Multi-Step Addition and Subtraction Word Problems - Third Grade Mathematics

Real-life mathematical problems rarely come with just a single calculation; they often present a story with multiple events happening one after another. In this chapter, you will learn how to unpack multi-step addition and subtraction word problems, identify the hidden question that must be answered first, and write complete mathematical equations to solve real-world challenges with poise and clarity.

The Nature of Multi-Step Word Problems

A multi-step problem requires two or more separate operations to find the final solution. The most critical step is identifying the "hidden question"—the piece of information you must calculate before you can answer the main question of the problem.

+---------------------------------------------------------------+
|                MULTI-STEP ROADMAP                             |
+---------------------------------------------------------------+
|  Given Info  -->  Find Hidden Answer (Step 1)                 |
|                   Then Use Hidden Answer to Find Final Result |
|                   (Step 2)                                    |
+---------------------------------------------------------------+

The Four-Phase Problem Solving Method

To solve multi-step problems systematically, use this structured four-phase approach:

  1. Understand: Read the story twice. Underline key numbers and identify what the question is asking you to find.
  2. Plan: Ask yourself: "What do I need to find first?" Draw a bar model or tape diagram to visualize the parts and the whole.
  3. Solve: Perform the first calculation carefully, then use that result in your second calculation.
  4. Check: Re-read the question. Does your answer answer what was asked? Is the number reasonable?

Bar Models and Tape Diagrams

Tape diagrams help you see how the different amounts in a story fit together visually.

Part-Part-Whole Model:
+-----------------------------------------------+
|                 Total Whole                   |
+-----------------------+-----------------------+
|        Part 1         |        Part 2         |
+-----------------------+-----------------------+

Comparison Model:
Quantity A: +-------------------------------+
Quantity B: +-----------------------+-----------+
                                     Difference

Worked Examples

Let us dissect two classic types of multi-step word problems.

Example 1: Add Then Subtract

Story: The zoo had 340 visitors on Saturday morning. In the afternoon, another 215 visitors arrived. By evening, 180 visitors had left the zoo. How many visitors were still inside the zoo?

Phase 1: Understand
- Morning visitors: 340

- Afternoon visitors: 215

- Visitors who left: 180

- Final question: How many visitors are still inside?


Phase 2: Plan
- Hidden question: How many total visitors arrived during the entire day?

- Step 1: Add morning + afternoon visitors.

- Step 2: Subtract the visitors who left from the total.


Phase 3: Solve
- Step 1: 340 + 215 = 555 total visitors.

- Step 2: 555 - 180 = 375 visitors remaining.


Phase 4: Check
- 375 + 180 = 555, and 555 - 215 = 340. The numbers check out completely!
Answer: 375 visitors were still inside the zoo.

Example 2: Subtract Then Add (Comparison Story)

Story: Liam had 450 trading cards. He gave 135 cards to his younger sister. Then his best friend gave him 80 new cards. How many trading cards does Liam have now?

Phase 1: Understand
- Started with: 450 cards

- Gave away: 135 cards

- Received: 80 cards

- Final question: How many cards does Liam have now?


Phase 2: Plan
- Hidden question: How many cards did Liam have after giving cards to his sister?

- Step 1: 450 - 135.

- Step 2: Take that result and add 80.


Phase 3: Solve
- Step 1: 450 - 135 = 315 cards.

- Step 2: 315 + 80 = 395 cards.


Answer: Liam has 395 trading cards now.

Example 3: Finding the Unknown Part from a Total

Story: An orchard has 700 fruit trees in total. There are 245 apple trees and 198 peach trees. The rest of the trees are plum trees. How many plum trees are in the orchard?

Method:
- Step 1: Combine apple and peach trees: 245 + 198 = 443 trees.

- Step 2: Subtract the known trees from the orchard total: 700 - 443 = 257 plum trees.
Answer: There are 257 plum trees.

Chapter Practice Exercises

  1. A school cafeteria prepared 500 sandwiches for lunch. The third graders ate 185 sandwiches, and the fourth graders ate 210 sandwiches. How many sandwiches were left over?
  2. Maya saved 275 dollars from babysitting. Her grandmother gave her 150 dollars for her birthday. Then Maya bought a new bicycle for 299 dollars. How much money does Maya have left?
  3. In a school library, there are 850 books. On Monday, 142 books were checked out. On Tuesday, another 98 books were checked out. How many books remained in the library?
  4. A toy store had 320 board games on the shelf. The store received a delivery of 175 more board games. Over the weekend, the store sold 248 board games. How many board games are on the shelf now?
  5. Write your own multi-step word problem that uses the numbers 100, 45, and 20, where the solution requires both addition and subtraction.

Solutions and Step-by-Step Answers

  1. Cafeteria sandwiches:
  2. Step 1 (Find total sandwiches eaten): 185 + 210 = 395 sandwiches.
  3. Step 2 (Subtract from whole): 500 - 395 = 105 sandwiches. There were 105 sandwiches left over.
  4. Maya's savings:
  5. Step 1 (Find total money before buying bicycle): 275 + 150 = 425 dollars.
  6. Step 2 (Subtract cost of bicycle): 425 - 299 = 126 dollars. Maya has 126 dollars left.
  7. Library books:
  8. Step 1 (Find total books checked out): 142 + 98 = 240 books.
  9. Step 2 (Subtract from library total): 850 - 240 = 610 books. There were 610 books remaining in the library.
  10. Board games:
  11. Step 1 (Total games after delivery): 320 + 175 = 495 games.
  12. Step 2 (Games left after sales): 495 - 248 = 247 games. There are 247 board games on the shelf now.
  13. Sample student word problem: "A baker baked 100 blueberry muffins in the morning. A customer came in and bought 45 muffins. Later that afternoon, the baker baked 20 more fresh muffins. How many muffins are in the bakery now?" Solution: 100 - 45 = 55 muffins, then 55 + 20 = 75 muffins.