Smart Math guide · Problem Solving

Use Understand–Plan–Solve–Check

A repeatable problem-solving cycle reduces rushed mistakes and makes reasoning visible.

All levelsWorked example includedSelf-check included
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The method

How to use it

  1. Restate what is known and asked.
  2. Choose a representation or method.
  3. Solve, then check units and reasonableness.
Worked example

See it in action

For a trip-cost problem, list miles, mpg, and fuel price before choosing formulas.

Check your thinking

How to verify it

Estimate fuel gallons first, then compare the exact cost.

Keep learning

More Problem Solving guides

Problem Solving

Draw a Diagram

A labeled sketch can reveal relationships that are hidden in words.

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Problem Solving

Make a Table

Tables organize repeated cases, patterns, and input-output relationships.

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Problem Solving

Work Backward

When the final result is known and operations are reversible, undo them in reverse order.

Read guide →
Problem Solving

Let Units Guide the Formula

Units can show which operations make sense and expose mismatched formulas.

Read guide →
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