Multiplication and Division Lowest common multiples and highest common factors Mental strategies in division and multiplication Objectives Day 1 Find lowest common multiples and highest common factors. Day 2 Use mental strategies (factors and multiples) to multiply by 5, 20, 6, 4 and 8. Day 3 Use mental strategies to divide by 5, 20, 6, 4 and 8. Before teaching, be aware that: On Day 1 children will need mini-whiteboards and pens. You may wish to use the ITP Number grid. On Days 2 & 3 children will need mini-whiteboards and pens. Year 5

Multiplication and Division Lowest common multiples and highest common factors Mental strategies in division and multiplication Starters Day 1 Divisibility by 2, 3 or 5 (pre-requisite skills) Day 2 Double 2-digit numbers (simmering skills) Day 3 ‘Fizz-Buzz-Whizz: Common multiples’ (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

Multiplication and Division Lowest common multiples and highest common factors Mental strategies in division and multiplication Starter Divisibility by 2, 3 or 5 Pre-requisite skills – to use this starter, drag this slide to the start of Day 1 Split the class into three teams, and assign the number 2, 3 or 5 to each team. Remind children of the test of divisibility for each number. Use a random number generator such as at: http://www.primaryresources.co.uk/maths/mathsA1.htm (click on Random Bingo Number Generator) to generate numbers between 1000 and 10,000. Children in a team hold up their hands if their number is a factor of the number generated. If they are correct, they score a point. Is this a fair game? Year 5

Multiplication and Division Lowest common multiples and highest common factors Mental strategies in division and multiplication Starter Double 2-digit numbers Simmering skills – to use this starter, drag this slide to the start of Day 2 Children play in pairs. They sketch a 0–200 line, making it as long as they can. They take it in turns to roll a 0–9 dice. They can use the digits in either order to make a 2-digit number, and then they double that number. They mark the answer on a blank 0–200 line in their chosen colour. The first to get three of their numbers in a line, without the opponent’s in-between, wins. Year 5

Multiplication and Division Lowest common multiples and highest common factors Mental strategies in division and multiplication Starter ‘Fizz-Buzz-Whizz: Common multiples’ Simmering skills – to use this starter, drag this slide to the start of Day 3 Beginning at 1, count around the class. If the number is a multiple of 3, you say ‘Fizz’ (instead of the number); if the number is a multiple of 5, you say ‘Buzz’ (instead of the number); if the number is a multiple of 7, you say ‘Whizz’ (instead of the number). If the number is a common multiple of any of 3, 5 and 7, you say each word necessary, e.g. 15 is Fizz-Buzz, 21 is Fizz-Whizz, 35 is Buzz-Whizz, and so on. Choose whether to start again at 1 if anyone makes a mistake. How far will we need to count to say ‘Fizz-Buzz-Whizz’?! Year 5

Multiplication and Division Lowest common multiples and highest common factors Mental strategies in division and multiplication Objectives Day 1 Find lowest common multiples and highest common factors. Year 5

Day 1: Find lowest common multiples and highest common factors. Write a list of the multiples of 2 up to 20. Then write a list of the multiples of 3 up to 21. Which numbers are in both lists? These are the common multiples of 2 and 3 – shaded pink and yellow on the grid. Which of these common multiples is the lowest? Six is the lowest common multiple of 2 and 3. Year 5

Which is the lowest common multiple? Day 1: Find lowest common multiples and highest common factors. Write three common multiples of 3 and 4 on your whiteboards, i.e. numbers divisible by both 3 and 4. Which is the lowest common multiple? Year 5

Which is the lowest common multiple? Day 1: Find lowest common multiples and highest common factors. Write three common multiples of 3 and 6 on your whiteboards, i.e. numbers divisible by both 3 and 6. Which is the lowest common multiple? Year 5

Day 1: Find lowest common multiples and highest common factors. Write three common multiples of 6 and 9 on your whiteboards. Which is the lowest common multiple? Year 5

List some numbers which are factors of all three of these numbers. Day 1: Find lowest common multiples and highest common factors. 32 16 24 List some numbers which are factors of all three of these numbers. 1 2 4 8 Which is the biggest number that goes exactly into all these numbers? We call this the highest common factor. Year 5

Day 1: Find lowest common multiples and highest common factors. 12 20 32 List some numbers which are factors of all three of these numbers. 1 2 4 Which is the highest common factor? Today would be a great day to use a problem-solving investigation – LCM Squares– as the group activity, which you can find in this unit’s IN-DEPTH INVESTIGATION box on Hamilton’s website. Alternatively, 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 on our website. WT/ARE: Investigate finding lowest common multiples. ARE/GD: Derive lowest common multiples and highest common factors. Year 5

The Practice Sheet on this slide is suitable for most children. You can download differentiated PRACTICE WORKSHEETS from Hamilton’s website in this unit’s PROCEDURAL FLUENCY box. WT: Finding highest common factor and lowest common multiple of pairs of numbers. ARE/GD: Finding highest common factor and lowest common multiple of sets of numbers. Challenge Year 5

Multiplication and Division Lowest common multiples and highest common factors Mental strategies in division and multiplication Objectives Day 2 Use mental strategies (factors and multiples) to multiply by 5, 20, 6, 4 and 8. Year 5

How can we use 23 × 10 = 230 to find the answer to 23 × 5? Day 2: Use mental strategies (factors and multiples) to multiply by 5, 20, 6, 4 and 8. How can we use 23 × 10 = 230 to find the answer to 23 × 5? We can multiply numbers by 5 by multiplying by 10, then halving. 23 x 10 = 230 23 x 10 = ? 23 x 5 = 115 What do we already know? How does that help? We can double the answer to 23 x 10. 23 x 20 = 460 23 x 19 = 437 What do we know? How does that help? We can subtract 23 from the answer to 23 x 20. Choose four other 2-digit numbers to multiply by 5 and 20, using the strategy of multiplying by 10 then either halving or doubling. Year 5

Day 2: Use mental strategies (factors and multiples) to multiply by 5, 20, 6, 4 and 8. Work out 23 x 3. One way to multiply a number by 6 is to multiply by 3, and then by 2. We are using a pair of factors of 6. How can we use 23 × 3 = 69 to work out the answer to 23 × 6? 23 x 6 = 138 Now use this strategy to multiply 25, 53 and 17 by 6. Also multiply each of these numbers by 6 using partitioning, e.g. (20 × 6) + (5 × 6). Which method did you prefer for each number? Choices may vary for different numbers, and because of personal preference, especially if children are not sure about the 6x table. Year 5

Double 23 , then double the answer. Day 2: Use mental strategies (factors and multiples) to multiply by 5, 20, 6, 4 and 8. Doubling twice Double 23 , then double the answer. Discuss how you would work out 23 × 4. Partitioning (20 x 4) + (3 x 4) Try both methods. We’ll vote for which you preferred. Doubling three times Double 23 , double the answer, then double again. Discuss how you would work out 23 × 8. Partitioning (20 x 8) + (3 x 8) 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 on our website. WT: Explore mental methods based on doubling and halving to multiply 42 and 62 by 5, 20, 6, 4 and 8. ARE: Explore mental methods based on doubling and halving to multiply 48 and 123 by 5, 20, 6, 4 and 8. GD: Explore mental methods based on doubling and halving to multiply their own numbers including 3-digit numbers by 5, 20, 6, 4 and 8. Try both. Vote for your preference… Year 5

Challenge The Practice Sheet on this slide is suitable for most children. You can download differentiated PRACTICE WORKSHEETS from Hamilton’s website in this unit’s PROCEDURAL FLUENCY box. WT: Use mental strategies (in particular doubling and halving) to multiply ‘friendly’ numbers by 5, 20, 6, 4 and 8. ARE/GD: Use mental strategies (in particular doubling and halving) to multiply by 5, 20, 6, 4 and 8. Year 5

Multiplication and Division Lowest common multiples and highest common factors Mental strategies in division and multiplication Objectives Day 3 Use mental strategies to divide by 5, 20, 6, 4 and 8. Take feedback, ensuring children understand when they need to double to give a bigger answer (÷ 5) and when they need to halve it to give a smaller answer (÷20). Year 5

We can divide numbers by 5 by dividing by 10, and then doubling. Day 3: Use mental strategies to divide by 5, 20, 6, 4 and 8. 240 ÷ 10 = 24 We can divide numbers by 5 by dividing by 10, and then doubling. How can we use 240 ÷ 10 = 24 to work out the answer to 240 ÷ 5? 240 ÷ 5 = 48 How can we use 240 ÷ 10 = 24 to work out the answer to 240 ÷ 20? 240 ÷ 20 = 12 We can halve the answer to 240 ÷ 10. If a number is split into bigger groups, there will be fewer groups, so dividing by a bigger number gives a smaller answer. Take feedback, ensuring children understand when they need to double to give a bigger answer (÷ 5) and when they need to halve it to give a smaller answer (÷20). Compare this to the previous day when they were multiplying. Emphasise how, if a number is split into bigger groups, there will be fewer groups, so dividing by a bigger number gives a smaller answer. If necessary model with smaller numbers. Year 5

Day 3: Use mental strategies to divide by 5, 20, 6, 4 and 8. Work out 270 ÷ 3. Hint: use the tables fact 27 ÷ 3. How can we use 270 ÷ 3 = 90 to work out the answer to 270 ÷ 6? We need to halve the answer to 270 ÷ 3. 270 ÷ 6 = Use this strategy to find 450 ÷ 3 then 450 ÷ 6. Work out 280 ÷ 4. Hint: halve twice, or use a tables fact. How can we use 280 ÷ 4 = 70 to work out the answer to 280 ÷ 8? We need to halve the answer to 280 ÷ 4. 280 ÷ 8 = Use this strategy to find 128 ÷ 4, then 124 ÷ 8. Year 5

Day 3: Use mental strategies to divide by 5, 20, 6, 4 and 8. Work with a partner to write the strategies for dividing by 5, 20, 6, 4 and 8. Together we’ll use what you have written to make a class poster about mental division strategies. 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 on our website. WT: Explore mental methods to divide by 5, 20 and 4. ARE/GD: Explore mental methods to divide by 5, 20, 6, 4 and 8. Year 5

The Practice Sheet on this slide is suitable for most children. You can download differentiated PRACTICE WORKSHEETS from Hamilton’s website in this unit’s PROCEDURAL FLUENCY box. WT/ARE: Use mental strategies (in particular doubling and halving) to divide by 5, 20, 6, 4 and 8; articulate strategies. GD: Use mental strategies (in particular doubling and halving) to divide ’less friendly’ numbers by 5, 20, 6, 4 and 8; articulate strategies. Year 5

Multiplication and Division Lowest common multiples and highest common factors Mental strategies in division and multiplication Well Done! You’ve completed this unit. Objectives Day 1 Find lowest common multiples and highest common factors. Day 2 Use mental strategies (factors and multiples) to multiply by 5, 20, 6, 4 and 8. Day 3 Use mental strategies to divide by 5, 20, 6, 4 and 8. 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 Is the lowest common multiple of 6 and 4 smaller than the highest common factor of 30 and 45? • Write common factors of 24 and 48. • Write common multiples of 3 and 5 up to 60. • Are any numbers in both sets? True or false? There are exactly four, 2-digit, common multiples of 3 and 7. 4 and 5 are common factors of all 2-digit multiples of 10. 15 is a factor of 100. If 350 ÷ 5 is 70, calculate 350 ÷ 10, 350 ÷ 20 and 350 ÷ 70. So, can you have a try at 350 ÷ 2.5? Year 5