Math101 · Independent Ontario learning library
Math101Problem Solving Toolkit
A problem-solving toolkit is a collection of decisions rather than one universal algorithm.
Use a flexible problem-solving toolkit to identify givens and constraints, choose a representation, carry out a justified plan, and interpret the result.
Intuition and core definition
A problem-solving toolkit is a collection of decisions rather than one universal algorithm. Strong solvers understand the question, represent the information, choose and carry out a plan, monitor assumptions, and interpret the result. When stuck, they change representation or solve a simpler related problem instead of performing random operations.
Notation, language, and conditions
Let given mean information supplied, unknown mean the requested quantity, constraint mean a condition any solution must satisfy, and model mean a mathematical representation of the situation. Useful tools include a diagram, table, equation, organized list, pattern, estimate, working backward, cases, and invariants—features that remain unchanged.
Why this idea matters
A modelling toolkit separates the unknown, constraints, operations, and reasonableness check so that an unfamiliar context becomes a sequence of mathematical decisions.
A dependable method
- Restate the question and list givens, unknowns, units, and constraints.
- Represent the relationships with a labelled diagram, table, equation, or smaller analogous case.
- Choose a plan and state why its conditions match the problem.
- Carry out the plan while monitoring signs, units, domain, and whether intermediate values remain plausible.
- Check against the original context, then communicate a conclusion that answers the actual question.
