MATH SCHEMAS
Find the structure in the story.
A word problem is a story with mathematical relationships. Understand those relationships before choosing an operation.
Stories first. Models next.
We ask: What is happening? How are the quantities related? What is known, and what do we need to find? Schemas give students a framework for recognizing the structure of a problem.
Begin with simple numbers and familiar situations. Use students’ names, interests, and sometimes delightfully ridiculous stories to bring the mathematics to life.
When the problem feels difficult
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Estimate before calculating.
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Try simpler numbers.
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Temporarily remove the numbers and discuss the story.
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Connect structures as students move into multi-step problems.
Different stories. Shared structures.
Combine
Change
Additive comparison
Parts come together to make a whole.
A starting amount increases or decreases.
Two amounts are compared to find a difference.
Equal groups
Multiplicative comparison
A number of groups contains the same amount in each group.
One amount is a certain number of times another.
See an example: Maya’s toy cats
Maya has 24 toy cats. Some are in a basket, and 9 are on a shelf. How many are in the basket?
9 + □ = 24
The two parts make a whole: this is a combine structure. Subtraction finds the missing part: 24 − 9 = 15 toy cats in the basket.
Try it
Change the story while keeping its structure. Move the unknown to a different position. Ask students to label the quantities, draw a model, and explain why their equation fits.
In equal-groups problems, the unknown might be the total, the number of groups, or the amount in each group. The relationship stays connected even when the question changes.
Students create and teach
Students write stories, create schema models and posters, and use the three reads to lead classmates through their thinking. Disagreement is a reason to explain, listen, and revise.
Math practices in action
Schema work supports sense-making (MP1), quantitative reasoning (MP2), discussion (MP3), modeling (MP4), precision (MP6), and recognizing structure across different stories (MP7).
Building confidence through connection.
© 2026 Heidi Fee · Math With Meaning
Music. Creativity. Student leadership.