How to help your child with maths word problems

Help your child with a maths word problem by asking them to explain what happens before choosing a calculation. A quick drawing can make the quantities and changes visible. Once they understand the story, work through one step at a time and check that the final answer matches the question.

You can read the problem aloud if the wording is getting in the way. The aim of this activity is to practise mathematical reasoning, so reading help is useful.

Understand the idea

A word problem describes a situation with something to find out. The numbers have jobs: one might describe the number of groups, another the amount in each group, and another what changes afterwards.

Start with: "Tell me this story in your own words. What are we trying to find?"

Ask your child to name the quantities, including their units. "Six pencils in each pack" means something different from "six packs". Then choose a drawing, objects or a short written plan to represent the situation.

Avoid teaching a list of trigger words such as "more always means add". In "Sam has eight stickers, which is three more than Ava", finding Ava's number requires subtraction. What matters is the relationship between the quantities.

See it worked through

Three packs, then five given away

There are three packs of pencils. Each pack contains six pencils. Five pencils are given to another class. How many pencils remain?

Draw three boxes with six marks in each. Ask: "How many pencils were there before giving any away?"

There were 3 × 6 = 18 pencils. Adding 6 + 6 + 6 is another valid way to find that total.

Now cross out five pencil marks. Ask: "What changed after we gave five pencils away?"

Five pencils were given away, so 18 − 5 = 13. The answer is 13 pencils remain.

The number 18 answers the first question we needed to solve. It does not answer the final question about what remains.

Ask your child to check by putting the five pencils that were given away back. The 13 remaining pencils and five pencils that were given away make 18, matching the original total. Writing the unit also helps them check that they found pencils, rather than packs.

Try it together

Draw the craft box

Read this new problem: A craft box holds four bags of beads. Each bag contains five beads. Eight beads are used to make a bracelet. How many beads remain?

Ask your child to retell the story and sketch the bags. Before they calculate, ask: "Will there be more or fewer beads than we started with?"

Let them write or say each step. If they answer 20, ask them to reread the final sentence and explain what happened to the eight beads.

Check the answer

Four groups of five make 4 × 5 = 20 beads. Eight are used, leaving 20 − 8 = 12 beads. Adding the 12 remaining beads to the eight used beads gives 20, so the answer fits the starting amount.

Check their understanding

Change the pencil problem so that five extra pencils are added instead of given away. Ask what changes in the drawing and calculation. There would be 18 + 5 = 23 pencils.

Then ask your child to explain why the first step still uses the same numbers. The original packs have not changed; only the later event has changed.

Make it easier or harder

Make it easier with two packs of three pencils and two pencils given away. Act it out with counters. Count the starting six, remove two and count the four remaining.

Make it harder by adding information that is not needed: the three packs sit in a blue box. Ask whether the colour changes the answer and why. Later, let your child write a two-step problem for you and check your solution.

Teaching notes

NSW Education's discussion of numeracy and mathematical language describes using multiple representations of word problems. These original activities use talk, drawings and calculations to connect the story with the maths.

Numeracy practice

Help your child apply their maths understanding with practice questions and explanations.

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