Maths word problems: when the calculation is not the problem

Why is maths a language subject too?

Pure calculation is language-free: 48 divided by 6 works the same in every language. But as soon as a situation is described, language decides which calculation is the right one in the first place.

From year 5 onwards, lessons shift exactly in that direction. Questions get longer, they contain conditions, restrictions and several quantities. The real achievement is no longer the calculation but turning a piece of running text into a mathematical model.

For children examined in German while living abroad there is an additional layer: they often think in the local language and calculate in it too. German technical language then has to be translated on the fly — under time pressure, in the test.

Which words cost the most marks?

There are surprisingly few of them and they come up again and again. Anyone who has them secure solves a large share of the exercises far more reliably.

• «by» versus «to»: «the price rises by 20 per cent» is not the same as «the price rises to 20 per cent».
• «at least» and «at most»: both include the stated value — «more than» and «fewer than» do not.
• «per» and «each»: they mark what a quantity refers to and decide between multiplying and dividing.
• «in total» versus «respectively»: an overall value or a value per unit.
• «twice as much as» versus «two times more than»: similar wording, very different error rates.
• «in proportion» and «proportionally»: they require a reference value that the text often names only indirectly.

How can my child turn the text into a calculation?

The translation step looks like intuition to many children: either you see the calculation or you don't. In fact it can be learnt as a fixed procedure that runs the same way for every exercise.

• Mark what is being asked. What exactly does the question want to know? Read that sentence first — it is often at the end.
• Collect what is given. Write down every number with its unit and its meaning, not just the figures.
• Write down the relationships. Which quantity depends on which, and how? This is where the operations come from.
• Calculate. Only now — and with units.
• Translate back. An answer sentence that answers the question asked, rather than just repeating the number.

Why the answer sentence is more than a formality

Many children treat it as a tiresome courtesy. In the marking scheme it is a mark of its own — and it is also the final check.

Anyone writing «The club needs 14 buses» notices while writing that 13.4 has to be rounded up. Anyone who just writes «13.4» does not.

My child only knows the terms in Spanish or English. Is that a problem?

Not for understanding, but for the exam it is. A child who knows «fractional equation» but not Bruchgleichung understands the matter completely but loses time and confidence as soon as the question is posed in German.

It gets tricky with terms that do not translate one to one. German lessons work in places with different labels and notations than other school systems — the decimal separator, the names of some geometric shapes, or the terminology for arithmetic laws.

The solution is not a separate vocabulary notebook but building German technical language on current material: each new term is introduced where it is needed and then used consistently.

Why doesn't simply doing more calculations help?

Because it practises exactly the part that already works. A child who cannot find the approach does not get better at recognising percentage problems through the thirtieth percentage exercise.

There is also a side effect families often describe: practice without effect is frustrating. The child spends longer at the desk, the grade stays the same, and they draw the obvious conclusion that they are simply not good at maths.

The more effective route starts with a marked test and the question of which of the five steps actually failed. In most cases it is always the same one.

How do we tell whether it is the language or the maths?

A simple test helps: read the question out to your child and explain it in your own words — without calculating, just the situation. If they then find the approach immediately, maths was not the problem.

• Pure calculation exercises are secure, word problems are not.
• The method is right, but the wrong quantity was calculated.
• Units are missing or do not match each other.
• The answer sentence is missing or answers a different question.
• In multi-step problems, work stops after the first step.
• At home the same exercise works, in the test it does not — there is no time to read it several times.

Frequently asked questions