Division Two Ways: Sharing on One Card, Grouping on the Other

The two cards on this 3rd grade word-problems page look different on purpose. On the first, twelve nectarines are pictured above two wide empty boxes, and Tom sorts them equally into 2 groups; on the second, ten cranberries lie in one unbroken row with no boxes at all, and Tom arranges them in rows of 5. Both stories are about fruits, both are division, and only the first supplies the containers. Each card carries the usual dot grid, a dashed answer box and a handwriting line for the sentence.

Putting the two shapes side by side is the point. Sharing gives the number of groups and asks for the size; grouping gives the size and asks for the number, and although both are written with a division sign, children who have only met one of them will try to run its method on the other and find no boxes to deal into. Seeing them on one sheet, in the same layout with the same kind of picture, is what makes the difference discussable: what does this story already tell me, and what is it asking for? That question, rather than any procedure, is what a word problems page is for.

Print the PDF free and ask, before any working, which card gives the boxes and which does not; the answer names the type without any vocabulary being required. If one card is much harder than the other, its single-type page is the repair: sharing for the dealt boxes, making groups for the rings. The mixed problems page adds a multiplication story to the same choice, and the multiplication word problems page is where the equal-groups picture is first built rather than broken up.