Year 4: The 7 and 11 times tables, square numbers and the whole grid
Part of the Year 4 times tables chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
The 7 and 11 times tables, square numbers and the whole grid
The 7 times table. This is often called the hardest table, but you already know almost all of it! 7 × 2, 7 × 3, 7 × 4, 7 × 5, 7 × 9, 7 × 10 and 7 × 12 come from tricks you know. The ones to practise are 6 × 7 = 42, 7 × 7 = 49 and 7 × 8 = 56. To remember 56 = 7 × 8, notice the digits in order: 5, 6, 7, 8. If you forget a fact, build it: 7 × 7 = 5 × 7 + 2 × 7 = 35 + 14 = 49.
The 11 times table. From 11 × 1 to 11 × 9, write the digit twice: 11 × 4 = 44 and 11 × 7 = 77. After that, use ten lots and one more lot: 11 × 10 = 110, 11 × 11 = 110 + 11 = 121 and 11 × 12 = 120 + 12 = 132.
Square numbers. When you multiply a number by itself, such as 5 × 5 = 25, the dots in the array make a perfect square. 1, 4, 9, 16, 25, ... are called square numbers. The first twelve are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121 and 144.
The whole grid. Here is the complete multiplication grid up to 12 × 12. The square numbers form a diagonal line (orange). The grid is a mirror image across this line, because 7 × 8 = 8 × 7 (blue). There are 144 facts in the grid, but because of commutativity only 78 of them are different. And you already know all of the × 0, × 1, × 2, × 5 and × 10 facts.
Key words. A square number is what you get when you multiply a whole number by itself. A grid is rows and columns of boxes.
Key ideas
- × 7: 5 lots + 2 lots. Learn 6 × 7 = 42, 7 × 7 = 49 and 7 × 8 = 56 (5, 6, 7, 8).
- × 11 (up to 11 × 9): write the digit twice. After that: × 10 and add one more lot.
- Square numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.
- There are 144 facts in the grid but only 78 different ones, because 7 × 8 = 8 × 7.
Method. Six is five and one more. Work out 5 lots, then add one more group.
- Work out 5 lots. The 5 times table is half of the 10 times table: 70 halved.5 × 7 = 35
- Add one more group. 6 = 5 + 1, so add the number once more.35 + 7 = 42
- Write the answer. 6 × 7 = 42
Check. Check by dividing: 42 ÷ 6 = 7. ✓
Watch out. Add one more group, not six more. 6 lots = 5 lots + 1 lot.
Method. Seven is five and two. Work out 5 lots and 2 lots, then add them.
- Work out 5 lots. The 5 times table is half of the 10 times table.5 × 7 = 35
- Work out 2 lots. Double the number.7 + 7 = 14
- Add them. 7 = 5 + 2.35 + 14 = 49
- Write the answer. 7 × 7 = 49
Check. Check by dividing: 49 ÷ 7 = 7. ✓
Watch out. Do not forget the 2 lots. 7 lots = 5 lots + 2 lots.
Method. Eight is double double double. Double the number three times.
- Swap the numbers round. Order does not matter in multiplication, so 7 × 8 = 8 × 7. Use the 8 times table trick.7 × 8 = 8 × 7
- Double once. This gives 2 lots.7 + 7 = 14
- Double again. This gives 4 lots.double 10 = 20, double 4 = 8, so 20 + 8 = 28
- Double a third time. This gives 8 lots.double 20 = 40, double 8 = 16, so 40 + 16 = 56
- Write the answer. 7 × 8 = 56
Check. Check by dividing: 56 ÷ 7 = 8. ✓
Watch out. Count your doubles. Three doubles give 8 lots. Two doubles only give 4.
Method. Twelve is ten and two. Multiply by 10, multiply by 2, then add.
- Multiply by 10. Move the digits one place to the left.10 × 7 = 70
- Multiply by 2. Double the number.7 + 7 = 14
- Add the two answers together. 12 = 10 + 2.70 + 14 = 84
- Write the answer. 12 × 7 = 84
Check. Check by dividing: 84 ÷ 7 = 12. ✓
Watch out. Do both parts, 10 lots and 2 lots, then add. Do not stop after 10 lots.
Method. Eleven is ten and one more. Multiply by 10, then add one more group.
- Multiply by 10. 10 lots of the number first.10 × 6 = 60
- Add one more group. 11 = 10 + 1, so add the number itself once more. You can also write the digit twice: 66.60 + 6 = 66
- Write the answer. 11 × 6 = 66
Check. Check by dividing: 66 ÷ 6 = 11. ✓
Watch out. The “write the digit twice” trick only works from 11 × 1 to 11 × 9. For 11 × 12 it does not give 1212. Use 10 lots + 1 lot.
Method. Eleven is ten and one more. Multiply by 10, then add one more group.
- Multiply by 10. 10 lots of the number first.10 × 12 = 120
- Add one more group. 11 = 10 + 1, so add the number itself once more.120 + 12 = 132
- Write the answer. 11 × 12 = 132
Check. Check by dividing: 132 ÷ 11 = 12. ✓
Watch out. The “write the digit twice” trick only works from 11 × 1 to 11 × 9. For 11 × 12 it does not give 1212. Use 10 lots + 1 lot.
Method. Twelve is ten and two. Multiply by 10, multiply by 2, then add.
- Multiply by 10. Move the digits one place to the left.10 × 12 = 120
- Multiply by 2. Double the number.double 10 = 20, double 2 = 4, so 20 + 4 = 24
- Add the two answers together. 12 = 10 + 2.120 + 24 = 144
- Write the answer. 12 × 12 = 144
Check. Check by dividing: 144 ÷ 12 = 12. ✓
Watch out. Do both parts, 10 lots and 2 lots, then add. Do not stop after 10 lots.
Method. A square number makes a square array: the same number of rows and columns.
- Find a pair of equal numbers that multiply to 49. Try the times tables. 7 × 7 is 49.7 × 7 = 49
- Check the array. The array has 7 rows and 7 columns. It is a square.7 rows of 7 dots
- Answer. Yes. 49 is a square number because 7 × 7 = 49.
Check. The square numbers in order: 1, 4, 9, 16, 25, 36, 49, 64. ✓
Watch out. The array must be a square. 7 × 8 = 56 is a rectangle, not a square, so 56 is not a square number.
Watch out
The “write the digit twice” trick for 11 only works up to 11 × 9. 11 × 12 is not 1212. It is 120 + 12 = 132. Also, 7 × 8 is 56, not 54 or 58. If you forget a fact, build it from ones you know, such as 5 lots and 3 lots of 7.Exercise 3D The 7 and 11 times tables, squares and the grid
Non-calculatorMethod. Three is double and one more. Double the number, then add the number once.
- Swap the numbers round. Order does not matter in multiplication, so 7 × 3 = 3 × 7. Use the 3 times table trick.7 × 3 = 3 × 7
- Double the number. This gives 2 lots.7 + 7 = 14
- Add one more group. 3 = 2 + 1, so add the number once more.14 + 7 = 21
- Write the answer. 7 × 3 = 21
Check. Check by dividing: 21 ÷ 3 = 7. ✓
Watch out. Add the number itself, not 3, as the extra group.
Method. Six is five and one more. Work out 5 lots, then add one more group.
- Swap the numbers round. Order does not matter in multiplication, so 7 × 6 = 6 × 7. Use the 6 times table trick.7 × 6 = 6 × 7
- Work out 5 lots. The 5 times table is half of the 10 times table: 70 halved.5 × 7 = 35
- Add one more group. 6 = 5 + 1, so add the number once more.35 + 7 = 42
- Write the answer. 7 × 6 = 42
Check. Check by dividing: 42 ÷ 6 = 7. ✓
Watch out. Add one more group, not six more. 6 lots = 5 lots + 1 lot.
Method. Seven is five and two. Work out 5 lots and 2 lots, then add them.
- Work out 5 lots. The 5 times table is half of the 10 times table.5 × 7 = 35
- Work out 2 lots. Double the number.7 + 7 = 14
- Add them. 7 = 5 + 2.35 + 14 = 49
- Write the answer. 7 × 7 = 49
Check. Check by dividing: 49 ÷ 7 = 7. ✓
Watch out. Do not forget the 2 lots. 7 lots = 5 lots + 2 lots.
Method. Eight is double double double. Double the number three times.
- Swap the numbers round. Order does not matter in multiplication, so 7 × 8 = 8 × 7. Use the 8 times table trick.7 × 8 = 8 × 7
- Double once. This gives 2 lots.7 + 7 = 14
- Double again. This gives 4 lots.double 10 = 20, double 4 = 8, so 20 + 8 = 28
- Double a third time. This gives 8 lots.double 20 = 40, double 8 = 16, so 40 + 16 = 56
- Write the answer. 7 × 8 = 56
Check. Check by dividing: 56 ÷ 7 = 8. ✓
Watch out. Count your doubles. Three doubles give 8 lots. Two doubles only give 4.
Method. Nine is one less than ten. Multiply by 10, then take away one group.
- Multiply by 10. 10 lots of the number first.10 × 7 = 70
- Take away one group. 9 = 10 − 1, so take away the number itself once.70 − 7 = 63
- Write the answer. Answers in the 9 times table have digits that add up to 9 (or 18).9 × 7 = 63
Check. The digits of 63 add up to 9: 6 + 3 = 9. ✓
Watch out. Take away 7, the other number, not 9. For 9 × 7 you work out 10 × 7 − 7.
Method. Eleven is ten and one more. Multiply by 10, then add one more group.
- Swap the numbers round. Order does not matter in multiplication, so 7 × 11 = 11 × 7. Use the 11 times table trick.7 × 11 = 11 × 7
- Multiply by 10. 10 lots of the number first.10 × 7 = 70
- Add one more group. 11 = 10 + 1, so add the number itself once more. You can also write the digit twice: 77.70 + 7 = 77
- Write the answer. 7 × 11 = 77
Check. Check by dividing: 77 ÷ 7 = 11. ✓
Watch out. The “write the digit twice” trick only works from 11 × 1 to 11 × 9. For 11 × 12 it does not give 1212. Use 10 lots + 1 lot.
Method. Twelve is ten and two. Multiply by 10, multiply by 2, then add.
- Multiply by 10. Move the digits one place to the left.10 × 7 = 70
- Multiply by 2. Double the number.7 + 7 = 14
- Add the two answers together. 12 = 10 + 2.70 + 14 = 84
- Write the answer. 12 × 7 = 84
Check. Check by dividing: 84 ÷ 7 = 12. ✓
Watch out. Do both parts, 10 lots and 2 lots, then add. Do not stop after 10 lots.
Method. Four is double double. Double the number, then double the answer.
- Swap the numbers round. Order does not matter in multiplication, so 7 × 4 = 4 × 7. Use the 4 times table trick.7 × 4 = 4 × 7
- Double the number. This gives 2 lots.7 + 7 = 14
- Double the answer again. Doubling twice gives 4 lots.double 10 = 20, double 4 = 8, so 20 + 8 = 28
- Write the answer. 7 × 4 = 28
Check. Check by dividing: 28 ÷ 4 = 7. ✓
Watch out. You must double twice. Doubling once gives the 2 times table.
Method. Five is half of ten. Multiply by 10 first, then halve the answer.
- Multiply by 10. This is easy: move the digits one place to the left.10 × 7 = 70
- Halve the answer. 5 is half of 10, so 5 lots of a number is half of 10 lots.half of 60 = 30, half of 10 = 5, so 30 + 5 = 35
- Write the answer. Answers in the 5 times table end in 0 or 5.5 × 7 = 35
Check. Check by dividing: 35 ÷ 5 = 7. ✓
Watch out. Halve the answer to 10 × the number. Do not halve the number before you multiply by 10 and then forget to multiply.
Method. To multiply by 10, every digit moves one place to the left. The ones become tens.
- Think about tens. 10 × 7 means 7 lots of 10, which is 7 tens.7 tens
- Move the digits one place to the left. A tens column needs a 0 in the ones place.7 → 70
- Write the answer. 10 × 7 = 70
Check. Check by dividing: 70 ÷ 7 = 10. ✓
Watch out. The 10 times table has a 0 in the ones place every time. Put the 0 on the end, but think “tens” so you understand why.
Method. Multiplying by 2 is the same as doubling. Double the number.
- Swap the numbers round. Order does not matter in multiplication, so 11 × 2 = 2 × 11. Use the 2 times table trick.11 × 2 = 2 × 11
- Double the number. Doubling means adding the number to itself.double 10 = 20, double 1 = 2, so 20 + 2 = 22
- Write the answer. 11 × 2 = 22
Check. Check by dividing: 22 ÷ 2 = 11. ✓
Watch out. Doubling is not adding 2. To double 7, add 7 + 7, not 7 + 2.
Method. Five is half of ten. Multiply by 10 first, then halve the answer.
- Swap the numbers round. Order does not matter in multiplication, so 11 × 5 = 5 × 11. Use the 5 times table trick.11 × 5 = 5 × 11
- Multiply by 10. This is easy: move the digits one place to the left.10 × 11 = 110
- Halve the answer. 5 is half of 10, so 5 lots of a number is half of 10 lots.half of 100 = 50, half of 10 = 5, so 50 + 5 = 55
- Write the answer. Answers in the 5 times table end in 0 or 5.11 × 5 = 55
Check. Check by dividing: 55 ÷ 5 = 11. ✓
Watch out. Halve the answer to 10 × the number. Do not halve the number before you multiply by 10 and then forget to multiply.
Method. Eleven is ten and one more. Multiply by 10, then add one more group.
- Multiply by 10. 10 lots of the number first.10 × 9 = 90
- Add one more group. 11 = 10 + 1, so add the number itself once more. You can also write the digit twice: 99.90 + 9 = 99
- Write the answer. 11 × 9 = 99
Check. The digits of 99 add up to 9: 9 + 9 = 18. ✓
Watch out. The “write the digit twice” trick only works from 11 × 1 to 11 × 9. For 11 × 12 it does not give 1212. Use 10 lots + 1 lot.
Method. Eleven is ten and one more. Multiply by 10, then add one more group.
- Swap the numbers round. Order does not matter in multiplication, so 3 × 11 = 11 × 3. Use the 11 times table trick.3 × 11 = 11 × 3
- Multiply by 10. 10 lots of the number first.10 × 3 = 30
- Add one more group. 11 = 10 + 1, so add the number itself once more. You can also write the digit twice: 33.30 + 3 = 33
- Write the answer. 3 × 11 = 33
Check. Check by dividing: 33 ÷ 3 = 11. ✓
Watch out. The “write the digit twice” trick only works from 11 × 1 to 11 × 9. For 11 × 12 it does not give 1212. Use 10 lots + 1 lot.
Method. To multiply by 10, every digit moves one place to the left. The ones become tens.
- Swap the numbers round. Order does not matter in multiplication, so 11 × 10 = 10 × 11. Use the 10 times table trick.11 × 10 = 10 × 11
- Think about tens. 10 × 11 means 11 lots of 10, which is 11 tens.11 tens
- Move the digits one place to the left. A tens column needs a 0 in the ones place.11 → 110
- Write the answer. 11 × 10 = 110
Check. Check by dividing: 110 ÷ 10 = 11. ✓
Watch out. The 10 times table has a 0 in the ones place every time. Put the 0 on the end, but think “tens” so you understand why.
Method. Eleven is ten and one more. Multiply by 10, then add one more group.
- Multiply by 10. 10 lots of the number first.10 × 11 = 110
- Add one more group. 11 = 10 + 1, so add the number itself once more.110 + 11 = 121
- Write the answer. 11 × 11 = 121
Check. Check by dividing: 121 ÷ 11 = 11. ✓
Watch out. The “write the digit twice” trick only works from 11 × 1 to 11 × 9. For 11 × 12 it does not give 1212. Use 10 lots + 1 lot.
Method. Eleven is ten and one more. Multiply by 10, then add one more group.
- Swap the numbers round. Order does not matter in multiplication, so 12 × 11 = 11 × 12. Use the 11 times table trick.12 × 11 = 11 × 12
- Multiply by 10. 10 lots of the number first.10 × 12 = 120
- Add one more group. 11 = 10 + 1, so add the number itself once more.120 + 12 = 132
- Write the answer. 12 × 11 = 132
Check. Check by dividing: 132 ÷ 11 = 12. ✓
Watch out. The “write the digit twice” trick only works from 11 × 1 to 11 × 9. For 11 × 12 it does not give 1212. Use 10 lots + 1 lot.
Method. Eleven is ten and one more. Multiply by 10, then add one more group.
- Swap the numbers round. Order does not matter in multiplication, so 7 × 11 = 11 × 7. Use the 11 times table trick.7 × 11 = 11 × 7
- Multiply by 10. 10 lots of the number first.10 × 7 = 70
- Add one more group. 11 = 10 + 1, so add the number itself once more. You can also write the digit twice: 77.70 + 7 = 77
- Write the answer. 7 × 11 = 77
Check. Check by dividing: 77 ÷ 7 = 11. ✓
Watch out. The “write the digit twice” trick only works from 11 × 1 to 11 × 9. For 11 × 12 it does not give 1212. Use 10 lots + 1 lot.
Method. Eleven is ten and one more. Multiply by 10, then add one more group.
- Multiply by 10. 10 lots of the number first.10 × 8 = 80
- Add one more group. 11 = 10 + 1, so add the number itself once more. You can also write the digit twice: 88.80 + 8 = 88
- Write the answer. 11 × 8 = 88
Check. Check by dividing: 88 ÷ 8 = 11. ✓
Watch out. The “write the digit twice” trick only works from 11 × 1 to 11 × 9. For 11 × 12 it does not give 1212. Use 10 lots + 1 lot.
Method. Eleven is ten and one more. Multiply by 10, then add one more group.
- Swap the numbers round. Order does not matter in multiplication, so 4 × 11 = 11 × 4. Use the 11 times table trick.4 × 11 = 11 × 4
- Multiply by 10. 10 lots of the number first.10 × 4 = 40
- Add one more group. 11 = 10 + 1, so add the number itself once more. You can also write the digit twice: 44.40 + 4 = 44
- Write the answer. 4 × 11 = 44
Check. Check by dividing: 44 ÷ 4 = 11. ✓
Watch out. The “write the digit twice” trick only works from 11 × 1 to 11 × 9. For 11 × 12 it does not give 1212. Use 10 lots + 1 lot.
Method. Three is double and one more. Double the number, then add the number once.
- Double the number. This gives 2 lots.3 + 3 = 6
- Add one more group. 3 = 2 + 1, so add the number once more.6 + 3 = 9
- Write the answer. 3 × 3 = 9
Check. Check by dividing: 9 ÷ 3 = 3. ✓
Watch out. Add the number itself, not 3, as the extra group.
Method. Five is half of ten. Multiply by 10 first, then halve the answer.
- Multiply by 10. This is easy: move the digits one place to the left.10 × 5 = 50
- Halve the answer. 5 is half of 10, so 5 lots of a number is half of 10 lots.half of 40 = 20, half of 10 = 5, so 20 + 5 = 25
- Write the answer. Answers in the 5 times table end in 0 or 5.5 × 5 = 25
Check. Check by dividing: 25 ÷ 5 = 5. ✓
Watch out. Halve the answer to 10 × the number. Do not halve the number before you multiply by 10 and then forget to multiply.
Method. Six is five and one more. Work out 5 lots, then add one more group.
- Work out 5 lots. The 5 times table is half of the 10 times table: 60 halved.5 × 6 = 30
- Add one more group. 6 = 5 + 1, so add the number once more.30 + 6 = 36
- Write the answer. 6 × 6 = 36
Check. Check by dividing: 36 ÷ 6 = 6. ✓
Watch out. Add one more group, not six more. 6 lots = 5 lots + 1 lot.
Method. Eight is double double double. Double the number three times.
- Double once. This gives 2 lots.8 + 8 = 16
- Double again. This gives 4 lots.double 10 = 20, double 6 = 12, so 20 + 12 = 32
- Double a third time. This gives 8 lots.double 30 = 60, double 2 = 4, so 60 + 4 = 64
- Write the answer. 8 × 8 = 64
Check. Check by dividing: 64 ÷ 8 = 8. ✓
Watch out. Count your doubles. Three doubles give 8 lots. Two doubles only give 4.
Method. Nine is one less than ten. Multiply by 10, then take away one group.
- Multiply by 10. 10 lots of the number first.10 × 9 = 90
- Take away one group. 9 = 10 − 1, so take away the number itself once.90 − 9 = 81
- Write the answer. Answers in the 9 times table have digits that add up to 9 (or 18).9 × 9 = 81
Check. The digits of 81 add up to 9: 8 + 1 = 9. ✓
Watch out. Take away 9, the other number, not 9. For 9 × 9 you work out 10 × 9 − 9.
Method. To multiply by 10, every digit moves one place to the left. The ones become tens.
- Think about tens. 10 × 10 means 10 lots of 10, which is 10 tens.10 tens
- Move the digits one place to the left. A tens column needs a 0 in the ones place.10 → 100
- Write the answer. 10 × 10 = 100
Check. Check by dividing: 100 ÷ 10 = 10. ✓
Watch out. The 10 times table has a 0 in the ones place every time. Put the 0 on the end, but think “tens” so you understand why.
Method. Eleven is ten and one more. Multiply by 10, then add one more group.
- Multiply by 10. 10 lots of the number first.10 × 11 = 110
- Add one more group. 11 = 10 + 1, so add the number itself once more.110 + 11 = 121
- Write the answer. 11 × 11 = 121
Check. Check by dividing: 121 ÷ 11 = 11. ✓
Watch out. The “write the digit twice” trick only works from 11 × 1 to 11 × 9. For 11 × 12 it does not give 1212. Use 10 lots + 1 lot.
Method. Twelve is ten and two. Multiply by 10, multiply by 2, then add.
- Multiply by 10. Move the digits one place to the left.10 × 12 = 120
- Multiply by 2. Double the number.double 10 = 20, double 2 = 4, so 20 + 4 = 24
- Add the two answers together. 12 = 10 + 2.120 + 24 = 144
- Write the answer. 12 × 12 = 144
Check. Check by dividing: 144 ÷ 12 = 12. ✓
Watch out. Do both parts, 10 lots and 2 lots, then add. Do not stop after 10 lots.
Method. Six is five and one more. Work out 5 lots, then add one more group.
- Work out 5 lots. The 5 times table is half of the 10 times table: 60 halved.5 × 6 = 30
- Add one more group. 6 = 5 + 1, so add the number once more.30 + 6 = 36
- Write the answer. 6 × 6 = 36
Check. Check by dividing: 36 ÷ 6 = 6. ✓
Watch out. Add one more group, not six more. 6 lots = 5 lots + 1 lot.
Method. Six is five and one more. Work out 5 lots, then add one more group.
- Work out 5 lots. The 5 times table is half of the 10 times table: 70 halved.5 × 7 = 35
- Add one more group. 6 = 5 + 1, so add the number once more.35 + 7 = 42
- Write the answer. 6 × 7 = 42
Check. Check by dividing: 42 ÷ 6 = 7. ✓
Watch out. Add one more group, not six more. 6 lots = 5 lots + 1 lot.
Method. Eight is double double double. Double the number three times.
- Swap the numbers round. Order does not matter in multiplication, so 6 × 8 = 8 × 6. Use the 8 times table trick.6 × 8 = 8 × 6
- Double once. This gives 2 lots.6 + 6 = 12
- Double again. This gives 4 lots.double 10 = 20, double 2 = 4, so 20 + 4 = 24
- Double a third time. This gives 8 lots.double 20 = 40, double 4 = 8, so 40 + 8 = 48
- Write the answer. 6 × 8 = 48
Check. Check by dividing: 48 ÷ 6 = 8. ✓
Watch out. Count your doubles. Three doubles give 8 lots. Two doubles only give 4.
Method. Seven is five and two. Work out 5 lots and 2 lots, then add them.
- Work out 5 lots. The 5 times table is half of the 10 times table.5 × 7 = 35
- Work out 2 lots. Double the number.7 + 7 = 14
- Add them. 7 = 5 + 2.35 + 14 = 49
- Write the answer. 7 × 7 = 49
Check. Check by dividing: 49 ÷ 7 = 7. ✓
Watch out. Do not forget the 2 lots. 7 lots = 5 lots + 2 lots.
Method. Eight is double double double. Double the number three times.
- Swap the numbers round. Order does not matter in multiplication, so 7 × 8 = 8 × 7. Use the 8 times table trick.7 × 8 = 8 × 7
- Double once. This gives 2 lots.7 + 7 = 14
- Double again. This gives 4 lots.double 10 = 20, double 4 = 8, so 20 + 8 = 28
- Double a third time. This gives 8 lots.double 20 = 40, double 8 = 16, so 40 + 16 = 56
- Write the answer. 7 × 8 = 56
Check. Check by dividing: 56 ÷ 7 = 8. ✓
Watch out. Count your doubles. Three doubles give 8 lots. Two doubles only give 4.
Method. Eight is double double double. Double the number three times.
- Double once. This gives 2 lots.8 + 8 = 16
- Double again. This gives 4 lots.double 10 = 20, double 6 = 12, so 20 + 12 = 32
- Double a third time. This gives 8 lots.double 30 = 60, double 2 = 4, so 60 + 4 = 64
- Write the answer. 8 × 8 = 64
Check. Check by dividing: 64 ÷ 8 = 8. ✓
Watch out. Count your doubles. Three doubles give 8 lots. Two doubles only give 4.
Method. Nine is one less than ten. Multiply by 10, then take away one group.
- Swap the numbers round. Order does not matter in multiplication, so 6 × 9 = 9 × 6. Use the 9 times table trick.6 × 9 = 9 × 6
- Multiply by 10. 10 lots of the number first.10 × 6 = 60
- Take away one group. 9 = 10 − 1, so take away the number itself once.60 − 6 = 54
- Write the answer. Answers in the 9 times table have digits that add up to 9 (or 18).6 × 9 = 54
Check. The digits of 54 add up to 9: 5 + 4 = 9. ✓
Watch out. Take away 6, the other number, not 9. For 9 × 6 you work out 10 × 6 − 6.
Method. Nine is one less than ten. Multiply by 10, then take away one group.
- Swap the numbers round. Order does not matter in multiplication, so 7 × 9 = 9 × 7. Use the 9 times table trick.7 × 9 = 9 × 7
- Multiply by 10. 10 lots of the number first.10 × 7 = 70
- Take away one group. 9 = 10 − 1, so take away the number itself once.70 − 7 = 63
- Write the answer. Answers in the 9 times table have digits that add up to 9 (or 18).7 × 9 = 63
Check. The digits of 63 add up to 9: 6 + 3 = 9. ✓
Watch out. Take away 7, the other number, not 9. For 9 × 7 you work out 10 × 7 − 7.
Method. Nine is one less than ten. Multiply by 10, then take away one group.
- Swap the numbers round. Order does not matter in multiplication, so 8 × 9 = 9 × 8. Use the 9 times table trick.8 × 9 = 9 × 8
- Multiply by 10. 10 lots of the number first.10 × 8 = 80
- Take away one group. 9 = 10 − 1, so take away the number itself once.80 − 8 = 72
- Write the answer. Answers in the 9 times table have digits that add up to 9 (or 18).8 × 9 = 72
Check. The digits of 72 add up to 9: 7 + 2 = 9. ✓
Watch out. Take away 8, the other number, not 9. For 9 × 8 you work out 10 × 8 − 8.
Method. Nine is one less than ten. Multiply by 10, then take away one group.
- Multiply by 10. 10 lots of the number first.10 × 9 = 90
- Take away one group. 9 = 10 − 1, so take away the number itself once.90 − 9 = 81
- Write the answer. Answers in the 9 times table have digits that add up to 9 (or 18).9 × 9 = 81
Check. The digits of 81 add up to 9: 8 + 1 = 9. ✓
Watch out. Take away 9, the other number, not 9. For 9 × 9 you work out 10 × 9 − 9.
Method. Twelve is ten and two. Multiply by 10, multiply by 2, then add.
- Swap the numbers round. Order does not matter in multiplication, so 6 × 12 = 12 × 6. Use the 12 times table trick.6 × 12 = 12 × 6
- Multiply by 10. Move the digits one place to the left.10 × 6 = 60
- Multiply by 2. Double the number.6 + 6 = 12
- Add the two answers together. 12 = 10 + 2.60 + 12 = 72
- Write the answer. 6 × 12 = 72
Check. Check by dividing: 72 ÷ 6 = 12. ✓
Watch out. Do both parts, 10 lots and 2 lots, then add. Do not stop after 10 lots.
Method. Twelve is ten and two. Multiply by 10, multiply by 2, then add.
- Swap the numbers round. Order does not matter in multiplication, so 8 × 12 = 12 × 8. Use the 12 times table trick.8 × 12 = 12 × 8
- Multiply by 10. Move the digits one place to the left.10 × 8 = 80
- Multiply by 2. Double the number.8 + 8 = 16
- Add the two answers together. 12 = 10 + 2.80 + 16 = 96
- Write the answer. 8 × 12 = 96
Check. Check by dividing: 96 ÷ 8 = 12. ✓
Watch out. Do both parts, 10 lots and 2 lots, then add. Do not stop after 10 lots.
Key words. A missing number is a number you have to find. Division and multiplication are inverses (opposites): they undo each other.
Method. Use the inverse operation. Multiplication and division undo each other.
- Say what the sentence means. We need the number that 7 is multiplied by to make 63.7 × ? = 63
- Use the inverse (opposite) operation. The opposite of multiplying is dividing. Divide 63 by 7.63 ÷ 7 = 9
- Write the missing number. 7 × 9 = 63
Check. Put it back: 7 × 9 = 63. ✓
Watch out. Do not just put the numbers in the box in the order you see them. Think about what the sentence means.
Key words. A missing number is a number you have to find. Division and multiplication are inverses (opposites): they undo each other.
Method. Use the inverse operation. Multiplication and division undo each other.
- Say what the sentence means. We need the number that, multiplied by 11, makes 88.? × 11 = 88
- Use the inverse (opposite) operation. Order does not matter in multiplication. Divide 88 by 11.88 ÷ 11 = 8
- Write the missing number. 8 × 11 = 88
Check. Put it back: 8 × 11 = 88. ✓
Watch out. Do not just put the numbers in the box in the order you see them. Think about what the sentence means.
Key words. A missing number is a number you have to find. Division and multiplication are inverses (opposites): they undo each other.
Method. Use the inverse operation. Multiplication and division undo each other.
- Say what the sentence means. We need the number that 8 is multiplied by to make 56.8 × ? = 56
- Use the inverse (opposite) operation. The opposite of multiplying is dividing. Divide 56 by 8.56 ÷ 8 = 7
- Write the missing number. 8 × 7 = 56
Check. Put it back: 8 × 7 = 56. ✓
Watch out. Do not just put the numbers in the box in the order you see them. Think about what the sentence means.
Key words. A missing number is a number you have to find. Division and multiplication are inverses (opposites): they undo each other.
Method. Use the inverse operation. Multiplication and division undo each other.
- Say what the sentence means. We need the number that, multiplied by 7, makes 84.? × 7 = 84
- Use the inverse (opposite) operation. Order does not matter in multiplication. Divide 84 by 7.84 ÷ 7 = 12
- Write the missing number. 12 × 7 = 84
Check. Put it back: 12 × 7 = 84. ✓
Watch out. Do not just put the numbers in the box in the order you see them. Think about what the sentence means.
Key words. A missing number is a number you have to find. Division and multiplication are inverses (opposites): they undo each other.
Method. Use the inverse operation. Multiplication and division undo each other.
- Say what the sentence means. We need the number that 12 is multiplied by to make 144.12 × ? = 144
- Use the inverse (opposite) operation. The opposite of multiplying is dividing. Divide 144 by 12.144 ÷ 12 = 12
- Write the missing number. 12 × 12 = 144
Check. Put it back: 12 × 12 = 144. ✓
Watch out. Do not just put the numbers in the box in the order you see them. Think about what the sentence means.
Key words. A missing number is a number you have to find. Division and multiplication are inverses (opposites): they undo each other.
Method. Use the inverse operation. Multiplication and division undo each other.
- Say what the sentence means. We need the number that, multiplied by 9, makes 81.? × 9 = 81
- Use the inverse (opposite) operation. Order does not matter in multiplication. Divide 81 by 9.81 ÷ 9 = 9
- Write the missing number. 9 × 9 = 81
Check. Put it back: 9 × 9 = 81. ✓
Watch out. Do not just put the numbers in the box in the order you see them. Think about what the sentence means.
Method. Eight is double double double. Double the number three times.
- Swap the numbers round. Order does not matter in multiplication, so 6 × 8 = 8 × 6. Use the 8 times table trick.6 × 8 = 8 × 6
- Double once. This gives 2 lots.6 + 6 = 12
- Double again. This gives 4 lots.double 10 = 20, double 2 = 4, so 20 + 4 = 24
- Double a third time. This gives 8 lots.double 20 = 40, double 4 = 8, so 40 + 8 = 48
- Write the answer. 6 × 8 = 48
Check. Check by dividing: 48 ÷ 6 = 8. ✓
Watch out. Count your doubles. Three doubles give 8 lots. Two doubles only give 4.
Method. Seven is five and two. Work out 5 lots and 2 lots, then add them.
- Work out 5 lots. The 5 times table is half of the 10 times table.5 × 7 = 35
- Work out 2 lots. Double the number.7 + 7 = 14
- Add them. 7 = 5 + 2.35 + 14 = 49
- Write the answer. 7 × 7 = 49
Check. Check by dividing: 49 ÷ 7 = 7. ✓
Watch out. Do not forget the 2 lots. 7 lots = 5 lots + 2 lots.
Method. Nine is one less than ten. Multiply by 10, then take away one group.
- Swap the numbers round. Order does not matter in multiplication, so 7 × 9 = 9 × 7. Use the 9 times table trick.7 × 9 = 9 × 7
- Multiply by 10. 10 lots of the number first.10 × 7 = 70
- Take away one group. 9 = 10 − 1, so take away the number itself once.70 − 7 = 63
- Write the answer. Answers in the 9 times table have digits that add up to 9 (or 18).7 × 9 = 63
Check. The digits of 63 add up to 9: 6 + 3 = 9. ✓
Watch out. Take away 7, the other number, not 9. For 9 × 7 you work out 10 × 7 − 7.
Method. Nine is one less than ten. Multiply by 10, then take away one group.
- Swap the numbers round. Order does not matter in multiplication, so 8 × 9 = 9 × 8. Use the 9 times table trick.8 × 9 = 9 × 8
- Multiply by 10. 10 lots of the number first.10 × 8 = 80
- Take away one group. 9 = 10 − 1, so take away the number itself once.80 − 8 = 72
- Write the answer. Answers in the 9 times table have digits that add up to 9 (or 18).8 × 9 = 72
Check. The digits of 72 add up to 9: 7 + 2 = 9. ✓
Watch out. Take away 8, the other number, not 9. For 9 × 8 you work out 10 × 8 − 8.
Method. Square numbers are made by multiplying a number by itself. Try the numbers in order until you go past 100.
- Start with numbers that are too small. 5 × 5 = 25 is less than 30.5 × 5 = 25 (too small)
- Try the next numbers. Keep going until the answer is more than 100.6 × 6 = 36 7 × 7 = 49 8 × 8 = 64 9 × 9 = 81 10 × 10 = 100
- Choose the ones between 30 and 100. 100 is not between 30 and 100.36, 49, 64, 81
Check. Look at the diagonal of the grid: 25, 36, 49, 64, 81, 100. ✓
Watch out. “Between 30 and 100” does not include 100.
Method. There are 8 equal groups, so multiply the number in one group by the number of groups.
- Draw a bar model. 8 equal bars show 8 equal weeks. Each bar is 7. We want the total.
- Choose the operation. Equal groups: multiply the number of groups by the amount in each group.8 × 7
- Work it out. Use a times table trick.7 + 7 = 14
double 10 = 20, double 4 = 8, so 20 + 8 = 28
double 20 = 40, double 8 = 16, so 40 + 16 = 56
8 × 7 = 56 - Write the answer. Include the unit.56 days
Check. Divide back: 56 ÷ 8 = 7. ✓
Watch out. Check that you multiplied. Equal groups mean the total is bigger than the size of one group.
Method. There are 9 equal groups, so multiply the number in one group by the number of groups.
- Draw a bar model. 9 equal bars show 9 equal teams. Each bar is 11. We want the total.
- Choose the operation. Equal groups: multiply the number of groups by the amount in each group.9 × 11
- Work it out. Use a times table trick.10 × 9 = 90
90 + 9 = 99
9 × 11 = 99 - Write the answer. Include the unit.99 players
Check. Divide back: 99 ÷ 9 = 11. ✓
Watch out. Check that you multiplied. Equal groups mean the total is bigger than the size of one group.
Method. The plants are in an array of 9 rows with 9 in each row, so multiply 9 × 9.
- Count the rows and columns. There are 9 rows and 9 plants in each row.9 rows of 9
- Multiply. Use the 9 times table: ten lots take away one lot.10 × 9 = 90
90 − 9 = 81
9 × 9 = 81 - Write the answer. The garden is a square, so 81 is a square number.81 plants
Check. The digits of 81 add up to 9: 8 + 1 = 9. ✓
Watch out. Rows and columns means multiply. Do not add 9 + 9.
Method. There are 6 equal groups, so multiply the number in one group by the number of groups.
- Draw a bar model. 6 equal bars show 6 equal pizzas. Each bar is £7. We want the total.
- Choose the operation. Equal groups: multiply the number of groups by the amount in each group.6 × £7
- Work it out. Use a times table trick.5 × 7 = 35
35 + 7 = 42
6 × 7 = 42 - Write the answer. Include the unit.£42
Check. Divide back: 42 ÷ 6 = 7. ✓
Watch out. Check that you multiplied. Equal groups mean the total is bigger than the size of one group.
Method. Check Ravi’s answer by building 7 × 8 from facts you know.
- Use 7 × 7 = 49. 7 × 8 is one more group of 7 than 7 × 7.7 × 7 = 49
- Add one more group of 7. 49 + 7 = 56
- Compare with Ravi. Ravi said 54. The digits in order are 5, 6, 7, 8, so the fact is 56 = 7 × 8.56, not 54
Check. Also 5 × 8 = 40 and 2 × 8 = 16, and 40 + 16 = 56. ✓
Watch out. Learn 7 × 8 = 56 by the pattern 5, 6, 7, 8.
Method. Try all the numbers from 1 to 9.
- Write the facts. 11 times a digit gives the digit twice.11, 22, 33, 44, 55, 66, 77, 88, 99
- Decide. Every answer has two matching digits.Always
Check. 11 × 9 = 99. ✓
Watch out. Be careful: it stops working after 11 × 9. 11 × 10 = 110.
Method. Look at some square numbers.
- List some. Some end in an even digit and some in an odd digit.4, 16, 36, 64 are even. 9, 25, 49, 81 are odd.
- Decide. We found some of each.Sometimes
Check. Even × even is even (4 × 4 = 16) and odd × odd is odd (5 × 5 = 25). ✓
Watch out. “Sometimes” needs an example that works and an example that does not.
Method. Look for a property that three numbers share. Try writing each number as a multiplication.
- Write each as a multiplication fact. See if any of them is a number times itself.49 = 7 × 7
64 = 8 × 8
56 = 7 × 8
81 = 9 × 9 - Choose the odd one out. 49, 64 and 81 are square numbers. 56 is 7 × 8, which is not a number times itself.56
Check. The square numbers are on the diagonal of the grid. 56 is not on it. ✓
Watch out. 56 can also be 4 × 14 or 2 × 28, but none of those have equal numbers.
Method. The grid is a mirror image across the diagonal. Count the boxes on one side of the diagonal, including the diagonal.
- Look at the picture. The shaded boxes are the diagonal and everything above it. Every other box is a mirror copy of a shaded box.Count the shaded boxes row by row.
- Count row by row. Row 1 has 12 shaded boxes, row 2 has 11, and each row has one fewer than the row before.12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1
- Add them up. Add in pairs: 12 + 1 = 13, 11 + 2 = 13, and so on. There are 6 pairs.6 × 13 = 78
- Write the answer. 78 different facts
Check. 144 − 12 = 132 boxes that are not on the diagonal. Half of 132 is 66. 66 + 12 = 78. ✓
Watch out. Do not count the diagonal twice. The square numbers (like 7 × 7) have no mirror partner.