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🗺️ Planning and Checking Multi-Step Problems

A good plan turns a tangled problem into simple steps — and a good check catches mistakes before they cost you. Learn to map out the steps, solve them, and prove your answer makes sense.

3
lessons
~15 min
to learn
🔢 Math
subject
Ages 6–12
level
Start the course →

What you’ll learn

  1. Make a PlanRepresent a multi-step problem with a bar model and order the steps before solving.Planning turns a messy problem into clear steps. A bar model pictures the maths — four equal parts of 32 shows 4 × 32 = 128. Then you decide the order of operations: for the cookie problem you must multiply to find the total baked before you can subtract the amount sold.
  2. Work the PlanSolve a two-step problem carefully, carrying the middle result into the next step.With a plan in hand, solving is orderly. For 6 trays of 24 cookies with 100 sold: step one gives 6 × 24 = 144, and step two gives 144 − 100 = 44. The middle number, 144, is the bridge between steps — keep it, and the answer follows.
  3. Check It Makes SenseCheck answers using estimation, inverse operations, and reasonableness.Checking catches mistakes. Estimate: 6 × 25 = 150, then 150 − 100 = 50 — close to 44, so it's sensible. Reverse it: 44 + 100 = 144 and 144 ÷ 6 = 24, proving the work. Finally, ask whether the answer fits the real world; if it clashes with the story, something went wrong.

Questions this course answers

For '4 buses with 32 children each', what does a bar model of four equal parts of 32 show?

Four equal parts of 32 joined together is 4 × 32 = 128 children.

In the cookie problem, what should the FIRST step of the plan be?

You must find the total baked (6 × 24) before you can take away the 100 sold.

6 trays of 24 cookies, then 100 are sold. How many are left?

6 × 24 = 144 baked, then 144 − 100 = 44 left.

What is the 'middle number' in the cookie problem?

144 (the total baked) is the middle number carried into the subtraction.

How can you CHECK that 144 − 100 = 44 using the inverse?

Addition undoes subtraction: 44 + 100 = 144, so the answer is right.

Which answer is NOT reasonable?

One bus alone holds 32 children, so 8 total for four buses is impossible.

Grounded in trusted sources

  • Khan Academy
  • NRICH — University of Cambridge
  • NCTM — teaching standards
  • PBS LearningMedia

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

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