40-minute lesson
Year 5 Mathematics: Multiplication and division facts
Lesson objective
- Recall multiplication facts up to 10 × 10 using efficient strategies.
- Use the link between multiplication and division to solve division facts.
- Solve simple everyday problems that involve equal groups.
Success criteria:
- I can recall multiplication facts up to 10 × 10.
- I can use a multiplication fact to work out a division fact.
- I can write the fact family for a multiplication fact.
- I can solve a word problem about equal groups.
Materials
- Counters, buttons or dried pasta pieces
- An egg carton or muffin tray
- Paper and pencil
- A pack of playing cards (optional)
Introduction
4 minIntroduce today's words:
- Multiply: To find the total of a number of equal groups. The symbol is ×.
- Divide: To share a total into equal groups, or to find how many equal groups fit into a total. The symbol is ÷.
- Product: The answer to a multiplication. The product of 4 and 5 is 20.
- Array: Objects arranged in equal rows and columns, which show a multiplication.
- Fact family: A group of related multiplication and division facts that use the same three numbers.
Ask your child what they already know about multiplication and division facts.
Explanation
8 minMultiplication is a quick way of adding equal groups. If you have 4 bags with 6 apples in each, you could add 6 + 6 + 6 + 6, or you could say 4 × 6 = 24.
An array shows multiplication clearly. An egg carton with 2 rows of 6 eggs shows 2 × 6 = 12. Turn the carton around and you see 6 columns of 2, which is 6 × 2 = 12. The order of the numbers does not change the product, so learning one fact gives you two.
Some facts can be built from easier ones:
- Doubling: to find 4 × 7, double 2 × 7. Double 14 is 28.
- Using tens: 9 × 6 is one group of 6 less than 10 × 6. So 60 − 6 = 54.
- Halving tens: 5 × 8 is half of 10 × 8. Half of 80 is 40.
Division is the opposite (inverse) of multiplication. To solve 35 ÷ 5, ask yourself: “5 times what makes 35?” Because 5 × 7 = 35, we know 35 ÷ 5 = 7.
A fact family uses three numbers. For 3, 8 and 24 the family is: 3 × 8 = 24, 8 × 3 = 24, 24 ÷ 3 = 8 and 24 ÷ 8 = 3. Knowing one fact helps you check the others.
Worked examples
6 minUsing doubling
Work out 6 × 8.
Step 1: 6 is double 3, so first find 3 × 8.
Step 2: 3 × 8 = 24.
Step 3: Double 24: 24 + 24 = 48.
Answer: 6 × 8 = 48
Using a multiplication fact to divide
Work out 56 ÷ 7.
Step 1: Ask: 7 times what makes 56?
Step 2: Count or recall the sevens: 7, 14, 21, 28, 35, 42, 49, 56. That is 8 sevens.
Step 3: So 7 × 8 = 56, which means 56 ÷ 7 = 8.
Answer: 56 ÷ 7 = 8
An equal-groups problem
At a family barbecue there are 3 packets of sausages with 8 sausages in each packet. How many sausages are there altogether?
Step 1: There are 3 equal groups of 8, so the number sentence is 3 × 8.
Step 2: 3 × 8 = 24.
Step 3: Check by adding: 8 + 8 + 8 = 24.
Answer: There are 24 sausages.
Guided practice (do together)
8 min1. What is 7 × 8?
(a) 54 (b) 56 (c) 63 (d) 48
2. Which division fact belongs to the same fact family as 6 × 9 = 54?
(a) 54 ÷ 9 = 6 (b) 54 ÷ 5 = 9 (c) 45 ÷ 9 = 5 (d) 60 ÷ 6 = 10
3. Mia packs 32 muffins into boxes that hold 4 muffins each. How many boxes does she fill?
(a) 6 (b) 7 (c) 8 (d) 9
4. Which of these gives the same answer as 4 × 7?
(a) 7 + 7 + 7 (b) 4 + 7 (c) 7 × 7 (d) double 2 × 7
Independent practice
10 min5. What is 9 × 6?
6. What is 63 ÷ 7?
7. Pool entry costs $4 for each child. How many dollars does it cost for 9 children?
8. An egg carton holds 6 eggs. How many full cartons can be made from 42 eggs?
Questions to check understanding
- Can you recall multiplication facts up to 10 × 10?
- Can you use a multiplication fact to work out a division fact?
- Can you write the fact family for a multiplication fact?
- Can you solve a word problem about equal groups?
- What was the trickiest part today?
Answer guide
1. 56 — 7 × 8 = 56. One way to check: 7 × 4 = 28, and double 28 is 56.
2. 54 ÷ 9 = 6 — The fact family uses 6, 9 and 54, so 54 ÷ 9 = 6 belongs to it.
3. 8 — 32 ÷ 4 = 8, because 4 × 8 = 32.
4. double 2 × 7 — 2 × 7 = 14 and double 14 is 28, which is the same as 4 × 7 = 28.
5. 54 — 10 × 6 = 60, and taking away one group of 6 gives 60 − 6 = 54.
6. 9 — 7 × 9 = 63, so 63 ÷ 7 = 9.
7. $36 — 9 groups of $4 is 9 × 4 = 36, so it costs $36.
8. 7 — 42 ÷ 6 = 7, because 6 × 7 = 42.
Review
4 minRecap the success criteria together. Watch for these common misconceptions:
- Thinking that 4 × 7 and 7 × 4 are different answers. Build both arrays with counters to show they contain the same number of objects.
- Believing division can be done in either order, so 24 ÷ 6 is the same as 6 ÷ 24. Share 24 counters among 6 people, then try sharing 6 counters among 24 people to see the difference.
- Adding instead of multiplying, for example writing 3 × 8 = 11. Ask the learner to draw 3 groups of 8 to see what the symbol means.
Extension activities
- Play a card game: remove the picture cards, flip two cards and race to say the product. Aces count as 1 and tens count as 10.
- Make a multiplication grid from 1 × 1 to 10 × 10 and colour in the facts you know. Look for patterns, such as the answers in the 5 column always ending in 0 or 5.
- Investigate: which numbers between 1 and 50 can be made into more than one rectangular array? (For example, 12 can be 1 × 12, 2 × 6 or 3 × 4.)
Suggested follow-up
- Revisit multiplication and division facts tomorrow with two or three quick questions from memory.
- Try the online practice check for this topic and look at any questions that need another go.
Tips for parents
- Practise a few facts often rather than many facts at once. Five minutes a day works better than a long session once a week.
- Focus on strategies, not just memory. Ask “How did you work that out?” and praise clever methods such as doubling.
- Use real moments: setting the table, packing lunch boxes or counting pairs of socks are all chances to multiply.