Mathematics Grade 3 Word Problems Multi-step

Grade 3 Mathematics Study Guide: Multi-Step Word Problems

1. The Driving Question

"If you have 24 stickers, give 7 to your friend, then buy 12 more, and finally split the rest equally with your sister—how do you figure out how many you each get without losing count or mixing up the steps? Why can’t you just add or subtract everything at once?"

2. The Core Idea — Built, Not Listed

Imagine you’re at the school fair with a $10 bill. You spend $3 on a ticket, then win $5 from a game, and finally buy a $2 snack. To know how much money you have left, you can’t just add or subtract everything at once—you have to follow the steps in order, like a recipe. First, subtract the ticket cost ($10 - $3 = $7). Then add the winnings ($7 + $5 = $12). Finally, subtract the snack cost ($12 - $2 = $10). Multi-step word problems work the same way: they give you a story with more than one action, and you have to solve them step by step, like climbing a ladder—one rung at a time.

Key Vocabulary:
- Operation – A math action like adding, subtracting, multiplying, or dividing.
Example: If you share 15 crayons equally with 2 friends, you’re using division (15 ÷ 3).
- Equation – A number sentence with an equals sign (e.g., 8 + 5 = 13).
Example: After buying 3 packs of gum with 5 pieces each, the equation is 3 × 5 = 15.
- Unknown – The missing number you’re trying to find in a problem.
Example: In "Liam has 9 marbles and gives some away. Now he has 4. How many did he give away?" the unknown is the number of marbles given away.
- Context – The real-life situation the problem is describing (e.g., buying, sharing, measuring).
Example: A problem about "slices of pizza" is in the context of food and sharing.

3. Assessment Translation

How This Appears in Classroom Assessments (Grade 3):
Multi-step word problems show up in exit tickets, worksheets, and short constructed-response questions. Teachers look for: - Proficient: The student solves the problem in order, shows each step clearly (even if the answer is wrong), and labels their work (e.g., "Step 1: 24 - 7 = 17").
- Developing: The student tries to solve it but mixes up the steps, skips a step, or doesn’t label their work. They might get the right answer by accident but can’t explain how.

What Teachers Look For:
1. Step-by-step work – Did you solve one part at a time? 2. Labels – Did you write what each number means (e.g., "17 stickers left")? 3. Correct operations – Did you add when you should’ve subtracted (or vice versa)?

Model Proficient Response:
Problem: Emma has 18 trading cards. She gives 5 to Jake, then buys 9 more. How many cards does she have now? Student Work: Step 1: 18 - 5 = 13 (cards left after giving to Jake) Step 2: 13 + 9 = 22 (cards after buying more) Answer: Emma has 22 trading cards now.

4. Mistake Taxonomy

Mistake 1: Solving Out of Order
Question: A bakery has 20 cupcakes. They sell 8 in the morning and 5 in the afternoon. How many are left? Common Wrong Answer: 20 - 8 = 12, then 12 + 5 = 17.
Why It Loses Credit: The student added instead of subtracting the second step. They didn’t read the context ("sell" means subtract).
Correct Approach: Step 1: 20 - 8 = 12 (cupcakes left after morning) Step 2: 12 - 5 = 7 (cupcakes left after afternoon) Answer: 7 cupcakes.

Mistake 2: Skipping a Step
Question: There are 12 kids on the bus. 4 get off at the first stop, and 3 more get off at the second stop. How many kids are still on the bus? Common Wrong Answer: 12 - 4 = 8 (stops here).
Why It Loses Credit: The student forgot the second stop. They only did one step.
Correct Approach: Step 1: 12 - 4 = 8 (kids after first stop) Step 2: 8 - 3 = 5 (kids after second stop) Answer: 5 kids.

Mistake 3: Mislabeling Numbers
Question: A farmer has 15 apples. He picks 10 more, then gives 7 to his neighbor. How many apples does he have now? Common Wrong Answer: 15 + 10 = 25, 25 - 7 = 18 (but writes "18 neighbors").
Why It Loses Credit: The student got the math right but labeled the answer wrong (it’s "18 apples," not "18 neighbors").
Correct Approach: Step 1: 15 + 10 = 25 (apples after picking) Step 2: 25 - 7 = 18 (apples after giving away) Answer: The farmer has 18 apples.

5. Connection Layer

1. Within Math: Multi-step problems → Order of Operations (Grade 5+)
   Why? Later, you’ll learn that some problems have parentheses or exponents that tell you which step to do first—just like how word problems give you clues in the story.

2. Across Subjects: Multi-step problems → Following Lab Procedures in Science
   Why? In science class, you might measure water, add salt, then heat it—each step changes the result, just like each step in a word problem changes the answer.

3. Outside School: Multi-step problems → Building a LEGO Set
   Why? The instructions tell you to snap pieces together in a certain order. If you skip a step, the spaceship won’t look right—just like skipping a step in a word problem gives the wrong answer.

6. The Stretch Question

"If a word problem has three steps, but the second step’s answer is zero, does the third step even matter? Why or why not?"

Pointer Toward the Answer:
Think about this: If you have 10 cookies, give all 10 away (10 - 10 = 0), then try to share the "rest" with a friend—there’s nothing left to share! The third step does matter because it changes what the answer means (e.g., "0 cookies to share" vs. "no cookies at all"). But if the problem asked for the total after all steps, the zero would make the third step irrelevant. The trick is to ask: What is the problem really asking me to find?