What is this skill?
This skill brings all four operations together in fourth grade word problems. A story might be about joining, taking away, comparing, equal groups, sharing or "times as many", and some stories need two steps, such as finding the cost of several tickets and then the change. Your child decides which operations fit, writes an equation with a letter standing for the unknown (n = 4 × 12 − 9), and uses rounding to judge whether an answer is reasonable.
The numbers are bigger than in earlier grades: adding and subtracting within 1,000, multiplying a two-digit number by a one-digit number, and dividing by a one-digit number. The practice asks which operation solves a story or which two steps solve it, which equation matches, whether a classmate’s answer is reasonable, and then the answer itself.
Why it matters
Fourth grade word problems are where keyword lists stop working for good. A two-step story can say "gives away" and "more" in the same paragraph, and a single word cannot tell a child what to do first. What works is a routine: what do I know, what am I looking for, what does the story look like as a picture, and only then which operation.
Writing an equation with a letter is a first step into algebra. It asks a child to describe the whole story in one line before calculating, which slows down guessing and makes the plan visible. Estimating is the safety net: if the story is about 4 packs of about 10 cards, an answer of 390 cannot be right, whatever the calculation said.
Common mistakes
- Using every number in the order it appears. Retelling the story in their own words, then drawing it, helps a child see which step comes first.
- Stopping after the first step of a two-step story. Reread the question and ask whether the number found is the one it asks for.
- Choosing the operation from one word, such as "times" or "more". Ask which amount is bigger and whether it is made of copies or has a piece added.
- Trusting an answer without checking it. Round the numbers, work out a quick estimate, and compare. A place-value slip often shows up as an answer ten times too big.
How to help at home
- Plan a real purchase: "3 notebooks at $4 each, paid with $20. What is the change?" Let your child write the equation before working it out.
- Ask for an estimate first and the exact answer second, and talk about whether they are close.
- Give an equation such as n = 5 × 8 + 6 and ask your child to make up a story that matches it.
- When your child is stuck, ask the three questions out loud: what do we know, what are we looking for, and what would the drawing look like?
Worked examples
These are real questions from the Tutorsaurus which operation? word problems practice, with the answers worked out.
Example 1
125 beads are shared equally by 5 friends. Then each friend gives away 18. How many beads does each friend have left? Which two steps solve it?
Choices: × then +, − then ÷, ÷ then −, + then −
Answer: ÷ then −. This is a two-step story. Each share: 125 ÷ 5 = 25. Each friend gives away 18: 25 − 18 = 7.
Example 2
The tent costs $963. The telescope costs $221. How much more does the tent cost than the telescope? Zoe says the answer is $742. Estimate first: is that reasonable?
Choices: Yes, No
Answer: Yes. Round to tens and the answer is about 740. The exact answer is 742, so $742 is reasonable. This is a compare story. 963 − 221 = 742.
Example 3
9 friends shared some raisins. Each friend got 26. How many raisins did they share?
Answer: 234. This is an equal-groups story. The word shared is a clue, not a rule: we know 9 equal shares of 26 and need the total, so multiply. 9 × 26 = 234.
Printable worksheet (PDF) — one page of which operation? word problems problems from the same practice, easier ones first, with an answer key on page 2. Free to print, no sign-up. See all 4th grade math worksheets.