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.
Before teaching, be aware that:
On Day 1 children will need mini-whiteboards and pens. You may wish to use the Number Grid ITP.
On Day 2 children will need mini-whiteboards and pens. You may wish to use real 1 to 10 cards.

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

3. Multiplication and division Multiples, factors and word problems
Starter Times tables
Pre-requisite skills – to use this starter, drag this slide to the start of Day 1
Children play in pairs. They each shuffle a set of 0–12 cards and place face down. On the count of three, they each turn their top card over. The first child to say the product keeps both cards. Carry on until all cards are gone. Who won most pairs? Play another round.

4. Multiplication and division
Multiples, factors and word problems
Starter
Double and halve numbers to 100
Simmering skills – to use this starter, drag this slide to the start of Day 2
Children in pairs to take it in turns to roll a 0-9 dice twice to generate a 2-digit number. They choose to double or halve it and mark it on a blank line. 1st to get 5 numbers without opponent’s numbers in between wins.

5. Multiplication and division Multiples, factors and word problems
Starter
Bar charts
Simmering skills – to use this starter, drag this slide to the start of Day 3
Show the bar chart of types of pizzas sold (see resources). Ask children to talk to a partner about what it shows including how many of each pizza were sold reading the scale carefully. How can we work out how many pizzas were sold? Which type of pizza was twice as popular as another? Ask children to sketch a graph where twice as many cheese and tomato were sold as tuna and sweetcorn and twice as many pepperoni pizzas were sold as ham and pineapple. There should still be a total of 20 pizzas. They share their graph with another pair.

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

7. Write at least four common multiples of 2 and 3 on your whiteboards.
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. The multiples of 2 are pink and the multiples of 3 are yellow.
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?
Draw out that common multiples of 2 and 3 are multiples of 6.

9. How can we recognise multiples of 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. Which of these multiples of 6 are also multiples of 8?
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. Which of these multiples of 6 are also multiples of 8?
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. Which of these multiples of 2 are also multiples of 7?
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. Which of these multiples of 2 are also multiples of 7?
Day 1: Use knowledge of times tables facts to help find common multiples.
Which of these multiples of 2 are also multiples of 7?
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: Use a Venn diagram to sort multiples, placing common multiples in the intersection.
ARE/GD: Find pairs of numbers which have common multiples, using a Venn diagram to help.

15. 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: Children play common multiples game using two 1 to 6 dice.
ARE/GD: Children play common multiples game using two 0 to 9 dice.

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

17. Numbers which divide into 24 exactly are factors of 24.
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…
What numbers divide into 24 exactly?
Work in pairs to write as many as you can on your whiteboards.
24 has lots of factors!
Together make an ordered list of the pairs of factors of 24: 1, 24; 2, 12; 3, 8; 4, 6. Point out the systematic approach to make sure we’ve got them all.

18. Day 2: Find factors of two-digit numbers.27
What numbers divide into 27 exactly?
Work in pairs to write as many as you can on your whiteboards.
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…

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

20. What do you notice about numbers with an odd number of factors?
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.
Children can now go on to do this whole class activity.
Sit with different groups and help them to find all the factor pairs of their chosen number. Ask children why they think some numbers have an even number of factors and others have an odd number of factors.
Afterwards, ask children to feedback the number they found with the most factors (48, with 10 factors). Also list the numbers which they found had an odd number of factors. What do they notice about these numbers? Draw out that square numbers have an odd number of factors because one number is multiplied by itself rather than another number to make a factor pair.
WT: Give children a 12 × 12 multiplication square to help. They just do the first part of the investigation.
GD: Also challenge children to find a number greater than 50 with more than 10 factors. (60, 72, 84, 90, and 96 each have 12 factors.)
What do you notice about numbers with an odd number of factors?

21. The Practice Sheet on this slide is probably suitable for most children.
Download this OPTIONAL PRACTICE WORKSHEET from this unit’s PROCEDURAL FLUENCY box.
ARE: Find factors of 2-digit numbers.

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?
Work in pairs to agree the calculation needed for the problem.
We’ll discuss the answers to the problems together!
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.
Does the answer need to be rounded up or down?
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.
Today would be a great day to use a problem-solving investigation – Long As You Like – 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.
WT/ARE/GD: Use sketches/cubes to represent division problems to help determine if answers need to be rounded up or down.
There are suggestions for support/challenge.
Challenge! Think of a division problem where we would need to round up, and one where we would need to round down.

24. The Practice Sheet on this slide is suitable for most children.
Downloadable PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box.
WT/ARE/GD: Solve division word problems with rounding.
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.
You can now use the Mastery: Reasoning and Problem-Solving questions to assess children’s success across this unit. Go to the next slide.

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 , 24 and 36
Write common multiples of 3, 4 and 5 up to 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?