Division and Multiplication Strategies for Lowest Common Multiples and Highest Common Factors

1. 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. Year 5

2. 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) Year 5

3. Multiplication and Division Lowest common multiples and highest common factors Mental strategies in division and multiplication Starter Divisibility by 2, 3 or 5 Year 5

4. Multiplication and Division Lowest common multiples and highest common factors Mental strategies in division and multiplication Starter Double 2-digit numbers Year 5

5. Multiplication and Division Lowest common multiples and highest common factors Mental strategies in division and multiplication Starter • ‘Fizz-Buzz-Whizz: Common multiples’ Year 5

6. 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

7. Day 1: Find lowest common multiples and highest common factors. • 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? • Write a list of the multiples of 2 up to 20. • Then write a list of the multiples of 3 up to 21. • Six is the lowest common multiple of 2 and 3. Year 5

8. 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

9. 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

10. 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

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

12. Day 1: Find lowest common multiples and highest common factors. 12 20 32 • Which is the highest common factor? 1 2 4 • List some numbers which are factors of all three of these numbers. Year 5

13. Challenge Year 5

14. 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

15. 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 = ? • What do we know? • How does that help? • What do we already know? • How does that help? 115 23 x 5 = • We can double the answer to 23 x 10. 460 23 x 20 = 23 x 19 = • We can subtract 23 from the answer to 23 x 20. 437 • 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

16. Day 2: Use mental strategies (factors and multiples) to multiply by 5, 20, 6, 4 and 8. • Which method did you prefer for each number? • How can we use 23 × 3 = 69 to work out the answer to • 23 × 6? • 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. 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). Work out 23 x 3. Year 5

17. 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. Partitioning (20 x 4) + (3 x 4) • Try both methods. • We’ll vote for which you preferred. • Try both. • Vote for your preference… Doubling three times Double 23 , double the answer, then double again. Partitioning (20 x 8) + (3 x 8) • Discuss how you would work out 23 × 4. • Discuss how you would work out 23 × 8. Year 5

18. Challenge Year 5

19. 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. Year 5

20. Day 3: Use mental strategies to divide by 5, 20, 6, 4 and 8. • How can we use 240 ÷ 10 = 24 to work out the answer to • 240 ÷ 5? 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 ÷ 20? 48 240 ÷ 5 = 12 240 ÷ 20 = • 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. Year 5

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

22. Day 3: Use mental strategies to divide by 5, 20, 6, 4 and 8. • Together we’ll use what you have written to make a class poster about mental division strategies. • Work with a partner to write the strategies for dividing by 5, 20, 6, 4 and 8. Year 5

23. Year 5

24. 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. Year 5

25. 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