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How to Solve Math Word Problems: A Step-by-Step Method
Many children who are good at calculating freeze when numbers come wrapped in a story. The fix is rarely more arithmetic practice. It is a routine for reading the problem, so they know what is being asked before they start computing.
The five-step routine
- Read it twice. The first time, just understand the story. The second time, notice the numbers.
- Underline the question. What exactly are we trying to find? "How many are left?" "How much more?" "How many in all?"
- Draw or act it out. A quick sketch, tally marks or a bar model turns words into something visible.
- Write a number sentence and solve it. Include a label (apples, dollars, minutes).
- Check. Does the answer make sense? Is it the right size? Did I answer the question that was asked?
Worked example 1: one step
Maya had 24 stickers. She gave 9 to her brother. How many does she have now?
The question is "how many now?" Maya starts with 24 and loses 9, so we subtract: 24 − 9 = 15 stickers. Check: 15 + 9 = 24, which matches what she started with.
Worked example 2: equal groups
There are 4 boxes. Each box has 6 pencils. How many pencils in all?
Equal groups call for multiplication: 4 × 6 = 24 pencils. A sketch of four boxes with six dots each confirms it.
Worked example 3: two steps
Leo buys 3 notebooks that cost $2 each and a pen for $1. He pays with a $10 bill. How much change does he get?
Step one: notebooks cost 3 × $2 = $6. Step two: add the pen, $6 + $1 = $7 total. Step three: change is $10 − $7 = $3. Writing each step on its own line prevents most errors.
Be careful with keywords
Many kids are taught that "in all" means add and "left" means subtract. That works often, but not always. Compare: "Sam has 5 marbles. Ana has 3 more than Sam. How many does Ana have?" The word "more" suggests adding, and that is right here (5 + 3 = 8). But "Sam has 8 marbles, which is 3 more than Ana. How many does Ana have?" needs subtraction, even though the word "more" is still there. Teach children to picture the situation, not just hunt for keywords.
Use a bar model
A bar model is a rectangle that represents the total, split into parts. For "Sam has 8 marbles, 3 more than Ana," draw a bar of 8 divided into a part for Ana and a part of 3. The missing part is 8 − 3 = 5. Bar models work from second grade through middle school ratios.
When your child is stuck
- Ask them to retell the problem in their own words.
- Replace big numbers with small ones to see the operation, then put the real numbers back.
- Ask "What do we know? What do we need to find out?"
- Have them write their own word problems about their toys, pets or hobbies; creating a problem builds understanding.
Practice problems
- A bakery made 36 muffins and sold 19. How many are left?
- Each bag holds 8 apples. How many apples are in 5 bags?
- Tara read 12 pages on Monday and 15 pages on Tuesday. How many pages did she read in all?
- There are 30 students going on a trip. Each van holds 6 students. How many vans are needed?
- Jon has $20. He buys a book for $8 and a snack for $3. How much money does he have left?
- A rope is 45 inches long. Ben cuts off 18 inches. How long is the piece left?
Answer key
1) 17 muffins 2) 40 apples 3) 27 pages 4) 5 vans (30 ÷ 6) 5) $9 ($20 − $8 − $3) 6) 27 inches
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