute, obtuse and right angles Children know that angles are measured in degrees and learn to say whether an angle is acute, obtuse or a right angle. Given a set of cards with pictures of angles on, they sort them into sets or order them from smallest to largest. They make sensible estimates of the size of angles less than 180 and then measure them to within 5 degrees, using a protractor or angle measurer. They apply this knowledge to work with shapes drawn on a coordinate grid. For example, they plot the missing vertex of a square with sides not parallel or perpendicular to the axes and then check that each angle is 90. Look at these angles. Estimate, draw and measure acute and obtuse angles using an angle measurer or protractor to a suitable degree of accuracy; calculate angles in a straight line I can draw angles less than 180 to within 5 I can calculate angles on a straight line Children know that a right angle is equal to 90. They recognise that a straight line can be formed from two right angles and is equivalent to 180. They use this to calculate angles on a straight line. They draw and measure angles, using a protractor. For example, children take four card semicircles. They draw a line from the centre of each semicircle to the edge, and cut along the line to form two card angles. They shuffle the eight angles on the table top and label them randomly from A to H. They estimate the size of each angle, recording their estimates and using these to suggest which pairs will go together to form a straight line. Children then use a protractor to measure each angle, and calculate whether their predictions were correct. They check by placing the angles together to form straight lines. Assessment opportunity: Ma3, Measures Look for evidence of children choosing and using appropriate units and measuring instruments, and interpreting different scales accurately, when they solve problems. Look for children who make reasonable estimates of angles and consistently measure angles accurately, for example, to the nearest 5 or 2. Estimate then use a protractor to measure these angles to the nearest 5 degrees. Which of them are acute angles? Which are obtuse angles? Estimate the size of each of the angles. Now use your protractor to measure the angles to the nearest 5 degrees. Use a protractor to draw an angle of 35. PQ is a straight line. Calculate the size of angle x.

22 Year 6 Block D: calculating, measuring and understanding shape progression map 2 weeks 10 lessons Framework objectives, children s learning outcomes and examples of assessment for learning questions in blue. Speaking & listening Y6 Block D Unit 1 Y6 Block D Unit 2 Y6 Block D Unit 3 Use a range of oral techniques to present persuasive argument Participate in a whole-class debate, using the conventions and language of debate Analyse and evaluate how speakers present points effectively through use of I can use different techniques to persuade people I can take part in a whole-class debate language, gesture, models and images Convince your partner that a good estimate for the perimeter of the classroom is 25 Debate with the class the usefulness of various benchmarks for estimating measurements. I can listen to someone explain their method or solution to a problem, and evaluate metres, and that a good estimate for its area is 35 square metres. For example, how useful is it to know that a door is roughly 2 metres tall? What other whether their explanation made sense Tim says a square with sides of 8 cm has an area of 32 cm 2. Do you agree with him? heights can be estimated, using this benchmark? Listen to and then discuss how someone explained to the class how they estimated the Why or why not? number of leaves of clover on the playing field. Could their method have been improved? Could their explanation have been improved? Would a table or diagram have helped? Word problems Solve multi-step problems, and problems involving fractions, decimals and percentages; choose and use appropriate calculation strategies at each stage, including calculator use I can solve problems with several steps and decide how to carry out the calculation Calculate mentally with integers and decimals: U.t ± U.t, TU U, TU U, U.t U, U.t U I can add, subtract, multiply and divide whole numbers and decimals in my head Use efficient written methods to add and subtract integers and decimals, to multiply and divide integers and decimals by a one-digit integer, and to multiply two-digit and three-digit integers by a two-digit integer I can add, subtract, multiply and divide whole numbers and decimals using efficient written methods Use a calculator to solve problems involving multi-step calculations I can use a calculator to solve problems with several steps Use approximations, inverse operations and tests of divisibility to estimate and check results I can estimate the result of a calculation I know several ways of checking answers Children solve multi-step problems involving measures. They decide what calculation(s) to do and estimate the answers. They choose appropriate and efficient methods, including mental methods, and using a calculator where appropriate. They check their answers against their estimates and consider them in the context of the problem, to make sure that they are reasonable. They compare different methods and justify their choices. For example, they solve problems such as: The temperature inside an aeroplane is 20 C. The temperature outside the aeroplane is 30 C. What is the difference between these temperatures? The area of a rectangle is 16 cm 2. One of the sides is 2 cm long. What is the perimeter of the rectangle? Peanuts cost 60p for 100 grams. What is the cost of 350 grams of peanuts? Raisins cost 80p for 100 grams. Jack pays 2 for a bag of raisins. How many grams of raisins does he get? Assessment focus: Ma2, Solving numerical problems Look for evidence of children s proportional reasoning. Look for the way in which children solve problems involving direct proportion. For example, when they solve problems about cost per unit of weight, look for children who scale up and those children who begin to use a sequence of calculator key presses including multiplication and division, for example: Solve multi-step problems, and problems involving fractions, decimals and percentages; choose and use appropriate calculation strategies at each stage, including calculator use I can solve problems with several steps and decide how to carry out the calculation Calculate mentally with integers and decimals: U.t ± U.t, TU U, TU U, U.t U, U.t U I can add, subtract, multiply and divide whole numbers and decimal numbers in my head Use efficient written methods to add and subtract integers and decimals, to multiply and divide integers and decimals by a one-digit integer, and to multiply two-digit and three-digit integers by a two-digit integer I can add, subtract, multiply and divide whole numbers and decimal numbers using efficient written methods Use a calculator to solve problems involving multi-step calculations I can use a calculator to solve problems with several steps Use approximations, inverse operations and tests of divisibility to estimate and check results I can estimate the result of a calculation I know several ways of checking answers Children use decimal notation in the context of measures and convert between units where necessary, for example, to solve word problems such as: How many 250 ml cups of tea can you pour from a tea urn that holds 8.5 litres? How many 30 cm square tiles would you need to buy to cover a rectangular floor that is 2.5 m wide by 3.5 m long? There is 60 g of rice in one portion. How many portions are there in a 3 kg bag of rice? A packet contains 1.5 kilograms of guinea pig food. Remi feeds her guinea pig 30 grams of food each day. How many days does the packet of food last? Assessment focus: Ma2, Operations, relationships between them Look for evidence of the range of relationships between operations that children use in their calculations, particularly when they use a calculator to work with larger numbers or decimal numbers. Look for children who understand that the missing number in 8.5 = 34 can be calculated by entering = into the calculator. Look for children who check the answer to a division calculation by entering the same calculation again, and those who check by using multiplication as the inverse operation. Look for evidence of children who are aware of the order of operations, particularly when using a four-function calculator that is not scientific. For example, look for children calculating the cost of three books at 3.75 and five at 2.45 and recognising the order in which this should be entered into their calculator. They might use the memory, for example, storing the result of , entering = and then using + MR (memory recall). Mr Singh buys paving slabs to go around his pond. Solve multi-step problems, and problems involving fractions, decimals and percentages; choose and use appropriate calculation strategies at each stage, including calculator use I can solve problems with several steps and decide how to carry out the calculation Calculate mentally with integers and decimals: U.t ± U.t, TU U, TU U, U.t U, U.t U I can add, subtract, multiply and divide whole numbers and decimals in my head Use efficient written methods to add and subtract integers and decimals, to multiply and divide integers and decimals by a one-digit integer, and to multiply two-digit and three-digit integers by a two-digit integer I can add, subtract, multiply and divide whole numbers and decimals using efficient written methods Use a calculator to solve problems involving multi-step calculations I can use a calculator to solve problems with several steps Use approximations, inverse operations and tests of divisibility to estimate and check results I can estimate the result of a calculation I know several ways of checking answers Children continue to solve word problems involving several steps, or involving decimals, applying their choice of mental, written or calculator method. They make sure that measurements are converted to the same unit before calculation. They record their methods efficiently, explaining how the problem was solved. For example: A box contains 220 matches and weighs 45 grams. The empty box weighs 12 grams. Calculate the weight of one match. Butter costs 4.50 for 1 kg. Marie buys 200 grams of butter. How much does she pay? Cream cheese costs 3.60 for 1kg. Robbie buys a pot of cream cheese for 90p. How many grams of cream cheese does he buy? Assessment focus: Ma2, Solving numerical problems Look for evidence of the mathematics children choose to use as they solve a wider range of word problems. Look out for children who independently use their knowledge of different units to solve problems such as finding how many 60 g portions can be served from a bowl containing 1 kg. As they solve problems involving ratio, look for evidence of children beginning to calculate, using multiplication rather than relying on trial and improvement. What clues do you look for in the wording of questions? What words mean you need to add, subtract, multiply or divide? This fence has three posts, equally spaced. Here is a design made with the tiles. Each tile is 4 centimetres by 9 centimetres. Calculate the width and height of the design. Write down the calculations that you did. Did you use a written method or a calculator? Explain why. Which of these subtractions can you do without writing anything down? Why is it possible to solve this calculation mentally? What clues did you look for? I need two shelves each 1.4 metres in length. I cut the two shelves from a plank 5 metres long. How much of the plank is left? Explain the mental calculations that you did He buys 4 rectangular slabs and 4 square slabs. What is the total cost of the slabs he buys? Mr Singh says: It would cost more to use square slabs all the way round. Explain why Mr Singh is correct. How did you decide whether Mr Singh was right or wrong? What calculations did you do? The answer is 10.6 kg. What was the question? In a cafe I buy two cups of coffee and a sandwich. Altogether I pay three pounds. The sandwich costs one pound sixty. What is the cost of one cup of coffee? Explain the mental calculations that you did to solve this problem. Cashew nuts cost 90p for 100 grams. What is the cost of 450 grams of cashew nuts? Currants cost 40p for 100 grams. Maria pays 3 for a bag of currants. How many grams of currants does she get? Show me the calculations that you did to solve these problems. Could there be a more Each post is 15 centimetres wide. The length of the fence is 153 centimetres. Calculate the length of one gap between two posts. Show me the calculations that you did. Did you use a written method or a calculator? Explain why. A packet of crisps costs 32 pence. Josh buys three packets. How much change does he get from one pound? Explain the mental calculations that you did to solve this problem. Make up an example of an addition/subtraction involving decimals that you would do in your head. Now make up an example you would do on paper. Explain why. Show me how to find the answer to the next problem, using an efficient written method. A packet contains 1.5 kilograms of guinea pig food. Remi feeds her guinea pig 30 grams of food each day. How many days does the packet of food last? Show me the calculator key presses you made to solve that problem. Could you do the calculation with fewer key presses? Julie is 92 cm tall. Tom is 1.34 m tall. Lisa's height is halfway between Julie's height and Tom's height. Calculate Lisa's height.