Math Word Problems: Turning a Sentence Into a Sum

Almost no child fails a word problem because of the arithmetic. They fail because they cannot decide which arithmetic to do — and reading it again more slowly does not help.

Three questions, in this order.

1. What is being asked? Have the child say the question in their own words, without numbers. "How many are left." "How much altogether." If they cannot, no method will save the answer.

2. Are things joining, separating, grouping, or sharing? Joining is addition. Separating or comparing is subtraction. Equal groups is multiplication. Splitting into equal groups is division. Four situations, four operations — this is more reliable than keyword lists.

3. Is the answer bigger or smaller than the numbers given? Estimating first catches most errors before they happen.

The keyword trap. Children are often taught that "more" means add. Then they meet "Tom has 5 more than Ann; Tom has 12; how many has Ann?" and add. Keywords are a shortcut that fails on exactly the problems that matter. Situations do not fail.

Multi-step problems add a memory load: there is an intermediate answer that is not the answer. Insist it gets written down and labelled. Half of all multi-step errors are a correct middle number that was forgotten.

Practical tip. Occasionally give a problem with a missing number or an impossible one and ask whether it can be solved. Children who only ever see solvable problems learn to grab numbers and combine them; children who have to check learn to read.

See also ratios and proportions, division facts, counting coins and games for 3rd graders.