Two-step word problems
Write down what you know, decide what the question actually asks, then plan the two steps before calculating anything.
Read it twice, calculate once
On the first read, work out the situation: who is doing what, and with what numbers.
On the second read, find the exact thing being asked for. It is almost never the number you meet first.
Only then start calculating. Rushing at the numbers is how you end up solving a question nobody asked.
Two steps, and the trap between them
A two-step problem hides a second question inside the first. Maya buys three notebooks at $4.50 and pays with $20. Working out what the notebooks cost is step one. It is not the answer.
The number you get at the end of step one always looks like an answer. It is sitting right there, it took work, and it is usually one of the options. That is not an accident — it is put there on purpose.
Write the plan down
Two short lines are enough, and they should be written before any arithmetic happens.
The plan is not for the marker. It is so that when you finish step one you can see, in your own handwriting, that there is a step two.
Check the answer against the question
When you have a number, read the question one last time and ask whether your number is the thing it asked for.
Change, not cost. How many are left, not how many there were. How much further, not how far.
The answer is in the last line
The commonest way to lose a mark on a two-step problem is to do both steps correctly and then write down the wrong one.
Maya buys three notebooks at $4.50 and pays with $20. Three times $4.50 is $13.50. That number is real, it is correct, and it is not what was asked. The question asked for the change.
Before you write anything in the answer box, read the final sentence of the question one more time and check that your number answers it.
Estimate before you start
A rough answer worked out in your head takes five seconds and catches the kind of mistake that is otherwise invisible.
Three notebooks at about $5 is about $15, so the change from $20 will be about $5. Now an answer of $6.50 looks reasonable and an answer of $65 does not.
This matters most in multiple choice, where a wrong option is usually the number you would get by slipping a decimal place or doing the last step backwards. An estimate rules those out before you have to think about them.
Worked examples
Maya buys 3 notebooks at $4.50 each and pays with a $20 note. How much change does she receive?
Step one: the notebooks cost 3 × $4.50 = $13.50.
Step two: the change is $20 − $13.50 = $6.50.
The question asked for change, not cost, so $13.50 is the trap and $6.50 is the answer.
Answer: $6.50
A bus has 52 seats. 18 people get on at the first stop and 13 at the second. How many seats are still empty?
Step one: 18 + 13 = 31 people on the bus.
Step two: 52 − 31 = 21 seats empty.
Stopping at 31 answers "how many people", which is not what was asked.
Answer: 21
Liam reads 24 pages on Monday and twice as many on Tuesday. How many pages did he read altogether?
Step one: Tuesday is 24 × 2 = 48 pages.
Step two: altogether is 24 + 48 = 72 pages.
Here the trap is 48 — the answer to "how many on Tuesday", which the question did not ask.
Answer: 72 pages
A box holds 6 pencils. A teacher buys 7 boxes and hands out 30 pencils. How many are left?
Step one: 7 × 6 = 42 pencils bought.
Step two: 42 − 30 = 12 pencils left.
Check against the question: it asked how many are left, and 12 is a count of pencils, so it is the right kind of answer.
Answer: 12
A class of 28 students goes to a museum. Tickets are $12 each and the school pays a $40 booking fee. What is the total cost?
First the tickets: 28 × $12 = $336. Then add the fee, because the question asks for the total, not the ticket cost.
Answer: $376
Liam has $50. He buys 4 books at $8.50 each. How much does he have left?
Estimate first: four books at about $8 is about $34, so he should have about $16 left. Now the working: 4 × $8.50 = $34, and $50 − $34 = $16.
Answer: $16
A baker makes 96 rolls and packs them into trays of 8. She sells 7 trays. How many rolls are left?
96 ÷ 8 = 12 trays. She sells 7, so 5 trays remain — but the question asks for rolls, not trays, so multiply back: 5 × 8.
Answer: 40 rolls
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