Times tables 3 and 4
By the end of this chapter you will be able to
- Know the 3 times table facts in any order
- Know the 4 times table facts in any order
- Find a missing number in a multiplication or division with the 3 and 4 facts
- Show that 3 x 4 and 4 x 3 give the same total
- Solve a word problem with equal groups of 3 or 4
You should already know
- Counting in twos, fives and tens (Level 3, chapter 7)
- Repeated addition (Level 3, chapter 6)
Where this leads
- Times tables 6, 8 and 9 (chapter 5)
Step-by-step practice: maths (Level 4). Small steps, repeated until fluent. Content: Recall and use the multiplication and division facts for the 3 and 4 times tables (MD1), Write and calculate multiplication statements using the tables known, including missing numbers (MD2, MD3), Understand that the order of the numbers in a multiplication does not change the answer (Year 4 paraphrase), Solve one-step problems with equal groups of 3 or 4 (MD3).
Exercise P Do you remember?
Non-calculatorMethod. Count in fives four times.
- Count in fives. Each count is one group of 5.5, 10, 15, 20
- The last number we said is the answer. We counted four groups of 5.5 × 4 = 20
- Write the answer. This is the total.20
Check. Check: 4 × 5 is also 20.
Watch out. Count in fives on your fingers.
Method. Count in twos six times.
- Count in twos. Each count is one group of 2.2, 4, 6, 8, 10, 12
- The last number we said is the answer. We counted six groups of 2.2 × 6 = 12
- Write the answer. This is the total.12
Check. Check: 6 × 2 is also 12.
Watch out. Doubling is the same as multiplying by 2.
Method. Add a zero to the end of the number.
- Write the number 3. Multiplying by 10 makes each group ten times bigger.3
- Add a zero to the end. A zero at the end makes the number ten times as big.3 with a zero = 30
- Write the answer. This is the total.30
Check. Check: 30 ÷ 10 = 3.
Watch out. Only the zero is added. The 3 does not change.
Method. Count in fives until you reach 35.
- Count in fives. Each count is one group of 5.5, 10, 15, 20, 25, 30, 35
- Count the numbers you said. Count each time you said a number.7 counts
- Write the answer. This is the number of groups.7
Check. Check: 7 × 5 = 35.
Watch out. Count the groups, not the total.
Method. Count in threes three times.
- Count in threes. Each count adds 3.3, 6, 9
- The last number we said is the answer. We counted three groups of 3.3 × 3 = 9
- Write the answer. This is the total.9
Check. Check: 9 ÷ 3 = 3.
Watch out. Count in threes on your fingers.
The 3 times table
The 3 times table counts in threes: 3, 6, 9, 12, 15, 18 and so on. Each answer is one more group of 3.
Learn the facts in order, then say them in any order.
Key ideas
- Count in threes for the 3 times table.
- Each answer is one more group of 3.
- The order of the numbers does not change the answer.
Method. Count in 3s to find 3 groups of 6. The order of the two numbers does not matter.
- Count in 3s, 6 times. Each count adds one more group of 3.3, 6, 9, 12, 15, 18
- The last number we said is the answer. We counted in equal groups.3 × 6 = 18
- Write the answer. The order of the numbers does not change the answer.18
Check. Check: 6 × 3 is also 18.
Watch out. Say the 3 times table in order until you reach the fact you need.
Method. Count in 3s to find 3 groups of 9. The order of the two numbers does not matter.
- Count in 3s, 9 times. Each count adds one more group of 3.3, 6, 9, 12, 15, 18, 21, 24, 27
- The last number we said is the answer. We counted in equal groups.3 × 9 = 27
- Write the answer. The order of the numbers does not change the answer.27
Check. Check: 9 × 3 is also 27.
Watch out. Say the 3 times table in order until you reach the fact you need.
Method. Count in 3s to find 3 groups of 12. The order of the two numbers does not matter.
- Count in 3s, 12 times. Each count adds one more group of 3.3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36
- The last number we said is the answer. We counted in equal groups.3 × 12 = 36
- Write the answer. The order of the numbers does not change the answer.36
Check. Check: 12 × 3 is also 36.
Watch out. Say the 3 times table in order until you reach the fact you need.
Watch out
Watch out. 3 × 8 is 24, not 21. Count in threes carefully and count the number of steps.
Exam tip
Grown-up tip. Count in threes on the fingers of both hands, with a finger for each step. Ask: “Which fact can you say quickly?”
Exercise 4A Practice: the 3 times table
Non-calculatorMethod. Count in 3s to find 3 groups of 8. The order of the two numbers does not matter.
- Count in 3s, 8 times. Each count adds one more group of 3.3, 6, 9, 12, 15, 18, 21, 24
- The last number we said is the answer. We counted in equal groups.3 × 8 = 24
- Write the answer. The order of the numbers does not change the answer.24
Check. Check: 8 × 3 is also 24.
Watch out. Say the 3 times table in order until you reach the fact you need.
Method. Count in 3s to find 3 groups of 3. The order of the two numbers does not matter.
- Count in 3s, 3 times. Each count adds one more group of 3.3, 6, 9
- The last number we said is the answer. We counted in equal groups.3 × 3 = 9
- Write the answer. The order of the numbers does not change the answer.9
Check. Check: 3 × 3 is also 9.
Watch out. Say the 3 times table in order until you reach the fact you need.
Method. Count in 3s to find 3 groups of 4. The order of the two numbers does not matter.
- Count in 3s, 4 times. Each count adds one more group of 3.3, 6, 9, 12
- The last number we said is the answer. We counted in equal groups.3 × 4 = 12
- Write the answer. The order of the numbers does not change the answer.12
Check. Check: 4 × 3 is also 12.
Watch out. Say the 3 times table in order until you reach the fact you need.
Method. Count in 3s to find 3 groups of 12. The order of the two numbers does not matter.
- Count in 3s, 12 times. Each count adds one more group of 3.3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36
- The last number we said is the answer. We counted in equal groups.3 × 12 = 36
- Write the answer. The order of the numbers does not change the answer.36
Check. Check: 12 × 3 is also 36.
Watch out. Say the 3 times table in order until you reach the fact you need.
Method. Count in 3s to find 3 groups of 6. The order of the two numbers does not matter.
- Count in 3s, 6 times. Each count adds one more group of 3.3, 6, 9, 12, 15, 18
- The last number we said is the answer. We counted in equal groups.3 × 6 = 18
- Write the answer. The order of the numbers does not change the answer.18
Check. Check: 6 × 3 is also 18.
Watch out. Say the 3 times table in order until you reach the fact you need.
Method. Count in 3s to find 3 groups of 4. The order of the two numbers does not matter.
- Count in 3s, 4 times. Each count adds one more group of 3.3, 6, 9, 12
- The last number we said is the answer. We counted in equal groups.3 × 4 = 12
- Write the answer. The order of the numbers does not change the answer.12
Check. Check: 4 × 3 is also 12.
Watch out. Say the 3 times table in order until you reach the fact you need.
Method. Count in 3s to find 3 groups of 2. The order of the two numbers does not matter.
- Count in 3s, 2 times. Each count adds one more group of 3.3, 6
- The last number we said is the answer. We counted in equal groups.3 × 2 = 6
- Write the answer. The order of the numbers does not change the answer.6
Check. Check: 2 × 3 is also 6.
Watch out. Say the 3 times table in order until you reach the fact you need.
Method. Count in 3s to find 3 groups of 6. The order of the two numbers does not matter.
- Count in 3s, 6 times. Each count adds one more group of 3.3, 6, 9, 12, 15, 18
- The last number we said is the answer. We counted in equal groups.3 × 6 = 18
- Write the answer. The order of the numbers does not change the answer.18
Check. Check: 6 × 3 is also 18.
Watch out. Say the 3 times table in order until you reach the fact you need.
Method. Count in 3s to find 3 groups of 11. The order of the two numbers does not matter.
- Count in 3s, 11 times. Each count adds one more group of 3.3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33
- The last number we said is the answer. We counted in equal groups.3 × 11 = 33
- Write the answer. The order of the numbers does not change the answer.33
Check. Check: 11 × 3 is also 33.
Watch out. Say the 3 times table in order until you reach the fact you need.
Method. Count in 3s to find 3 groups of 12. The order of the two numbers does not matter.
- Count in 3s, 12 times. Each count adds one more group of 3.3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36
- The last number we said is the answer. We counted in equal groups.3 × 12 = 36
- Write the answer. The order of the numbers does not change the answer.36
Check. Check: 12 × 3 is also 36.
Watch out. Say the 3 times table in order until you reach the fact you need.
Method. Count in 3s to find 3 groups of 1. The order of the two numbers does not matter.
- Count in 3s, 1 times. Each count adds one more group of 3.3
- The last number we said is the answer. We counted in equal groups.3 × 1 = 3
- Write the answer. The order of the numbers does not change the answer.3
Check. Check: 1 × 3 is also 3.
Watch out. Say the 3 times table in order until you reach the fact you need.
Method. Count in 3s to find 3 groups of 10. The order of the two numbers does not matter.
- Count in 3s, 10 times. Each count adds one more group of 3.3, 6, 9, 12, 15, 18, 21, 24, 27, 30
- The last number we said is the answer. We counted in equal groups.3 × 10 = 30
- Write the answer. The order of the numbers does not change the answer.30
Check. Check: 10 × 3 is also 30.
Watch out. Say the 3 times table in order until you reach the fact you need.
Method. Count in 3s to find 3 groups of 1. The order of the two numbers does not matter.
- Count in 3s, 1 times. Each count adds one more group of 3.3
- The last number we said is the answer. We counted in equal groups.3 × 1 = 3
- Write the answer. The order of the numbers does not change the answer.3
Check. Check: 1 × 3 is also 3.
Watch out. Say the 3 times table in order until you reach the fact you need.
Method. Count in 3s to find 3 groups of 10. The order of the two numbers does not matter.
- Count in 3s, 10 times. Each count adds one more group of 3.3, 6, 9, 12, 15, 18, 21, 24, 27, 30
- The last number we said is the answer. We counted in equal groups.3 × 10 = 30
- Write the answer. The order of the numbers does not change the answer.30
Check. Check: 10 × 3 is also 30.
Watch out. Say the 3 times table in order until you reach the fact you need.
Method. Count in 3s to find 3 groups of 7. The order of the two numbers does not matter.
- Count in 3s, 7 times. Each count adds one more group of 3.3, 6, 9, 12, 15, 18, 21
- The last number we said is the answer. We counted in equal groups.3 × 7 = 21
- Write the answer. The order of the numbers does not change the answer.21
Check. Check: 7 × 3 is also 21.
Watch out. Say the 3 times table in order until you reach the fact you need.
Method. Count in 3s to find 3 groups of 7. The order of the two numbers does not matter.
- Count in 3s, 7 times. Each count adds one more group of 3.3, 6, 9, 12, 15, 18, 21
- The last number we said is the answer. We counted in equal groups.3 × 7 = 21
- Write the answer. The order of the numbers does not change the answer.21
Check. Check: 7 × 3 is also 21.
Watch out. Say the 3 times table in order until you reach the fact you need.
The 4 times table
The 4 times table counts in fours: 4, 8, 12, 16, 20 and so on. Each answer is one more group of 4.
Doubling twice gives the 4 times table. For 4 × 6, double 6 to get 12, then double 12 to get 24.
Key ideas
- Count in fours for the 4 times table.
- Double twice: 4 × 5 is 5 doubled to 10, then 10 doubled to 20.
- The order of the numbers does not matter.
Method. Count in 4s to find 4 groups of 5. The order of the two numbers does not matter.
- Count in 4s, 5 times. Each count adds one more group of 4.4, 8, 12, 16, 20
- The last number we said is the answer. We counted in equal groups.4 × 5 = 20
- Write the answer. The order of the numbers does not change the answer.20
Check. Check: 5 × 4 is also 20.
Watch out. Say the 4 times table in order until you reach the fact you need.
Method. Count in 4s to find 4 groups of 7. The order of the two numbers does not matter.
- Count in 4s, 7 times. Each count adds one more group of 4.4, 8, 12, 16, 20, 24, 28
- The last number we said is the answer. We counted in equal groups.4 × 7 = 28
- Write the answer. The order of the numbers does not change the answer.28
Check. Check: 7 × 4 is also 28.
Watch out. Say the 4 times table in order until you reach the fact you need.
Method. Count in 4s to find 4 groups of 11. The order of the two numbers does not matter.
- Count in 4s, 11 times. Each count adds one more group of 4.4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44
- The last number we said is the answer. We counted in equal groups.4 × 11 = 44
- Write the answer. The order of the numbers does not change the answer.44
Check. Check: 11 × 4 is also 44.
Watch out. Say the 4 times table in order until you reach the fact you need.
Watch out
Watch out. 4 × 7 is 28, not 24. Count in fours and check the number of counts.
Exam tip
Grown-up tip. Ask the child to double twice to check the answer: double 6 is 12, double 12 is 24.
Exercise 4B Practice: the 4 times table
Non-calculatorMethod. Count in 4s to find 4 groups of 12. The order of the two numbers does not matter.
- Count in 4s, 12 times. Each count adds one more group of 4.4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48
- The last number we said is the answer. We counted in equal groups.4 × 12 = 48
- Write the answer. The order of the numbers does not change the answer.48
Check. Check: 12 × 4 is also 48.
Watch out. Say the 4 times table in order until you reach the fact you need.
Method. Count in 4s to find 4 groups of 10. The order of the two numbers does not matter.
- Count in 4s, 10 times. Each count adds one more group of 4.4, 8, 12, 16, 20, 24, 28, 32, 36, 40
- The last number we said is the answer. We counted in equal groups.4 × 10 = 40
- Write the answer. The order of the numbers does not change the answer.40
Check. Check: 10 × 4 is also 40.
Watch out. Say the 4 times table in order until you reach the fact you need.
Method. Count in 4s to find 4 groups of 8. The order of the two numbers does not matter.
- Count in 4s, 8 times. Each count adds one more group of 4.4, 8, 12, 16, 20, 24, 28, 32
- The last number we said is the answer. We counted in equal groups.4 × 8 = 32
- Write the answer. The order of the numbers does not change the answer.32
Check. Check: 8 × 4 is also 32.
Watch out. Say the 4 times table in order until you reach the fact you need.
Method. Count in 4s to find 4 groups of 7. The order of the two numbers does not matter.
- Count in 4s, 7 times. Each count adds one more group of 4.4, 8, 12, 16, 20, 24, 28
- The last number we said is the answer. We counted in equal groups.4 × 7 = 28
- Write the answer. The order of the numbers does not change the answer.28
Check. Check: 7 × 4 is also 28.
Watch out. Say the 4 times table in order until you reach the fact you need.
Method. Count in 4s to find 4 groups of 3. The order of the two numbers does not matter.
- Count in 4s, 3 times. Each count adds one more group of 4.4, 8, 12
- The last number we said is the answer. We counted in equal groups.4 × 3 = 12
- Write the answer. The order of the numbers does not change the answer.12
Check. Check: 3 × 4 is also 12.
Watch out. Say the 4 times table in order until you reach the fact you need.
Method. Count in 4s to find 4 groups of 4. The order of the two numbers does not matter.
- Count in 4s, 4 times. Each count adds one more group of 4.4, 8, 12, 16
- The last number we said is the answer. We counted in equal groups.4 × 4 = 16
- Write the answer. The order of the numbers does not change the answer.16
Check. Check: 4 × 4 is also 16.
Watch out. Say the 4 times table in order until you reach the fact you need.
Method. Count in 4s to find 4 groups of 8. The order of the two numbers does not matter.
- Count in 4s, 8 times. Each count adds one more group of 4.4, 8, 12, 16, 20, 24, 28, 32
- The last number we said is the answer. We counted in equal groups.4 × 8 = 32
- Write the answer. The order of the numbers does not change the answer.32
Check. Check: 8 × 4 is also 32.
Watch out. Say the 4 times table in order until you reach the fact you need.
Method. Count in 4s to find 4 groups of 5. The order of the two numbers does not matter.
- Count in 4s, 5 times. Each count adds one more group of 4.4, 8, 12, 16, 20
- The last number we said is the answer. We counted in equal groups.4 × 5 = 20
- Write the answer. The order of the numbers does not change the answer.20
Check. Check: 5 × 4 is also 20.
Watch out. Say the 4 times table in order until you reach the fact you need.
Method. Count in 4s to find 4 groups of 11. The order of the two numbers does not matter.
- Count in 4s, 11 times. Each count adds one more group of 4.4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44
- The last number we said is the answer. We counted in equal groups.4 × 11 = 44
- Write the answer. The order of the numbers does not change the answer.44
Check. Check: 11 × 4 is also 44.
Watch out. Say the 4 times table in order until you reach the fact you need.
Method. Count in 4s to find 4 groups of 12. The order of the two numbers does not matter.
- Count in 4s, 12 times. Each count adds one more group of 4.4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48
- The last number we said is the answer. We counted in equal groups.4 × 12 = 48
- Write the answer. The order of the numbers does not change the answer.48
Check. Check: 12 × 4 is also 48.
Watch out. Say the 4 times table in order until you reach the fact you need.
Method. Count in 4s to find 4 groups of 9. The order of the two numbers does not matter.
- Count in 4s, 9 times. Each count adds one more group of 4.4, 8, 12, 16, 20, 24, 28, 32, 36
- The last number we said is the answer. We counted in equal groups.4 × 9 = 36
- Write the answer. The order of the numbers does not change the answer.36
Check. Check: 9 × 4 is also 36.
Watch out. Say the 4 times table in order until you reach the fact you need.
Method. Count in 4s to find 4 groups of 6. The order of the two numbers does not matter.
- Count in 4s, 6 times. Each count adds one more group of 4.4, 8, 12, 16, 20, 24
- The last number we said is the answer. We counted in equal groups.4 × 6 = 24
- Write the answer. The order of the numbers does not change the answer.24
Check. Check: 6 × 4 is also 24.
Watch out. Say the 4 times table in order until you reach the fact you need.
Method. Count in 4s to find 4 groups of 9. The order of the two numbers does not matter.
- Count in 4s, 9 times. Each count adds one more group of 4.4, 8, 12, 16, 20, 24, 28, 32, 36
- The last number we said is the answer. We counted in equal groups.4 × 9 = 36
- Write the answer. The order of the numbers does not change the answer.36
Check. Check: 9 × 4 is also 36.
Watch out. Say the 4 times table in order until you reach the fact you need.
Method. Count in 4s to find 4 groups of 6. The order of the two numbers does not matter.
- Count in 4s, 6 times. Each count adds one more group of 4.4, 8, 12, 16, 20, 24
- The last number we said is the answer. We counted in equal groups.4 × 6 = 24
- Write the answer. The order of the numbers does not change the answer.24
Check. Check: 6 × 4 is also 24.
Watch out. Say the 4 times table in order until you reach the fact you need.
Method. Count in 4s to find 4 groups of 5. The order of the two numbers does not matter.
- Count in 4s, 5 times. Each count adds one more group of 4.4, 8, 12, 16, 20
- The last number we said is the answer. We counted in equal groups.4 × 5 = 20
- Write the answer. The order of the numbers does not change the answer.20
Check. Check: 5 × 4 is also 20.
Watch out. Say the 4 times table in order until you reach the fact you need.
Method. Count in 4s to find 4 groups of 1. The order of the two numbers does not matter.
- Count in 4s, 1 times. Each count adds one more group of 4.4
- The last number we said is the answer. We counted in equal groups.4 × 1 = 4
- Write the answer. The order of the numbers does not change the answer.4
Check. Check: 1 × 4 is also 4.
Watch out. Say the 4 times table in order until you reach the fact you need.
Missing numbers and dividing with 3 and 4
Division is the opposite of multiplication. 24 ÷ 3 asks: how many groups of 3 make 24?
To find a missing number, think of the times table. 4 × ___ = 28 asks: what times 4 makes 28?
Key ideas
- Division asks how many groups of the number make the total.
- Find the missing number by counting in steps.
- Division is the inverse of multiplication.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think: how many groups of 4 make 28? Count in steps of the first number.4, 8, 12, 16, 20, 24, 28
- Count the groups. We said 7 numbers, so there are 7 groups.7 groups of 4
- Write the missing number. This is the number of groups.7
Check. Check: 4 × 7 = 28.
Watch out. The times table of 4 is the key. Division is the opposite of multiplication.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think of the multiplication: 3 × ___ = 24. Division asks how many groups.3 × ___ = 24
- Count in 3s until you reach 24. Count the steps as you go.3, 6, 9, 12, 15, 18, 21, 24
- Write the answer. This is the number of groups.8
Check. Check: 3 × 8 = 24.
Watch out. The times table of 3 is the key. Division is the opposite of multiplication.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think of the times table of 3. The missing number is the number of groups of this size.3, 6, 9, 12, 15, 18, 21
- Find the number of counts. We counted 7 times to reach 21.7 counts
- Write the missing number. It goes in the gap.7
Check. Check: 3 × 7 = 21.
Watch out. The times table of 3 is the key. Division is the opposite of multiplication.
Watch out
Watch out. 24 ÷ 3 is 8, because 3 × 8 = 24. Do not divide 3 by 24.
Exam tip
Grown-up tip. Ask: “What times the number makes this answer? Count in steps until you get there.”
Exercise 4C Practice: missing numbers and division
Non-calculatorMethod. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think of the times table of 4. The missing number is the number of groups of this size.4, 8, 12, 16
- Find the number of counts. We counted 4 times to reach 16.4 counts
- Write the missing number. It goes in the gap.4
Check. Check: 4 × 4 = 16.
Watch out. The times table of 4 is the key. Division is the opposite of multiplication.
Method. Division can find how many equal groups fit. Count the groups in steps of the group size.
- Think of the division: 27 ÷ 3. Each bag holds the same number, so count how many groups of this size there are.27 ÷ 3 = ___
- Count in 3s until you reach 27. Count one bag at a time.3, 6, 9, 12, 15, 18, 21, 24, 27
- Write the answer. This is the number of bags.9
Check. Check: 9 bags of 3 is 27.
Watch out. Count the groups, not the number in each group.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think: how many groups of 4 make 48? Count in steps of the first number.4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48
- Count the groups. We said 12 numbers, so there are 12 groups.12 groups of 4
- Write the missing number. This is the number of groups.12
Check. Check: 4 × 12 = 48.
Watch out. The times table of 4 is the key. Division is the opposite of multiplication.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think: how many groups of 4 make 12? Count in steps of the first number.4, 8, 12
- Count the groups. We said 3 numbers, so there are 3 groups.3 groups of 4
- Write the missing number. This is the number of groups.3
Check. Check: 4 × 3 = 12.
Watch out. The times table of 4 is the key. Division is the opposite of multiplication.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think of the times table of 4. The missing number is the number of groups of this size.4, 8, 12, 16, 20, 24
- Find the number of counts. We counted 6 times to reach 24.6 counts
- Write the missing number. It goes in the gap.6
Check. Check: 4 × 6 = 24.
Watch out. The times table of 4 is the key. Division is the opposite of multiplication.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think of the multiplication: 4 × ___ = 44. Division asks how many groups.4 × ___ = 44
- Count in 4s until you reach 44. Count the steps as you go.4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44
- Write the answer. This is the number of groups.11
Check. Check: 4 × 11 = 44.
Watch out. The times table of 4 is the key. Division is the opposite of multiplication.
Method. Division can find how many equal groups fit. Count the groups in steps of the group size.
- Think of the division: 30 ÷ 3. Each bag holds the same number, so count how many groups of this size there are.30 ÷ 3 = ___
- Count in 3s until you reach 30. Count one bag at a time.3, 6, 9, 12, 15, 18, 21, 24, 27, 30
- Write the answer. This is the number of bags.10
Check. Check: 10 bags of 3 is 30.
Watch out. Count the groups, not the number in each group.
Method. Division can find how many equal groups fit. Count the groups in steps of the group size.
- Think of the division: 48 ÷ 4. Each bag holds the same number, so count how many groups of this size there are.48 ÷ 4 = ___
- Count in 4s until you reach 48. Count one bag at a time.4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48
- Write the answer. This is the number of bags.12
Check. Check: 12 bags of 4 is 48.
Watch out. Count the groups, not the number in each group.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think of the times table of 4. The missing number is the number of groups of this size.4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44
- Find the number of counts. We counted 11 times to reach 44.11 counts
- Write the missing number. It goes in the gap.11
Check. Check: 4 × 11 = 44.
Watch out. The times table of 4 is the key. Division is the opposite of multiplication.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think: how many groups of 4 make 44? Count in steps of the first number.4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44
- Count the groups. We said 11 numbers, so there are 11 groups.11 groups of 4
- Write the missing number. This is the number of groups.11
Check. Check: 4 × 11 = 44.
Watch out. The times table of 4 is the key. Division is the opposite of multiplication.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think of the times table of 3. The missing number is the number of groups of this size.3, 6, 9, 12, 15, 18, 21, 24
- Find the number of counts. We counted 8 times to reach 24.8 counts
- Write the missing number. It goes in the gap.8
Check. Check: 3 × 8 = 24.
Watch out. The times table of 3 is the key. Division is the opposite of multiplication.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think of the multiplication: 4 × ___ = 8. Division asks how many groups.4 × ___ = 8
- Count in 4s until you reach 8. Count the steps as you go.4, 8
- Write the answer. This is the number of groups.2
Check. Check: 4 × 2 = 8.
Watch out. The times table of 4 is the key. Division is the opposite of multiplication.
Method. Division can find how many equal groups fit. Count the groups in steps of the group size.
- Think of the division: 24 ÷ 3. Each bag holds the same number, so count how many groups of this size there are.24 ÷ 3 = ___
- Count in 3s until you reach 24. Count one bag at a time.3, 6, 9, 12, 15, 18, 21, 24
- Write the answer. This is the number of bags.8
Check. Check: 8 bags of 3 is 24.
Watch out. Count the groups, not the number in each group.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think: how many groups of 3 make 9? Count in steps of the first number.3, 6, 9
- Count the groups. We said 3 numbers, so there are 3 groups.3 groups of 3
- Write the missing number. This is the number of groups.3
Check. Check: 3 × 3 = 9.
Watch out. The times table of 3 is the key. Division is the opposite of multiplication.
Method. Division can find how many equal groups fit. Count the groups in steps of the group size.
- Think of the division: 40 ÷ 4. Each bag holds the same number, so count how many groups of this size there are.40 ÷ 4 = ___
- Count in 4s until you reach 40. Count one bag at a time.4, 8, 12, 16, 20, 24, 28, 32, 36, 40
- Write the answer. This is the number of bags.10
Check. Check: 10 bags of 4 is 40.
Watch out. Count the groups, not the number in each group.
Method. Division can find how many equal groups fit. Count the groups in steps of the group size.
- Think of the division: 24 ÷ 3. Each bag holds the same number, so count how many groups of this size there are.24 ÷ 3 = ___
- Count in 3s until you reach 24. Count one bag at a time.3, 6, 9, 12, 15, 18, 21, 24
- Write the answer. This is the number of bags.8
Check. Check: 8 bags of 3 is 24.
Watch out. Count the groups, not the number in each group.
Order in multiplication and equal groups
Swapping the two numbers in a multiplication does not change the total. 3 × 4 = 12 and 4 × 3 = 12.
For a word problem, the number of groups is one number and the number in each group is the other.
Key ideas
- The order of the numbers does not change a multiplication.
- Equal groups: multiply the number of groups by the number in each group.
- Read the question to find the groups and the number in each group.
Method. Swap the numbers round. The total stays the same.
- Work out the first fact: 3 × 4. This tells us the total.3 × 4 = 12
- Swap the two numbers round. The order of the numbers in a multiplication does not change the answer.4 × 3 = 12
- Write the missing number. It is the number that moved to the front.4
Check. Check: 3 × 4 and 4 × 3 are both 12.
Watch out. Multiplication works in any order, but division does not: 12 ÷ 3 is not the same as 3 ÷ 12.
Method. Multiply the number of groups by the number in each group.
- Write 4 groups of 3 as a multiplication. Each bag holds the same number.4 × 3
- Count in 3s, 4 times. Each count is one bag.3, 6, 9, 12
- Write the answer. This is the total altogether.12
Check. Check: 3 × 4 = 12, and 4 × 3 is the same.
Watch out. The number of bags is the number of groups. The number in each bag is the group size.
Method. Multiply the number of groups by the number in each group.
- Write 3 groups of 4 as a multiplication. Each bag holds the same number.3 × 4
- Count in 4s, 3 times. Each count is one bag.4, 8, 12
- Write the answer. This is the total altogether.12
Check. Check: 4 × 3 = 12, and 3 × 4 is the same.
Watch out. The number of bags is the number of groups. The number in each bag is the group size.
Watch out
Watch out. Multiplication can go in any order, but division cannot. 12 ÷ 3 is 4, but 3 ÷ 12 is not a whole number.
Exam tip
Grown-up tip. Ask: “How many bags? How many in each bag?” before the child writes the sum.
Exercise 4D Practice: order and equal groups
Non-calculatorMethod. Swap the numbers round. The total stays the same.
- Work out the first fact: 3 × 2. This tells us the total.3 × 2 = 6
- Swap the two numbers round. The order of the numbers in a multiplication does not change the answer.2 × 3 = 6
- Write the missing number. It is the number that moved to the front.2
Check. Check: 3 × 2 and 2 × 3 are both 6.
Watch out. Multiplication works in any order, but division does not: 12 ÷ 3 is not the same as 3 ÷ 12.
Method. Multiply the number of groups by the number in each group.
- Write 8 groups of 4 as a multiplication. Each bag holds the same number.8 × 4
- Count in 4s, 8 times. Each count is one bag.4, 8, 12, 16, 20, 24, 28, 32
- Write the answer. This is the total altogether.32
Check. Check: 4 × 8 = 32, and 8 × 4 is the same.
Watch out. The number of bags is the number of groups. The number in each bag is the group size.
Method. Multiply the number of groups by the number in each group.
- Write 6 groups of 4 as a multiplication. Each bag holds the same number.6 × 4
- Count in 4s, 6 times. Each count is one bag.4, 8, 12, 16, 20, 24
- Write the answer. This is the total altogether.24
Check. Check: 4 × 6 = 24, and 6 × 4 is the same.
Watch out. The number of bags is the number of groups. The number in each bag is the group size.
Method. Swap the numbers round. The total stays the same.
- Work out the first fact: 4 × 12. This tells us the total.4 × 12 = 48
- Swap the two numbers round. The order of the numbers in a multiplication does not change the answer.12 × 4 = 48
- Write the missing number. It is the number that moved to the front.12
Check. Check: 4 × 12 and 12 × 4 are both 48.
Watch out. Multiplication works in any order, but division does not: 12 ÷ 3 is not the same as 3 ÷ 12.
Method. Multiply the number of groups by the number in each group.
- Write 6 groups of 3 as a multiplication. Each bag holds the same number.6 × 3
- Count in 3s, 6 times. Each count is one bag.3, 6, 9, 12, 15, 18
- Write the answer. This is the total altogether.18
Check. Check: 3 × 6 = 18, and 6 × 3 is the same.
Watch out. The number of bags is the number of groups. The number in each bag is the group size.
Method. Swap the numbers round. The total stays the same.
- Work out the first fact: 3 × 5. This tells us the total.3 × 5 = 15
- Swap the two numbers round. The order of the numbers in a multiplication does not change the answer.5 × 3 = 15
- Write the missing number. It is the number that moved to the front.5
Check. Check: 3 × 5 and 5 × 3 are both 15.
Watch out. Multiplication works in any order, but division does not: 12 ÷ 3 is not the same as 3 ÷ 12.
Method. Multiply the number of groups by the number in each group.
- Write 5 groups of 4 as a multiplication. Each bag holds the same number.5 × 4
- Count in 4s, 5 times. Each count is one bag.4, 8, 12, 16, 20
- Write the answer. This is the total altogether.20
Check. Check: 4 × 5 = 20, and 5 × 4 is the same.
Watch out. The number of bags is the number of groups. The number in each bag is the group size.
Method. Multiply the number of groups by the number in each group.
- Write 8 groups of 3 as a multiplication. Each bag holds the same number.8 × 3
- Count in 3s, 8 times. Each count is one bag.3, 6, 9, 12, 15, 18, 21, 24
- Write the answer. This is the total altogether.24
Check. Check: 3 × 8 = 24, and 8 × 3 is the same.
Watch out. The number of bags is the number of groups. The number in each bag is the group size.
Method. Swap the numbers round. The total stays the same.
- Work out the first fact: 4 × 7. This tells us the total.4 × 7 = 28
- Swap the two numbers round. The order of the numbers in a multiplication does not change the answer.7 × 4 = 28
- Write the missing number. It is the number that moved to the front.7
Check. Check: 4 × 7 and 7 × 4 are both 28.
Watch out. Multiplication works in any order, but division does not: 12 ÷ 3 is not the same as 3 ÷ 12.
Method. Swap the numbers round. The total stays the same.
- Work out the first fact: 4 × 10. This tells us the total.4 × 10 = 40
- Swap the two numbers round. The order of the numbers in a multiplication does not change the answer.10 × 4 = 40
- Write the missing number. It is the number that moved to the front.10
Check. Check: 4 × 10 and 10 × 4 are both 40.
Watch out. Multiplication works in any order, but division does not: 12 ÷ 3 is not the same as 3 ÷ 12.
Method. Multiply the number of groups by the number in each group.
- Write 9 groups of 3 as a multiplication. Each bag holds the same number.9 × 3
- Count in 3s, 9 times. Each count is one bag.3, 6, 9, 12, 15, 18, 21, 24, 27
- Write the answer. This is the total altogether.27
Check. Check: 3 × 9 = 27, and 9 × 3 is the same.
Watch out. The number of bags is the number of groups. The number in each bag is the group size.
Method. Swap the numbers round. The total stays the same.
- Work out the first fact: 4 × 2. This tells us the total.4 × 2 = 8
- Swap the two numbers round. The order of the numbers in a multiplication does not change the answer.2 × 4 = 8
- Write the missing number. It is the number that moved to the front.2
Check. Check: 4 × 2 and 2 × 4 are both 8.
Watch out. Multiplication works in any order, but division does not: 12 ÷ 3 is not the same as 3 ÷ 12.
Method. Multiply the number of groups by the number in each group.
- Write 3 groups of 4 as a multiplication. Each bag holds the same number.3 × 4
- Count in 4s, 3 times. Each count is one bag.4, 8, 12
- Write the answer. This is the total altogether.12
Check. Check: 4 × 3 = 12, and 3 × 4 is the same.
Watch out. The number of bags is the number of groups. The number in each bag is the group size.
Method. Swap the numbers round. The total stays the same.
- Work out the first fact: 3 × 7. This tells us the total.3 × 7 = 21
- Swap the two numbers round. The order of the numbers in a multiplication does not change the answer.7 × 3 = 21
- Write the missing number. It is the number that moved to the front.7
Check. Check: 3 × 7 and 7 × 3 are both 21.
Watch out. Multiplication works in any order, but division does not: 12 ÷ 3 is not the same as 3 ÷ 12.
Method. Swap the numbers round. The total stays the same.
- Work out the first fact: 3 × 4. This tells us the total.3 × 4 = 12
- Swap the two numbers round. The order of the numbers in a multiplication does not change the answer.4 × 3 = 12
- Write the missing number. It is the number that moved to the front.4
Check. Check: 3 × 4 and 4 × 3 are both 12.
Watch out. Multiplication works in any order, but division does not: 12 ÷ 3 is not the same as 3 ÷ 12.
Method. Swap the numbers round. The total stays the same.
- Work out the first fact: 4 × 5. This tells us the total.4 × 5 = 20
- Swap the two numbers round. The order of the numbers in a multiplication does not change the answer.5 × 4 = 20
- Write the missing number. It is the number that moved to the front.5
Check. Check: 4 × 5 and 5 × 4 are both 20.
Watch out. Multiplication works in any order, but division does not: 12 ÷ 3 is not the same as 3 ÷ 12.
Chapter summary
| Skill | Method |
|---|---|
| The 3 times table | Count in threes; each answer is one more group of 3 |
| The 4 times table | Count in fours; double twice to check |
| Missing numbers and division | Ask what times the number makes the total; count in steps |
| Order of the numbers | Swapping the numbers in a multiplication gives the same total |
| Equal groups | Groups × the number in each group = total |
Can you…?
- I can recall the 3 times table facts, in any order
- I can recall the 4 times table facts, in any order
- I can find a missing number in a multiplication or division
- I can show that 3 × 4 and 4 × 3 give the same total
- I can solve a one-step word problem with equal groups of 3 or 4
Key terms
- times table
- the list of multiples of one number
- multiple
- a number in the times table of another, such as 12 is a multiple of 3
- equal groups
- groups with the same number in each
- inverse
- the operation that undoes another; division undoes multiplication
Exercise 4Z Check-up
Non-calculatorMethod. Multiply the number of groups by the number in each group.
- Write 3 groups of 4 as a multiplication. Each bag holds the same number.3 × 4
- Count in 4s, 3 times. Each count is one bag.4, 8, 12
- Write the answer. This is the total altogether.12
Check. Check: 4 × 3 = 12, and 3 × 4 is the same.
Watch out. The number of bags is the number of groups. The number in each bag is the group size.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think: how many groups of 3 make 24? Count in steps of the first number.3, 6, 9, 12, 15, 18, 21, 24
- Count the groups. We said 8 numbers, so there are 8 groups.8 groups of 3
- Write the missing number. This is the number of groups.8
Check. Check: 3 × 8 = 24.
Watch out. The times table of 3 is the key. Division is the opposite of multiplication.
Method. Count in 4s to find 4 groups of 1. The order of the two numbers does not matter.
- Count in 4s, 1 times. Each count adds one more group of 4.4
- The last number we said is the answer. We counted in equal groups.4 × 1 = 4
- Write the answer. The order of the numbers does not change the answer.4
Check. Check: 1 × 4 is also 4.
Watch out. Say the 4 times table in order until you reach the fact you need.
Method. Multiply the number of groups by the number in each group.
- Write 5 groups of 4 as a multiplication. Each bag holds the same number.5 × 4
- Count in 4s, 5 times. Each count is one bag.4, 8, 12, 16, 20
- Write the answer. This is the total altogether.20
Check. Check: 4 × 5 = 20, and 5 × 4 is the same.
Watch out. The number of bags is the number of groups. The number in each bag is the group size.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think of the multiplication: 4 × ___ = 28. Division asks how many groups.4 × ___ = 28
- Count in 4s until you reach 28. Count the steps as you go.4, 8, 12, 16, 20, 24, 28
- Write the answer. This is the number of groups.7
Check. Check: 4 × 7 = 28.
Watch out. The times table of 4 is the key. Division is the opposite of multiplication.
Method. Count in 3s to find 3 groups of 2. The order of the two numbers does not matter.
- Count in 3s, 2 times. Each count adds one more group of 3.3, 6
- The last number we said is the answer. We counted in equal groups.3 × 2 = 6
- Write the answer. The order of the numbers does not change the answer.6
Check. Check: 2 × 3 is also 6.
Watch out. Say the 3 times table in order until you reach the fact you need.
Method. Swap the numbers round. The total stays the same.
- Work out the first fact: 4 × 5. This tells us the total.4 × 5 = 20
- Swap the two numbers round. The order of the numbers in a multiplication does not change the answer.5 × 4 = 20
- Write the missing number. It is the number that moved to the front.5
Check. Check: 4 × 5 and 5 × 4 are both 20.
Watch out. Multiplication works in any order, but division does not: 12 ÷ 3 is not the same as 3 ÷ 12.
Method. Count in 3s to find 3 groups of 3. The order of the two numbers does not matter.
- Count in 3s, 3 times. Each count adds one more group of 3.3, 6, 9
- The last number we said is the answer. We counted in equal groups.3 × 3 = 9
- Write the answer. The order of the numbers does not change the answer.9
Check. Check: 3 × 3 is also 9.
Watch out. Say the 3 times table in order until you reach the fact you need.
Method. Count in 3s to find 3 groups of 10. The order of the two numbers does not matter.
- Count in 3s, 10 times. Each count adds one more group of 3.3, 6, 9, 12, 15, 18, 21, 24, 27, 30
- The last number we said is the answer. We counted in equal groups.3 × 10 = 30
- Write the answer. The order of the numbers does not change the answer.30
Check. Check: 10 × 3 is also 30.
Watch out. Say the 3 times table in order until you reach the fact you need.
Method. Count in 4s to find 4 groups of 10. The order of the two numbers does not matter.
- Count in 4s, 10 times. Each count adds one more group of 4.4, 8, 12, 16, 20, 24, 28, 32, 36, 40
- The last number we said is the answer. We counted in equal groups.4 × 10 = 40
- Write the answer. The order of the numbers does not change the answer.40
Check. Check: 10 × 4 is also 40.
Watch out. Say the 4 times table in order until you reach the fact you need.
Total 19 marks. Allow about 19 minutes.
Exercise 4X Practice test questions
Non-calculatorMethod. Swap the numbers round. The total stays the same.
- Work out the first fact: 4 × 7. This tells us the total.4 × 7 = 28
- Swap the two numbers round. The order of the numbers in a multiplication does not change the answer.7 × 4 = 28
- Write the missing number. It is the number that moved to the front.7
Check. Check: 4 × 7 and 7 × 4 are both 28.
Watch out. Multiplication works in any order, but division does not: 12 ÷ 3 is not the same as 3 ÷ 12.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think of the times table of 4. The missing number is the number of groups of this size.4, 8, 12, 16, 20, 24, 28, 32, 36
- Find the number of counts. We counted 9 times to reach 36.9 counts
- Write the missing number. It goes in the gap.9
Check. Check: 4 × 9 = 36.
Watch out. The times table of 4 is the key. Division is the opposite of multiplication.
Method. Count in 4s to find 4 groups of 6. The order of the two numbers does not matter.
- Count in 4s, 6 times. Each count adds one more group of 4.4, 8, 12, 16, 20, 24
- The last number we said is the answer. We counted in equal groups.4 × 6 = 24
- Write the answer. The order of the numbers does not change the answer.24
Check. Check: 6 × 4 is also 24.
Watch out. Say the 4 times table in order until you reach the fact you need.
Method. Count in 3s to find 3 groups of 1. The order of the two numbers does not matter.
- Count in 3s, 1 times. Each count adds one more group of 3.3
- The last number we said is the answer. We counted in equal groups.3 × 1 = 3
- Write the answer. The order of the numbers does not change the answer.3
Check. Check: 1 × 3 is also 3.
Watch out. Say the 3 times table in order until you reach the fact you need.
Method. Count in 3s to find 3 groups of 10. The order of the two numbers does not matter.
- Count in 3s, 10 times. Each count adds one more group of 3.3, 6, 9, 12, 15, 18, 21, 24, 27, 30
- The last number we said is the answer. We counted in equal groups.3 × 10 = 30
- Write the answer. The order of the numbers does not change the answer.30
Check. Check: 10 × 3 is also 30.
Watch out. Say the 3 times table in order until you reach the fact you need.
Method. Count in 3s to find 3 groups of 11. The order of the two numbers does not matter.
- Count in 3s, 11 times. Each count adds one more group of 3.3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33
- The last number we said is the answer. We counted in equal groups.3 × 11 = 33
- Write the answer. The order of the numbers does not change the answer.33
Check. Check: 11 × 3 is also 33.
Watch out. Say the 3 times table in order until you reach the fact you need.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think of the multiplication: 4 × ___ = 32. Division asks how many groups.4 × ___ = 32
- Count in 4s until you reach 32. Count the steps as you go.4, 8, 12, 16, 20, 24, 28, 32
- Write the answer. This is the number of groups.8
Check. Check: 4 × 8 = 32.
Watch out. The times table of 4 is the key. Division is the opposite of multiplication.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think of the multiplication: 3 × ___ = 21. Division asks how many groups.3 × ___ = 21
- Count in 3s until you reach 21. Count the steps as you go.3, 6, 9, 12, 15, 18, 21
- Write the answer. This is the number of groups.7
Check. Check: 3 × 7 = 21.
Watch out. The times table of 3 is the key. Division is the opposite of multiplication.
Method. Multiply the number of groups by the number in each group.
- Write 8 groups of 4 as a multiplication. Each bag holds the same number.8 × 4
- Count in 4s, 8 times. Each count is one bag.4, 8, 12, 16, 20, 24, 28, 32
- Write the answer. This is the total altogether.32
Check. Check: 4 × 8 = 32, and 8 × 4 is the same.
Watch out. The number of bags is the number of groups. The number in each bag is the group size.
Method. Count in 4s to find 4 groups of 1. The order of the two numbers does not matter.
- Count in 4s, 1 times. Each count adds one more group of 4.4
- The last number we said is the answer. We counted in equal groups.4 × 1 = 4
- Write the answer. The order of the numbers does not change the answer.4
Check. Check: 1 × 4 is also 4.
Watch out. Say the 4 times table in order until you reach the fact you need.