Addition and Subtraction Mental addition and subtraction – revision of strategies Objectives Day 1 Add and subtract near multiples of 10, 100, 1000. Day 2 Use pairs to 100, other facts and place value to mentally add and subtract, including decimal numbers and money. Day 3 Understand and use equivalence. Before teaching, be aware that: On Day 1 children will need mini-whiteboards and pens. On Day 3 each group of four children will need a sheet of A4 paper. Year 5

Addition and Subtraction Mental addition and subtraction – revision of strategies Starters Day 1 Add/subtract 1-digit numbers to/from 4-digit numbers (pre-requisite skills) Day 2 Complements to 100 (pre-requisite skills) Day 3 Double numbers with one decimal place (simmering skills) Choose starters that suit your class by dragging and dropping the relevant slide or slides below to the start of the teaching for each day. Year 5

Addition and Subtraction Mental addition and subtraction – revision of strategies Starter Add/subtract 1-digit numbers to/from 4-digit numbers Pre-requisite skills – to use this starter, drag this slide to the start of Day 1 Count round the class in steps of 6, beginning at 1456: 1456, 1462, 1468, 1474… until every child has had a turn. If we keep going, will anyone say 2056? (Yes – it’s 600 more than 1456 – that’s another 100 steps of 6!) Repeat this time counting back in steps of 6 from 1456. If we keep going, will anyone say zero? (No – 1456 is not a multiple of 6 [multiples of 6 are even multiples of 3]) Year 5

Addition and Subtraction Mental addition and subtraction – revision of strategies Starter Complements to 100 Pre-requisite skills – to use this starter, drag this slide to the start of Day 2 Throw a bean bag/soft ball to a child saying a number less than 100. They reply by giving the complement to 100. Repeat, differentiating by giving a few children multiples of 10, some multiples of 5 but mostly other 2-digit numbers. Year 5

Addition and Subtraction Mental addition and subtraction – revision of strategies Starter Double numbers with one decimal place Simmering skills – to use this starter, drag this slide to the start of Day 3 Play ‘Maths Fishing – Multiplication’ at https://mathsframe.co.uk/en/resources/resource/306/Maths-Fishing-Multiplication. Choose game 17 (Double decimals 1dp). Click ‘Play’, then follow the on-screen instructions to select questions. Children must quickly calculate doubles, then call out answers or click on-screen. Play switches from child to child around the class, or children can play individually on portable devices. Year 5

Addition and Subtraction Mental addition and subtraction – revision of strategies Objectives Day 1 Add and subtract near multiples of 10, 100, 1000. Year 5

You are going to work in pairs, one to solve each calculation. Day 1: Add and subtract near multiples of 10, 100, 1000. 4658 + 198 4658 + 205 You are going to work in pairs, one to solve each calculation. They are near multiples of 100. BUT before you do, what do you notice about 198 and 205? Now work out the answers. What calculation could you do that will help both of you? What is the difference between your two answers? +200 -2 +5 Agree that 4658 + 200 will be a useful step towards calculating both additions. 4658 4856 4858 4863 Year 5

Day 1: Add and subtract near multiples of 10, 100, 1000. 4658 + 68 658 + 73 Work in pairs, one to solve each calculation. What is the difference between your two answers? What calculation was useful to both of you this time? 4658 + 2997 4658 + 3004 Work in pairs, one to work out each calculation. What will the difference be between your answers this time? How do you know? Agree that 4658 + 200 will be a useful step towards calculating both additions. Year 5

Day 1: Add and subtract near multiples of 10, 100, 1000. 4658 – 82 4658 – 79 Solve one calculation each. Now find the answers. What calculation could you do that will help both of you? 4658 –703 4658 – 698 You are going to work in pairs, one to work out each calculation. Now find the answers. What calculation could you do that will help both of you? Year 5

Day 1: Add and subtract near multiples of 10, 100, 1000. 4658 – 2005 4658 – 1998 Solve one calculation each. Now find the answers. What calculation could you do that will help both of you? What is the difference between your two answers? Children can now go on to do differentiated GROUP ACTIVITIES. You can find Hamilton’s group activities in this unit’s TEACHING AND GROUP ACTIVITIES download. WT: Add/subtract near multiples of 10, 100, 1000 to/from 5468. ARE/GD: Add/subtract near multiples of 10, 100, 1000 to/from 23,456. Year 5

The Practice Sheet on this slide is suitable for most children. Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box. WT: Add/subtract multiples of 10, 100, 1000, then related near multiples (Sheet 1) ARE/GD: Add/subtract near multiples of 10, 100 and 1000 (Sheet 2) Year 5

Addition and Subtraction Mental addition and subtraction – revision of strategies Objectives Day 2 Use pairs to 100, other facts and place value to mentally add and subtract, including decimal numbers and money. Year 5

All these calculations can be worked out mentally! Day 2: Use pairs to 100, other facts and place value to mentally add and subtract, including decimal numbers and money. All these calculations can be worked out mentally! Sometimes it helps to jot something down to help keep track of the steps in a mental method….but no written column methods are allowed today! Spot another calculation where a ‘place value’ calculation might be an efficient strategy. Discuss in pairs what number fact could be used to help find the answer. What number fact can help this time? What might be a useful mental strategy here? £2.68 + □ = £3. Take feedback and agree that pairs to 100 will help (68 + 32). □ = 45. + 0.6. Take feedback, e.g. pair to 1 (0.7 and 0.3) to help ‘bridge’ 46, or 6 + 7 = 13. 3.25 – 0.26. Suggest that ‘place value’ can be used to subtract 0.25, and then another 0.01 needs to be subtracted. Children can now go on to do differentiated GROUP ACTIVITIES. You can find Hamilton’s group activities in this unit’s TEACHING AND GROUP ACTIVITIES download. WT: Play fluency challenges – pairs to 100, £1 and 1 (numbers with 2dp), then play an online game using pairs to 1. ARE/GD: Match mental calculations to answers, against the clock. Year 5

The Practice Sheet on this slide is suitable for most children. Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box. WT/ARE/GD: Mental calculations using number facts and place value (Sheet 1) Year 5

Addition and Subtraction Mental addition and subtraction – revision of strategies Objectives Day 3 Understand and use equivalence. Year 5

Day 3: Understand and use equivalence. Tell me what you see… What do these equations mean? Each side of the equals sign must be equal - the equation must balance. 134 + 8 = 200 – □ 32 × 4 = □ × 2 48 ÷ 4 = 12 x □ 3.6 × □ = 10 – 2.8 58 64 1 2 Calculate what number belongs in this box. Year 5

Day 3: Understand and use equivalence. Work in groups of four. One person writes an addition with an answer of 72 at the top of the page, then folds it over. Pass to the next person who writes a subtraction with an answer of 72, then folds it over. The next person writes a multiplication with an answer of 72. The last person writes a division with an answer of 72. Open out the paper, then use these calculations to write lots of ‘balancing’ equations. Choose a few to share with the class to check. Year 5

Whole class activity: in pairs Solve: 45 × □ = 180 ÷ 2 Day 3: Understand and use equivalence. Whole class activity: in pairs   Solve: 45 × □ = 180 ÷ 2 □ + 78 = 135 – 35 86 ÷ □ = 2 × 4.3 Then work in pairs to write your own set of three balancing equations, using a mix of operations in each one. The complete set of equations must include all four operations, some whole numbers and some decimals. I’ll be looking out for equations to use to challenge everybody at the end of the lesson…! Today’s GROUP ACTIVITY is a whole class activity. You can find more details in the unit’s TEACHING AND GROUP ACTIVITIES download. WT/ARE/GD: Write sets of balancing equations, using a mix of operations in each equation and across each set. Year 5

The Practice Sheet on this slide is suitable for most children. Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box. WT/ARE/GD: Find missing numbers to maintain equalities (Sheet 1). Challenge Year 5

Addition and Subtraction Mental addition and subtraction – revision of strategies Well Done! You’ve completed this unit. Objectives Day 1 Add and subtract near multiples of 10, 100, 1000. Day 2 Use pairs to 100, other facts and place value to mentally add and subtract, including decimal numbers and money. Day 3 Understand and use equivalence. You can now use the Mastery: Reasoning and Problem-Solving questions to assess children’s success across this unit. Go to the next slide. Year 5

Problem solving and reasoning questions How many times must I add 7 to 7,728 get to 7,777? Subtract 205 from each of… • 12,321 45,254 20,062 What will the ones digit of your answer be if you carry out the following sequence? Start with 30,460. 2. Add 9999 3. Subtract 999 4. Add 99 5. Subtract 9 6. What’s your final number? What numbers must be subtracted from 21,234 to leave: • 9999 19,235 21,035 Complete each sentence: £4.36 + [__] = £5 £6.72 + [___] = £10 4.83 + [__] = 10 Write the value of each shape. 701 – ★ = 3 x 152 (6.25 x 6) + [__] = 120 ÷ 3 100 – 55.68 = ½ of Δ Here is an equation with two empty spaces. What ONE number will make the equation balance? (34 x 5) – [_] = 4 x [_] x 4 Year 5

Problem solving and reasoning questions How many times must I add 7 to 7,728 get to 7,777? 7 times Subtract 205 from each of… • 12,321 12,116 45,254 45,049 20,062 19,857 If done mentally, check children are jotting down part-answers, e.g. 12,321, 12,121 (subtracting 200), 12,116 (subtracting 5 more). Encourage children to add 205 back to their answers to check. What will the ones digit of your answer be if you carry out the following sequence? 0, same as the starting number since nine 1s are twice added and twice subtracted 1. Start with 30,460. 2. Add 9999 40,459 3. Subtract 999 39,460 4. Add 99 39,559 5. Subtract 9 39,550 6. What’s your final number? 39,550 Check children make the right adjustments, e.g. when adding 9999, add 10,000 then subtract 1; when subtracting 999, subtract 1000 then add 1 What numbers must be subtracted from 21,234 to leave: • 9999 11,235 19,235 1,999 21,035 199 Complete each sentence: £4.36 + 64p or £0.64 = £5 £6.72 + £3.28 = £10 4.83 + 5.17 = 10 Write the value of each shape. 701 – 245 = 3 x 152 (6.25 x 6) + 2.5 = 120 ÷ 3 100 – 55.68 = ½ of 88.64 Here is an equation with two empty spaces. What ONE number will make the equation balance? (34 x 5) – 10 = 4 x 10 x 4 Year 5