Solving maths word problems step by step
Many pupils who calculate well still freeze when numbers arrive inside a story. The difficulty is rarely arithmetic. It is the move from words to a mathematical structure. A routine they can follow every time makes that move less frightening.
Read it twice
On the first reading, pupils get the story: who, what and where. On the second, they look for the question and the numbers. Ask them to retell the problem in their own words without numbers. If they cannot, the trouble is comprehension, not maths, and a short discussion will help more than a hint about the operation.
Draw it
A quick sketch makes the structure visible. For part-whole problems, a bar model works well, as in the figure above: the long bar is the whole, and the short bars are the parts. For comparison, draw two bars of different lengths. For rates, draw a table. The picture does not need to be neat, only useful.
Decide the operation, with reasons
Avoid keyword tricks such as "altogether means add". They fail often: "Sam has 45 stickers altogether, 18 of which are red" asks for subtraction. Instead, ask what is happening. Are parts being joined, separated, compared, shared equally or repeated? Each has its operation. Pupils should say the reason aloud: "I am finding a part, so I take away from the whole."
Estimate first
Rounding the numbers gives a range for the answer. Forty-five take away eighteen is about forty-five take away twenty, so roughly twenty-five. When the exact answer of twenty-seven appears, it passes the sense check. An estimate also catches slips such as adding when subtraction was needed.
Solve and write a sentence
Write the calculation, solve it, and then answer in a full sentence with units: "There are 27 blue stickers." This last step ties the number back to the story and avoids answers like "27" that do not say what was counted.
Check in a different way
Use the inverse operation: 27 plus 18 is 45. For multi-step problems, check that each step answers a part of the question. If a result is unreasonable, such as a person with a negative number of apples, go back to the picture.
Build up gradually
Begin with one-step problems in familiar contexts, then add a second step, then extra information that is not needed. Vary the context and the position of the unknown. Our sheets mix these in the show-working format so that pupils must set out their reasoning. See the Year 4 and Grade 4 level pages for suitable topics: Year 4 and Grade 4.
Let pupils write their own
Writing a problem for a given calculation shows understanding more clearly than solving one. Give a calculation, such as 45 minus 18, and ask for two different stories. Add a few of the best to a sheet as custom questions in the editor, with the answer in the key.
Read more in the guide to fraction misconceptions or return to the guides index.