Find relationships and unknowns before calculating

Adding every number in a problem or subtracting the smaller number from the larger can miss the situation’s structure. Ask students to restate the problem, distinguish known quantities from the changing relationship, and identify what is unknown. Then choose a drawing, table, or equation that makes that relationship visible.

Explain the representation and check transfer

Model aloud why a drawing or equation fits the situation, and compare why a tempting incorrect approach may seem plausible. Present a new story with the same mathematical structure to check whether students recognize the relationship when wording changes. Pair it with a superficially similar problem that requires a different operation so keyword matching becomes visible. These are illustrative teaching moves; no single formula fits every word problem.

A small numeric pair separates keywords from relationships. “Mina had 4 shells and found 3 more. How many now?” gives 4 + 3 = 7. “Mina has 7 shells, 3 more than Jun. How many does Jun have?” uses the same word *more* but asks for the comparison amount’s other quantity: 7 − 3 = 4. By contrast, “Mina read 4 pages and then 3 more” has the same combine structure as the first shell problem: 4 + 3 = 7. These illustrative examples show how the unknown’s position changes the operation, while a changed story can preserve a relationship.

Check the answer against the original conditions

Review units, magnitude, and whether the answer addresses the quantity asked for; then place it back into the situation. Asking students to explain their representation can help distinguish a calculation error from difficulty interpreting the structure. Choose a follow-up task based on that explanation without assuming unobserved classroom outcomes.

Questions for review

Which relationship, rather than which surface phrase, led the student to choose an operation or representation? Can the student explain why the answer fits the conditions and units?

Sources: WWC: Improving Mathematical Problem Solving in Grades 4 Through 8 · Mathematical Knowledge for Teaching and the Mathematical Quality of Instruction: An Exploratory Study