L4 · Division as equal sharing and equal grouping

Learning goal

“I can divide by sharing fairly and by making groups. I can check every division with multiplication, because division and multiplication are inverse operations.”

Division — splitting a total into equal parts, or measuring it out in equal groups. The sign is /.

Equal sharing — dealing a total out fairly: "12 shared among 3 friends - how many does each friend get?"

Equal grouping — packing a total into groups of a set size: "12 cookies, 4 to a bag - how many bags?"

Quotient — the result of a division: in sharing it is the size of each share; in grouping it is the number of groups.

Worked example

12 cookies are shared equally among 3 friends. How many cookies does each friend get? Step 1 (name the question): SHARING. The total is 12. The shares are 3. We want the size of each share. Step 2 (deal them out): deal one cookie to each friend, round and round: after 4 rounds every friend holds 4 and the cookies are gone. Step 3 (write it): 12 / 3 = 4. Each friend gets 4 cookies. Step 4 (check by the inverse): division is checked by multiplication: 3 x 4 = 12.

Check yourself — explain it

The answer 4 is checked by multiplying 3 x 4 because...

Paired problem — example still visible

20 stickers shared equally among 5 children: 20 / 5 = 4 each (check: 5 x 4 = 20)

Faded completion — last step is yours

"18 / 6 = ___ - and the check is 6 x ___ = 18" -> 3; 3

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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