Choosing an operation and number range that match the lesson
Ms. Chen needs 10 word problems for pupils who can add confidently within 20 but are only beginning to read mathematical stories. She chooses Addition and a range of 1 to 20. The arithmetic stays familiar, so the new work is identifying the two quantities and the question. Moving the range to 1 to 100 on the same day would test place value and reading at once, making a wrong answer harder to diagnose.
The selected range controls the numbers stated in the story, not necessarily the answer. A multiplication problem with 8 groups of 7 uses two numbers inside a 1 to 12 range, while the answer is 56. Two-step problems can also produce a larger intermediate total. That is useful when the method is familiar, but it should be planned rather than accidental.
- Addition and subtraction: use 1 to 10 for first stories, then 1 to 20. Subtraction stories always leave zero or more, so the wording never asks a pupil to give away items that were not there.
- Multiplication: use 2 to 12 for times-table facts. Equal groups, rows, and containers make the repeated quantity explicit.
- Division: keep whole answers on while equal sharing is the lesson. A 1 to 20 range provides familiar dividends and divisors without division by zero.
- Two-step reasoning: begin with a smaller known range. Selecting and ordering two operations is already the new challenge.
A narrow range is not a weakness. It isolates the skill you want to observe. Increase the numbers only when a pupil can explain why the chosen operation fits the story.