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YEAR 2 UNIT 2 – BLOCK B – 3 WEEKS Learning overview Block B Year 2 Children consolidate their ability to read and write two- and three-digit numbers, using practical equipment such as arrow cards and number grids. They identify missing numbers in a 100-square. Children use their knowledge of addition and subtraction facts for numbers to 10 to find sums and differences of multiples of 10, for example 80 - 50. They recognise pairs of multiples of 10 that total 100. They use their knowledge of pairs of numbers that sum to 10 to identify what must be added to any two-digit number to reach the next multiple of 10. For example, they know that 56 4 60 because 6 4 10. They describe the patterns in the sequence 0 20 20, 1 19 20, predict the next calculation in the sequence and continue the pattern to generate all the pairs of numbers with a total of 20. Children use their knowledge and experience of counting from zero in steps of 2, 5 and 10 to learn the 2, 5 and 10 multiplication facts. They answer questions such as: How many twos make 12? and recognise that this can be recorded as 12 2. They recognise multiples of 2, 5 and 10; they know that multiples of 2 are called even numbers and that numbers which are not even are odd. Children choose and use appropriate calculations to solve problems and puzzles involving all four operations, supporting their methods with practical equipment or drawings. They record their thinking using jottings, including number lines. For example, they use jumps on a number line to solve problems such as: 17 people are on a bus. 8 more get on and 3 get off. How many people are on the bus now? You have 50 litres of water. How many 10-litre buckets can you fill? Desi needs 18 balloons. The shop sells balloons in packs of 5. How many packs does he need to buy? Children make and describe symmetrical patterns, for example, using ink blots or pegboards. They recognise symmetry in objects and pictures; they check for symmetry with a mirror or by folding. They complete a symmetrical picture by making or drawing the 'other half', and solve puzzles involving symmetry. For example, they place two red squares, two green squares and two blue squares in a line so that the squares make a symmetrical pattern, and explore the number of different ways of doing it. Children make and draw 2-D shapes, patterns and 3-D models, and explore their properties. For example, they use construction kits to make simple 3-D shapes and count the number of edges or corners. They understand and use appropriate vocabulary to describe the properties of shape, for example selecting from a group of shapes those that match a particular description. Learning overview for Year 1 can be used to Learning overview for Year 3 can be used to support pupils working below Year 2 support pupils working above Year 2 expectations. expectations. 1 Y2, BLOCK B, UNIT 2 Speaking and BLOCK B listening objectives Assessment for Learning YEAR for the block 2 Use language and Links to 1999 Framework and Supplements of Hold your shape up and describe it to the class. Point to its gesture to support the Examples Unit 2 features when you talk about them. use of models, Sort these shapes. Point to one of your shapes and explain diagrams or displays 3 Weeks why you have placed it in that group. when explaining STRAND CODE Year 2 Objectives Year 2 Year 2 Describe patterns What is special about the way I have ordered these Solve mathematical problems or Year 2 and relationships counters? puzzles, recognise simple patterns and 63, 65 involving numbers or Can you make a different pattern using the same relationships, generalise and predict. shapes, make counters? Can you make me a pattern where the eighth Suggest extensions by asking „What predictions and test counter is blue? Is that the only way it could be done? if…?‟ or „What could I try next?‟ these with examples What is wrong with this pattern? Can you put it right? Investigate a general statement about Is this picture/object symmetrical? How can you check? familiar numbers or shapes by finding I have begun to make a symmetrical shape with these examples that satisfy it. coloured blocks. Can you complete the shape? How can Using and you check that it is symmetrical? Applying Solve problems Rosie spent 24p. She spent 8p more than Suzy. How much Use mental addition and subtraction, Year 2 involving addition, did and simple multiplication and division, 67, 69 subtraction, Suzy spend? What calculation is needed? How did you to solve simple word problems involving multiplication or decide? numbers in „real life‟, money or division in contexts of How did you work out the calculation? How did you record measures, using one or two steps. numbers, measures it? Recognise all coins; begin to use £.p or pounds and pence Look at this next problem. What do you need to find out? notation for money (e.g. know that How do you know you need to add/subtract/double/halve? £4.65 indicates £4 and 65p). Find What clues are there? totals, give change; work out which coins to pay. Read and write two- I have made a three-digit number with some cards. Read and write whole numbers to at Year 2 digit and three-digit least 100 in figures and words. 9 numbers in figures Describe and extend simple number 3, 5, 7 and words describe sequences; recognise odd and even Counting and and extend number Write all the other three-digit numbers that you can make numbers to at least 30. Understanding sequences and with the same cards. Number recognise odd and [Point to one of the numbers.] Write this number in words. even numbers Think of an even number which is more than 20 and less than 40. Write the two missing numbers in this sequence. 41 43 45 47 49 53 Derive and recall all How many different pairs of numbers can you remember Know by heart: all addition and Year 2 addition and that have a total of 20? How can you be sure you have subtraction facts for each number to at 31 subtraction facts for remembered them all? least 10; all pairs of numbers with a each number to at Look at these multiples of 10. Which pair of numbers has a total of 20 (e.g. 13 + 7, 6 + 14); all pairs least 10, all pairs total of of multiples of 10 with a total of with totals to 20 and 100? Are there any other possibilities? 100 (e.g. 30 + 70). all pairs of multiples 10 20 30 40 50 60 70 80 90 of 10 with totals up + ¯ = 100. What two numbers could go in the boxes? Knowing and to 100 Are there any other possibilities? Using Number Derive and recall What are the missing numbers? Know by heart multiplication facts for Year 2 Facts multiplication facts for × 2 = 16 10 × = 40 × ¯ = 20 the 2 and 10 times-tables; begin to 53 the 2, 5 and 10 times- How do you know? know multiplication facts for the 5 times- tables and the related Harriet knows that 2 × 10 = 20. What is 2 × 11? How do table. division facts; you know? Derive quickly the corresponding recognise multiples of Which are the even numbers in this list? division facts. 2, 5 and 10 13, 4, 12, 8, 19, 16 Know by heart multiplication facts for Year 3 Draw rings around all the multiples of 5. the 5 times-table. 53 45, 20, 54, 17, 40 Visualise common Describe the shape or solid in the cloth bag as you feel it. Use the mathematical names for Year 2 2D shapes and 3D What might it be? Why? How do you know this shape is a common 3D and 2D shapes, including 81, 83 solids; identify …? How do you know this shape isn‟t a …? the pyramid, cylinder, pentagon, shapes from Imagine a cube. Four faces are yellow; the rest are blue. hexagon, octagon. pictures of them in How many faces are blue? Relate solid shapes to pictures of them. different positions Describe this shape/solid to a friend. Can they guess what Sort shapes and describe some of their and orientations; it is? features, such as the number of sides sort, make and Sort these 2D shapes. Put all the pentagons in this circle. and corners, symmetry. describe shapes, Now choose another way to sort them. What do all the Make and describe shapes, pictures referring to their shapes that you have put in the circle have in common? and patterns, e.g. using solid shapes, properties pinboard and elastic bands, squared paper, a programmable robot, … Identify reflective Two of these shapes have no lines of symmetry. Which are Begin to recognise line symmetry. Year 2 symmetry in patterns they? 85 and 2D shapes and Understanding draw lines of Shape symmetry in shapes This shape has been folded in half along the dotted line. Imagine opening it up. How many sides does the opened shape have? Draw the shape that you think will be made when the folded shape is opened up. Look at the symmetrical picture that I have given you. Draw a line of symmetry on it. 2 Y2, BLOCK B, UNIT 2 BLOCK B - YEAR 2 UNIT 2 USING AND APPLYING MATHEMATICS Describe patterns and relationships involving numbers or shapes, make predictions and test these with examples (Objective repeated in Block B Units 1, 2 & 3) Q What is this shape called and can you tell me something about it? Do all hexagons look like this one? Explain that you want the children to work in pairs on the carpet and to make some more hexagons with elastic bands and pinboards which are different to the one which you have just shown them. Expect some children to still make a regular hexagon of a different size, . Q Who can show me a different shaped hexagon? Look for examples of irregular hexagons which must still have 6 sides and 6 corners. Repeat the exercise with triangles, squares, rectangles, pentagons, etc. Q Which is the only shape that will always be the same shape although it may be a different size? Show children 4 interlocking cubes and demonstrate one way in which they fit together to give one layer only. Tell the children that you want them to find other ways of fitting the cubes together and they are to record their findings on squared paper. Children work on the task in pairs Using a magnetic board or OHP display 13 counters. Explain that two players take turns to remove 1 or 2 counters. The player that removes the last counter wins. Choose two volunteers to play. Repeat the game, this time arranging the counters on a track numbered 1 – 15. Begin at 15. The player to remove the counter from number 1 wins. 11 12 13 14 15 (track here 1-15 with some counters on). Ask the children to play several games, keeping count of the number of wins. After 5 minutes stop the children and ask: Q. Who won a lot of games? Did you have a special way of winning (a strategy)? Q. Is it better to go first or second? Allow the children to play several more games, trying out some of the ideas discussed. Stop the children and ask: Q. Did any of the ideas work? Did you win more games? (Have the children noticed that when there are 3 counters left you can predict the winner?) Invite two children to demonstrate on the magnetic board or OHP. Stop them when 3 counters remain. Ask: Q. Do you know who will win? Q. How do you know? Allow children to play a final game. 3 Y2, BLOCK B, UNIT 2 Show the children 3 boxes (with lids). Tell the children that there are 9 teddies inside the boxes. Ask: Q. How many teddies do you think there are in this box? Take several suggestions. Ask: Q. What is the most there could be? The least? Open the box and show the children the contents. Repeat for the second and third boxes. Empty all the boxes and ask the children to think how the teddies could be arranged in the three boxes. Give them two or three minutes to discuss with a partner and then ask for suggestions, recording several on the board. Example 3 + 3 + 3 Children work in pairs with boxes and counters, finding as many ways as possible of arranging the counters in the boxes. After 5 or 10 minutes stop the children and collect responses. If any pair has been systematic ask them to explain their method. Ask: Q. Have we found them all? How do you know? Q. How many ways do you think there are? Allow children a few more minutes to try to find more. Show Resource sheet Y2 B1, and ask the children in pairs to write an answer to the first question on their whiteboards. Collect the answers. Q Have we got some answers that are the same? Q Have we got all ten answers between us? Tell the children that it helps to record the answers in order so that we don‟t miss any or repeat any. Ask them to talk to their partner about how we could do this and where we would start. Collect answers and suggest that one way would be to find all the possible ways of making 12 if the first card is zero. Q If we have to find three numbers which total 12 and one is zero, what must our two remaining numbers total? Ask the children to work in pairs to find the pairs to 12 and remind them to put them in order. Collect answers: 9 + 3, 8 + 4, 7 + 5 and then write them on the board putting the zero first. 0 + 9 + 3 = 12 0 + 8 + 4 = 12 0 + 7 + 5 = 12 Q Is 0 + 5 + 7 = 12 a different answer? Why don‟t we need this? Q Why haven‟t we used 1 or 2 with zero? Why haven‟t we used 6 and 6? Ensure that the children understand that if one card is 0 and another is 1, the other card would have to be 11 and we don‟t have that card. Also emphasise that there is only one of each card. Q What number shall we start with next? Ask the children to find a total of 12 using 1 as the first card and record it in number sentences on the whiteboards. Collect and record answers on the board following on from the set beginning with zero. 1 + 9 + 2 = 12 1 + 8 + 3 = 12 1 + 7 + 4 = 12 1 + 6 + 5 + 12 Q Can you see any patterns? Discuss the pattern 9, 8, 7, 6 and 2, 3, 4, 5. Q Which number shall we use as our first card now? Q If we have to find three numbers which total 12 and one is 2, what must our two remaining numbers total? Ask children to record answers as before, collect responses and record on the board: 4 Y2, BLOCK B, UNIT 2 2 + 9 + 1 = 12 2 + 7 + 3 = 12 2 + 6 + 4 = 12 Q Can you see a set of three numbers that we have already used? Agree that 2 + 9 + 1 and 1 + 9 + 2 are the same and explain that as you don‟t want any repeats you will cross out 2 + 9 + 1. Ask the children to start with 3 and record as before. Collect answers and help the children to see that the only new answer is 3 + 4 + 5 = 12. Ask the children to start with 4 and see if this gives any new answers. Agree that it does not as the other two cards will have a total of 8 and all pairs with a total of 8 have been used. Say that starting with higher numbers will also only give answers we already have and so we don‟t need to go any further. Check that you have ten answers as it suggests in the question. Ask the children to work in pairs to look at question 2 on Resource sheet Y2 B1. Remind them that we have been learning to record systematically and they should do the same. If there is time, the children should move on to answer question 3. Remind the children of the importance of being systematic to ensure all the answers are found. Put a bucket inside a hoop. Ask a child to throw three different coloured beanbags into the hoop or bucket one at a time. If the beanbag goes in the bucket, the score is 10 and if it goes into the hoop the score is 5. If it goes in neither, the child throws again. Record the score on the board, e.g. 5 + 5 + 10. Q What is the total score? Agree that it is 20. Q What do you think the largest score could be? Why? Agree that this will be 30 as the biggest score is 10 + 10 + 10. Q What do you think the smallest score could be? Why? Agree that this is 15 made from 5 + 5 + 5. Tell the children to work in pairs, and find all the possible scores with the totals. Remind them to record in order in their books. Collect children‟s responses and agree that the possible totals are 15, 20, 25 and 30. Ask for the ways that 25 can be made. (10 + 10 + 5; 10 + 5 + 10; 5 + 10 + 10). Point out that the total is the same; the order they are shown in does not matter. Read Resource sheet Y2 B2 and point out that this time there are four beanbags. Ask them to work in pairs to find all the possible totals. Suggest that they start with largest or smallest total first 5 Y2, BLOCK B, UNIT 2 Count in tens starting at 2. Ring each number on the hundred square. Q What do you notice? Draw out that each number ends in 2. Start at 2 and count on in fives. Use a different colour and ring each number on the hundred square. Q What do you notice? Is there a pattern? Draw out that each number ends in 2 or 7. Q Will there always be a pattern when we count in 5s whatever number we start at? Collect children‟s responses. Write on the board: When I count in 5s from any number, the number always ends in one of two digits and one digit is the same as in the start number. Tell the children that this was true when we started counting from 2 as the numbers all ended in 2 or 7. Q Will it be true if we start counting on from another number? Give out Activity sheet Y2 B3. Ask the children to choose a number to count on from in fives. Ask them to record their numbers by ringing the numbers on hundred squares as you did when you started counting on in fives from 2. When they have finished discuss the patterns they have found. Q Do all the numbers end in one of two digits? Ask for some examples e.g. 3, 8, 13, 18… Point out that the last digit is either 3 or 8. Now ask the children to do the same but start with a two-digit number. When they have all finished one, discuss the patterns they have found. Q Do all the numbers end in one of two digits? Ask for some examples e.g. 11, 16, 21, 26… Point out that the last digit is either 1 or 6. If they started with an even number, ask them to find a pair who started at an odd number to see if the rule still applied and compare their answers. 6 Y2, BLOCK B, UNIT 2 Write on the board When I subtract 10 from a number the ones digit stays the same. Explain that we are going to find examples to test whether this statement is correct. Write on the board 12 – 10 = Ask the children to work out the answer. Q How did you work it out? Collect methods. Point to 12 and 2 on the hundred square and ask: Q Why does moving up one square give the answer? Check that they realise that this is the same as counting back 10 squares from 12 to 2. Show the 12 beads on the bead string and move 10 back. Draw attention to the pattern as you do so. Record 12 – 10 = 2. Q Did the ones digit stay the same? Agree that it did. Write on the board 24 – 10 = Ask the children to work out the answer. Q How did you work it out? Collect methods. Repeat the demonstration of subtracting 10 using the hundred square and bead string. Record 24 – 10 = 14. Q Did the ones digit stay the same? Ask the children to think of another calculation where subtracting 10 will give the same ones digit. Collect their suggestions. Q Do you think this will always work? Discuss the fact that we cannot test every number. Q Which numbers should we choose to test? Collect ideas such as odd numbers, even numbers, two-digit numbers, three-digit numbers, multiples of ten. Q How many of each sort of number should we try, to convince ourselves that it is true? Ask the children to try three of each, working in pairs. Write on the board It doesn‟t matter which order you add numbers together because the answer will always be the same. In pairs ask the children to show their partner examples that show this is true. They can use their whiteboards. Collect examples. Q Do you think it will always be true? Q Have we tried enough different numbers to convince us? Q Would it make any difference if we were adding with amounts of money? Give out Activity sheet Y2 B4. Ask the children to find the pairs of calculations and work out the answers. When they have finished they should share their answers with a partner and see if they all show the statement to be true. Ask them to say what kind of numbers have been used in each pair e.g. two two-digit numbers, two odd numbers. 7 Y2, BLOCK B, UNIT 2 Q What is 4 + 5? Children to show answers quickly using number fans. Q If we know 4 + 5 = 9 do we know 40 + 50? Children to discuss quickly with partners and show answers using number fans. Q How do we know 40 + 50 = 90? Children to explain that 4 tens add 5 tens makes 9 tens or 90. Q What is 20 + 40? Children to show answers quickly on number fans. Q 20 + = 60. What is the value of ? Children to show answers and explain methods. Q Using these 3 numbers can you think of any different number sentences? Children to discuss with partner and write sentences on whiteboards 60 - 20 = 40 60 - 40 = 20 Repeat using different tens values. Q What is 300 + 500? Children to discuss quickly with partners and write answers on whiteboard. Take children‟s answers and ask for methods. Children to explain that 3 hundreds add 5 hundreds makes 8 hundreds or 800. Demonstrate this practically if necessary. Q 300 + = 800. What is ? Children to write answer on whiteboard and explain methods. Repeat using different hundred values. Activities. Children to respond to selection of tens and hundreds, additions and find inverse sentences. 8 Y2, BLOCK B, UNIT 2 Q What are the first ten multiples of 3? Write a list on the board. Tell the children that when we count in threes, starting at zero, we are saying the multiples of 3. Continue the pattern further until the 20th multiple. Ask the children, in pairs, to find out whether there are any multiples of 3 that are also multiples of 4, recording any working in their books. Suggest they count in fours starting at 0 to find the multiples of 4 and write these out. Collect answers and compare working out. Q Why is 12 a multiple of 3 and 4? Show the children two bead strings. Count in threes on the first string and stop at 12. Q How many threes in 12? Agree there are four. Count in fours on the second string and stop at 12. Q How many fours in 12? Agree there are three. Record: 3 x 4 = 12, 4 x 3 = 12 Q Which is the next multiple of 3 and 4? Agree that it is 24. Check with the bead strings. Q What do you notice about the first and second of these numbers? (12 and 24) Draw out that 24 is 12 more than 12. Q What will be the next multiple of 3 and 4? Count on in fours until you reach a multiple of 3. Agree that it is 36, 12 more than 24. Q How would you find multiples of 3 that are also multiples of 2? Ask the children to work in pairs to do this up to the 20th multiple. If they finish ask them to repeat the problem with 2 and 5. 9 Y2, BLOCK B, UNIT 2 Write on the board, 3, 12, 21, 30 Q What is the next number in this sequence? How do you know? Ask the children to discuss this with a partner. Discuss with the whole class and agree that 9 is added each time. Ask the children to continue the sequence for another five terms on their whiteboards. Record the answers. Ask if the children notice any patterns. Q What do you notice about the ones digits and the tens digits? Why do you think this is happening? Draw out that we can add 9 by adding 10 and then subtracting 1 so the tens digit will increase by 1 and the units will decrease by 1 each time. Write on the board 2, 4. Q Can you predict the next number in this sequence? Draw out that it could be, e.g. 6 or 8, and agree that we need more terms to establish the rule. Write on the board 2, 4, 6. Q Can you be sure of the rule now? (Some children may say that the next term is 10 because 2 + 4 = 6, 4 + 6 = 10. If so give the next term, 8.) Q What is the rule? Agree that the rule is to add on 2 each time. Ask the children to write 2, 4, 6 and the next five numbers in the sequence in their books. Q What if the rule was the same but the start number was 1, what would the sequence be? Ask the children to record the first eight numbers in the sequence in their books. Q What do you notice about the sequence? Q How is it the same as the previous sequence? How is it different? Draw out that both sequences contain alternate numbers, but the numbers in the first sequence are all even, whereas the numbers in the second are all odd. Ask each child to think of their own rule for a sequence then write the first few numbers on their whiteboards and ask their partner to guess their rule. Q How many numbers did you need before you could work out the rule? 10 Y2, BLOCK B, UNIT 2 Draw a square on the whiteboard and say that this is a table. Q How many children can sit around it if one chair fits on each side? Draw the following: Q If we put two tables next to each other how many children can sit around them? Draw the extra table: Ask the children to work in pairs to find out how many children can sit around three tables put together side by side. Ask them to draw the tables on their whiteboards. Collect responses and agree the answer. Q How many children could sit around four tables put together? Collect answers and agree the answer. Point out that drawing the diagrams helped to give us the answer. Ask if anyone noticed a pattern in the numbers. Use the children‟s responses to draw up the following table: Number of tables Number of children sitting around 1 4 2 6 3 8 4 10 5 12 Q How many children could sit round six tables? Give out Activity sheet Y2 B5, read it and ask the children to complete it in pairs 11 Y2, BLOCK B, UNIT 2 Draw a triangle on the board. Then draw one line to make it into two triangles. For example: Q How many triangles are there now altogether? Draw out that there are three triangles altogether, because there is still the original triangle. Draw a second line to create another triangle. For example: Q How many triangles are there? Ask the children to draw this picture on their whiteboards and to discuss this with their partners. Take feedback and agree that there are five. Use Resource sheets Y2 B6, Y2 B7 and Y2 B8 to show the triangles cut up and put on top of each other to convince them that there are five triangles altogether. Give out Resource sheet Y2 B9. Ask the children, in pairs, to solve the problem. Ask each pair to join with another pair to discuss their methods of working this out. Collect the answers. Discuss setting about the problem systematically. Encourage the children to draw the shape on their whiteboards in the same way as you did above. Q Where would you start to count the triangles? Q Is there a pattern? Draw out that there are 9 triangles. 1 3 6 9 Ask the children to complete question 2 on the Resource Sheet Y2 B9 in pairs. Ask each pair to join with another pair to discuss their methods of working this out. Collect answers. Point out the steps 1 3 9 16 12 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B1 13 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B2 14 Y2, BLOCK B, UNIT 2 ACTIVITY SHEET Y2 B3 15 Y2, BLOCK B, UNIT 2 ACTIVITY SHEET Y2 B4 16 Y2, BLOCK B, UNIT 2 ACTIVITY SHEET Y2 B5 17 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B6 18 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B7 19 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B8 20 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B9 21 Y2, BLOCK B, UNIT 2 BLOCK B - YEAR 2 UNIT 2 Solve problems involving addition, subtraction, multiplication or division in contexts of numbers, measures or pounds and pence (Objective repeated in Blocks B & D Units 1, 2 & 3 and Block E Unit 2) Display large money – coins to 50p – and ask children to identify them. Q: What different coins can you see? Who can tell me what the value of this coin is? Draw attention to the value written on the coins whilst saying the value clearly. Ask children to identify the coin with the smallest value, then the next highest value – so ordering the coins and displaying them on the board with their value written underneath. Ask the children to discuss in pairs which coins they might choose that would have the same value as the 10p coin. Children could choose coins from small money trays and write their selection on a whiteboard and then share the different equivalents with the class. Repeat with 20p and 50p coins. Q: Which coins have you chosen that together total 10p/20p/50p? Direct attention to a `shop/stall‟ pre-arranged with a selection of toys for sale – items up to 50p. Choose a child to be the shopkeeper and one to choose a toy from the stall to buy. Identify the price on the tag and ask children in pairs again to find the right coins they would need to pay for the item. Discuss the different combinations and show on board. Ask children to explain how they decided on which coins to pick. Q: What coins would I need to buy this toy? Choose one of the items and say this time you want them to try and find the fewest number of coins that they would need to be able to pay for it. Check understanding of language `fewest` by referring to the different combinations of coins on the board and showing, for example, the fewest number of coins for the price tag 27p would be 20p, 5p and 2p. Repeat with other items in the shop – below 50p and one above 50p but less than £1 Revise ordering coins and show £ coin. What is the value of this coin? How many pennies equal £1? Teacher chooses coins from the large money and displays them grouped randomly. 50p, 10p, 5p, 2p, 1p, Children work out the total value of the coins and show on whiteboards. How did you count up the value of the coins? Which coins did you add together first? Teacher reinforces correct answer by counting up and then showing the amount written on board. Repeat for a few totals, both under and over £1 Use „shop‟ with a selection of different items clearly labelled with large price tags – both under and over £1 – and explain to children that you (or a hand puppet/class toy) have 86p and that you would like to buy a certain two items from the shop but you are not sure if you have enough money. Can they help out? Children work in pairs to total the two items. How did you know I had enough money/not enough money? Did anyone find the cost of the two items in a different way? Repeat with different items as appropriate. Ask one of the children to come up and choose an item from the shop that costs less than 10p. (stock the shop with small items like rubbers, pencils etc.) Choose another child and give him/her 25p Explain that you want the children to work out how many of that item can be bought for the 25p. Allow time for the children to work on the problem using whiteboards. Then take answers. How many ________ could you buy? How did you calculate how many you could buy? How much money would s/he have left over? Draw the children‟s attention to the link between repeated addition and multiplication and their knowledge of the multiplication tables. Highlight fact that they are finding out how many groups of 6p/7p/8p/etc. there are in any total amount they have to spend. 22 Y2, BLOCK B, UNIT 2 Show the different methods on board and discuss. Ask the children how much money they would have left over or the amount of change they would have. How do you know how much change there was? What kind of calculation would you need to do to find out what change s/he would have? Draw a number line on board to show counting on to find out how much money would be left over. Repeat with other small items from the shop and different totals up to £1 Encourage children to make links between the totals and what they find out – for example 3 pencils costing 8p could be bought with 25p with 1p change, so 6 pencils could be bought for 50p with 2p change. Show £2 coin. Who can tell me the value of this coin? If 100 pennies equal £1, how many pennies will be equal to this coin? How many 10 pence pieces would make £2? Explain you are going to give them some larger amounts to total. Display randomly grouped large money coins. E.g. £2 coin, £1 coin, 50p coin, 2x 20p coins, 3x 1p coins Children work in pairs to find totals and show on whiteboards. Which coins did you add up first? Does anyone have a different way? Ask volunteers to write the amounts correctly on board. Include one total where the children have to use zero place holder in tens column. Next, show a simple problem written on card (resource sheet Y2 B10) Which operation do we need to use to solve this problem? Which words tell you it is an addition? Elicit addition and ask children to solve the problem and find a way of recording what they do on paper/whiteboard. Take one way of calculating the answer and put on the board. 7p + 12p + 19p = If we want to be absolutely sure of our answer we need to find a way of checking our work. What different ways are there of doing this calculation? Could we use any of these ways to check our answer? Elicit that we can do this by calculating in an alternative way – take children‟s alternative ways of mentally totalling the prices whilst looking at the calculation written on board. Next write the calculation in a different order. 19p + 7p + 12p = Ask the children if they think the answer will stay the same. Demonstrate that the total is the same and highlight the fact that changing the order of the numbers to be added will not affect the answer. Set the children differentiated problems to work on in small groups explaining that they should read the problem and decide on the appropriate operation, perform the calculation and check their method 23 Y2, BLOCK B, UNIT 2 Set the class a problem (resource sheet Y2 B11). One of the children is going to have a small birthday party and seven friends are to attend. Choose children in the class or toys/book characters etc. Explain you want them to work in pairs to choose the appropriate operation and record their working out and answer in any way they like on the whiteboard. Discuss the different ways of recording. 7 x 5p = 35p 7 lots of 5p is 35p 5p+5p+5p+5p+5p+5p+5p=35p Revise the link between multiplication and repeated addition. Demonstrate using groups of pennies the different methods. Ask the children if they think the answer will be the same if the calculation is set out: - 5p x 7 = Show that it is the same. Highlight the fact that they are able to check using a related method. Give the children second problem from resource sheet Y2 B12. As before ask them to discuss with a partner the best way to solve the problem and to record in any way they like. How did you solve the problem? What operation did you choose? Which words told you which operation to choose? How did you calculate the answer? Take examples of the different ways of recording and show on board. Value all jottings/pictures as well as any formal calculations. Elicit from children that they were dividing the original sum of money up fairly so that each child could buy a required number of the item. Demonstrate using coins both grouping and sharing. First demonstrate with a child taking groups of 5p away from the amount and then seeing how many groups you have and so how many items could be bought. Second demonstrate sharing the money out equally between the number of friends. Discuss and make links between division and multiplication/repeated addition as a way to check work. Write on the board 2 + 7 = 9 On a 100 square, ring 2, draw an arrow to 9 and write + 7 above the arrow. +7 1 2 3 4 5 6 7 8 9 10 Q What is 12 + 7? What is 22 + 7? Record each calculation on a number square as above. Q What do you think 72 + 7 is? Why? Q 2 + 7 = 9 so what is 9 – 7? Determine the answer and record on number square as above. (Ring 9, draw an arrow to 2 and write −7 above the arrow.) Q What is 19 − 7? 29 – 7? 39 – 7? Record each calculation on a 100 square as above. Q So what is 89 – 7? How do you know? Q What is 20 + 70? How do you know? 20 is 2 tens and 70 is 7 tens, how many tens altogether? Explain that it is 2 tens plus 7 tens which total 9 tens and 9 tens are 90. Q What is 200 + 700? Establish that it is 2 hundreds plus 7 hundreds which is 9 hundreds. Q What is 2000 + 7000? 2 000 000 + 7 000 000? Write on the board: 3 + 6 = 9 and ask children to write this number sentence in their books. Now write 13 + 6 = 9 and ask them to write this. 24 Y2, BLOCK B, UNIT 2 Q What are the next two in the pattern? Check that they are correct. Now ask them to complete the sentence 53 + 6 = .ٱ Now write 9 – 6 = 3, 19 – 6 = 13 and ask them to write these two and the next two number sentences. Check that they are correct. Now ask them to complete the sentence 79 – 6 = .ٱ Q What is 90 – 60? 900 – 600? 9000 – 6000? 9 000 000 – 6 000 000? Write 2 + 5 = 7 and 7 – 5 = 2 on the board and ask children to use these to generate other number sentences. They should record them in their books. Show a toy with a £2.21 price tag. Q How many pounds and how many pennies does this toy cost? Establish that the toy costs two pounds and twenty-one pennies. Draw attention to the £ sign and the decimal point and the fact that we don‟t use the p sign as well. Q What coin or coins could we use to make £2? What coins could we use to make 21p? Use the large coins to show different ways of making the amounts, e.g. a £2 coin, two £1 coins, a 20p, two 10p coins and 1 penny. Establish that one way is to use two £1 coins, two 10p coins and one penny. Record this as: £1 10p 1p £1 10p Repeat for other prices e.g. £3.42 and £4.13, drawing out using £ coins, 10p coins and pennies as one way to make the amounts and recording these as above. Show a price tag of £3.05. Q How many £1 coins would we use? 10p coins? 1p coins? Establish that there are no 10p coins, and we write a zero in this place. Write £5.09 and £5.90 on the board. Q Which is more? Why? Draw out the explanation that £5.90 is 5 pounds and 90 pence and £5.09 is 5 pounds and 9 pence. Show the two amounts with the large coins and record as above. Show the top part of OHT Y2 B14. Q I have 68p. I spend 30p. How much have I got left? Q Which operation do you need to use? How did you know? Did any of the words help you decide which operation to use? Ring the operation on OHT Y2 B14. Show OHT Y2 B15. Ask the children to work in pairs to find the answer and write it on their whiteboards. Q How did you work it out? Show the two ways on OHT Y2 B15 and explain them. Ask if any of them worked it out like that, or if they used another way. Model the recording of any other efficient methods. Show the calculation using large coins. Record the number sentence 68p – 30p = 38p. Repeat using OHT Y2 B16. Q Which operation do you need to use? How did you know? Did any words help? Ring the operation and then write the calculation £2.40 + £3.20 on OHT Y2 B16. Ask children to work in pairs to find the answer and write it on their whiteboards. Encourage the use of the jottings to explain how they got the answer. Gather some explanations, show the recording of them on OHT Y2 B15 and explain it. Model the recording of any other efficient methods you can see on their whiteboards. Show the calculation using large coins and then record the number sentence. Give out a sheet of appropriate word problems. Ask the children to work in pairs, ring the operation, write the calculation, record any jottings as you did on OHTs Y2 B14 and Y2 B16 and write the complete number sentence. After most children have completed the first two questions, share children‟s use of using jottings to help their calculations and then ask them to continue. 25 Y2, BLOCK B, UNIT 2 Write question on board: Every day at break Sam has 5 grapes for his snack. How many grapes does he eat at school during the week? Q What calculation do we need to do? Establish that Sam eats grapes on Monday, Tuesday, Wednesday, Thursday and Friday. Q How many days does he eat grapes? Explain it is 5 days. Q How many grapes does he eat each day? Explain it is 5. Q So how can we work out 5 lots of 5? Discuss 5 + 5 + 5 + 5 + 5 = 25 Q Do you know another way to write this? Explain it can be written as 5 lots of 5. Q Do we know a sign that represents lots of? Discuss the x sign and what it means. Write up vocabulary related to x eg lots of, groups of, multiply, times. Q How do we work out 5 x 5? Represent 5 x 5 as an array, using grapes 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Explain by adding 5 + 5 + 5 + 5 + 5 or we could use the 5 times table and count up in 5‟s. Q So how many grapes does Sam eat during a week at school? Establish answer is 25 grapes. Discuss methods used. Children make up own problems involving the vocabulary of x and show answer using array of repeated addition. Start with question. Q How many wheels are there on 3 cars? Q What calculation do we need to do? Discuss with partner and take responses, 4 x 3 or 3 x 4 Q Are these the same? Do they give the same answer? Discuss they are the same and prove drawing 2 arrays xxxx xxx xxxx xxx xxxx xxx xxx Q How do we work out 4 x 3? Children talk to partner and explain methods, ie 4 + 4 + 4, using an array, counting up in 4‟s 3 times or 3 + 3 + 3 + 3, counting up in 3‟s 4 times. Write 6 x 2 = Q What could be the possible question to go with this calculation? Discuss in pairs, take responses. Model how to work it out using repeated + and arrays. Children given multiplications with to represent answer, which they invent own questions for. Show working in arrays and repeated +. 26 Y2, BLOCK B, UNIT 2 Q. I think of a number then double it. My answer is 18. What is my number? Ask the children to discuss with their partners how to solve this problem, then share their ideas with the rest of the class. Q. What is the calculation we need to solve? x 2 = 18 Ask children to explain methods to find the answer. e.g. use an array or knowing double 9 is 18. Q. Two people have 8 cakes each. How many cakes altogether? One person gives 2 cakes to the other person. How many cakes does each have now? Ask the children to discuss how they will solve this problem and to share their methods. Establish that there are two parts to this problem: How many cakes altogether? How many cakes will each person have at the end? The calculations are: Double 8 = 16 8 - 2 = 6 8 + 2 = 10 Work through this problem with the children. Children to devise 2 step problems involving multiplication and addition and then produce an answer sheet showing the calculations and the answers. Set out large money coins and revise their values with the class What is the name of this coin? What is the value of this coin? How much is this coin worth? How many 10p coins are equal to this coin? How many 2p coins would be equal to this coin? Show the class different amounts of money and ask them to work in pairs to find an equivalent sum of money using different coins – for example, show 50p and the children find small coins that make 50p then record the coins they have chosen on their whiteboards. Discuss and show some of the different combinations. To vary this activity, ask them to match the value of the amount you show them using the fewest coins possible or tell them they must try and match the value without using a specific coin such as no 20p coins allowed. Set up a very simple „café‟ area – couple of chairs, table, plates, etc. Have a large poster price list and show the children the café menu. Ask questions. What is the price of a cup of coffee? What would you pay for 2 ice creams? How much is it for a portion of chips? Ask a child to sit at the café table and decide on two/three items to order. The class make a note of the price of each item and then mentally find a way of doing the addition to find the total. Discuss what strategies they used – doubling for two of the same items, using known facts, adding the tens first etc. Children can go on to differentiated activities finding totals and using the café menu and bill sheet. 27 Y2, BLOCK B, UNIT 2 Set up a very simple „café‟ area – couple of chairs, table, plates, etc. Have a large poster price list and show the children the café menu. Choose a child to be the waiter and a couple of children to go to the café and order something simple each – e.g. one thing to eat, one drink.. Explain that you want the class to help the waiter to total the prices so that s/he can present the bill. Children use mental addition strategies to total the bill. Share and discuss their methods. What did you add together first? What do you know about these numbers that might help you? The „waiter‟ then gives correct bill to the „customers‟ Repeat with a few different children. Today they are to imagine that they have enough money but not the exact amount. Make a list of prices and total, under £1 – give one of the children a one pound coin. Has s/he got enough to pay this bill? What will the waiter have to work out? Establish the idea of giving back change. What calculation will the waiter do to find the change? What do we call this operation? Establish that we are subtracting the total for the items from the £1 and what is left will be the change. Ask the children how many pennies equal £1 and establish 100. Draw a number line on the board labelled 0 to 100 Where do you think I should put a mark on this number line to show how much the bill came to? Take estimates and discuss where the line should be marked. Model counting on in different steps to the 100 mark and find the amount of change due. Start with totals that are multiples of 10, then multiples of 5 moving to other totals. If necessary, demonstrate the number line using actual money. Children can work in differentiated groups finding totals and giving change. Using a price list from the cafe ask the children to find a way of working out what several of one item would cost. If a chocolate biscuit costs 5p, how much would 10 biscuits cost? Can you show me the right money to pay for 7 cakes at 4p each? How much will 8 ice lollies cost? Discuss the ways that children found the answers and make links to the multiplication tables that they know and „multiples of‟ using number square etc. Repeat for different items in the café. Set out a selection of toys/puppets and a teddy bear that the children are familiar with and explain that it is teddy‟s birthday and he has invited 9 friends along to the café to have a special birthday tea (extra items could be priced on a separate price list if necessary). Outline the food and drinks/party hats etc. that are ordered – e.g. three chocolate biscuits each, one balloon each, 5 coca colas and five lemonades and so. Explain to the class that this is going to be a much larger bill than the previous ones and that they are all going to work together to find the total. Divide the children into groups and allocate each specific items to find the cost of such as, all of the drinks, cakes and biscuits. They are to work on finding the totals – checking with other pairs in the group the answer is correct and recording their answer in a number sentence using mathematical signs. 28 Y2, BLOCK B, UNIT 2 Show the children a selection of small sweets and lollies. Put a card by each to clearly show the prices – a selection of prices up to 10p. What is the price of this sweet? Which coin/s could I use to pay for it? How much would I need to buy one for each of teddy‟s guests? If each toy at the party got 3 lollies, how much money would I need to pay for them? Can you find the coins? Discuss with children how they find the totals and make links to the multiplication used to solve the problem on day three. Ask the children to work out how much change they would receive if they paid one of the prices using a 20p/50p/£1 coin. Revisit using the number line to count on. Next, explain that as part of the birthday celebrations the group of friends are going to the fair/a theme park etc and show cards that state the price of entry and various rides. Keep the prices in whole £s and none more than £10. Repeat questions How much would it cost them all to get into the theme park? Can you give me the right money to buy each toy a burger? How much change would you get from a £10/£20 note? How did you find the total? Investigate finding the totals and working out the necessary change. Children can find the correct money or „pay‟ using a note and another child give change Which is less 36 or 63? Children to show answer using number fans. Ask one child to indicate where these numbers are on number line and show which is less. Q Give me a number between 36 and 63 Children to show answers using number fans. Ask selection of children to indicate where their numbers are on number line and check they come between 36 and 63. Q What even numbers lie between 36 and 63? Children to talk to partner and then show number on number fans. Q If Ali has 16 pens and Ben has 22 pens who has more pens? Children to talk to partner and then write answer on whiteboard. Q How many more pens does Ben have? Children to discuss again with a partner and write calculation on whiteboard. Ask some children to explain how they found the answer. How did they decide on the calculation? Children to answer questions on problem sheet and then devise own problems giving solutions. 29 Y2, BLOCK B, UNIT 2 Write this number problem on the board 51 + + = 100 Using number lines or squares children to suggest solutions. Take responses and check on number line. Q 33 + + = 70 Children to talk to partners and use apparatus to find solutions. Write answers on whiteboards. Choose some children to demonstrate methods and answers for rest of class. Ask the children to help you solve a problem. Q I have 17 red crayons, 19 blue crayons and 12 yellow. How many crayons do I have altogether? Ask children to talk to their partners and decide how to solve this problem. Q What sort of calculation do we need? Take responses - children should suggest addition. Q How do we know it is an addition calculation? Children should know that altogether implies addition. If this is not suggested - explain. Ask the children to explain how they would do calculation. Get children to demonstrate using number lines, number squares or partitioning 17 + 19 + 12 (10 + 7) + (10 + 9) + (10 + 2) = 30 + 9 + 9 = 48 Children to choose 3 of these numbers 14, 15, 16, 19. How many different totals can they make? I have £14. I am given another £9. How much do I have now? With partners children to discuss calculation and show answer using fans. Discuss methods. Repeat for these questions. Q A pear costs 15p more than an apple. An apple costs 12p. What does a pear cost? Q Patrick bought 3 choc bars at 15p each. How much change did he get from 50p? Discuss methods in both cases and provide apparatus for children eg number lines, squares, rods, whiteboards. Q How many different ways can you make 50p using only silver coins? Children to spend some time in groups investigating different ways to make 50p using silver money and recording. Bring class back together and discuss solutions. 50p 20p + 20p + 10p 20p + 20p + 5p + 5p 20 + 10 + 10 + 10 Look at ways to ensure finding all answers by being systematic. Children to investigate. Joe has 3 20p and 2 15p stamps. What values can he make using 1 or more of the stamps. 30 Y2, BLOCK B, UNIT 2 I have 8 ribbons and I want to share them between Jo and Nicola. (Substitute names of 2 children in class). Show the children the ribbons and ask another child to come out and share the ribbons between the 2 children. When each child has 4 ribbons each show the children how to write the calculation 82=4 8 shared between 2 gives 4. Q I have 9 sweets to share between 3 friends. How many do they get? Ask children to work with a partner using whiteboards and multilink to write the calculation and find the answer. Work through calculation together and check answers. We know that (division sign) can mean sharing but it can also be used for grouping - or repeated subtraction. Q There are 18 apples in the box. How many bags, each with 3 apples, can be filled? Do this question practically with the children using balls or multilink to represent the apples. Explain that this can be written as 18 3 = 6 Q How many sticks of 4 cubes can you make from a stick of 20 cubes? Children to work with partners using multilink to solve problem and writing calculation on whiteboards. Discuss methods and answers. Children to work with a partner to write a sharing problem and a grouping problem and to solve problem. Swap problems with another group and solve. Remind children about the difference between grouping and sharing. Q 24 = 6 With partners children to discuss method and then share with rest of class. Ask 2 children to demonstrate different methods. Having found 24 4 = 6 explain that we can check this answer using another calculation. Ask children for any suggestions. Remind children that when checking subtraction they could use addition. When checking division can use multiplication. Q What calculation could we use to check 24 4 = 6 Children to talk to partners and suggest 4 x 6 = 24 or 6 x 4 = 24 Resource sheet Y2 B19 then check answers using multiplication. 31 Y2, BLOCK B, UNIT 2 Explain that in this lesson you will use or to stand for an unknown number - the challenge is to discover what the number is. The children need to be detectives! Q + 4 = 20. What is ? Something add 4 equals 20. Ask the children what the square represents and what method they used to work this out. Discuss methods - using number line to count on from 4 or number square or using inverse 20 - 4 = Stress that we have only one answer for this question. Q + = 20. What are and ? Children to talk with their partners and write 2 numbers on whiteboard. Ask several children for answers and list on board. Q What have we found out about this question? Children explain that there are several answers to this question. Q Why can we have more than one answer? Ask children for suggestions then explain we have two unknown numbers in this problem so they can keep changing but giving the right answer - as one gets more the other gets less. In pairs find all the answers to + = 20 and + + = 20 Try to ensure that the children find all the answers by working systematically Q I have £1.50 and I find 20p - how much do I have altogether? Children to talk to partners to decide on calculation. Take responses. £1.50 + 20p Q How did they know to add these together? Children explain „altogether‟ implies adding amounts together. Q How could we make this calculation easier? Again children to discuss and suggest turning £1.50 into pence. Q What is calculation now? 150p + 20p Children to show answers using money fans or whiteboards. Get children to explain methods of working out answer eg partitioning. Q How many ways can I make £1.00 using only 10p, 20p or 50p? Children to work with partner to find solution. 50p + 50p 50p + 20p + 20p + 10p 50p + 20p + 10p + 10p + 10p 50p + 10p + 10p + 10p + 10p + 10p etc As class work through this solution systematically showing how to make sure we find all the answers. Investigate - you have £5.00, toys are priced at £1.20, £1.80, £1.60, £1.40, £2.20 and £2.70. Which 3 could you buy. Find all the solutions. 32 Y2, BLOCK B, UNIT 2 Set out large money coins and revise their values with the class What is the name of this coin? What is the value of this coin? How much is this coin worth? How many 10p coins are equal to this coin? How many 20p coins would be equal to this coin? Show the class different amounts of money. Ask them to work in pairs to find an equivalent sum of money using different coins – for example, show 50p.The children find small coins that make 50p then record the coins they have chosen on their whiteboards. Discuss and show some of the different combinations. To vary this activity, ask them to match the value of the amount you show them using the fewest coins possible or tell them they must try and match the value without using a specific coin such as no 20p coins allowed. Introduce Post Office resources to the children. Read together prices labelled on the items and ask children appropriate questions such as What is the price of a stamp? What would you pay for 2 birthday cards? How much is it for an envelope? Ask a child to decide on two/three items to buy. The class make a note of the price of each item and then mentally find a way of doing the addition to find the total. Discuss what strategies they used – doubling for two of the same items, using known facts, adding the tens first etc. Ask the children: Can you find the exact coins to match a total? What coins would you use to pay the bill? Can anyone show me a different way of using the coins to match the total? Children can go on to differentiated activities finding totals and choosing the correct amount of money from the “money pots”. Choose a child to be the post office master and a couple of children to go to the post office to buy two items. Explain that you want the class to help the post office master to total the prices so that s/he can present the bill. Children use mental addition strategies to total the bill. Share and discuss their methods making links with previous day. What did you add together first? What do you know about these numbers that might help you? The post office master then gives correct bill to the „customers‟ Repeat with a few different children. They are to imagine that they have enough money but not the exact amount. Use one of the previous totals as an example - under £1 – and give one of the children a one pound coin. Has s/he got enough to pay this bill? What will the post office master have to work out? Establish the idea of giving back change. What calculation will the post office master do to find the change? What do we call this operation? Establish that we are subtracting the total for the items from the £1 and what is left will be the change. Ask the children how many pennies equal £1 and establish 100. Draw a number line on the board labelled 0 to 100 Where do you think I should put a mark on this number line to show how much the bill came to? Take estimates and discuss where the line should be marked. Model counting on in different steps to the 100 mark and find the amount of change due. Start with totals that are multiples of 10, then multiples of 5 moving to other totals. If necessary, demonstrate the number line using actual money. Children can work in differentiated groups finding totals and giving change. 33 Y2, BLOCK B, UNIT 2 Using Post Office Resources ask the children to find a way of working out what several of one item would cost. If a stamp costs 7p, how much would 10 stamps cost? Can you show me the right money to pay for 7 envelopes at 5p each? How much will 8 cards cost? Discuss the ways that children found the answers and make links to the multiplication tables that they know and „multiples of‟ using number square etc. Repeat for different items in the Post Office. Q. Can you show me the exact coins to pay for the 10 stamps? Accept several examples and then tell the children that they have to: Q. Show the exact amount using the least number of coins. Allow the children time to solve this problem in pairs. Establish that the least number of coins to show 70p would be 2 coins. Then ask the children Q. Can you show 70p using 4 coins? There is more than one possible correct answer Collect children‟s answers and confirm both possible solutions have been found. Q. Can you show 70p using 5 coins? Is there more than one correct answer? Collect children‟s answers and confirm both possible solutions have been found. Q. Can you show 70p using 6 coins? Is there more than one correct answer? Ask the children to work out how much change they would receive if they paid one of the prices calculated earlier using a £1 coin. Repeat for different items in the Post Office. Show the children a selection of items from the post office. Put a price card by each item to show the prices. Ask the children to work out how much change they would receive if they paid one of the prices using a 20p/50p/£1 coin. Revisit using the number line to count on. Discuss with children how they find the totals and make links to the multiplication. Put an amount on the board e.g. 50p. Ask the children questions such as: If a birthday card costs 15p, how many cards can I buy with 50p. How much change would I receive? Work through the problem as a class. Model the appropriate calculations on the whiteboard. 15p x 3 = 45p. Count on from 45 to 50 on the number line to find the difference. Repeat using £1. E.g. If a birthday card costs 15p, how many cards can I buy with 50p. How much change would I receive? Repeat using different examples. 34 Y2, BLOCK B, UNIT 2 Show OHT Y2 B20. Read the first question through together. Ask the children which operation they would need to solve the problem and to show this operation on their whiteboards. Ask them to discuss with their partner how they decided which operation they needed. Q How do you decide which operation to use? Agree that the words „another‟ and „how much now‟ suggest addition. Underline these words on the OHT. Ask the children to write the calculation for this problem: 13 + 5. Ask the children to decide with their partner which words in the second problem tell us which operation is needed. Collect answers and underline the words. Ask the children to write the calculation needed on their whiteboards, i.e. 13 – 5. Repeat for question 3. Draw attention to the two calculations needed: £3.50 + £2.50 and £10.00 £6.00 (or £10.00 – £3.50 and £6.50 – £2.50). Ask the children to write the calculations needed for the other questions with a partner and then to make up a question of their own. Ask the children to choose two of the questions and work out the answers to them. Display the „Seaside Shop‟ resource sheets (Resource sheets Y2 B21 and Y2 B22) or set out a selection of similar, real items and add appropriate price labels. Ask questions such as: If I bought a sun hat how much would I pay? Which costs more, a kite or a ball? How much more does a towel cost than a fishing net? What would I have to pay to buy a beach chair? Does anything cost more than 50p but less than £1? Ask the children to talk in pairs to agree similar questions they could ask or statements they could make using the price information. Encourage the use of a range of vocabulary. Share ideas. Ask a child to choose 2/3 items to buy from the shop. Ask: How much will (s)he have to pay to buy these items? Can you explain how you worked out the total cost? What coins could (s)he use to pay the exact amount? Children work in pairs to find answer and record their methods on whiteboards. Discuss strategies used e.g. known facts, adding tens first, doubling etc. Compare methods to see if some are more efficient and discuss how we can check our answers by doing the addition in another order. Agree that there are different ways to pay and find which uses the fewest coins. Repeat Children could work in differentiated groups to find totals of sets of items appropriately priced. or Give groups of children sets of cards made from the resource sheets, differentiated by the prices used. Place the cards face down on the table. Each pair chooses 2/3 cards and calculates the total cost of the items chosen, recording their methods. The pair that has the highest total scores a point. Replace cards and repeat. Display the Seaside Shop resources. (Resource Sheet Y2 B21 and Y2 B22) Give a child a £2 coin. Ask him/her to choose 2 items from the shop. Ask: If he/she buys these items and pays with a £2 coin how can we work out how much change he/she will get? Allow time to discuss how we can solve this problem. Establish that there are two steps to this problem: Finding the total cost of items and Calculating the change Ask: Which number operation do we use to find the total cost? Which number operation do we need to find the change? Agree that we use addition to find the total cost and discuss children‟s methods. 35 Y2, BLOCK B, UNIT 2 Establish that we need to subtract the total for the two items from £2 and what is left will be the change. Ask how many pennies equal £2 and establish 200. Write the subtraction e.g. 200p – 125p = Draw a number line on the board labelled 0 to 200. Mark on the total cost of the items e.g. 125p Model counting on to 200 using appropriate steps to find the amount of change due. Explain that you are subtracting by counting up. Use coins to show how a shopkeeper might count up to give change to a customer. Repeat Children can work in differentiated groups finding totals and giving change from different amounts as appropriate. Emphasise the importance of recording how each step of the problem was worked out. Use a selection of the seaside shop resources priced appropriately. Ask: If I want to buy more than one of the same item, how could I work out the total cost? How much would I pay for 6 ice creams if the price for one is 5p? What would be the total cost of 7 fishing nets at 10p each? Discuss children‟s methods for finding answers. Remind them of the multiplication tables they know and the link between multiplication and repeated addition. Record number sentences. Ask similar questions for children to respond to by recording their methods on their whiteboards. Tell the children ice creams cost 5p and drinks cost 3p. Ask: If I have 30p to spend how many drinks and ice creams could I buy? Prompt thinking by asking: If I bought just ice creams how many could I buy? How do you know? If I bought just drinks how many could I buy? How do you know? What if I buy some ice creams and some drinks, how many of each could I buy? Would I have any change? Model one or two solutions and how to record them. Allow time and paired working to find more solutions. Provide lots of 3p / 5p price labels using Resource sheet Y2 B23. Encourage children to record any solutions they find. Support as necessary. Take feedback and model some solutions and recording methods in a mini plenary. Children continue to work on finding solutions. More able could be encouraged to work systematically or to investigate other amounts. Less able could find cost of one drink, two drinks, three drinks etc. Today the children are going to solve some problems. What do we need to find out? What is the important information here? What operation do we need to use? How did you find the answer? What did you do first? How can we write a number sentence for that calculation? One of the problem solving approach resource sheets (Resource sheets Y2 B24 AND Y2 B25) could be used to focus children on how they solve problems. Show the class a problem from Resource sheet Y2 B25a. Read then solve the problem together using the prompt questions from the problem solving approach. Choose a suggested approach to the problem and model how to record the workings using number sentences or an empty number line. Ask if anyone can suggest a way to check the answer. Repeat the process with another problem, identifying the important information and choosing the appropriate number operation. Children could work on sets of word problems differentiated by the numbers involved, the number of steps required and/or the range of operations involved. Remind children of the problem solving approach (using Resource sheet Y2 B24 or Y2 B25). Show the children the table of train ticket prices on Resource sheet Y2 B26 (Change prices as appropriate for class).Tell them they are going to solve problems using the information in the table. Check that they understand the table: How much is a child‟s single ticket? What is the price of an adult return ticket? Or Tell me something I can find out from this table? Ask questions: How much does it cost for one adult and one child to buy return tickets to the seaside? 36 Y2, BLOCK B, UNIT 2 How much change would I get from £5 if I bought a child‟s single ticket? How much would it cost for 4 adult return tickets? How many children‟s single tickets could I buy with a £10 note? How many return tickets? If I buy single tickets for 1 adult and 2 children how much change will I get from £10? Ensure questions asked include all number operations and some involve more than one step. Focus discussions on how to identify the number operation(s) and steps required. Give the children a small set of word problems to sort according to the number operation needed to solve them. Which number operation do you need to solve each problem? How do you decide which number operation you need? Give children time to sort the problems. Work with groups as appropriate to help them identify the number operations. Discuss how we know which number operations are needed. Ask children to solve some of problems after they have sorted them. Some could work on a restricted range of operations; others could be given problems that involve more than one operation. What we do during the day; get up; get washed and dressed, go to school; have break; have lunch etc. Q How many seconds in a minute? Look at the minute hand of the clock and count to 60. Q. What kind of things does it take a minute to do? Give children one minute to carry out tasks e.g. read for one minute, write for one minute, talk for one minute . Q. What kind of tasks does it take 2 minutes to do? Children work with a partner; estimate how long you think it takes for your partner to do a task. If appropriate, then time the task to see how near your estimate is (See Resource sheet. Y2 B27) Some tasks can only be timed when appropriate e.g. lining up or running in P.E. This will encourage children to use measurement of time in all areas of the curriculum. Encourage children to think of their own tasks. 37 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B10 38 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B11 39 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B12 40 Y2, BLOCK B, UNIT 2 OHT Y2 B14 I have 68p, I spend 30p How much have I got left? + - x 41 Y2, BLOCK B, UNIT 2 OHT Y2 B15 68p – 30p = 42 Y2, BLOCK B, UNIT 2 OHT Y2 B16 I have £2.40 I save £3.20 How much have I got altogether? + -x 43 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B19 25 =5 15 3 = 10 = 4 27 =9 20 = 10 5=6 50 5 = 4=2 44 Y2, BLOCK B, UNIT 2 OHT Y2 B20 1. I win 13p at the fair. I find another 5p. How much do I now have? 2. I have 13 sweets. I eat 5. How many sweets do I have left? 3. I spend £3.50 on books and £2.50 on sweets. I have £10. How much change do I get? 45 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B21 46 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B22 47 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B23 48 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B24 49 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B25 50 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B25a 51 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B26 52 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B27 53 Y2, BLOCK B, UNIT 2 BLOCK B - YEAR 2 UNIT 2 KNOWING AND USING NUMBER FACTS Derive and recall all addition and subtraction facts for each number to at least 10, all pairs with totals to 20 and all pairs of multiples of 10 with totals up to 100 (Objectives repeated in Block B Units 1, 2 & 3) Q What is 6 + 7 =? Children to talk to partners and show answers using number fans. Q How did you work out the answer? Children to explain their methods. Explain that it is always easier to add something to 10 so we need to partition these numbers so we can make a 10. Q How could we do this? Take responses from children. Explain we need to split the 7 into 4 and 3 to give us 6 + 4 + 3 = Q Do we have a number bond to 10? 6 + 4 = 10 Therefore 10 + 3 = 13. Explain we can use this method with bigger numbers. Q What is 16 + 7? Ask children to talk to their partners about how they would do this calculation. Take children‟s responses and model 16 + 7 16 + 4 + 3 20 + 3 = 23 Q Why is it easier to add to 20? Take children‟s responses and then explain that as 20 is a multiple of 10 it makes it easier to add another number to. Q What do we mean by a multiple? Take responses – if children are unsure of this term explain that it means 20 is in the 10 times table. Children to use digit cards to add single digit to 2 digit numbers by bridging through multiples of 10. Ask a child to come out and pick two of the large digit cards. e.g. 4 and 2 Ask the children to use these cards to make a multiplication sum and write this on their whiteboards. Take responses. e.g. 4 x 2 or 2 x 4 On the board stick coloured circles to show the arrays to represent these calculations. o o o o o o o o o o o o Q. How many circles? Does it matter if we do 4 x 2 or 2 x 4? Children to realise that the answer is the same whichever way they do the multiplication. Repeat using other digit cards showing arrays and the calculations. Children to pick digit cards from the range 1 – 9 and make arrays on pegboards then write the calculations to represent the array. 54 Y2, BLOCK B, UNIT 2 Present children with groups of four numbers that they are to add in their head. Ensure that, they are within each group of numbers, there are two numbers which are familiar totals to 10, for example: 8+3+5+2 Discuss ways in which they did the addition and see if any of them chose to add 8 + 2 first and then add on the 5 + 3, or linked 3 + 5 and added 8 + (3 + 5) + 2. Give them other similar examples and encourage them to look for pairs that add to make 10 or make doubles before beginning to add. Get them to make up similar examples for each other. Have regular short, brisk pace practice sessions where children are given ten question such as 2 + 7 + 8 + 5 + 4 + 3 with at least five numbers such that some pairs total 10. Encourage children to time their responses, keep a personal record of their times and try to beat their personal best. When children can find pairs of numbers that add to make multiples of 10, they can make use of this information when adding several numbers together. For example, when adding 14 + 39 + 16 + 25 + 21, it is sensible to pair numbers: 14 39 16 25 21 30 60 90 In some particular sequence of numbers, the re-ordering strategy is useful and can provide opportunities for an investigative approach. For example: Find quick ways of answering these: 1+2+3+4+5+6=? 5 + 7 + 11 + 13 = ? 3 + 6 + 9 + 12 + 15 + 18 = ? 1 + 2 + 3 + 4 +….. + 98 + 99 = ? Use a set of number cards, making sure that there are pairs that make multiples of 10. Divide the class into groups of three and give each child a card. Ask each group to add their numbers together. Encourage them to look for pairs of numbers to link together. List all the totals on a board or projector. Q. Whose numbers give the largest projection? After each round, get each group to add all the three totals together. Check that the three totals add up to the same „grand total‟. The numbers on the cards can depend on the knowledge of the children. For example they could be: 23 30 17 52 24 8 70 16 12 30 60 140 170 50 80 You can arrange that each group gets cards that match their number skills. 55 Y2, BLOCK B, UNIT 2 Use a die marked: 1, 1, 10, 10, 100, 100 for the game „Target 500‟ with a group of children. Each player may roll it as many times as they wish, adding the score from each roll and aiming at the target of 500. They must not „overshoot‟. If they do, they go bust! For example a sequence of rolls may be: 10, 10, 1, 100, 1, 100, 100, 1, 1, 10, 100 At this point with a total of 434, a player might decide to not risk another roll (in case a 100 is rolled) and stop, or to hope for another 10. Who gets nearest to 500? Use place value cards 1 to 9, 10 to 90 and 100 to 900: 1 1 0 1 0 0 2 2 0 2 0 0 3 3 0 3 0 0 Ask the children to use the cards to make a two-digit or three-digit number by selecting the cards and placing them on top of each other. For example to make 273, the cards 2 0 0 7 0 3 Can be placed over each other to make 2 7 3 A group of three to five players, play a game using the place value cards 1 to 9, 10 to 90 and 100 to 900. Deal these 27 place value cards between the players. Give the children a set of cards containing two and three digit numbers; for example: 153 307 682 914 530 890 745 201 26 79 468 96 Place these numbers in a pile and turn them over, the top card is the target number. Player A inspects his or her own place value cards to see if he or she has any part of that number and if so places it on the table. Play continues anticlockwise round the group and player B checks to see whether he or she has another part of the number, followed by player C, D, and so on. Whoever completes the target number keeps it. Turn over next card, and repeat until the pile of target numbers is completed. Who wins the most target numbers? Use the empty number line to add or subtract two-digit numbers: e.g. 76 + 35: +10 +10 +10 +1 +1 +1 +1 +1 ~ ~ ~ ~ ~ = 111 76 86 96 106 111 or 54 – 28 -4 -4 -10 -10 = 26 26 30 34 44 54 or +10 +10 +4 +1 +1 = 26 ~ ~ 28 30 40 50 54 56 Y2, BLOCK B, UNIT 2 BLOCK B - YEAR 2 UNIT 2 Derive and recall multiplication facts for the 2, 5 and 10 times-tables and the related division facts; recognise multiples of 2, 5 and 10 (Objective repeated in Blocks B & E Units 1, 2 & 3) Give out large number cards with multiples of 5 to 50 5, 10, 15 etc. Demonstrate counting to five on one hand showing one finger at a time. When you get to five ask the child with the number 5 card to come out to the front. Continue counting to 10, 15, 20. Demonstrating counting on with your fingers each time. Each time calling a child out to the front with the appropriate multiple of 5 cards. Ask: Q. What comes next? Q. Continue up to 50. Ask: Q. What do you notice about the numbers? Q. Is any number the same? Q. Can you see a pattern? Repeat on number line jumping in 5s. Record jumps on the board. In pairs prepare a set of number cards with multiples of 5 to 50. Extend to 100 where appropriate. Deal the cards to each pair. Child with the number 5 card starts. The children place their cards in sequence. Children can record their sequence in their books Extend by asking children to count backwards. Again children can record in their books starting with 50 or 100. Using bead strings and or number line from zero children to count in tens up to 100 and back again to zero. Now using a100 square children to count in tens up to 100 and back again to zero. Ask: Q. What do you notice? Q. Can you see a pattern? Encourage children to recognise that multiples of 10 end in 0. Using the 100 square ask children to count up in fives from zero. Shade the numbers on the number square as the children count. Teachers could use ITP Number grid. Ask: Q. What do you notice? Q. What number will come next? Q. What will be the last number? Multiples of 5 end in 0 or 5. Children could have straws or similar to bundle into 10s or 5s to count. Extension: Provide children with a blank 100 square and encourage them to explore the pattern created when counting in 10s, 5s or 2s as appropriate. 57 Y2, BLOCK B, UNIT 2 Around the circle count up in 10s from zero and back again. Repeat counting in 5s and 2s. Show 10 pence coins, discuss how 10 pence is equivalent to 10, 1 penny coins. Drop 10 pence coins into a tin. Ask children to count in their head as you drop the coins. Ask the children to show the answer on their whiteboards. Repeat with 5 pence coins. Repeat with 2 pence coins. Challenge and extend children by asking: Q. How many more coins will I need to make 50p? Q. How many more coins will I need to make £1 etc. Children can complete the activity sheet Y2 B29 practising recognising multiples of 10 and 5. Children who are able to count in twos, fives and tens can use this knowledge to work out other facts such as 2 x 6, 5 x 4, 10 x 9. Show children how to hold out the appropriate number of fingers and, touching each one in turn, to count in twos, fives or tens. For 2 x 6, hold up 6 fingers. As children touch each of the six fingers in turn, they say „2, 4, 6, 8, 10, 12‟ to get the answer 12. For 5 x 4, hold up four fingers. This time say „5, 10, 15, 20‟ to get the answer 20. For 10 x 9, hold up nine fingers. Count ‟10, 20, 30, 40, 50, 60, 70, 80, 90‟ to give the answer 90. Discuss ways of grouping a number of dots in a rectangular array. For example, 12 can be represented as follows: ●●● ●●●● ●●●●●● ●●● ●●●● ●●●●●● ●●● ●●●● ●●● Children can use this idea to play this game: Player A takes a handful of counters, counts them and announces to player B how many there are. Player B then says how he or she can this into a rectangular array and then proceeds to make the array with counters. If they both agree it is correct player B gets a point. (Single line arrays are not allowed in this game.) Both players record the multiplication fact that this represents. For example, player A takes 15 counters. Player B says, „I can make three lots of five,‟ and proceeds to arrange the counters: ●●●●● ●●●●● ●●●●● They record their result as 15 = 3 x 5 or 15 = 5 x 3 Or 3 x 5 = 15 or 5 x 3 = 15 At the end of the game, discuss the numbers that could not be made into a rectangular array, ie the prime numbers. Place tracing paper over a random collection of numbers such as: 3 4 9 8 7 8 1 2 3 2 6 8 5 4 9 9 6 7 To practice recalling multiples of a given number, eg multiples of four, children write the appropraite multiple over each printed number. 12 16 36 32 28 32 4 8 12 8 24 32 20 16 36 36 24 28 How many can they do in two minutes? 58 Y2, BLOCK B, UNIT 2 Have a series of cards (related to one of the multiplaction tables) which show a multiplication on one side and the answer on the other. Children play a game on their own where they lay the cards out in front of them with either all the multiplactions or all the results showing. 1x5 5x9 4x5 9x5 5x5 5x6 2x5 6x5 7x5 3x5 10 x 5 5x7 The player touches a card, says what is on the other side and turns it over. This continues until all the cards are turned over. If the answer on the card is wrong, it has to be turned back over and another card tried. Use a rectangular array to show multiplication by 10. For example, 3 x 10 How many in each row? How many rows? How many altogether? Similarly for 3 x 20. And for 27 x 10 59 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B29 60 Y2, BLOCK B, UNIT 2 BLOCK B - YEAR 2 UNIT 2 Read and write two-digit and three-digit numbers in figures and words; describe and extend number sequences and recognise odd and even numbers (Objective repeated in Block A Units 1, 2 & 3 and Block B Unit 2) Display 100-square. Rehearse counting forwards in „twos‟, starting at 1, to at least 30. Ask a child to cover/circle the numbers as you count. Ask: Q. What do you notice about the covered numbers? Q. What would we cover next? Count back again. Ask: Q. What do we call these numbers? (Bring children‟s attention to the final digits.) Repeat starting at 1. Demonstrate the activity to the class. Put number cards from 1 – 30 in a bag. Ask for two volunteers. Decide who will be „odd‟ and who will be „even‟. Take turns to take a number card from the bag. The „odd‟ child keeps any odd numbers selected; the „even‟ child keeps any „even‟ numbers selected. The game finishes when one child has 6 cards. Change „odd and even‟ and play again. 61 Y2, BLOCK B, UNIT 2 Call out a sequence of numbers such as 21, 23, 25, 27. When you stop the children must continue. Repeat several times, varying the sequence and counting on and back. Challenge individuals and the whole class. Ask volunteers to begin the sequence for the class to continue. Peg the following numbers on the line – 4, 6, 8 and 10. Ask: Q. Which number will be next? How do you know? Encourage children to describe the sequence in their own words and discuss. Repeat for other sequences such as: 5, 10, 15 …. 32, 31, 30 …… 23, 33, 43 ….. Encourage children to extend sequences in both directions, explaining the „rule‟ each time. Demonstrate the activity. Each pair needs a set of number cards from 1 to at least 30. Children take turns to choose 3 cards to lay out in sequence. Their partner must complete the sequence by adding 2 more cards. Children check the sequence and record in their books. Examples: [ ], 8, 9, 10 [ ] [ ], [ ], 12, 14, 16 Count in tens from 0 to 50. Ask the children to write the words for 10, 20, 30, 40, 50 on their whiteboards. Check these. Write on the board sixty, seventy, eighty, ninety. Q What do you notice? Draw out that unlike twenty, thirty, forty, fifty, the numbers sixty, seventy, eighty and ninety are spelt by writing 'ty' after the number of tens. Write 77 in words on the board: seventy-seven. Ask the children to partition the number into tens and ones: 7 tens and 7 ones. Ask a child to find it on the class number line. Q Which number comes next? Ask the children to write 65 in figures and words. Ask a child to find it on the class number line. Ask which number comes next. Repeat with other numbers in this decade. Ask the children to write 52 in figures and words. Ask a child to find it on the class number line. Ask which number comes next. Repeat with other numbers in this decade. Ask the children to work in pairs. Give each pair a selection of 10 numbered cards from 0 to 100. One child picks a card and says the number and the other child writes the number in words. They also have to say which number comes next. They take turns to write and say. If they use all the cards they should make up some of their own. Q If I ask you to write ninety-seven in figures, how do you know which digits to use? 62 Y2, BLOCK B, UNIT 2 Write eighty-four and seventy-three on the board. Ask a child to write these numbers in figures. Q Which is more? How do you know? Which digit do you look at to find the larger number? Write 23 and 32 on the board. Q Which is more? How do you know? Which digit do you look at to find the larger number? Share the answers. Ask the children to discuss this in pairs and then take feedback. Show 23 and 32 using the place value cards. Demonstrate by partitioning that 32 is more because 30 is more than 20. Emphasise again that we look at the largest digit – the tens in this case – to show us that the whole number is more. Show 32 and 23 on the number line. Emphasise that we first look at the largest digit – the tens in this case – to show us that the whole number is more. Point to the numbers on the number line and show that 32 is more than 23. Q Show me a number on the number line that lies between 23 and 32. Ask the children to work in pairs to choose an odd number that is greater than 40 and less than 75, and an even number greater than 45 and less than 70. Ask them to discuss with a partner which of the two numbers is less and how they know. Share the answers. Q Which digit did you look at to find the smaller number? Give two dice to each pair of children – one marked in tens and the other in ones. Children throw both dice and then write the number they make. They then mark and label the number on an empty number line. They then throw both the dice again and write the number and mark and label it on the empty number line. They write M under the number which is more and L under the number which is less. They then mark and label a number which lies between the two numbers, e.g. 0 34 50 76 100 L M They should repeat this, sketching a new „empty number line‟ each time. Using a number line ask a volunteer to jump on from 0 in twos and record where they land with a marker pen. 0 1 2 3 4 5 6 7 8 ………. Say the numbers together, then ask Q. What pattern have we made? (Talk to „maths partner‟ before taking suggestions) Repeat with steps of 3. Count round the class – pat, pat, clap – 1, 2, 3 (on clap), 4, 5, 6 ….continue to at least 30. Using a bead string horizontally, move beads 3 at a time, counting as you go – 3, 6, 9, 12 etc. Ask a volunteer to pick out the multiples of 3 and sequence them along a washing line. Read in unison from 0-30 and back again. Ask children to close eyes and remove several multiples of 3 from the washing line. Q. Can you see what numbers are missing? Explain how you know (give children an opportunity to explain reasoning to their „maths partner‟). Give each pair a set of cards with the multiples of 3 on them. Children take turns to order the cards and turn up to 3 over whilst their partner looks away. Partner has to identify the numbers turned over. Children should play several times, shuffling the cards between each turn. Repeat ordering from 30-0. 63 Y2, BLOCK B, UNIT 2 Using a collection of objects with 4 legs or wheels etc. (mini-motors, dinosaurs or similar). Invite a volunteer to take a handful and arrange them in a line. Q. How many motors are there here? Q. How many wheels are there altogether? Q. How do you know? Spend one minute to allow children to discuss in pairs. nvite suggestions. (Encourage children to count other than in ones). Q. Did you need to count each wheel? Q. Is there a quicker way? Establish counting in 4‟s would be useful. Count around the circle in 4‟s, each child to say next 4 numbers (add actions, such as, knee, knee, click, click). Ask a volunteer to write down the last number said by each child (4, 8, 12 etc). Invite a volunteer to take a small number of cars and try counting together the number of wheels in 4‟s – repeat several times. Display multiples of 4, invite a volunteer to choose one and count back from that number in multiples of 4 to 0. Provide each pair with a collection with 4 as an attribute (at least 10 of each) e.g. squares (4 corners), bears (4 paws), animals (4 legs). Get children to take a handful for their partner to count in 4‟s and record final number on a post-it. Repeat several times and order the post-its from lowest to highest Challenge: Order „Post-it‟s from highest to lowest and identify missing multiples. Using ITP or 100 square highlight any 3 consecutive multiples of 3 e.g. 9, 12, 15 … invite a volunteer to highlight the next three and explain their thinking. (Look for responses such as, “It‟s counting in 3‟s” “Multiples of 3” “There are 2 squares between each number” etc.) Repeat for other sequences involving multiples of 3 or 4. Using laminated number ladder (horizontally or vertically) add consecutive multiples of 2, 3, 4 or 5. Challenge children to describe and extend the sequence. Ask: Q. Can you describe the pattern? Is it getting higher or lower? What comes after / before this number? Repeat several times, including multiples of 3 and 4. Create a worksheet with similar ladders for children to work on individually or in pairs completing each sequence. 64 Y2, BLOCK B, UNIT 2 Use a bead string up to 50 to count the beads in tens. Q How many beads are there? Do we need to count them in ones like this, one, two, three…? Or can we count them in a quicker way? Q Where will 20 beads come up? Do we need to count them in ones? Write 25 on a tag. Ask a child to come and write 20 on a tag and hang it after the 20th bead. Q What does this number say? Where shall we hang the tag? How did you know? Did you have to count the beads from the beginning? Write 40 on a tag. Q What does this number say? Where shall we hang the tag? How did you know? Count on 6 beads after 40. Q What tag should we hang here? Why? Draw the following number line on the board: Say that this line starts at zero and goes up in tens and discuss where numbers should be placed on it. Q What does this line go up to? Where would 50 be? Why? Where should we put 10? 20? And 25? And 40? What number is halfway between 40 and 50? Where should we put 46? Will it be closer to 45 or 50? Where would we put 49? Ask other questions to help children become familiar with the marked number line. Q Where is 90? How do you know? What are the numbers in between 90 and 100? Ask the children to record the numbers on their whiteboards. Ask for volunteers to come up and mark on 5, 15, 25… 95. Count in tens along these numbers. Ask the children to work in pairs, taking it in turns to roll two 0-9 dice. They choose which number they want to be the tens digit and which they want to be the ones digit. One child should try and make a small number and the other a large number. They each place the number they made on their number line. Demonstrate this first with the class. Q If you roll a 6 and a 1, what large number can you make? What small number can you make? Are 16 and 61 near to each other or far apart? If you roll a 3 and a 4, what numbers can you make? Are 34 and 43 closer or further apart than 16 and 61? Show 46 beads on the string. Point out the four groups of ten, counting them, 10, 20, 30, and 40. Say that the digit 4 tells us how many groups of ten there are in 46. Count on the 6 ones, saying 1, 2, 3, 4, 5, 6. Say that the digit 6 tells us how many ones there are. Q What did we add onto 40 to get 46? What would be left if we took away the 6 beads? What if we took away 40 beads from 46? Count on 6 from the 40, saying 41, 42, 43, 44, 45, 46. Write 46 = 40 + 6 on the board. Write 37 = 30 + ? on the board. Q What would we add onto 30 to get 37? Demonstrate this on the bead string. Write 18 on the board. Q What does this number say? What would it look like on a bead string? What number sentence could we write to show how many tens and ones there are? Give out Activity sheet Y2 B30 and ask the children to complete the number sentences. If they finish they should make up their own tens and ones number sentences. 65 Y2, BLOCK B, UNIT 2 ACTIVITY SHEET Y2 B30 53 = 50 + 40 + = 47 9+ = 19 70 = =74 25 = 5 + 60 + = 68 + = 45 5+ = 85 + 40 = 41 22 = + 7+ = 67 66 Y2, BLOCK B, UNIT 2 BLOCK B - YEAR 2 UNIT 2 UNDERSTANDING SHAPE Visualise common 2-D shapes and 3-D solids; identify shapes from pictures of them in different positions and orientations; sort, make and describe shapes, referring to their properties (Objective repeated in Block B Units 1, 2 & 3) Show children a selection of 2-D shapes in various colours and sizes Q Who can tell me the name of one of these shapes? Q Are there any other shapes which have this name? Q what is the same about them, and what is different? Eg. Colour, size but still all rectangles. Discuss all the 2-D shapes and encourage children to count the number of sides as they name the shapes. Q Is there an easy way to remember some of the names of these shapes? Play `Guess my shape` I am thinking of a shape and it has got 5 sides, what is its name? Etc. Encourage children to come out and choose a shape from a feely bag and give the rest of the class clues. Encourage the children to describe the shapes in terms of number of sides and number of corners, as well as straight or curved sides and their lengths. Introduce two set rings and place a circle in one and a square and pentagon in the other Q What label could we give these two sets? Eg curved sides, straight sides Ask a volunteer to put different shapes into the two sets and then to describe their properties by giving the two sets labels Q Can you see anything in the classroom which is the same shape as the ones we have been talking about? eg. A table may be hexagonal. Check it has six sides and six corners In pairs children play a matching game. They turn over 2 cards (Resource sheet Y2 B31) If they match they keep them, if not they go back face down on the table. When all cards have been chosen, the children count them and the winner is the child with the most cards. Remind children of all the 2-D shapes previously met and briefly discuss number of sides and corners. Point out that the shapes you are looking at today will stand up because they are 3 dimensional, not flat (2 dimensional) Hold up a cylinder Q Can you see any of the shapes we looked at yesterday on this 3-D shape? Demonstrate that two of the faces of the cylinder are circles by matching the 2-D shape to the 3-D one. Look at other 3-D shapes Q Can you see any shapes which are faces on the 3-D shapes Go through all 3-D shapes mentioned in the vocabulary list and give children time to feel the shapes and look for the shapes of their faces and also to count the number of edges Sort shapes with curved faces and flat faces. Collect all the 3-D shapes in and put them in a feely bag. Select a shape from the bag without the children seeing it and give them clues. The child who guesses the shape correctly then takes over from the teacher. In groups of 4 or 5, give out a selection of wooden, plastic or cardboard 3-D shapes. Tell the groups you would like them to build a palace using the shapes and they are to record all the shapes they have chosen on a recording sheet (Activity sheet Y2 B32) Whilst building the palace you want the children to consider which of the shapes are better for building walls and which shapes you would use elsewhere eg on the roof 67 Y2, BLOCK B, UNIT 2 Hand out a selection of 2-d shapes to volunteers. Q Who can describe their shape using mathematical words like side, corner, straight and curved? Q Who can tell me the names of all these shapes? Write the names of the shapes on the board, recapping on difficult spellings. Show ITP polygon, or use a pinboard and elastic bands. Q This shape has 5 sides and 5 corners. What is it called? Q If I stretch it so it looks different but still has 5 sides and 5 corners, is it still a pentagon? If I stretch it again, is it still a pentagon? Repeat with other shapes. Model using a pinboard and elastic bands to make shapes if you haven‟t already. Q Who can show us how to make a pentagon using these interlocking cubes? Use cards on Resource sheet Y2 B33. Take a card with a shape name on it. Use pinboards and elastic bands/ interlocking cubes to make different forms of that shape. Q Are there any types of shape we can‟t make? Why not? Give each group the name of a shape to make using interlocking cubes. Draw and colour your shape on squared paper. (Could be used to make a class shape book.) Sit children in pairs, face to face. Play the mirror game, one of the pair makes a movement and the other has to match the movement like a mirror. Q When your partner moved their left arm, if you wanted to be their mirror, which arm did you move? Why? Hand out an even number of interlocking cubes to each pair. One of the pair makes a shape in interlocking cubes. Use a mirror to find a mirror image of the shape and then try and make this mirror image in cubes. Q How can we check that you have made a mirror image of your partner‟s shape, not just a copy? (Use mirrors/ put them together, along an imaginary line of symmetry). You may need to repeat this activity with cubes and extend to other equipment such as pegboards. Fold a piece of squared paper in half to make a line of symmetry. Choose one of the shapes you or your partner made and draw it on the squared paper along the line of symmetry. Then draw its symmetrical mirror image. Children have cubes in pairs. Using multilink make a single layer shape using 3 cubes (in the shape of a right angle). Q: Can you make a shape the same as this? Discuss how they were made. Now join 3 cubes in a line. Q: Can you make this shape? Q: How many did you move? Ask children to see how many shapes they can make using 4 cubes. Bring the children together after a while and discuss the shapes. Pupils to explain how they made them. N.B. Learning and Teaching Using ICT has a useful video clip which provides an alternative lesson using whiteboards. 68 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B31 69 Y2, BLOCK B, UNIT 2 RESOURCE SHEET B33 70 Y2, BLOCK B, UNIT 2 BLOCK B - YEAR 2 UNIT 2 Identify reflective symmetry in patterns and 2-D shapes and draw lines of symmetry in shapes. (Objective repeated in Block B Unit 2) Sit children in pairs, face to face. Play the mirror game, one of the pair makes a movement and the other has to match the movement like a mirror. Q When your partner moved their left arm, if you wanted to be their mirror, which arm did you move? Why? Hand out an even number of interlocking cubes to each pair. Activity: Q How can we check that you have made a mirror image of your partner‟s shape, not just a copy? (Use mirrors/ put them together, along an imaginary line of symmetry). You may need to repeat this activity with cubes and extend to other equipment such as pegboards. Activity: One of the pair makes a shape in interlocking cubes. Use a mirror to find a mirror image of the shape and then try and make this mirror image in cubes. Fold a piece of squared paper in half to make a line of symmetry. Choose one of the shapes you or your partner made and draw it on the squared paper along the line of symmetry. Then draw its symmetrical mirror image. Provide a selection of kaleidoscopes, mirrors and shiny surfaces and ask the children, in pairs, to investigate them and talk about what they see. Introduce the fact that they all produce reflections. Explain the words „symmetry‟ and „symmetrical‟. Provide paint or ink for children to make quick, simple patterns on half the paper, folding it over to make the picture symmetrical. Ask the children to discuss what has happened and how the picture looks now. Stress the reflection and check with mirrors. Show the children a selection of symmetrical pictures on an OHP or whiteboard. (See Resource sheets Y2 B34 – B40 for examples.) Ask a child to come up and draw in the line of symmetry. (Try to provide a mixture of vertical and horizontal lines of symmetry.) Give children a simple „half‟ picture or pattern with the line of symmetry included and ask them to complete the picture. (Stars, arrows, a clown‟s face, a simple house all make good pictures that are not too difficult to draw!) Using the Symmetry ITP on an interactive whiteboard ask a child to come up and create a simple pattern on one side of the mirror. Ask another child to complete the symmetrical pattern using the whiteboard pens. Ask the class in pairs to discuss whether it is correct. Take feedback and check by revealing the pattern on the ITP. Repeat several times until the children are secure. Give out pegboards and pegs to pairs of children (with a line of symmetry drawn on the board) or alternatively use squared paper. One child is to create a pattern on one side of the line of symmetry and the other is to copy it. Take turns as to who starts. Ask children to share patterns on tables, checking that they are correct. Seeking a symmetrical leaf Collect a variety of leaves and give them to the children on their tables to compare: which one is the most symmetrical? Is any leaf perfectly symmetrical? Suggestions: 1) Record the leaf's shape using one of these methods: a) Lay each leaf on a sheet of paper and trace around it with a pencil. b) Make a crayon rubbing of each leaf by placing a piece of paper over it and rubbing gently with the side of a crayon. c) Flatten a piece of clay with a rolling pin or bottle, then make a leaf imprint. 2) After you have preserved the shape of the leaf with one of the above methods, flip the leaf over and set it down onto its recorded shape. How well does it fit? The better the fit, the more symmetrical the leaf. 3) Another method of checking symmetry after transferring the leaf's shape to paper is to cut out the paper outline and fold it in half. How well do the edges match up? Variation: On graph paper, trace around one-half of a leaf, making sure that the stem points straight down. Remove the leaf. Try to draw the mirror image of this half-leaf to form a completely symmetrical leaf. Can you do it? If not, why not? If it's not symmetrical, make minor adjustments to both halves of the drawing until you can complete a symmetrical leaf. 71 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B34 72 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B35 73 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B36 74 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B37 75 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B38 76 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B39 77 Y2, BLOCK B, UNIT 2 RESOURCE SHEET Y2 B40 78 Y2, BLOCK B, UNIT 2

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