More than one step
A multi-step problem needs two or more calculations. The answer to the first step becomes part of the next one. Many real problems are like this: buying several items, working out change, planning a trip.
A four-step approach
| Step | Ask yourself |
|---|---|
| 1. Understand | What is the question? What key information do I have? |
| 2. Plan | What steps and operations will I need, and in what order? |
| 3. Solve | Do each calculation carefully, one at a time. |
| 4. Check | Does the answer make sense? Did I answer the question asked? |
Finding the hidden question
Most multi-step problems have a hidden question: something you need to work out first that the problem doesn’t ask directly.
Problem: Maya buys 3 books at $8 each and pays with a $50 bill. How much change does she get?
- Hidden question: How much do the books cost? 3 × $8 = $24.
- Main question: How much change? $50 − $24 = $26.
Organizing your work
Write each step on its own line with a label:
- Step 1: Cost of books = 3 × 8 = 24
- Step 2: Change = 50 − 24 = 26
Labelling makes it easy to find mistakes.
Draw a picture or bar model
A bar model helps you see the parts. Draw one long bar for the $50 Maya pays. Split off three equal boxes of $8 for the books. The part of the bar that is left over is the change.
| Book | Book | Book | Change |
|---|---|---|---|
| $8 | $8 | $8 | ? |
Another example
Problem: A class of 28 students is going to a museum. Tickets cost $6 each. The school pays $50 and the rest is split equally among students. How much does each student pay?
- Total cost: 28 × $6 = $168.
- After the school pays: $168 − $50 = $118.
- Per student: $118 ÷ 28 ≈ $4.21.
Each student pays about $4.21.
Worked examples
Example 1: A farmer has 4 rows of 12 apple trees. 9 trees are sick. How many healthy trees?
4 × 12 = 48; 48 − 9 = 39.
Example 2: Liam reads 15 pages each day for 6 days, then 22 pages on day 7. Total?
15 × 6 = 90; 90 + 22 = 112 pages.
Example 3: 3 packs of 8 juice boxes are shared among 6 friends. How many each?
3 × 8 = 24; 24 ÷ 6 = 4 each.
Common mistakes
- Stopping after the first step and giving the hidden answer instead of the final one.
- Using numbers in the wrong order, especially with subtraction and division.
- Using information that isn’t needed. Some problems include extra numbers.
- Not checking whether the answer is reasonable.
Try it yourself
- Pens cost $2 each. Ana buys 7 pens and pays $20. What is her change?
- A bus has 48 seats. 3 buses carry 130 people. How many empty seats?
- Sam earns $12 an hour for 5 hours and spends $25. How much does he have left?
Answers: 1) $6 2) 14 (144 − 130) 3) $35
Quick recap
- A multi-step problem needs more than one operation.
- Find the hidden question and plan the order of steps.
- Label each step and check the final answer.