How to Solve Math Word Problems

Word problems are where maths meets real life - and where many students struggle. The good news? Solving word problems is a skill that can be learned with the right strategy and practice. This guide teaches you a reliable four-step approach that works for any type of problem, from simple addition stories to multi-step challenges.

The RUCS Strategy: 4 Steps to Solve Any Word Problem

R
Read
Read the problem carefully - at least twice. Do not start calculating after the first read. Underline important numbers and words.
U
Understand
Ask yourself: what is the question? What information is given? What operation do I need? Draw a picture or diagram if it helps.
C
Calculate
Write the number sentence and solve. Show your working so you can check each step.
S
Solution Check
Does the answer make sense? Reread the question and make sure you answered what was asked. Estimate to verify.

Print this strategy and keep it next to your homework. With practice, these four steps become automatic.

How to Spot Which Operation to Use

Word problems do not always say "add" or "multiply" directly. Learning common signal words helps you decode the question.

Addition (+)

altogether, total, combined, sum, in all, more than, increased by, how many together

Subtraction (−)

left, remaining, difference, fewer, less than, how many more, decreased by, took away

Multiplication (×)

each, every, per, times, groups of, rows of, twice, triple, product

Division (÷)

share equally, split, divide, per person, how many groups, how many in each, quotient

Caution: Keywords are helpful clues, not rules. "How many more does Anna have than Ben?" uses "more" but requires subtraction. Always think about what the question is really asking rather than relying solely on keywords.

The Power of Drawing a Diagram

Many students skip this step, but research shows that students who draw diagrams solve word problems more accurately and with less anxiety.

Bar models: Draw rectangles to represent quantities. For comparison problems, put two bars side by side to see the difference.
Part-whole diagrams: Draw a large circle (the whole) split into sections (the parts). Label what you know and what you need to find.
Number lines: Great for problems involving distance, time, or counting on/back.
Tables and charts: For multi-step problems, organise the information into a table before calculating.

Your diagram does not need to be artistic - just accurate enough to show the relationships between numbers.

Worked Examples

Example 1 (Addition): “Maria collected 47 seashells on Monday and 35 on Tuesday. How many seashells does she have in total?”

R: Two amounts (47 and 35), asked for total.
U: Combining two groups > addition. 47 + 35 = ?
C: 47 + 35 = 82.
S: 82 seashells. Check: 50 + 35 = 85, minus 3 = 82. ✓

Example 2 (Multi-step): “A bakery made 120 cookies. They sold 45 in the morning and 38 in the afternoon. How many cookies are left?”

R: Started with 120, sold two batches, asked for remaining.
U: Two subtractions: 120 – 45 – 38. Or add sold first: 45 + 38 = 83, then 120 – 83.
C: 45 + 38 = 83. 120 – 83 = 37.
S: 37 cookies left. Check: 37 + 83 = 120. ✓

Example 3 (Division): “There are 48 children going on a trip. Each minibus holds 8 children. How many minibuses are needed?”

R: 48 children, groups of 8, how many groups.
U: Grouping > division. 48 ÷ 8 = ?
C: 48 ÷ 8 = 6.
S: 6 minibuses. Check: 6 × 8 = 48. ✓

Common Traps and How to Avoid Them

Extra information: Some problems include numbers you do not need. Underline only the relevant ones.
Not answering the question: You calculated correctly but answered "how many in total" when the question asked "how many more." Always re-read the question before writing your final answer.
Units mismatch: If the problem uses centimetres and metres, convert before calculating.
Forgetting to label: An answer of "37" means nothing without "37 cookies" or "37 cm."

Practice makes permanent:Goldy's math games include word problem challenges that train you to pick the right operation and solve step by step.

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