Step-by-step Maths Level 3: Equal groups and repeated addition
Part of the Step-by-step Maths Level 3 multiplication as repeated addition chapter. Chapter overview · whole chapter on one page
Equal groups and repeated addition
Equal groups are the same number of things in each group. Three groups of 4 means 4 + 4 + 4.
Add the same number once for each group. Count the groups first, then add.
Key ideas
- Equal groups: the same number in each group.
- Repeated addition: add the group size once for each group.
- Count the groups, then add them up.
Method. Repeated addition: add the same number once for each group.
- Write one 4 for each group. There are 3 groups, so there are 3 lots of 4.4 + 4 + 4
- Add them up. Add the groups one after another, or count in steps of the group size.4 + 4 + 4 = 12
- Write the answer. This is the total altogether.12
Check. Count in 4s 3 times and you reach 12.
Watch out. Add 4 3 times. Do not add 3 4 times.
Method. Repeated addition: add the same number once for each group.
- Write one 3 for each group. There are 4 groups, so there are 4 lots of 3.3 + 3 + 3 + 3
- Add them up. Add the groups one after another, or count in steps of the group size.3 + 3 + 3 + 3 = 12
- Write the answer. This is the total altogether.12
Check. Count in 3s 4 times and you reach 12.
Watch out. Add 3 4 times. Do not add 4 3 times.
Method. Repeated addition: add the same number once for each group.
- Write one 2 for each group. There are 5 groups, so there are 5 lots of 2.2 + 2 + 2 + 2 + 2
- Add them up. Add the groups one after another, or count in steps of the group size.2 + 2 + 2 + 2 + 2 = 10
- Write the answer. This is the total altogether.10
Check. Count in 2s 5 times and you reach 10.
Watch out. Add 2 5 times. Do not add 5 2 times.
Watch out
Watch out. 3 groups of 4 is 4 + 4 + 4, which is 12. It is not 3 + 4.
Exam tip
Grown-up tip. Use egg boxes or cups. Put the same number in each box, then count the boxes and the total together.
Exercise 6A Practice: equal groups and repeated addition
Non-calculatorMethod. Repeated addition: add the same number once for each group.
- Write one 2 for each group. There are 3 groups, so there are 3 lots of 2.2 + 2 + 2
- Add them up. Add the groups one after another, or count in steps of the group size.2 + 2 + 2 = 6
- Write the answer. This is the total altogether.6
Check. Count in 2s 3 times and you reach 6.
Watch out. Add 2 3 times. Do not add 3 2 times.
Method. Repeated addition: add the same number once for each group.
- Write one 3 for each group. There are 2 groups, so there are 2 lots of 3.3 + 3
- Add them up. Add the groups one after another, or count in steps of the group size.3 + 3 = 6
- Write the answer. This is the total altogether.6
Check. Count in 3s 2 times and you reach 6.
Watch out. Add 3 2 times. Do not add 2 3 times.
Method. Repeated addition: add the same number once for each group.
- Write one 4 for each group. There are 4 groups, so there are 4 lots of 4.4 + 4 + 4 + 4
- Add them up. Add the groups one after another, or count in steps of the group size.4 + 4 + 4 + 4 = 16
- Write the answer. This is the total altogether.16
Check. Count in 4s 4 times and you reach 16.
Watch out. Add 4 4 times. Do not add 4 4 times.
Method. Repeated addition: add the same number once for each group.
- Write one 4 for each group. There are 5 groups, so there are 5 lots of 4.4 + 4 + 4 + 4 + 4
- Add them up. Add the groups one after another, or count in steps of the group size.4 + 4 + 4 + 4 + 4 = 20
- Write the answer. This is the total altogether.20
Check. Count in 4s 5 times and you reach 20.
Watch out. Add 4 5 times. Do not add 5 4 times.
Method. Repeated addition: add the same number once for each group.
- Write one 2 for each group. There are 5 groups, so there are 5 lots of 2.2 + 2 + 2 + 2 + 2
- Add them up. Add the groups one after another, or count in steps of the group size.2 + 2 + 2 + 2 + 2 = 10
- Write the answer. This is the total altogether.10
Check. Count in 2s 5 times and you reach 10.
Watch out. Add 2 5 times. Do not add 5 2 times.
Method. Repeated addition: add the same number once for each group.
- Write one 2 for each group. There are 4 groups, so there are 4 lots of 2.2 + 2 + 2 + 2
- Add them up. Add the groups one after another, or count in steps of the group size.2 + 2 + 2 + 2 = 8
- Write the answer. This is the total altogether.8
Check. Count in 2s 4 times and you reach 8.
Watch out. Add 2 4 times. Do not add 4 2 times.
Method. Repeated addition: add the same number once for each group.
- Write one 3 for each group. There are 3 groups, so there are 3 lots of 3.3 + 3 + 3
- Add them up. Add the groups one after another, or count in steps of the group size.3 + 3 + 3 = 9
- Write the answer. This is the total altogether.9
Check. Count in 3s 3 times and you reach 9.
Watch out. Add 3 3 times. Do not add 3 3 times.
Method. Repeated addition: add the same number once for each group.
- Write one 2 for each group. There are 4 groups, so there are 4 lots of 2.2 + 2 + 2 + 2
- Add them up. Add the groups one after another, or count in steps of the group size.2 + 2 + 2 + 2 = 8
- Write the answer. This is the total altogether.8
Check. Count in 2s 4 times and you reach 8.
Watch out. Add 2 4 times. Do not add 4 2 times.
Method. Repeated addition: add the same number once for each group.
- Write one 4 for each group. There are 6 groups, so there are 6 lots of 4.4 + 4 + 4 + 4 + 4 + 4
- Add them up. Add the groups one after another, or count in steps of the group size.4 + 4 + 4 + 4 + 4 + 4 = 24
- Write the answer. This is the total altogether.24
Check. Count in 4s 6 times and you reach 24.
Watch out. Add 4 6 times. Do not add 6 4 times.
Method. Repeated addition: add the same number once for each group.
- Write one 3 for each group. There are 2 groups, so there are 2 lots of 3.3 + 3
- Add them up. Add the groups one after another, or count in steps of the group size.3 + 3 = 6
- Write the answer. This is the total altogether.6
Check. Count in 3s 2 times and you reach 6.
Watch out. Add 3 2 times. Do not add 2 3 times.
Method. Repeated addition: add the same number once for each group.
- Write one 4 for each group. There are 4 groups, so there are 4 lots of 4.4 + 4 + 4 + 4
- Add them up. Add the groups one after another, or count in steps of the group size.4 + 4 + 4 + 4 = 16
- Write the answer. This is the total altogether.16
Check. Count in 4s 4 times and you reach 16.
Watch out. Add 4 4 times. Do not add 4 4 times.
Method. Repeated addition: add the same number once for each group.
- Write one 6 for each group. There are 3 groups, so there are 3 lots of 6.6 + 6 + 6
- Add them up. Add the groups one after another, or count in steps of the group size.6 + 6 + 6 = 18
- Write the answer. This is the total altogether.18
Check. Count in 6s 3 times and you reach 18.
Watch out. Add 6 3 times. Do not add 3 6 times.
Method. Repeated addition: add the same number once for each group.
- Write one 6 for each group. There are 6 groups, so there are 6 lots of 6.6 + 6 + 6 + 6 + 6 + 6
- Add them up. Add the groups one after another, or count in steps of the group size.6 + 6 + 6 + 6 + 6 + 6 = 36
- Write the answer. This is the total altogether.36
Check. Count in 6s 6 times and you reach 36.
Watch out. Add 6 6 times. Do not add 6 6 times.
Method. Repeated addition: add the same number once for each group.
- Write one 3 for each group. There are 4 groups, so there are 4 lots of 3.3 + 3 + 3 + 3
- Add them up. Add the groups one after another, or count in steps of the group size.3 + 3 + 3 + 3 = 12
- Write the answer. This is the total altogether.12
Check. Count in 3s 4 times and you reach 12.
Watch out. Add 3 4 times. Do not add 4 3 times.
Method. Repeated addition: add the same number once for each group.
- Write one 5 for each group. There are 6 groups, so there are 6 lots of 5.5 + 5 + 5 + 5 + 5 + 5
- Add them up. Add the groups one after another, or count in steps of the group size.5 + 5 + 5 + 5 + 5 + 5 = 30
- Write the answer. This is the total altogether.30
Check. Count in 5s 6 times and you reach 30.
Watch out. Add 5 6 times. Do not add 6 5 times.
Method. Repeated addition: add the same number once for each group.
- Write one 3 for each group. There are 6 groups, so there are 6 lots of 3.3 + 3 + 3 + 3 + 3 + 3
- Add them up. Add the groups one after another, or count in steps of the group size.3 + 3 + 3 + 3 + 3 + 3 = 18
- Write the answer. This is the total altogether.18
Check. Count in 3s 6 times and you reach 18.
Watch out. Add 3 6 times. Do not add 6 3 times.