Multiplication and division Multiples, factors and word problems

1. Multiplication and division Multiples, factors and word problems Objectives Day 1 Use knowledge of times tables facts to help find common multiples. Day 2 Find factors of two-digit numbers. Day 3 Divide mentally, deciding whether to round up or down depending on the context.

2. Multiplication and division Multiples, factors and word problems Starters Day 1Times tables (pre-requisite skills) Day 2Double and halve numbers to 100 (simmering skills) Day 3Bar charts (simmering skills)

3. Multiplication and division Multiples, factors and word problems StarterTimes tables

4. Multiplication and division Multiples, factors and word problems Starter Double and halve numbers to 100

5. Multiplication and division Multiples, factors and word problems Starter Bar charts

6. Multiplication and division Multiples, factors and word problems Objectives Day 1 Use knowledge of times tables facts to help find common multiples.

7. Day 1: Use knowledge of times tables facts to help find common multiples. Can you see a number that is a multiple of 3 and also a multiple of 2? We call these common multiples of 2 and 3. Write at least four common multiples of 2 and 3 on your whiteboards.

8. Day 1: Use knowledge of times tables facts to help find common multiples. The multiples of 2 are pink and the multiples of 3 are yellow. The common multiples have pink and yellow stripes. Use these to check your list of common multiples. What do you notice about these numbers?

9. Day 1: Use knowledge of times tables facts to help find common multiples. How can we recognise multiples of 9? Some are also multiples of 6. Write three common multiples of 6 and 9 on your whiteboards.

10. Day 1: Use knowledge of times tables facts to help find common multiples. See how the common multiples have pink and yellow stripes. Check yours.

11. Day 1: Use knowledge of times tables facts to help find common multiples. Which of these multiples of 6 are also multiples of 8?

12. Day 1: Use knowledge of times tables facts to help find common multiples. Which of these multiples of 6 are also multiples of 8?

13. Day 1: Use knowledge of times tables facts to help find common multiples. Which of these multiples of 2 are also multiples of 7?

14. Day 1: Use knowledge of times tables facts to help find common multiples. Which of these multiples of 2 are also multiples of 7?

16. Multiplication and division Multiples, factors and word problems Objectives Day 2 Find factors of two-digit numbers.

17. Day 2: Find factors of two-digit numbers. 24 Numbers which divide into 24 exactly are factors of 24. Let’s use the numbers on your whiteboards to make an ordered list of pairs of factors… 24 has lots of factors! • What numbers divide into 24 exactly? • Work in pairs to write as many as you can on your whiteboards.

18. Day 2: Find factors of two-digit numbers. 27 Let’s use the numbers on your whiteboards to make an ordered list of pairs of factors. Although 27 is a bigger number than 24, it does not have as many factors as 24: it is not in as many times tables… • What numbers divide into 27 exactly? • Work in pairs to write as many as you can on your whiteboards.

19. Day 2: Find factors of two-digit numbers. 15 18 12 30 Which were ‘good’ numbers to choose? Why? 25 36 21 Here come some number cards… If the number that appears is a factor of your number, score a point! Choose one of these numbers. 8 5 4 9 3 1 7 2 6 10

20. Day 2: Find factors of two-digit numbers. Whole class activity Work in pairs to find the number less than 50 with the greatest number of factors. Also try to find numbers which have an even number of factors and numbers which have an odd number of factors. What do you notice about numbers with an odd number of factors?

22. Multiplication and division Multiples, factors and word problems Objectives Day 3 Divide mentally, deciding whether to round up or down depending on the context.

23. Day 3: Divide mentally, deciding whether to round up or down depending on the context. 1. Sarah is taking free range chicks to sell at the farmers’ market. She can put five chicks in each cage. She has 62 chicks. How many cages does she need to take all the chicks? 2. She’s also taking eggs. She has 75. How many full boxes of six eggs can she take? 3. Mrs Holes is ordering some group reading books for Year 5. She needs 65 books. They come in packs of four. How many packs does she need to order? 4. She has 89 handwriting pens for the year group. How many pots of 6 pens can she make? Does the answer need to be rounded up or down? The answer to the division is 12 r 2, but if Sarah only takes 12 cages she will leave 2 chicks behind, so the answer needs to be rounded up to 13 so that she can take all the chicks, and the cages won’t be full. The answer is 12 r 3, but Sarah can only fill 12 boxes, so the answer is rounded down. She will have 3 eggs she can’t put into boxes. Work in pairs to agree the calculation needed for the problem. We’ll discuss the answers to the problems together! Challenge! Think of a division problem where we would need to round up, and one where we would need to round down.

24. Challenge

25. Multiplication and division Multiples, factors and word problems Well Done! You’ve completed this unit. Objectives Day 1 Use knowledge of times tables facts to help find common multiples. Day 2 Find factors of two-digit numbers. Day 3 Divide mentally, deciding whether to round up or down depending on the context.

26. Multiplication and Division Problem solving and reasoning questions Are there more or fewer common multiples of 2 and 3 under 30 than of 3 and 5? Explain your answer… Write common multiples of 2, 3 and 4 up to 40. Write common multiples of 3, 4 and 5 up to 40. Which set has more numbers? True or false • 5 is a factor of 20 and a factor of 40. • 3 is a factor of seven numbers less than 20. • 15 is a factor of 100. Sunil says that whenever a problem involves working out the number of cars or coaches needed, we have to round up. Is he correct? Invent a problem where the remainder is the answer.

27. Problem solving and reasoning answers Are there more or fewer common multiples of 2 and 3 under 30 than of 3 and 5? Explain your answer… Common multiples of 2 and 3 < 30: 6, 12, 18 and 24. Common multiples of 3 and 5 < 30: 15 Common multiples of 2 and 3 are all multiples of 6, common multiples of 3 and 5 are all multiples of 15; there are far more of the former under 30. Write common multiples of 2, 3 and 4 up to 40. 12, 24 and 36 Write common multiples of 3, 4 and 5 up to 40. Did I catch you out? There are no common multiples of 3, 4 and 5 up to 40, the smallest is 60. Which set has more numbers? The first… True or false • 5 is a factor of 20 and a factor of 40. True • 3 is a factor of 7 numbers less than 20. False, 3 is a factor of only 6 numbers less than 20: 3,6,9,12,15 and 18. • 15 is a factor of 100. False, since 6 x 15 = 90 and 7 x 15 = 105 Sunil says that whenever a problem involves working out the number of cars or coaches needed, we have to round up. Is he correct? He is sometimes correct. If you want to transport all passengers, and do not round up then some passengers will be left out. For example 4 people fit in a car. If there are 19 people how many cars are needed? Answer = 5 cars. However, if the question (using the same numbers) asks ‘How many cars can you fill?’, then you would round down. Answer = 4 cars Invent a problem where the remainder is the answer. Various, check – the answer will be something left over or left out. e.g. A farmer has 32 eggs. He puts them into boxes of 6, how many are left over?