Problem-solving Strategies

Every word problem can be tackled with the same four steps: Understand, Plan, Solve, and Check. The Plan step is where you pick a strategy. Some problems are easier to draw, some are easier in a table, and some are easier when you work backward from the answer. Picking the right strategy makes the work shorter and the answer easier to trust.

The Four Problem-Solving Steps

1. Understand — read the problem twice, mark what is asked, and list what you are given.
2. Plan — choose a strategy that fits. Decide which operations and which order to use.
3. Solve — carry out the plan step by step, showing your work neatly.
4. Check — does the answer make sense? Estimate or work backward to confirm it.

Six Strategies to Choose From

• Draw a picture — turn words into a quick sketch when shapes, distances, or arrangements are described.
• Make a table — line up values in rows and columns when a problem lists rates, prices, or repeated counts.
• Work backward — start from the final answer and undo each step, useful when the end result is given.
• Look for a pattern — list a few cases and spot what repeats or grows.
• Guess and check — try a reasonable value, test it, then adjust up or down.
• Use simpler numbers — solve the same shape of problem with smaller, friendlier numbers first, then redo with the real numbers.

Picking the Right Strategy

• Distances, areas, parts of a whole — try Draw a picture.
• Rates, prices over time, repeated counts — try Make a table.
• You know the ending and need the start — try Work backward.
• A list keeps growing the same way — try Look for a pattern.
• Two unknowns that must add or multiply to a target — try Guess and check.
• The numbers feel scary — try Use simpler numbers, then scale back up.