Introduction
Two-Step Word Problems is an important Grade 3 math skill because students are moving from simple answers toward explaining how the math works.
In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with two-step word problems.
What Is Two-Step Word Problems?
Two-Step Word Problems means choosing a model, naming what each number means, and explaining the strategy.
The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.
Understanding Two-Step Word Problems
Before solving, students should slow down and decide what each number, shape, unit, or label represents.
- Read the question carefully and identify what is being asked.
- Choose a model, equation, table, or diagram that matches the situation.
- Solve one step at a time and keep units or labels attached.
- Use the answer explanation to check that the result makes sense.
Visual Models
Visual Model 1
Question: Eva collects \(5\) bags with \(8\) shells in each bag. She gives away \(12\) shells to her friend. How many shells does Eva keep?
- A. \(12\)
- B. \(24\)
- C. \(28\)
- D. \(40\)
Why it works: Step 1: Total shells: \(5\times8=40\) shells. Step 2: Subtract given away: \(40-12=28\) shells kept.
Answer: \(28\) shells
Visual Model 2
Question: Ms. Chen's class has \(4\) rows of desks with \(6\) desks in each row. Then she brings in \(8\) more desks for group work. How many desks are there altogether?
| Item | Count |
|---|---|
| Desks per row | \(6\) |
| Number of rows | \(4\) |
| Additional desks | \(8\) |
- A. \(24\)
- B. \(28\)
- C. \(30\)
- D. \(32\)
Why it works: Step 1: Desks in rows: \(4\times6=24\) desks. Step 2: Add more: \(24+8=32\) desks total.
Answer: \(32\) desks
Worked Examples
Example 1
Question: A farmer has \(3\) groups of chickens with \(7\) chickens in each group. He sells \(6\) chickens. How many chickens does the farmer have left?
- A. \(12\)
- B. \(27\)
- C. \(21\)
- D. \(15\)
- Step 1: Total chickens: \(3\times7=21\) chickens.
- Step 2: Subtract sold: \(21-6=15\) chickens left.
Answer: \(15\) chickens
Example 2
Question: Tommy has \(42\) marbles. He divides them into \(7\) equal groups for a game. Then he loses \(3\) marbles from one group. How many marbles are in that group now?
- A. \(3\)
- B. \(6\)
- C. \(7\)
- D. \(42\)
- Step 1: Marbles per group: \(42\div7=6\) marbles.
- Step 2: Lose from one group: \(6-3=3\) marbles.
Answer: \(3\) marbles
Example 3
Question: At a carnival, \(3\) booths each have \(9\) prizes. The organizers give away \(10\) prizes. How many prizes are left?
- A. \(10\)
- B. \(37\)
- C. \(27\)
- D. \(17\)
- Step 1: Total prizes: \(3\times9=27\) prizes.
- Step 2: Give away: \(27-10=17\) prizes left.
Answer: \(17\) prizes
Real-World Word Problems
Problem 1
Question: Lily collects \(9\) marbles and her friend collects \(6\) marbles. They put the marbles together and split them into \(3\) equal groups. How many marbles are in each group?
- A. \(3\)
- B. \(5\)
- C. \(9\)
- D. \(15\)
Why it works: Step 1: Add the marbles: \(9+6=15\). Step 2: Divide into \(3\) equal groups: \(15\div3=5\) marbles in each group. (Choice D is the answer to step 1 only.)
Answer: \(5\) marbles
Problem 2
Question: Ava buys \(4\) packs of crayons with \(9\) crayons in each pack. She already has \(7\) crayons. Let \(c\) be the total number of crayons. Which equation shows how to find \(c\)?
- A. \(c = 4 + 9 + 7\)
- B. \(c = 9 + 7 - 4\)
- C. \(c = 4 \times 9 \times 7\)
- D. \(c = (4 \times 9) + 7\)
Why it works: First multiply the number of packs by crayons per pack: \(4\times9=36\). Then add the crayons she has: \(36+7=43\).
Answer: \(c = (4 \times 9) + 7\)
Common Mistakes
- Rushing before identifying what the numbers represent.
- Choosing an operation that does not match the situation.
- Dropping labels, units, or context from the answer.
- Skipping the estimate or reasonableness check.
Strategy Tips
- Underline the question being asked.
- Use a model before jumping to computation.
- Write an equation that matches the story or picture.
- Explain the final answer in a sentence.
Practice Questions
Question 1
Mia has \(24\) stickers. She gets \(3\) packs of \(8\) more stickers. How many stickers does Mia have now?
- A. \(24\)
- B. \(32\)
- C. \(40\)
- D. \(48\)
Question 2
Ben has \(5\) bags with \(6\) pencils in each bag. He gives away \(10\) pencils. How many pencils does Ben have left?
- A. \(20\)
- B. \(25\)
- C. \(30\)
- D. \(35\)
Question 3
Noah has \(12\) cookies. His mom bakes \(8\) more cookies. Then Noah eats \(6\) cookies. How many cookies are left?
- A. \(12\)
- B. \(14\)
- C. \(20\)
- D. \(26\)
Question 4
Eli has \(35\) apples. He uses \(5\) apples to make a pie. He divides the remaining apples equally among \(6\) friends. How many apples does each friend get?
- A. \(5\)
- B. \(6\)
- C. \(7\)
- D. \(30\)
Question 5
Sam plants \(7\) rows of tomato seeds with \(8\) seeds in each row. Some seeds do not grow and only \(50\) seeds sprout. How many seeds did not sprout?
- A. \(6\)
- B. \(8\)
- C. \(15\)
- D. \(56\)
Question 6
A store has \(3\) shelves with \(12\) books on each shelf. Plus \(9\) more books on a table. What is the total number of books?
- A. \(24\)
- B. \(36\)
- C. \(45\)
- D. \(63\)
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(48\)
Step 1: Find the new stickers: \(3\times8=24\). Step 2: Add to her original: \(24+24=48\) stickers. (Choice A is just the original amount; choice B is step 1 only.)
Question 2
Answer: \(20\) pencils
Step 1: Find total pencils: \(5\times6=30\). Step 2: Subtract: \(30-10=20\) pencils. (Choice C is the answer to step 1 only—students must complete both steps.)
Question 3
Answer: \(14\) cookies
Step 1: Add: \(12+8=20\) cookies. Step 2: Subtract: \(20-6=14\) cookies. (Choice C is step 1 only; choice A ignores new cookies.)
Question 4
Answer: \(5\) apples
Step 1: Subtract: \(35-5=30\) apples. Step 2: Divide: \(30\div6=5\) apples per friend. (Choice D is step 1 only.)
Question 5
Answer: \(6\) seeds
Step 1: Find total seeds: \(7\times8=56\) seeds. Step 2: Subtract sprouted seeds: \(56-50=6\) seeds did not sprout. (Choice D is step 1 only; choice C is incorrect subtraction.)
Question 6
Answer: \(45\) books
Step 1: Multiply for shelf books: \(3\times12=36\) books. Step 2: Add table books: \(36+9=45\) books. (Choice B is step 1 only.)
Connection to Standards
This lesson supports Grade 3 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.
Summary
Two-Step Word Problems becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Understand the model before choosing the operation.
