What Children Who Can't Do Word Problems Have in Common — Behind "But the Arithmetic Is Fine"
"The arithmetic is fine, but word problems don't work." Whatever the grade, this is the thing I hear most.
I thought at first that it was a reading problem too — that we'd have to work on language instead. Looking into it, that's not it. Look at the actual papers and the stumbles are far more specific, each needing its own remedy. And what the national curriculum commentary asks for isn't reading ability either. It's moving between the situation, the diagram and the equation.
Four types
Type 1: can't turn the situation into a picture
Your child reads the problem and can't draw the scene. Ask them to draw "four bags with three oranges in each" and you get three oranges and four bags drawn separately. It's a sign that the sentence is being processed as a lump of words rather than reconstructed as a scene.
Japan's Ministry of Education, in its commentary on the national curriculum guidelines for elementary mathematics (2017), says teaching should deepen understanding of equations "while relating expression in words — such as 'the number of oranges on four plates with five on each' — to expression with diagrams such as circles and tapes, and to expression with concrete objects" (Grade 2, Numbers and Calculation). Words → diagram → equation is one continuous piece of work in the classroom too.
Type 2: choosing the operation from keyword cues
A child solving by a lookup table — "altogether means add", "left over means subtract" — falls apart on problems without those words, and on problems that run the other way. "I ate 5 oranges and 3 were left. How many were there to begin with?" says "left", but it's addition. This type is such a fixture that it has its own topic: Working Backward Word Problems.
Type 3: not looking at what's actually asked
The equation and the arithmetic are right, but the answer is to a different question — giving the total when asked for the difference. The habit is to build an equation reflexively from the numbers in view, before reading to the end.
Type 4: doing only the first stage of a two-stage problem
"You buy three rolls at 80 yen each and pay with a 500-yen note. What's the change?" and the answer is 240 yen. Practising only single-equation problems builds the reflex that an answer means you're finished.
How to teach it at home
Step 1: have days for drawing only
Ask for no equation and no answer — just draw the scene. If "four bags with three oranges each" comes out right, the multiplication equation follows by itself. If they can draw it, they can write the equation: that's the basic principle of word problems. For younger children, the problem texts in Multiplication Word Problems and Difference Word Problems make good drawing material.
Step 2: practise the reverse — make a problem from an equation
The commentary lists the reverse activity as well: from the equation 3 × 5, a child writes their own problem, such as "there are packs with three puddings in each, and five packs — how many puddings altogether?" If equation → situation works, situation → equation will too. Writing "4 × 6" on a piece of paper and saying "make me a story from this" is all it takes.
Step 3: ask "what are you being asked?" first
After reading, before writing anything: say what's being asked. If they can name the unit of the answer too — oranges? yen? people? — that's a pass. Type 3 all but disappears with this one move.
Step 4: write the equation in words first
Write "(price of one) × (how many bought) = (total)" and then substitute the numbers. It shifts the choice of operation away from keyword cues and onto the relationship between quantities.
Step 5: ask "why that equation?" about the ones they got right
More effective than grilling them on the ones they got wrong is asking them to explain one they got right. If they can explain, the understanding is real; if they get stuck, the right answer was luck. Ask from a "teach me" position, not an interrogating one.
How to practise
- Grade 2 splits word problems by situation type. Difference Word Problems, Order and Position Word Problems, then Working Backward Word Problems, in rising order of reading load
- Various Word Problems in grade 3 and Various Word Problems in grade 4 mix the types. If your child manages topic by topic but breaks down on mixed sets, suspect Type 2
- One problem a day is fine. Word problems are about the quality of the sequence — draw it, say what's asked, write the equation in words — not the volume
Frequently asked questions
Q. They can solve it when reading aloud, but not silently
A. Common, and nothing to worry about. Reading aloud forces the pace down and prevents skimming. Make "word problems are read out loud" the rule for a while, then return to silent reading once it's stable.
Q. Should we work through a reading comprehension book?
A. Most word-problem trouble is a math-side skill — turning a situation into a diagram of quantities — rather than general reading ability. Step 1 above works more directly than a language workbook. That said, if the vocabulary itself (what "difference" or "altogether" means) hasn't landed with a younger child, start by explaining the words.
Word problems don't improve much through volume; they change with the quality of one problem a day. Fewer worksheets doesn't mean less progress.
This article is written by a parent who builds diglabo. I am not a teacher or an education specialist. The general guidance here is based on how the topic is taught in Japanese primary schools, checked against Japan's national curriculum guidelines.
diglabo's worksheets follow the Japanese curriculum. What that means if you are outside Japan