Word Problems: Multiplication

Multiplication, in sentences

A number of boxes, the same number of things in each, and the question asks for the total. Equal groups, which is the meaning of multiplication a child can picture.

Easy keeps both factors small. Medium runs to eight by nine. Hard reaches twelve by twelve, which is the whole tables grid.

Equal groups first, arrays second

Boxes with the same number in each is the most concrete image available, and it is where multiplication should start.

It is not the only one. Arrays — rows and columns — make commutativity obvious, since turning the array sideways plainly does not change the count. Scaling is a third and the hardest. A child who has only met one of these can be fluent in tables and still lost on a question that uses another, so introduce the others alongside these sheets rather than after them.

What changes with difficulty

The factors get larger. Nothing else does.

Holding the sentence steady while the numbers grow is what makes the sheets diagnostic: it separates a tables gap, which shows up only on the hard band, from a comprehension gap, which shows up on all three equally and needs entirely different help.

The failure is upstream of the arithmetic

Children rarely get these wrong at the multiplication. They get them wrong having decided, on the strength of two numbers in a sentence, that some other operation was called for.

Insist on a sequence. Pencil down. Read it all. Say what is going on. Find the question. Then, and not before, look at the numbers.

Why keyword lists let you down

"Each means times" works while the questions are built like the examples and fails the moment one is not.

Ask instead what the situation is doing — combining things, taking them away, repeating a group, or splitting one up. That holds regardless of the wording, which is the whole point.

In practice

Twelve problems, answer key optional. The names and objects are drawn from a pool, so a second sheet on the same settings is genuinely a different sheet.

Ask for a few worksheets in one go if you want a set.

Companion sheets: addition, subtraction and division. For tables drill, the multiplication table generator.