Year 4 Times Tables: check-up and SATs-style questions

Method. Eight is double double double. Double the number three times.

1. Double once. This gives 2 lots.
   7 + 7 = 14
2. Double again. This gives 4 lots.
   double 10 = 20, double 4 = 8, so 20 + 8 = 28
3. Double a third time. This gives 8 lots.
   double 20 = 40, double 8 = 16, so 40 + 16 = 56
4. Write the answer.
   8 × 7 = 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.

1. Multiply by 10. 10 lots of the number first.
   10 × 12 = 120
2. Take away one group. 9 = 10 − 1, so take away the number itself once.
   120 − 12 = 108
3. Write the answer. Answers in the 9 times table have digits that add up to 9 (or 18).
   9 × 12 = 108

Check. Check by dividing: 108 ÷ 9 = 12. ✓

Watch out. Take away 12, the other number, not 9. For 9 × 12 you work out 10 × 12 − 12.

Method. Use the 9 times table. Count up in 9s until you reach 72.

1. Turn the division into a missing multiplication. 72 ÷ 9 asks: what do we multiply 9 by to get 72?
   72 ÷ 9 = ? means ? × 9 = 72
2. Count up in 9s until you reach 72. Each number you say is one more group of 9.
   9, 18, 27, 36, 45, 54, 63, 72
3. Count how many numbers you said. The number of jumps is the answer.
   I said 8 numbers, so 8 × 9 = 72
4. Write the answer.
   72 ÷ 9 = 8

Check. Multiply back: 8 × 9 = 72. ✓

Watch out. Know your 9 times table facts, then division is quick.

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.

1. Say what the sentence means. We need the number that, multiplied by 6, makes 54.
   ? × 6 = 54
2. Use the inverse (opposite) operation. Order does not matter in multiplication. Divide 54 by 6.
   54 ÷ 6 = 9
3. Write the missing number.
   9 × 6 = 54

Check. Put it back: 9 × 6 = 54. ✓

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 fact family is a group of multiplication and division facts that use the same three numbers.

Method. A fact family uses three numbers. Two multiplication facts and two division facts use the same three numbers.

1. Put the numbers in a fact triangle. The product goes at the top and the two factors at the bottom.
2. Write the two multiplication facts. Multiply the bottom numbers in either order.
   4 × 9 = 36
   9 × 4 = 36
3. Write the two division facts. Start at the top and divide by one factor to get the other.
   36 ÷ 4 = 9
   36 ÷ 9 = 4

Check. Check one fact: 4 × 9 = 36, so 36 ÷ 9 = 4. ✓

Watch out. In a division fact, the biggest number (the product) always comes first.

Key words. A known fact is a multiplication fact you can already recall. A derived fact is a new fact you work out from a known fact.

Method. Use the fact you know, 7 × 6 = 42, and place value. 70 is 7 tens, so the answer is 42 tens.

1. Spot the fact you know. Take away the zeros and look at the digits that are left.
   7 × 6 = 42
2. Say the bigger number in tens. 70 is 7 tens.
   70 = 7 tens
3. Multiply, using the known fact. 7 tens × 6 = 42 tens, because 7 × 6 = 42.
   7 × 6 = 42, so 7 tens × 6 = 42 tens
4. Change 42 tens back to a number. 1 ten is 10, so 42 tens is 42 × 10.
   42 tens = 420
5. Write the answer.
   70 × 6 = 420

Check. Divide back: 420 ÷ 6 = 70. ✓

Watch out. The answer is 42 tens, which has 1 zero on the end. Count the zeros carefully.

Key words. A factor of a number is a whole number that divides into it exactly. A factor pair is two factors that multiply to make the number.

Method. A factor pair is two numbers that multiply to make 18. Test 1, 2, 3, ... in order, and write down every pair you find.

1. Start at 1 and try each number in turn. A factor pair is two numbers that multiply to make the number. We test 1, 2, 3, ... using the times tables.
   1 × 18 = 18  (a pair: 1 and 18)
   2 × 9 = 18  (a pair: 2 and 9)
   3 × 6 = 18  (a pair: 3 and 6)
   4 × 4 = 16 and 4 × 5 = 20: 18 is in between, so 4 is not a factor
2. Stop when the numbers meet. After 4, the next factors would just be pairs we have already found the other way round.
   We can stop at 4.
3. Write the factor pairs.
   1 × 18 = 18
   2 × 9 = 18
   3 × 6 = 18
4. Picture them. Each pair makes a different array of the same number of squares.
5. List all the factors in order. Each number in a pair is a factor.
   1, 2, 3, 6, 9, 18

Check. There are 6 factors: 1, 2, 3, 6, 9, 18. Every factor pairs up with another. ✓

Watch out. Do not forget 1 and the number itself. Every number has the pair 1 and itself.

Key words. You can multiply three numbers in any order and the answer is the same.

Method. Multiplication can be done in any order, so look for two numbers that are easy to multiply first.

1. Choose two numbers to multiply first. 2 × 5 = 10, and multiplying by 10 is easy.
   2 × 5 = 10
2. Multiply the answer by the last number, 6. 10 × 6 is a times table fact.
   6 tens
   6 → 60
   10 × 6 = 60
3. Write the answer.
   2 × 5 × 6 = 60

Check. Try a different order: 5 × 6 = 30, then 30 × 2 = 60. ✓

Watch out. You can multiply in any order. Pick the pair that gives an easy answer, like a pair that makes 10.

Method. There are 9 equal groups, so multiply the number in one group by the number of groups.

1. Draw a bar model. 9 equal bars show 9 equal boxes. Each bar is 6. We want the total.
2. Choose the operation. Equal groups: multiply the number of groups by the amount in each group.
   9 × 6
3. Work it out. Use a times table trick.
   10 × 6 = 60
   60 − 6 = 54
   9 × 6 = 54
4. Write the answer. Include the unit.
   54 cupcakes

Check. Divide back: 54 ÷ 9 = 6. ✓

Watch out. Check that you multiplied. Equal groups mean the total is bigger than the size of one group.

Method. Dividing is the opposite of multiplying. Use the times table to find how many times the number fits.

1. Draw a bar model. The whole is 96. Each bar is 8. We want to know how many bars. (The picture shows only some of the bars.)
2. Choose the operation. We want to know how many groups of 8 fit into 96. That is a division.
   96 ÷ 8
3. Use the times tables. Think: what do we multiply 8 by to get 96?
   12 × 8 = 96, so 96 ÷ 8 = 12
4. Write the answer. Include the unit.
   12 bags

Check. Multiply back: 12 × 8 = 96. ✓

Watch out. Read the question carefully. Does it ask for the size of each group, or for how many groups?

Method. Nine is one less than ten. Multiply by 10, then take away one group.

1. Multiply by 10. 10 lots of the number first.
   10 × 6 = 60
2. Take away one group. 9 = 10 − 1, so take away the number itself once.
   60 − 6 = 54
3. Write the answer. Answers in the 9 times table have digits that add up to 9 (or 18).
   9 × 6 = 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. Use the 12 times table. Count up in 12s until you reach 96.

1. Turn the division into a missing multiplication. 96 ÷ 12 asks: what do we multiply 12 by to get 96?
   96 ÷ 12 = ? means ? × 12 = 96
2. Count up in 12s until you reach 96. Each number you say is one more group of 12.
   12, 24, 36, 48, 60, 72, 84, 96
3. Count how many numbers you said. The number of jumps is the answer.
   I said 8 numbers, so 8 × 12 = 96
4. Write the answer.
   96 ÷ 12 = 8

Check. Multiply back: 8 × 12 = 96. ✓

Watch out. Know your 12 times table facts, then division is quick.

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.

1. Say what the sentence means. A number divided by 7 gives 9.
   ? ÷ 7 = 9
2. Use the inverse (opposite) operation. The opposite of dividing by 7 is multiplying by 7.
   9 × 7 = 63
3. Write the missing number.
   63 ÷ 7 = 9

Check. Put it back: 63 ÷ 7 = 9. ✓

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 known fact is a multiplication fact you can already recall. A derived fact is a new fact you work out from a known fact.

Method. Use the fact you know, 6 × 8 = 48, and place value. 60 is 6 tens, so the answer is 48 tens.

1. Spot the fact you know. Take away the zeros and look at the digits that are left.
   6 × 8 = 48
2. Say the bigger number in tens. 60 is 6 tens.
   60 = 6 tens
3. Multiply, using the known fact. 6 tens × 8 = 48 tens, because 6 × 8 = 48.
   6 × 8 = 48, so 6 tens × 8 = 48 tens
4. Change 48 tens back to a number. 1 ten is 10, so 48 tens is 48 × 10.
   48 tens = 480
5. Write the answer.
   60 × 8 = 480

Check. Divide back: 480 ÷ 8 = 60. ✓

Watch out. The answer is 48 tens, which has 1 zero on the end. Count the zeros carefully.

Method. There are 9 equal groups, so multiply the number in one group by the number of groups.

1. Draw a bar model. 9 equal bars show 9 equal packs. Each bar is 12. We want the total.
2. Choose the operation. Equal groups: multiply the number of groups by the amount in each group.
   9 × 12
3. Work it out. Use a times table trick.
   10 × 12 = 120
   120 − 12 = 108
   9 × 12 = 108
4. Write the answer. Include the unit.
   108 pencils

Check. Divide back: 108 ÷ 9 = 12. ✓

Watch out. Check that you multiplied. Equal groups mean the total is bigger than the size of one group.

Method. Work out 6 × 8 first. Then work out each choice and find the two that match.

1. Work out 6 × 8. Use the 8 times table: double three times.
   8 × 6 = 48
2. Work out each choice.
   A: 4 × 12 = 48
   B: 7 × 7 = 49
   C: 8 × 6 = 48
   D: 9 × 5 = 45
3. Choose the two that make 48. C is 8 × 6, the same numbers swapped. A is another pair of factors of 48.
   A and C

Check. 48 ÷ 4 = 12 and 48 ÷ 8 = 6. ✓

Watch out. 2 marks: 1 mark for each correct box. If you tick three boxes you lose the marks.

Key words. A factor of a number is a whole number that divides into it exactly. A factor pair is two factors that multiply to make the number.

Method. A factor pair is two numbers that multiply to make 28. Test 1, 2, 3, ... in order, and write down every pair you find.

1. Start at 1 and try each number in turn. A factor pair is two numbers that multiply to make the number. We test 1, 2, 3, ... using the times tables.
   1 × 28 = 28  (a pair: 1 and 28)
   2 × 14 = 28  (a pair: 2 and 14)
   3 × 9 = 27 and 3 × 10 = 30: 28 is in between, so 3 is not a factor
   4 × 7 = 28  (a pair: 4 and 7)
   5 × 5 = 25 and 5 × 6 = 30: 28 is in between, so 5 is not a factor
2. Stop when the numbers meet. After 5, the next factors would just be pairs we have already found the other way round.
   We can stop at 5.
3. Write the factor pairs.
   1 × 28 = 28
   2 × 14 = 28
   4 × 7 = 28
4. Picture them. Each pair makes a different array of the same number of squares.
5. List all the factors in order. Each number in a pair is a factor.
   1, 2, 4, 7, 14, 28

Check. There are 6 factors: 1, 2, 4, 7, 14, 28. Every factor pairs up with another. ✓

Watch out. Do not forget 1 and the number itself. Every number has the pair 1 and itself.

Key words. You can multiply three numbers in any order and the answer is the same.

Method. Multiplication can be done in any order, so look for two numbers that are easy to multiply first.

1. Choose two numbers to multiply first. 4 × 5 = 20, a multiple of 10, which is easy to multiply.
   4 × 5 = 20
2. Multiply the answer by the last number, 7. 20 is 2 tens. Work out 2 × 7, then say that many tens.
   2 × 7 = 14, so 2 tens × 7 = 14 tens
   14 tens = 140
3. Write the answer.
   4 × 5 × 7 = 140

Check. Try a different order: 5 × 7 = 35, then 35 × 4 = 140. ✓

Watch out. You can multiply in any order. Pick the pair that gives an easy answer, like a pair that makes 10.

Method. Check Leo’s answer with the digit test for the 9 times table, then work out the right answer.

1. Add the digits of Leo’s answer. Every answer in the 9 times table has digits that add to 9.
   6 + 2 = 8
2. Compare with 9. 8 is not 9, so 62 is not in the 9 times table.
   Leo is wrong.
3. Work out 9 × 7. Ten lots take away one lot.
   10 × 7 = 70, then 70 − 7 = 63
4. Check the new answer.
   6 + 3 = 9. ✓   9 × 7 = 63

Check. 63 ÷ 9 = 7. ✓

Watch out. 2 marks: 1 mark for showing Leo is wrong (the digits do not add to 9) and 1 mark for the correct answer, 63.

Method. Work out how many pens and how many pencils, then add the two totals.

1. Pens. 7 packs of 8 pens.
   7 + 7 = 14
   double 10 = 20, double 4 = 8, so 20 + 8 = 28
   double 20 = 40, double 8 = 16, so 40 + 16 = 56
   7 × 8 = 56
2. Pencils. 9 packs of 6 pencils.
   10 × 6 = 60
   60 − 6 = 54
   9 × 6 = 54
3. Add the two totals.
   56 + 54 = 110

Check. 110 − 56 = 54 and 54 ÷ 6 = 9. ✓

Watch out. 3 marks: 1 for 7 × 8, 1 for 9 × 6, and 1 for adding to get 110.