Your first grader reads the problem out loud: "Jo has 5 toy cars. Lin has 3 toy cars. How many more toy cars does Jo have?" Then, without a pause: "Eight!" The word "more" said add, so they added. The answer is 2, and your child is now upset that the right-looking answer is wrong.
Your child can add 5 + 3, so arithmetic is not the problem. First-grade addition and subtraction word problems come in five types, and each type has its own typical mistake. Once you can name the type, you can see where your child's thinking went wrong, and help without giving the answer away.
Why first-grade word problems feel hard
In first grade, word problems put the missing number in different places: sometimes the total is missing, sometimes one of the parts, sometimes the change (Common Core Standard 1.OA.A.1). Researchers sorted these stories decades ago into a handful of types, and found that children solve some types far more easily than others, even when the numbers are the same (Riley, Greeno & Heller, 1983; Carpenter et al., 2015).
A child who has only met "how many altogether" stories learns a shortcut: grab the two numbers and add. The shortcut works until the story changes shape. Then it fails, and from the outside it looks as if your child "can't do word problems." Usually they can. They are using a rule that worked last week.
The 5 types of addition and subtraction word problems
Researchers sort these stories in slightly different ways. These are the five types SmartyPants Math practices. Each uses a real problem from its Grade 1 lessons, the slip children typically make, and something calm to say.
1. Add to: something joins
Pia has 2 balloons. A friend gives her 3 more balloons. How many balloons does Pia have now?
The story starts with 2, 3 more join, and we want the total: 2 + 3 = 5. This is the type children meet first and solve best.
The typical slip: counting everything from one ("one, two... three, four, five") instead of starting at 2 and counting on. The answer comes out right, but the method will not survive bigger numbers.
Say: "Pia already has 2. Hold the 2 in your head and count on the new ones."
2. Take from: something goes away
Mia has 7 balloons. 3 balloons pop. How many balloons are left?
The story starts with 7, 3 leave, and we want what remains: 7 − 3 = 4.
The typical slip: adding anyway, 7 + 3 = 10, because two numbers in a story have always meant "add." Another common one is counting back and including the starting number ("seven, six, five"), which gives 5.
Say: "Did Mia end up with more balloons or fewer? So will the answer be bigger than 7, or smaller?"
3. Change unknown (adding): how many joined?
Nate has 3 toy cars. His uncle gives him some more. Now Nate has 5 toy cars. How many toy cars did his uncle give him?
Here the start (3) and the end (5) are known. The missing number is the change in the middle: 3 + ? = 5, so the uncle gave him 2.
The typical slip: answering 8. The story says "gives him some more," so the child adds the two numbers they can see. But 5 is already the total after the gift. This is where the add-the-numbers shortcut breaks most often.
Say: "Is 5 how many he started with, or how many he has at the end? So what are we looking for?"
4. Change unknown (taking away): how many left?
Ali has 6 cookies. He gives some away. Now Ali has 4 cookies. How many cookies did he give away?
Start 6, end 4, the change is missing: 6 − ? = 4, so Ali gave away 2.
The typical slip: adding 6 + 4 = 10, or answering 4 because 4 is the last number in the story. Both come from grabbing numbers before picturing what happened.
Say: "Show me with your fingers: 6 cookies. Now fold some down until 4 are left. How many did you fold?"
5. Compare: how many more, how many fewer
Jo has 5 toy cars. Lin has 3 toy cars. How many more toy cars does Jo have?
Nothing joins and nothing leaves. Two groups sit side by side, and we want the difference: 5 − 3 = 2. Compare stories are often the hardest of the five for young children, because the question asks about a difference you cannot see as a separate pile.
The typical slip: adding, 5 + 3 = 8, because the question says "more." This is the key-word trap from the opening of this guide.
Say: "Line up Jo's cars and Lin's cars, one under the other. How many of Jo's cars have no partner?"
Why key words backfire
Many worksheets teach children to hunt for key words: "altogether" means add, "left" means subtract, "more" means add. It feels helpful, and it works on easy problems. Then it fails where the five types above get harder. "How many more does Jo have?" contains "more" and needs subtraction. "He gives him some more" contains "more" and is solved with a missing addend, not by adding the two numbers. Teacher educators list "use key words" among the rules that expire, because it stops working as problems grow and teaches children to skip the story (Karp, Bush & Dougherty, 2014).
The alternative is simple to say and slower to build: understand the story first, then choose the operation. Ask your child to retell the story in their own words, or act it out with toys, before any number is written.
A picture that works for every type
A part-whole bar is one drawing that fits all five types. Draw one long bar for the whole, split into two parts. Write the numbers you know where they belong, and a question mark where the number is missing.
Nate's cars
┌──────┬─────┐
│ 3 │ ? │ parts
└──────┴─────┘
│ 5 │ wholeOnce the bar is filled in, the operation is usually clear. If you know both parts and need the whole, you add. If you know the whole and one part, you subtract, or think "3 and what make 5?" For compare problems, draw two bars, one under the other, and look at the piece that sticks out.
Children do not need to know the names of the five types. They need the habit of asking "what do I know, and what is missing?" before they reach for a sign.
How SmartyPants Math practices word problems
SmartyPants Math has five Grade 1 word-problem lessons today, one for each type above. In each, Barnaby the owl first works one story out loud while your child watches. Then your child solves stories with help, and finally alone, with no timers.
The help fades as your child gets stronger. In the first problem the story's numbers are already on a bar. Next, your child places them. In the last three, they build the bar themselves. From the third problem on, your child also decides whether to add or take away, reading it from the bar instead of being handed the sign. If they choose the wrong sign, they get a hint about the bar, not a red mark, and the app records it as a wrong choice of sign, separate from a counting mistake. The app is built to find the step where your child's thinking went wrong, not only to mark the answer. You can see how it works.
Tonight's homework, calmer
Before solving, ask your child to tell you the story. Name the type quietly in your head: did something join, leave, or are two groups being compared? When an answer is wrong, ask which number is the total, instead of saying "no." And when the story makes sense to your child, stop while it still feels good. Understanding one story is more useful than guessing through a page.
References
- Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (2015). Children's Mathematics: Cognitively Guided Instruction (2nd ed.). Heinemann.
- Karp, K. S., Bush, S. B., & Dougherty, B. J. (2014). 13 rules that expire. Teaching Children Mathematics, 21(1), 18–25.
- National Governors Association Center for Best Practices & Council of Chief State School Officers (2010). Common Core State Standards for Mathematics (1.OA.A.1 and Table 1, common addition and subtraction situations).
- Riley, M. S., Greeno, J. G., & Heller, J. I. (1983). Development of children's problem-solving ability in arithmetic. In H. P. Ginsburg (Ed.), The Development of Mathematical Thinking (pp. 153–196). Academic Press.