1. Multiplication and Division
Solve problems using mental multiplication and division
Objectives
Day 1
Multiply and divide numbers mentally drawing on known facts.
Day 2
Solve word problems needing mental multiplication or division.
Day 3
Solve single and multi-step problems, working out which calculation(s) are necessary.
Before teaching, be aware that:
On Days children will need mini-whiteboards and pens.
Year 5

2. Multiplication and Division
Solve problems using mental multiplication and division
Starters
Day 1
7 times table (pre-requisite skills)
Day 2
8 times table (pre-requisite skills)
Day 3
24-hour clock (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

3. Multiplication and Division
Solve problems using mental multiplication and division
Starter
7 times table
Pre-requisite skills – to use this starter, drag this slide to the start of Day 1
Children work in pairs to shuffle a set of 0–12 cards and place face down. Start a timer. Turn over each card and multiply by 7. Can they get through their pack in under 2 minutes? Under 1 minute? Repeat as time allows, shuffling the cards between turns.
Year 5

4. Multiplication and Division
Solve problems using mental multiplication and division
Starter
8 times table
Pre-requisite skills – to use this starter, drag this slide to the start of Day 2
Children work in groups. They pass a 1–12 (or 1–10) dice round, roll, then multiply the number on it by 8. How many times can they get around the group in 3 minutes? Repeat.
Year 5

5. Multiplication and Division
Solve problems using mental multiplication and division
Starter
24-hour clock
Simmering skills – to use this starter, drag this slide to the start of Day 3
Practise telling the time using
Select 24-hour clock, let children watch the animation with the sun and moon changing with am and pm times, then click next. Ask a child to hit ‘stop the clock’. Children read the time on the analogue clock look at the moon/sun and write the 24-hour time on their whiteboards. Enter the most common time shown and click on ‘check’. Repeat.
Year 5

6. Multiplication and Division
Solve problems using mental multiplication and division
Objectives
Day 1
Multiply and divide numbers mentally drawing on known facts.
Year 5

7. What else can we work out using this fact?
Day 1: Multiply and divide numbers mentally drawing on known facts.
10 × 46 = 460
What else can we work out using this fact?
We can find 5 × 46, 15 × 46, 20 × 46, 21 × 46…
How could we work out 19 × 46?
19 × 46
= (20 x 46) – 46
= 920 – 46
= 874?
Quick finishers could also be directed to multiply by 15 and 19.
Work in pairs to choose an even 2-digit number, multiply it by 10, then use this to multiply the number by 5, 20 and 21.
Year 5

8. Day 1: Multiply and divide numbers mentally drawing on known facts.
20 × × × × × × 8
Write the answers on your whiteboard.
20 x 6
Which fact can we use to help us work out the answer?
123 ÷ 6
If we want an exact answer, 3 is half of a group of 6, so the exact answer is 201/2.
What is the remainder?
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: Multiply 3, 4 and 6 by 10, 20 and 30; use to help work out divisions, writing remainders as fractions.
ARE/GD: Multiply 6, 7 and 8 by 20, 30 and 40, then find divisions with answers in given ranges.
154 ÷ 7
Which fact can we use to help us work out the answer?
20 x 7
30 x 8
244 ÷ 8
Which fact can we use to help us work out the answer?
Year 5

9. 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: Multiply 6, 7 and 8 by 10, 20 and 30. Use these facts to help solve divisions, writing remainders as fractions (Sheet 1)
ARE: Multiply 6, 7 and 8 by 20, 30 and 40. Use these facts to help solve divisions, writing remainders as fractions (Sheet 2)
GD: Multiply 6, 7 and 8 by 20, 30 and 40. Use these facts to help solve divisions, writing remainders as fractions. Complete the challenge. (Sheet 3)
Year 5

10. Multiplication and Division
Solve problems using mental multiplication and division
Objectives
Day 2
Solve word problems needing mental multiplication or division.
Year 5

11. How many pieces of shortbread are there?
Day 2: Solve word problems needing mental multiplication or division.
A tea shop has 27 trays of shortbread. Each tray is divided so it holds 20 pieces of shortbread.
How many pieces of shortbread are there?
What we need to do to the numbers in this problem to solve it?
Write the necessary calculation on your whiteboards.
We can double 27, then multiply by 10.
Is this a multiplication we can work out mentally?
Read the problem above.
Were any children caught out by the word ‘divided’!?
Year 5

12. What we need to do to the numbers in this problem to solve it?
Day 2: Solve word problems needing mental multiplication or division.
A coach party of 46 people has come to the tea shop. They all want cream teas. Scones come in packs of 4. How many packs are needed?
What we need to do to the numbers in this problem to solve it?
Write the necessary calculation on your whiteboards then work out the answer.
The answer to the calculation is 11 r 2, or 111/2. But what is the answer to the problem?
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: Collaborate to use mental strategies alongside written jottings to solve a series of multiplication and division word problems.
They need to open 12 packs, but will only use 111/2 packs.
Year 5

13. 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: Work in pairs to read word problems, visualise or represent the context, agree the necessary calculation(s) then answer the problems (Sheet 1)
ARE: Work in pairs to read word problems, visualise or represent the context, agree the necessary calculation(s) then answer the problems (Sheet 2)
GD: Work in pairs to read word problems, visualise or represent the context, agree the necessary calculation(s) then answer the problems (Sheet 3)
Year 5

14. Multiplication and Division
Solve problems using mental multiplication and division
Objectives
Day 3
Solve single and multi-step problems, working out which calculation(s) are necessary.
Year 5

15. A Boeing 747 can carry 416 passengers.
Day 3: Solve single and multi-step problems, working out which calculation(s) are necessary.
Happy Holidays!
Today, we’re going to use our multiplication and division skills to solve holiday-related number problems…
Read this problem.
A Boeing 747 can carry 416 passengers.
How many passengers were carried on three such planes if a total of 27 seats were empty?
Discuss with a neighbour - do you Understand what you need to do with the numbers in the problem? What Calculation is needed to Solve the problem?
We first need to find how many passengers could fly on the three planes, then subtract the empty seats.
Make sure you read the words in red.
Take feedback after the paired discussion.
(3 x 416) – 27
Now find the Answer to the problem.
As you are off on holiday, did you remember your RUCSAC?
This is a useful acronym to help you through the stages of solving a word problem…
A quick Check – does the answer look sensible? Did we need the number 747?
Year 5

16. A seaside town has a population of 19,426 people.
Day 3: Solve single and multi-step problems, working out which calculation(s) are necessary.
A seaside town has a population of 19,426 people.
During one hot weekend, 27,428 people came to stay, while 2,183 residents were away.
How many people were in the town that day?
Read the problem.
Understand what you need to do.
Calculation: Which operation do you need?
Solve the calculation.
Answer the problem.
Check - does the answer seem reasonable?
Today would be a great day to use a problem-solving investigation – One O Five – 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: Solve single and multi-step word problems using a strategy to lead step-wise through the problem.
ARE/GD: Create and solve single and multi-step word problems.
Year 5

17. 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: Work in pairs to solve ‘holiday’ word problems (Sheet 1)
ARE/GD: Work in pairs to solve ‘holiday’ word problems (Sheet 2)
Challenge
Year 5

18. Multiplication and Division
Solve problems using mental multiplication and division
Well Done! You’ve completed this unit.
Objectives
Day 1
Multiply and divide numbers mentally drawing on known facts.
Day 2
Solve word problems needing mental multiplication or division.
Day 3
Solve single and multi-step problems, working out which calculation(s) are necessary.
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

19. Problem solving and reasoning questions
Write the correct symbol (<, = or >) in each box to make the statements correct:
15 x 10 □ 7 x 20
120 ÷ 6 □ 180 ÷ 9
70 x 30 □ 4 x 500
440 ÷ 4 □ 720 ÷ 60
A box contains trays of oranges. There are 12 oranges in a tray. There are 5 trays in a box. A grocer sells 30 boxes of oranges.
How many oranges does the grocer sell?
Write the missing number in each calculation:
252 ÷ 6 = [__]
[__] ÷ 6 = 10 remainder 3
102 ÷ [__] = 123/4
Year 5

20. Problem solving and reasoning: Answers
Write the correct symbol (<, = or >) in each box to make the statements correct:
15 x 10 > 7 x 20 since 150 > 140
120 ÷ 6 = 180 ÷ 9 since each equal 20
70 x 30 > 4 x 500 since > 2000
440 ÷ 4 > 720 ÷ 60 since 110 > 12
A box contains trays of oranges. There are 12 oranges in a tray. There are 5 trays in a box. A grocer sells 30 boxes of oranges. How many oranges does the grocer sell?
He sells 1800 oranges (12 x 5 x 30) – an answer of 60 or 150 suggests the question hasn’t been read carefully. This is a 2-step problem requiring all three numbers to be multiplied together; they can be multiplied in any order
Write the missing number in each calculation:
252 ÷ 6 = 42
63 ÷ 6 = 10 remainder 3
102 ÷ 8 = 123/4
Year 5