L6 · Remainders: the quantity left over

Learning goal

“I can divide when the total does not split evenly. I name the remainder, and I know it must be smaller than the divisor. I can say what the remainder means in a story.”

Remainder — the quantity left over after dividing, when one more equal group or share cannot be made. Written "r": 17 / 5 = 3 r 2.

Left over — the plain-language meaning of remainder: what remains after fair sharing or full grouping, too small to make another.

Quotient — the main answer of a division: the share size or the number of full groups. (Pre-taught in L4; the remainder now stands beside it.)

Share — one equal part in a sharing division. A remainder means the sharing stops before everyone can get one more.

Worked example

17 cookies are shared equally among 5 children. How many cookies does each child get? Step 1 (divide): deal in rounds: 5, 10, 15 cookies dealt after 3 rounds. Each child holds 3. Step 2 (what is left): 17 - 15 = 2 cookies remain - too few for another round. Step 3 (write it): 17 / 5 = 3 r 2. Each child gets 3 cookies; 2 are left over. Step 4 (the rule): a remainder must be smaller than the divisor. Here 2 < 5. If the leftover were 5 or more, another full round would fit - the division would not be finished. Step 5 (check): divisor x quotient + remainder = total: 5 x 3 + 2 = 17.

Check yourself — explain it

The dealing stops with cookies still on the table because...

Paired problem — example still visible

23 / 4: 4 x 5 = 20, leftover 3 -> 5 r 3 (check: 4 x 5 + 3 = 23, and 3 < 4)

Faded completion — last step is yours

"29 / 7: 7 x 4 = 28, leftover ___ -> 29 / 7 = 4 r ___" -> 1; 1

Ready to practise?

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

Start practice →Take the unit quiz