Here is how to help kids with math word problems: use the same four steps every time. Read the story, picture it with objects or a quick sketch, solve it with a number sentence, then check that the answer makes sense. Skip keyword tricks like "in all means add," because they often point to the wrong operation.
A word problem is really three jobs at once. Your child has to read and understand a short story, figure out what the question is asking, and choose the math that fits. A 2021 What Works Clearinghouse practice guide on elementary math makes the point that learning calculations alone does not necessarily help students solve word problems. The understanding part needs its own practice.
The good news is that most early word problems follow a handful of patterns. Once a child can see the pattern, the math is often the easy part.
Read. Read the problem aloud together, then ask your child to tell it back in their own words. Ask, "What is the question?" The practice guide also suggests rereading and restating the problem, and underlining what you need while crossing out what you don't.
Picture. Act it out with toys or snacks, or make a quick sketch. Circles and stick figures are plenty. The same guide suggests teaching simple sketches so drawing does not eat up all the time.
Solve. Write a number sentence with a box for the unknown, such as 6 + ? = 11. The Common Core standards for grades 1 and 2 describe using drawings and equations with a symbol for the unknown number.
Check. Put the answer back into the story. Does it make sense? If 6 kids plus some more makes 11, the answer can't be 17.
The Common Core groups early addition and subtraction stories into four situations: adding to, taking from, putting together or taking apart, and comparing. The unknown can show up in any position. These original examples go from grade 1 to grade 3.
1. Add to. Something joins a group.
Result unknown: Maya has 6 stickers. Her friend gives her 5 more. How many does she have now? (6 + 5 = 11)
Change unknown: Maya had 6 stickers. Her friend gave her some more. Now she has 11. How many did her friend give her? (6 + ? = 11, so 5)
Start unknown: Maya had some stickers. She got 5 more. Now she has 11. How many did she have at first? (? + 5 = 11, so 6)
2. Take from. Something leaves a group.
There are 14 crackers on a plate. Dad eats 4. How many are left? (14 - 4 = 10)
There were 14 crackers. Some got eaten. Now 9 are left. How many were eaten? (14 - ? = 9, so 5)
3. Put together or take apart. Two parts make a whole, and nothing moves.
A bowl has 8 red grapes and 7 green grapes. How many grapes are there? (8 + 7 = 15)
A bowl has 15 grapes. 8 are red and the rest are green. How many are green? (8 + ? = 15, so 7)
4. Compare. Two amounts are measured against each other.
Leo read 12 pages. Ava read 7 pages. How many more pages did Leo read? (7 + ? = 12, so 5)
Ava read 5 fewer pages than Leo. Ava read 7 pages. How many pages did Leo read? (7 + 5 = 12. The word is "fewer," but you add.)
Grades 2 and 3: two steps. The grade 2 standards add one- and two-step problems within 100. Try: A class had 23 crayons. They got a box of 24, then lost 9. How many crayons now? (23 + 24 = 47, then 47 - 9 = 38.) A grade 3 version might mix operations: There are 4 bags with 6 apples in each. We eat 5 apples. How many are left? (4 x 6 = 24, then 24 - 5 = 19.)
Many kids learn that "in all" means add and "left" means subtract. The What Works Clearinghouse panel advises avoiding key words that link specific words to operations. Key words let a child skip reading the whole problem, and they often point to the wrong operation. Problems without a familiar key word can leave a child stuck, and two-step problems may contain more than one.
See how these original examples trip up a keyword hunter:
"Altogether": Sam has 3 bags with 5 marbles in each. How many marbles altogether? Adding 3 + 5 gives 8, but the answer is 15.
"More": Nina got 4 more books. Now she has 10. How many did she have before? Adding 10 + 4 gives 14, but the answer is 6.
"In all": There are 9 kids in all. 4 are boys. How many are girls? Adding gives 13, but the answer is 5.
"Fewer": the compare problem above. "Fewer" sounds like subtraction, but you add.
Instead of hunting for words, ask, "What is happening in this story? Is something joining, leaving, being split up, or being compared?"
Tell the whole story first. The practice guide suggests starting with a story that gives every number, then telling the same story with one number missing. Kids see that the problem is just a story with a hole in it.
Shrink the numbers. If big numbers get in the way, swap in small ones to understand the story, then go back.
Add a distractor. Older kids can practice spotting extra information: "Priya has 2 dogs. She picked 6 carrots and 5 beans. How many vegetables did she pick?"
Use real life. Snacks, stairs, toy cars and bedtime minutes all make good stories. Our guide to math talk at home has more everyday prompts.
Flip roles. Let your child write a word problem for you. Writing one shows whether they understand the structure.
Praise the thinking. Say "I like how you drew the two groups" more often than "Good job."
If subtraction stories are the sticking point, our guide on how to teach subtraction covers the basics.
For early addition and subtraction, the Common Core uses four situations: add to, take from, put together or take apart, and compare. Each can have the unknown in different places.
A What Works Clearinghouse panel advises against it. Key words often point to the wrong operation. Asking what is happening in the story works better.
In the Common Core, kindergartners already solve addition and subtraction word problems within 10 using objects or drawings. First graders work within 20, and second graders within 100.
Read the problem aloud together, act it out with objects, and ask your child to retell it. If reading itself is hard, mention it to the teacher, since reading support may help.
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Common Core State Standards: Kindergarten, Operations and Algebraic Thinking
Common Core State Standards: Grade 1, Operations and Algebraic Thinking
Common Core State Standards: Grade 2, Operations and Algebraic Thinking