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Year 5 · Mathematics · Number

Multiplication and division facts

Recall multiplication facts up to 10 × 10 and use them to work out related division facts, using strategies such as doubling and fact families.

Awaiting educator review. This material was drafted by our content team with AI assistance and is waiting for review by a qualified educator. Please check it suits your child before using it. Created 10 October 2026.

These lessons were written around Australian Curriculum strands and matched to New Zealand year levels by age (NZ Year 1 is the first year of school). They are not yet mapped to The New Zealand Curriculum, so check them against your own learning programme.

Learning goals

Learners will

  • 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 looks like

  • 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.

The big idea

Multiplication 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

Using doubling

Work out 6 × 8.

  1. 6 is double 3, so first find 3 × 8.
  2. 3 × 8 = 24.
  3. Double 24: 24 + 24 = 48.

Answer: 6 × 8 = 48

Using a multiplication fact to divide

Work out 56 ÷ 7.

  1. Ask: 7 times what makes 56?
  2. Count or recall the sevens: 7, 14, 21, 28, 35, 42, 49, 56. That is 8 sevens.
  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?

  1. There are 3 equal groups of 8, so the number sentence is 3 × 8.
  2. 3 × 8 = 24.
  3. Check by adding: 8 + 8 + 8 = 24.

Answer: There are 24 sausages.

Practice check

Have a go, then check your answers. Each answer comes with an explanation.

  1. 1.What is 7 × 8?
  2. 2.Which division fact belongs to the same fact family as 6 × 9 = 54?
  3. 3.Mia packs 32 muffins into boxes that hold 4 muffins each. How many boxes does she fill?
  4. 4.Which of these gives the same answer as 4 × 7?
  5. 5.What is 9 × 6?
  6. 6.What is 63 ÷ 7?
  7. 7.Pool entry costs $4 for each child. How many dollars does it cost for 9 children?
  8. 8.An egg carton holds 6 eggs. How many full cartons can be made from 42 eggs?
Answer guide for parents

  1. What is 7 × 8?

    56 — 7 × 8 = 56. One way to check: 7 × 4 = 28, and double 28 is 56.

  2. Which division fact belongs to the same fact family as 6 × 9 = 54?

    54 ÷ 9 = 6 — The fact family uses 6, 9 and 54, so 54 ÷ 9 = 6 belongs to it.

  3. Mia packs 32 muffins into boxes that hold 4 muffins each. How many boxes does she fill?

    8 — 32 ÷ 4 = 8, because 4 × 8 = 32.

  4. Which of these gives the same answer as 4 × 7?

    double 2 × 7 — 2 × 7 = 14 and double 14 is 28, which is the same as 4 × 7 = 28.

  5. What is 9 × 6?

    54 — 10 × 6 = 60, and taking away one group of 6 gives 60 − 6 = 54.

  6. What is 63 ÷ 7?

    9 — 7 × 9 = 63, so 63 ÷ 7 = 9.

  7. Pool entry costs $4 for each child. How many dollars does it cost for 9 children?

    $36 — 9 groups of $4 is 9 × 4 = 36, so it costs $36.

  8. An egg carton holds 6 eggs. How many full cartons can be made from 42 eggs?

    7 — 42 ÷ 6 = 7, because 6 × 7 = 42.

Watch out for

  • 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.

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.

Go further

  • 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.)