Division • Topic 2 of 6

Equal Grouping

Equal grouping is the flip side of sharing. This time you know how big each group should be, and you want to know how many such groups you can make. The sentence is Total divided by Size of each group equals Number of groups. Put 20 students into teams of 4 and you get 5 teams, because 20 divided by 4 is 5. The same answer, but the question is now "how many groups?" rather than "how many each?". Grouping is also the clearest way to see division as repeated subtraction: take 4 away from 20 again and again -- 20 minus 4 is 16, 16 minus 4 is 12, 12 minus 4 is 8, 8 minus 4 is 4, 4 minus 4 is 0 -- you subtracted 4 a total of 5 times, so 20 divided by 4 is 5. On a number line this is five backward jumps of 4 from 20 to 0. The error CTET watches for is treating the divisor as the number of groups instead of the group size, which is exactly the sharing-grouping mix-up, so a good teacher keeps the two stories side by side: 20 sweets shared among 4 children gives 5 each, while 20 sweets packed in boxes of 4 gives 5 boxes.

✅ Solved examples

1. A shopkeeper packs 24 eggs into trays that hold 6 eggs each. How many trays does he fill, and which meaning of division is this?
He fills 4 trays. This is equal grouping: Total / Size of each group = Number of groups, so 24 / 6 = 4. The group size (6) is known and we find the number of groups.
2. Show how 20 / 4 = 5 can be found by repeated subtraction.
20 - 4 = 16, 16 - 4 = 12, 12 - 4 = 8, 8 - 4 = 4, 4 - 4 = 0. The number 4 was subtracted 5 times to reach 0, so 20 / 4 = 5.
3. A number line runs from 0 to 24, and a child makes equal backward jumps of 6 landing on 18, 12, 6 and 0. What division fact has the child shown?
24 / 6 = 4. There are 4 jumps of 6 from 24 down to 0, so 24 divided by 6 is 4 -- a grouping interpretation of division.

✏️ Practice — try these, take hints as needed

1. There are 30 chairs to be arranged in rows of 5 chairs each. How many rows can be made?
Size of each group is known (5).
Total / Size of group = Number of groups.
6 rows (30 / 5 = 6)
2. A child finds 18 / 3 by jumping backward in 3s on a number line from 18 to 0. How many jumps will there be?
Each jump removes 3.
Count the jumps to reach 0.
6 jumps (18 / 3 = 6)
3. "15 sweets are packed in bags of 5." Is this a sharing or a grouping problem, and what is the answer?
The bag size is fixed, the number of bags is unknown.
Grouping; 3 bags (15 / 5 = 3)

📝 Topic test — 8 questions

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