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🧗 Solving Complex Math Problems

Big, twisty problems are beatable with the right approach. Learn a four-step method and a toolkit of strategies — draw a picture, work backwards, list systematically — then carry a hard problem all the way to a checked answer.

3
lessons
~30 min
to learn
🔢 Math
subject
Ages 6–12
level
Start the course →

What you’ll learn

  1. Understand and PlanApply Pólya's four-step method and choose an appropriate problem-solving strategy.Hard problems reward a calm, planned approach. Pólya's four steps — Understand, Plan, Carry it out, Look back — organize the work. Understanding comes first, then a chosen strategy: draw a picture, work backwards, list systematically, or try a simpler case. Matching the strategy to the problem is half the battle.
  2. Powerful StrategiesSolve problems by working backwards and by listing possibilities systematically.Working backwards undoes operations in reverse order: for '×3 then +4 = 19', do 19 − 4 = 15 then 15 ÷ 3 = 5. Systematic listing counts possibilities without missing any: 2 shirts and 3 pants give 2 × 3 = 6 outfits when you pair them in an orderly grid.
  3. Carry It Out and CheckCarry out a multi-step solution in order and verify it by working backwards.The pizza problem shows the whole arc: 156 + 12 = 168 people, 168 × 2 = 336 slices, 336 ÷ 8 = 42 pizzas. The final 'look back' step reverses the work — 42 × 8 = 336 and 336 ÷ 2 = 168 — matching the group exactly. A checked answer is a trusted answer.

Questions this course answers

What is the FIRST step of Pólya's four-step method?

You must understand what is known and asked before planning or solving.

Which strategy best fits 'A number is doubled and the result is 30 — what was it?'

The problem gives the ending (30) and hides the start, so undo the steps: 30 ÷ 2 = 15.

Why is drawing a picture such a useful strategy?

A diagram or bar model makes the relationships in a problem visible and easier to reason about.

A number is multiplied by 3, then 4 is added, giving 19. What was the number?

Undo in reverse: 19 − 4 = 15, then 15 ÷ 3 = 5.

How many outfits can you make from 2 shirts and 3 pairs of pants?

Each of the 2 shirts pairs with each of the 3 pants: 2 × 3 = 6.

A number is divided by 2, then 1 is subtracted, giving 4. What was the number?

Undo in reverse: 4 + 1 = 5, then 5 × 2 = 10.

Grounded in trusted sources

  • Khan Academy
  • NRICH — University of Cambridge
  • George Pólya — How to Solve It
  • NCTM — teaching standards

Every Wunder lesson is built from real, reputable sources — never invented.

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🗺️Planning and Checking Multi-Step Problems🧩Solving Multi-Step Word Problems💷Solving Money and Measurement Problems🍎Solving Two-Step Word Problems🧺Sorting and Counting🗂️Sorting Data into Categories🍰Splitting Shapes into Equal Parts🔎Spotting Number Patterns

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