Word Problems: Division

Division, in sentences

A quantity is shared equally among a number of children, and the question asks how many each one gets. The totals are constructed by multiplying up from the answer, so every division comes out exactly — no remainders on these sheets.

Easy stays inside the small tables. Medium reaches eight groups of nine. Hard goes to twelve by twelve.

Sharing and grouping are different questions

Twelve divided by three can mean two things, and children meet them as separate problems long before anyone tells them they are the same operation.

Sharing: twelve sweets between three children, how many each. Grouping: twelve sweets in bags of three, how many bags. The first is the version these sheets use, because it is the one children meet first and the one they can act out. The second is worth introducing separately, and the moment a child sees that both are 12 ÷ 3 is a genuinely useful one.

The three bands

Only the numbers move between the bands. The sentence pattern stays exactly where it is.

This matters for diagnosis. A child who copes on the easy sheet and not the hard one has an arithmetic problem you can fix with tables practice; a child stuck across all three has a reading problem, and no amount of extra division drill will touch it.

Read it before touching it

The mistake is nearly never the division. It is deciding that division was wanted.

Children scan for numbers and reach for the last operation they were taught, which succeeds often enough to become entrenched. The counter-routine is short: read the whole question with the pencil down, say what is happening in your own words, find the sentence that asks something, underline that one.

Against keyword spotting

"Shared means divide" holds up until a question describes the same sharing without using the word, which examiners do on purpose.

Better to ask what the story is doing. Combining, removing, repeating equal groups, splitting into equal parts. That question does not care how the sentence was phrased.

Using them

Twelve questions and an answer key. The names and objects and places all rotate between sheets, so the same settings twice give you two different worksheets — handy for a second attempt.

Generate a few at once to cover a week.

Companion sheets: addition, subtraction and multiplication.