Year 2: Any order, and division is different
Part of the Year 2 multiplying and dividing chapter. Chapter overview · whole chapter on one page
Any order, and division is different
Multiplication can be done in any order. Look at 2 rows of 5 stars. Turn the array round: 5 rows of 2 stars. Both arrays have 10 stars.
So 2 × 5 = 10, and 5 × 2 = 10.
Division is different. Sharing 10 into 2 equal groups gives 5 in each group: 10 ÷ 2 = 5. But 2 ÷ 10 is not the same. The order matters.
Key ideas
- Multiplication can be done in any order.
- Turning an array round keeps the same total.
- Division cannot be done in any order.
- Check a multiplication by counting the array the other way.
Method. Work out both ways. If the answers match, the order does not matter.
- Work out the first way. 5 groups of 2 is 10.5 × 2 = 10
- Swap the numbers and work out the other way. 2 groups of 5 is also 10.2 × 5 = 10
- Compare the answers. The two answers are the same, so the order does not matter.Yes. 5 × 2 = 2 × 5
Check. Both ways make 10. Count the array the other way to check. ✓
Watch out. Multiplication works in any order. Division does not.
Method. Division cannot be done in any order. Try both ways and compare.
- Work out the first way. Share 10 into 2 equal groups. Each group has 5.10 ÷ 2 = 5
- Try the other way. Now try to share 2 into 10 equal groups. There are not enough things.2 ÷ 10 is not a whole number
- Compare the answers. The answers are not the same, so the order matters for division.No. 10 ÷ 2 is not 2 ÷ 10
Check. 10 ÷ 2 = 5, but 2 ÷ 10 is not 5. ✓
Watch out. Division needs the number being shared first. Swapping the numbers changes the answer.
Method. Swapping the two numbers does not change the total when you multiply.
- Look at the fact you know. 6 groups of 3 make 18.6 × 3 = 18
- Swap the numbers. Now there are 3 groups of 6.3 × 6
- Work out the answer. Swapping the numbers does not change the total.18
Check. 3 groups of 6 add up to 18: 6 + 6 + 6 = 18. ✓
Watch out. Multiplication can be done in any order. Check by counting the other way.
Watch out
Watch out: 10 ÷ 2 is 5, but 2 ÷ 10 is not 5. You cannot swap the numbers in a division.
Exam tip
Grown-up tip. Use 2 rows of 5 buttons. Turn the tray round and ask: “Is it still 10?” Then share 10 buttons between 2 plates and ask: “Can we do it the other way round?”
Exercise 3F Any order, and division is different
Non-calculatorMethod. Swapping the two numbers does not change the total when you multiply.
- Look at the fact you know. 2 groups of 6 make 12.2 × 6 = 12
- Swap the numbers. Now there are 6 groups of 2.6 × 2
- Work out the answer. Swapping the numbers does not change the total.12
Check. 6 groups of 2 add up to 12: 2 + 2 + 2 + 2 + 2 + 2 = 12. ✓
Watch out. Multiplication can be done in any order. Check by counting the other way.
Method. Swapping the two numbers does not change the total when you multiply.
- Look at the fact you know. 5 groups of 4 make 20.5 × 4 = 20
- Swap the numbers. Now there are 4 groups of 5.4 × 5
- Work out the answer. Swapping the numbers does not change the total.20
Check. 4 groups of 5 add up to 20: 5 + 5 + 5 + 5 = 20. ✓
Watch out. Multiplication can be done in any order. Check by counting the other way.
Method. Swapping the two numbers does not change the total when you multiply.
- Look at the fact you know. 10 groups of 3 make 30.10 × 3 = 30
- Swap the numbers. Now there are 3 groups of 10.3 × 10
- Work out the answer. Swapping the numbers does not change the total.30
Check. 3 groups of 10 add up to 30: 10 + 10 + 10 = 30. ✓
Watch out. Multiplication can be done in any order. Check by counting the other way.
Method. Work out both ways. If the answers match, the order does not matter.
- Work out the first way. 4 groups of 5 is 20.4 × 5 = 20
- Swap the numbers and work out the other way. 5 groups of 4 is also 20.5 × 4 = 20
- Compare the answers. The two answers are the same, so the order does not matter.Yes. 4 × 5 = 5 × 4
Check. Both ways make 20. Count the array the other way to check. ✓
Watch out. Multiplication works in any order. Division does not.
Method. Division cannot be done in any order. Try both ways and compare.
- Work out the first way. Share 8 into 2 equal groups. Each group has 4.8 ÷ 2 = 4
- Try the other way. Now try to share 2 into 8 equal groups. There are not enough things.2 ÷ 8 is not a whole number
- Compare the answers. The answers are not the same, so the order matters for division.No. 8 ÷ 2 is not 2 ÷ 8
Check. 8 ÷ 2 = 4, but 2 ÷ 8 is not 4. ✓
Watch out. Division needs the number being shared first. Swapping the numbers changes the answer.
Method. Swapping the two numbers does not change the total when you multiply.
- Look at the fact you know. 3 groups of 5 make 15.3 × 5 = 15
- Swap the numbers. Now there are 5 groups of 3.5 × 3
- Work out the answer. Swapping the numbers does not change the total.15
Check. 5 groups of 3 add up to 15: 3 + 3 + 3 + 3 + 3 = 15. ✓
Watch out. Multiplication can be done in any order. Check by counting the other way.
Key words. Equal groups have the same number of things in each group.
Method. Add the same number once for each group. Count the groups first.
- Look at one group. Each group has 7 shoes.7 in one group
- Add the same number once for each group. There are 2 groups, so add 7 2 times.7 + 7
- Write the total. The total is 14 shoes.14
Check. Count in 7s: 7, 14. ✓
Watch out. Count the groups first. Then add one number for each group.
Key words. Equal groups have the same number of things in each group.
Method. Add the same number once for each group. Count the groups first.
- Look at one group. Each group has 2 shoes.2 in one group
- Add the same number once for each group. There are 7 groups, so add 2 7 times.2 + 2 + 2 + 2 + 2 + 2 + 2
- Write the total. The total is 14 shoes.14
Check. Count in 2s: 2, 4, 6, 8, 10, 12, 14. ✓
Watch out. Count the groups first. Then add one number for each group.
Method. Count each array. Compare the totals.
- Count Mo’s sweets. 4 rows of 2 sweets make 8 sweets.2 + 2 + 2 + 2 = 8
- Count Ruby’s sweets. 2 rows of 4 sweets make 8 sweets.4 + 4 = 8
- Compare. Both have the same number of sweets.Same. Both have 8.
Check. Turning an array round keeps the total the same. ✓
Watch out. Count the sweets, not the rows.
Method. Try to make 4 rows of 3 with the same 12 cups.
- Count the cups. Dev has 12 cups in total.12 cups
- Make 4 rows of 3. Put 3 cups in each of 4 rows.3 + 3 + 3 + 3 = 12
- Write the answer. The same 12 cups fit into 4 rows of 3.Yes. 3 + 3 + 3 + 3 = 12.
Check. 4 rows of 3 make 12, the same as 3 rows of 4. ✓
Watch out. The same number of things can make arrays of different shapes.
Method. Division cannot be done in any order. Try both ways and compare.
- Work out the first way. Share 12 into 3 equal groups. Each group has 4.12 ÷ 3 = 4
- Try the other way. Now try to share 3 into 12 equal groups. There are not enough things.3 ÷ 12 is not a whole number
- Compare the answers. The answers are not the same, so the order matters for division.No. 12 ÷ 3 is not 3 ÷ 12
Check. 12 ÷ 3 = 4, but 3 ÷ 12 is not 4. ✓
Watch out. Division needs the number being shared first. Swapping the numbers changes the answer.
Method. Check each sum on its own. Then find the one that is wrong.
- Check 24 ÷ 6. Share 24 into 6 equal groups. Each group has 4.24 ÷ 6 = 4
- Check 6 ÷ 24. Share 6 into 24 equal groups. There are not enough.6 ÷ 24 is not 4
- Write the answer. Sam’s wrong statement is the one about 6 ÷ 24.6 ÷ 24 = 4
Check. 4 × 6 = 24, but 6 ÷ 24 is not a whole number of groups. ✓
Watch out. Division is not in any order. Check each statement the right way round.