Interpret Remainders in Word Problems

Students solve division-based word problems and make sense of the remainder by deciding whether to ignore it, round up the quotient, use only the remainder, or treat it as a fractional part. They justify their interpretation based on the real-world context.

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Grade 4 · Multistep Word Problems · question 1 of 3

0 of 20

20 rungs. A star at the top.

Ana packs 14 muffins into boxes that hold 4 each. How many muffins are left after every full box is packed?

How it is taught

0:00 of 4:18

A remainder is what is left after equal groups.

The story decides whether you ignore it, use it, or round up.

Read it: The question says what is left

23 students ride in vans of 5. 23 ÷ 5 = 4 R 3: 4 vans are full, and 3 students still need a seat. So 5 vans are needed.

Divide, and write the quotient and the remainder.
Read the question again: what does it ask for?
Round up, drop the remainder, give the remainder, or share it, as the question says.

Vans needed must carry everyone, so a remainder means one more van.

Full boxes count only the full ones, so the remainder is dropped.

A question about what is left wants the remainder itself.

Divide first. The question decides what the remainder means.

Answering 4 vans, the quotient, when 3 students are left without a seat.

Every student must ride, so the 3 left over need one more van: 5.

A boat holds 6 people. 40 people want a ride. How many boat trips are needed so everyone rides? — 7. 40 ÷ 6 = 6 R 4, and the 4 people left need one more trip: 7.

23 students ÷ 4 per van

Twenty-three students are going on a field trip. Each van holds four students. How many vans do we need?

Let's divide twenty-three by four using long division.

How many fours fit inside twenty-three?

Five! Write five on top.

Five times four is twenty. Write twenty underneath.

Twenty-three minus twenty is three. Three is our remainder.

Grade 4 · What does the remainder mean?

Five vans carry twenty students. But three students are still waiting!

Those three students need a ride too. So we need one more van.

Five vans plus one extra van equals six vans.

We need six vans. When leftover people still need a ride, we round up!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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