Multi-step word problems

Multi-step word problems

A multi-step problem hides two or more calculations inside one story. The numbers and the question are usually clear; what's tricky is figuring out the order: which calculation comes first, and which uses the answer of the first one as input.

The big idea — partial answers

In a multi-step problem you almost always have to compute a partial answer and then keep going. Treat the partial answer like a brand-new number that you can use in step 2.

A school has 8 classes. Each class has 24 children. On Monday 17 children were absent. How many children were at school on Monday?

Step 1 — find the total in school: 8 × 24 = 192 children.

Step 2 — subtract the absent ones: 192 − 17 = 175 children at school.

Notice: the answer to step 1 (192) becomes one of the inputs in step 2.

Choosing the operation — what each word suggests

The words in the story often hint at the operation, but they don't decide it on their own. Use this table as a starting suggestion, then check with common sense.

Story phraseOften means
altogether, in total, sum, combinedadd (+)
how many more, how many fewer, left oversubtract (−)
each, per, times, groups ofmultiply (×)
share equally, split into groups of, how many fitdivide (÷)
times as many, times as muchmultiplicative comparison (× or ÷)

⚠️ "Less than" usually signals subtraction, but be careful — sometimes you subtract one way ("3 less than 10") and sometimes the other (" twice as many minus 4 ").

A two-step worked example

Maya bought 4 packs of pens. Each pack had 6 pens. She gave 5 pens to her brother. How many pens does Maya have now?

Plan:

  • Step 1 — total pens bought: 4 × 6.
  • Step 2 — subtract the pens given away.

Compute:

  • 4 × 6 = 24.
  • 24 − 5 = 19 pens.

Write the answer in a sentence: Maya has 19 pens left.

A three-step worked example

A bakery makes 12 trays of buns each day. Each tray has 18 buns. On Tuesday the baker burned 9 buns and threw them away. The rest were sold in bags of 6. How many bags did the baker sell?

Plan:

  • Step 1 — buns made: 12 × 18.
  • Step 2 — subtract the burned ones.
  • Step 3 — divide into bags of 6.

Compute:

  • 12 × 18 = 216.
  • 216 − 9 = 207.
  • 207 ÷ 6 = 34 r 3.

But you can't sell three-buns-in-a-bag if a bag is supposed to have 6. So 34 full bags were sold, and 3 buns were left over.

Answer: The baker sold 34 bags, with 3 buns left over.

Common mistakes

  • Doing the calculations in the wrong order. "Plan first, compute second" is the rule. If you start computing as soon as you read a number, you usually end up doing them backwards.
  • Forgetting a step. Three-step problems are sneaky. The third calculation is easy to miss if you stopped after computing the first big number.
  • Mixing units. "Maya has 1 m 20 cm of ribbon. She uses 35 cm." You must convert to one unit first (1 m 20 cm = 120 cm) before subtracting.
  • Ignoring extra information. Some Year-4 problems give a number you don't actually need. Cross it out so it doesn't tempt you.

Drawing helps

For tough multi-step problems, draw a picture or a bar model — a long rectangle divided into the parts the story describes. Seeing the parts makes the steps obvious.

What's next

Try it out