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Word Problems

Level 1 — Beginning Word Problems: Understand the Story

Children learn that a word problem describes a mathematical situation.

Start with concrete, hands-on problems:

“You have 3 bears. I give you 2 more. How many do you have?”

Skills include identifying numbers, understanding more, less, altogether, left, acting out problems, using objects/pictures, identifying the question and solving one-step addition/subtraction situations.

Level 2 — Developing Word Problems: Choose the Operation

Now the emphasis is not relying solely on keywords.

Students learn to ask:

What do I know? → What am I trying to find? → What is happening to the quantities? → Which operation makes sense?

Include addition, subtraction, equal groups, sharing, comparison, missing-part and beginning multiplication/division problems.

Level 3 — Intermediate Word Problems: Represent & Solve

Students encounter problems with more information and must create a mathematical representation.

Teach them to use drawings, number lines, tables, bar models, equations and diagrams.

Include multi-digit operations, multiplication/division, money, measurement, time and beginning fraction problems.

Level 4 — Advanced Word Problems: Multi-Step Reasoning

Students solve problems requiring two or more operations and must determine the correct sequence.

Problems incorporate fractions, decimals, percentages, elapsed time, measurement, area/perimeter, money, graphs and data.

Some problems should intentionally contain irrelevant information so students learn to distinguish necessary from unnecessary information.

Level 5 — Mathematical Problem Solving & Application

This becomes higher-level mathematical reasoning.

Instead of:

“Solve 25% of $80.”

Give students something like:

“You have $100 to plan a class party for 12 children. Food is 20% off, but 6% sales tax will be added. Determine what you can purchase without exceeding your budget.”

Students must determine what information they need, select operations, develop a plan, calculate, evaluate whether their answer is reasonable, revise when necessary and explain/defend their solution.