What is this skill?
This skill is about deciding whether a story problem needs addition or subtraction, before doing any arithmetic. Second graders meet four kinds of add-and-subtract stories. In an adding-to story something joins ("Omar had 16 cards and got some more"). In a taking-from story something leaves ("Some birds flew away"). In a putting-together story two parts make a whole ("12 red marbles and 5 blue ones"). In a compare story two amounts are measured against each other ("Maya has 5 more stickers than Leo").
Any of the three numbers in a story can be the missing one. "Omar had 16 cards. He got some more. Now he has 27. How many did he get?" is an adding-to story, yet it is solved by subtracting 27 − 16. "Jamal gave away 13 shells and has 7 left. How many did he start with?" is a taking-from story that is solved by adding. The practice mixes all four kinds of story with the unknown in every position, using numbers up to 100, and asks four kinds of question: which operation fits, what the question is asking for, which number sentence or bar model matches, and finally the answer itself.
Why it matters
Many children are taught a list of keywords: "in all" means add, "left" means subtract, "more" means add. The list works on easy problems and then quietly fails. "Maya has 5 more stickers than Leo. Maya has 12. How many does Leo have?" contains the word more, and the answer is 12 − 5. A child who relies on the list gets it wrong and does not know why, and the problems only get harder in third and fourth grade.
What works instead is picturing the story. A bar model, sometimes called a tape diagram, is a quick drawing of rectangles: one long bar for a whole made of two parts, or two bars side by side for a comparison. Once the numbers are in the boxes and a question mark marks the missing piece, the operation is easy to see. If the whole bar is missing, add the parts. If a part is missing, take the known part away from the whole. Children who learn to draw the story keep a tool that still works for multiplication, fractions and multi-step problems later on.
Common mistakes
- Choosing the operation from one word. The fix is to ask what happens in the story before talking about plus or minus, and to act it out with objects if the child is unsure.
- Mixing up who has more in a compare story. In "Maya has 5 more than Leo", Maya has the bigger amount. Drawing Maya’s bar first, longer than Leo’s, settles it.
- Solving start-unknown stories by subtracting because something was given away. Rereading the question ("How many did he start with?") and pointing at the start of the story usually helps.
- Adding the two numbers in a parts-and-whole story where the whole is already given. "Mateo and Noah have 34 altogether. Mateo has 20." The 34 is the whole, so the missing part is 34 − 20.
How to help at home
- Tell stories with the unknown at the start: "I had some grapes, I ate 6, and now I have 9. How many did I have?" Let your child use real grapes or coins to check.
- Draw the bars together on scrap paper. One long bar for a whole, two bars for a comparison, and a big question mark in the box you are looking for.
- When your child says "it says more, so I add", do not correct the answer right away. Ask "who has more?" and let them draw it. Finding their own mistake sticks better.
- Ask your child to make up a story where the word "more" means subtract. Writing trap stories is one of the best ways to understand them.
Worked examples
These are real questions from the Tutorsaurus add or subtract? story problems practice, with the answers worked out.
Example 1
Ava has 16 seeds. Ava has 14 fewer seeds than Priya. How many seeds does Priya have? What is the question asking for?
Choices: The bigger amount, The smaller amount, The difference
Answer: The bigger amount. It asks for the bigger amount. This is a compare story. The word fewer is a clue, not a rule: Priya has the bigger amount. 16 + 14 = 30.
Example 2
Zoe had some seeds. Zoe planted 4 of them. Now Zoe has 35 left. How many seeds did Zoe have at the start? Which bar model matches the story?
One bar in two parts, 4 and ?, with 35 in all.
One bar in two parts, 35 and 4, with ? in all.
Answer: One bar in two parts, 35 and 4, with ? in all. One bar made of two parts, 35 and 4. The whole bar is the ?. This is a taking-from story. Some left, but the missing number is the start, and the start was the whole before any left. We are looking for the whole, so add: 35 + 4 = 39.
Example 3
Amara had some balloons. Amara popped 26 of them. Now Amara has 48 left. How many balloons did Amara have at the start?
Answer: 74. This is a taking-from story. Some left, but the missing number is the start, and the start was the whole before any left. We are looking for the whole, so add: 48 + 26 = 74.
Printable worksheet (PDF) — one page of add or subtract? story problems problems from the same practice, easier ones first, with an answer key on page 2. Free to print, no sign-up. See all 2nd grade math worksheets.