Multi-step word problems
By Year 5 you've met one-step word problems — "Sam has 4 bags of 6 marbles, how many in total?" This year the problems get longer. They need two or three calculations to reach the answer.
The arithmetic isn't harder than what you already know. The hard part is reading the problem carefully and figuring out which operations to use, in what order.
A typical example
A school has 24 classrooms. Each classroom has 8 tables, and each table has 4 chairs. After a renovation, 18 chairs are removed. How many chairs are left in the school?
Two facts:
- The school has 24 × 8 × 4 chairs in total.
- 18 chairs are removed.
In math:
chairs left = 24 × 8 × 4 − 18 = 768 − 18 = 750.
It's a single calculation — but you had to combine multiplication and subtraction.
The reading routine
- Read the whole problem once. Don't compute anything yet. Just understand the story.
- Find every number. Write them down with a one-word label so you don't lose track. (24 classrooms, 8 tables, 4 chairs, 18 removed.)
- Find the action words. They tell you the operations.
- "each", "every", "per", "of" → usually × (multiplying equal groups).
- "altogether", "total", "combined" → usually + or × (combining).
- "left", "remaining", "taken away", "fewer" → usually − (removing).
- "share equally", "divided into", "how many groups" → usually ÷.
- Decide the order. Multiplications usually come first (when forming "groups of groups"). The combine/remove operations come second.
- Write one expression for the whole problem and compute it using order of operations.
- Write the answer in a sentence. "There are 750 chairs left." Not just "750".
Worked examples
Example 1
A bookshop receives 12 boxes of books. Each box holds 40 books. The shop sells 150 books in the first week. How many books are left?
- Books delivered = 12 × 40 = 480.
- Books left = 480 − 150 = 330.
Or in one expression: 12 × 40 − 150 = 330.
Example 2
Mia bakes cupcakes. She fills 6 trays with 12 cupcakes each. Then she takes 3 of the trays to school. How many cupcakes does she keep at home?
- She still has 6 − 3 = 3 trays at home.
- Each tray has 12 cupcakes, so cupcakes at home = 3 × 12 = 36.
Or: (6 − 3) × 12 = 36. Order matters — brackets here!
Example 3
A bus has 42 seats. 8 buses go on a school trip. 12 seats are empty on each bus. How many children are on the trip?
- Filled seats per bus = 42 − 12 = 30.
- 8 buses × 30 children = 240 children.
Or: 8 × (42 − 12) = 240.
Common pitfalls
Doing operations in the wrong order
"6 trays of 12 cupcakes, take 3 away" gives 6 × 12 − 3 = 69 if you read it wrong. But the "3" is trays, not cupcakes — so you remove 3 × 12 = 36, leaving 6 × 12 − 3 × 12 = 36.
Fix: keep the units with each number. "3 trays" not "3". Convert trays to cupcakes before subtracting.Adding when you should multiply
"4 boxes of 5 marbles" is 4 × 5 = 20, not 4 + 5 = 9.
Fix: when you see "each", "per", "every" — that's almost always multiplication.Subtracting in the wrong direction
If you're left with negative chairs, you flipped the subtraction. Always subtract the smaller from the larger.
Forgetting a step
You computed total chairs but forgot to subtract the removed ones. Always re-read the question at the end: "Did I answer what was actually asked?"
A puzzle
A pizza place sells 8 slices per pizza. A school orders 15 pizzas for the canteen. 24 slices are eaten by lunchtime, and 18 more in the afternoon. How many slices are still in the box?
- Total slices: 15 × 8 = 120.
- Eaten: 24 + 18 = 42.
- Left: 120 − 42 = 78.
One expression: `15 × 8 − (24 + 18) = 120 − 42 = 78`.