Reading the maths in word problems
It is a familiar scene. A child who can add and subtract perfectly well on a worksheet of bare numbers stares at a word problem as though it were written in another language. "I don't know what to do." Often, they are right: the difficulty is not the arithmetic, it is the reading. A word problem is a short story with a mathematical question hidden inside, and learning to find that question is a skill in its own right. This article describes why word problems are hard, and gives practical habits that help children read the mathematics in a story.
Written for children aged 7 to 11.
Why word problems are hard
A word problem asks a child to do several things at once:
- Read and understand the language of the story, including words that may be unfamiliar.
- Picture the situation: what is happening, who is involved, what changes.
- Choose the operation: do I add, subtract, multiply or divide?
- Do the calculation.
- Interpret the answer in the context of the story and check that it makes sense.
Only step 4 is arithmetic. Children who struggle are often tripped by steps 1 to 3, and many are never taught how to carry them out. Teaching "key words" (such as "altogether means add" or "left means subtract") is a tempting shortcut, but it frequently misleads: "Sam has 5 marbles, which is 3 more than Ben" has the word "more" but requires subtraction to find Ben's marbles. Understanding the situation beats keyword spotting every time.
Habit 1: read it slowly, and more than once
The first reading is for the story. The second is for the numbers and the question. Ask your child to read the problem aloud or listen as you read it. Then ask, "Tell me the story in your own words." A child who can retell it correctly has taken the first big step.
Habit 2: find the question
Ask: "What is the problem asking us to find out?" Underline or say it aloud. Many mistakes come from answering a different question than the one asked: finding how many apples Maya has, when the problem asks how many more she needs. Writing the question as a short sentence with a blank, "Maya needs ___ more apples", helps to keep it in focus.
Habit 3: picture it or act it out
Drawing a quick sketch, even a rough one, lets a child see what is happening. Little circles for objects, a bar or a number line for amounts, a stick figure for each person. For younger children, using real objects or toys to act out the story is even better. A sketch needs no artistic skill, and it often makes the operation obvious.
Bar models are especially powerful for older children. A bar represents a quantity, divided into parts. For "Ali has 12 stickers. He gives 5 away. How many does he have left?", draw a bar of 12, mark off 5, and see that the remaining part is 12 − 5. For comparison problems ("Sam has 5 more than Ben"), two bars of different lengths show the difference visibly.
Habit 4: know the types of story
Most word problems fall into a small number of types, and recognising them helps children choose the operation.
- Joining and separating: some, then more arrive (add), or some leave (subtract).
- Part and whole: two parts make a whole; finding a missing part uses subtraction.
- Comparing: "how many more", "how many fewer". These are often subtraction, but the story is about a difference.
- Equal groups: 4 bags with 6 apples each (multiplication); 24 apples shared among 4 bags (division).
- Multi-step: a problem that needs two or more operations, such as "buy 3 pencils at 30 cents and pay with a dollar."
You do not need to teach these labels. Just talk about what is going on: "Is something being put together or taken apart? Are we comparing? Are there equal groups?"
Habit 5: estimate before calculating
Ask: "About what do you think the answer will be?" Estimating makes children think about size. If a problem has 48 children going on a bus, and the answer comes out as 2,000, estimation tells them something is wrong. A habit of checking "Does my answer make sense?" is one of the most valuable protections against careless errors.
Habit 6: write a number sentence and then label the answer
Write the calculation and the answer with units: "12 − 5 = 7 stickers". A bare number is not an answer to a story. Labelling forces the child to link the calculation back to the situation, and often reveals a mismatch: "7 what?"
Habit 7: reread and check
Finally, return to the original question and ask: "Does this answer the question? Does it fit the story?" A quick check is a mark of a good problem solver. Even better is to check with a different method, for instance counting up where subtraction was used.
Making your own word problems
One of the best ways to learn what makes a word problem work is to write one. Ask your child to make up a story for a number sentence such as 3 × 4. They might say, "There are three plates with four cookies each." Next, swap: you write a story, they solve it. Children enjoy writing silly stories about their pets or favourite characters, and the exercise turns problem solving from a chore into creative play.
You can also change a problem slightly: "What if there were 5 plates instead of 3?" or "What if the question asked how many cookies were left after we ate 7?" Variation builds flexibility.
Everyday maths stories
Home life is full of word problems that matter to children. "We need 2 apples for each of the 5 people. How many apples should we buy?" "The film starts at 4:30 and lasts 90 minutes. When does it end?" "The pizza costs $12 and there are 4 of us. What's each person's share?" The context makes the question real, and children often solve in their heads what they would struggle with on paper.
When language is the barrier
For children who are learning in a second language, or who find reading difficult, a word problem may be hard simply because of the vocabulary. Read the problem aloud together, explain unfamiliar words, use pictures or objects, and, if useful, restate the problem in your home language. Understanding the story comes first; the mathematics will follow.
A calm, repeatable routine
If your child gets stuck, try a short routine: read it, say it in your own words, find the question, draw a picture, choose, calculate, check. With practice, the steps become automatic. Over time, children come to see word problems not as traps, but as little puzzles in which mathematics helps to understand a story. And that is what mathematics is for.
Try it in the app
Practise this at the screen too: Two-step problems, Two-step word problems, Draw a bar model. You may also like our articles on learning the times tables and money at home.