Solved Exercises on Multi-Step Word Problems in Grade 3

Master multi-step word problems: addition and subtraction, multiplication and division, and mixed operations through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Addition and Subtraction
Exercise 1
Emma had 45 stickers. Her friend gave her 23 more stickers. Then Emma gave 15 stickers to her little brother. How many stickers does Emma have now?
Definition:

Multi-step word problem: A problem that requires more than one mathematical operation to solve. Keywords: Words that indicate operations (more, gave, total, left, etc.).

Multi-step problem solving method:
  1. Read the problem carefully
  2. Identify the question being asked
  3. Find the important information
  4. Determine the operations needed
  5. Solve step by step
  6. Check your answer
Original Problem
Emma had 45 stickers. Her friend gave her 23 more stickers. Then Emma gave 15 stickers to her little brother. How many stickers does Emma have now?
1
Emma starts with 45 stickers
2
Her friend gives her 23 more stickers (addition: 45 + 23)
3
Emma gives 15 stickers to her brother (subtraction: result - 15)
4
Find the final number of stickers
Step Operation Calculation Result 1 Initial 45 45 2 Addition 45 + 23 68 3 Subtraction 68 - 15 53
45
+
23
=
68
68
-
15
=
53
Final answer:

Emma has 53 stickers now.

Applied rules:

• Sequential operations: Perform operations in the order they occur in the problem

• Keywords: "gave her" means addition, "gave to" means subtraction

• Step-by-step: Solve one operation at a time

2 Multiplication and Division
Exercise 2
A bakery made 72 cookies. They packed the cookies into boxes with 8 cookies in each box. Then they sold 5 boxes. How many cookies are left unpacked?
Definition:

Groups: Sets of equal quantities. Per: Indicates division or rate (cookies per box).

Original Problem
A bakery made 72 cookies. They packed the cookies into boxes with 8 cookies in each box. Then they sold 5 boxes. How many cookies are left unpacked?
1
Total cookies = 72
2
Packed into boxes of 8 (division: 72 ÷ 8)
3
Sold 5 boxes (multiplication: 5 × 8 to find cookies sold)
4
Subtract sold cookies from total
Step Operation Calculation Result 1 Initial 72 cookies 72 2 Boxes made 72 ÷ 8 9 boxes 3 Cookies sold 5 × 8 40 cookies 4 Remaining 72 - 40 32 cookies
72
÷
8
=
9
5
×
8
=
40
72
-
40
=
32
Final answer:

There are 32 cookies left unpacked.

Applied rules:

• Division: "8 cookies in each box" means divide total by 8

• Multiplication: "5 boxes" of 8 cookies each = 5 × 8

• Remaining: Subtract sold amount from total

3 Mixed Operations
Exercise 3
Tom has 3 bags of marbles. Each bag contains 12 marbles. He gives 5 marbles to his friend and then buys 2 more bags of marbles (each with 12 marbles). How many marbles does Tom have now?
Definition:

Each: Indicates multiplication (3 bags, each with 12 marbles). Combined operations: Problems requiring different types of operations.

Original Problem
Tom has 3 bags of marbles. Each bag contains 12 marbles. He gives 5 marbles to his friend and then buys 2 more bags of marbles (each with 12 marbles). How many marbles does Tom have now?
1
Tom has 3 bags × 12 marbles each (multiplication)
2
Gives away 5 marbles (subtraction)
3
Buys 2 more bags × 12 marbles each (multiplication)
4
Add new marbles to remaining
Step Operation Calculation Result 1 Initial marbles 3 × 12 36 marbles 2 After giving away 36 - 5 31 marbles 3 New marbles bought 2 × 12 24 marbles 4 Final total 31 + 24 55 marbles
3
×
12
=
36
36
-
5
=
31
2
×
12
=
24
31
+
24
=
55
Final answer:

Tom has 55 marbles now.

Applied rules:

• Each: Multiply number of groups by amount per group

• Sequence: Follow the order of events in the problem

• Keywords: "gives" means subtraction, "buys" means addition

Problem Solving Strategy
1
Read the problem carefully
2
Identify what is being asked
3
Find important information
4
Determine operations needed
5
Solve step by step
6
Check your answer
\(\text{Total} = \text{Initial} + \text{Additions} - \text{Subtractions}\)
General Formula for Multi-Step Problems
Keywords Indicators
Addition: more, total, altogether, combined, in all
Subtraction: left, remaining, less, difference, gave away
Multiplication: each, per, groups of, times, product
Division: shared equally, each, per, split, quotient
📖
Read Carefully
🔍
Find Key Info
🧠
Plan Solution
✅
Check Work
Rules and Methods for Multi-Step Problems
\(\text{Result} = \text{Start} \pm \text{Changes}\)
Multi-Step Equation Model
Key Definitions:

Multi-step word problem: A problem that requires performing more than one mathematical operation to find the solution.

Keywords: Words in a problem that indicate which operation to use.

Sequence: The order in which operations should be performed based on the problem's story.

Problem Solving Strategy:
  1. Read: Carefully read the entire problem
  2. Identify: What is the question asking?
  3. Information: What numbers and facts are given?
  4. Operations: What operations are needed and in what order?
  5. Solve: Perform calculations step by step
  6. Check: Does the answer make sense?
Important: The order of operations follows the sequence of events in the problem, not just mathematical order.
Key Concept: Each step builds on the previous one, so errors in early steps affect later results.
Essential Rules for Multi-Step Problems:

• Keyword identification: "more" = addition, "left" = subtraction, "each" = multiplication, "shared" = division

• Sequential processing: Solve in the order events happen in the story

• Step tracking: Keep track of intermediate results

• Verification: Check if the final answer is reasonable

• Organization: Write down each step clearly

Summary: Multi-Step Word Problems
Core Concepts:

Multi-Step Word Problems: Problems that require more than one operation to solve. These problems mirror real-life situations where multiple calculations are needed.

Keywords: Words that signal which mathematical operation to use. Learning to identify these is crucial for problem solving.

Problem Sequence: The order of operations follows the story in the problem, not necessarily the order of operations in mathematics.

Problem Solving Methods:

Step-by-Step Method:

  1. Read thoroughly: Understand the entire problem before starting
  2. Identify the question: What exactly are you trying to find?
  3. Highlight key information: Numbers and important details
  4. Find keywords: Determine operations needed
  5. Plan the sequence: Decide order of operations
  6. Calculate: Solve each step carefully
  7. Verify: Check if answer makes sense

Keyword Recognition:

  • Addition: more, total, altogether, combined, in all, sum, increase
  • Subtraction: left, remaining, difference, less, gave away, decreased
  • Multiplication: each, per, groups of, times, product, area
  • Division: shared, each, per, split, quotient, equal groups

Verification Method:

  1. Does the answer make sense in the context?
  2. Are the units correct?
  3. Is the answer reasonable?
  4. Can you work backwards to check?
Tip 1: Underline or circle important numbers and keywords.
Tip 2: Draw pictures or diagrams to visualize the problem.
Tip 3: Solve one step at a time and write down intermediate results.
Tip 4: Always check if your answer is reasonable.
Common errors: Misreading keywords, solving in wrong order, calculation mistakes, not checking if answer makes sense.
Exam preparation: Practice identifying keywords, work through problems step-by-step, and always verify your answer.
Key Rules and Properties:

• Sequence matters: Follow the story order in the problem

• Keywords guide: Use keywords to identify operations

• Step-by-step: Solve one operation at a time

• Verification: Always check if the answer is reasonable

• Organization: Keep work neat and labeled

Questions & Answers

Question: How do I know which operation to do first in a multi-step problem? Does it always follow the order of operations (PEMDAS)?

Answer: In multi-step word problems, you follow the sequence of events as they happen in the story, not necessarily the order of operations (PEMDAS). For example:

"Sarah had 10 apples, bought 5 more, then ate 3" → You add first (10 + 5 = 15), then subtract (15 - 3 = 12).

PEMDAS applies to expressions like 10 + 5 × 3, but in word problems, you follow the story sequence.

The key is to identify the sequence of events in the problem and solve them in that order.

Question: What if there are no clear keywords in the problem? How do I know what to do?

Answer: Even without obvious keywords, you can identify operations by understanding the situation:

  • Getting more: Addition (receiving, buying, earning)
  • Having less: Subtraction (giving, spending, losing)
  • Equal groups: Multiplication (bags with same number, rows with same items)
  • Sharing equally: Division (splitting into equal parts)

Read the problem multiple times and think about what's happening. Draw a picture if it helps visualize the situation.

Ask yourself: "Is something being added, taken away, grouped, or shared?"

Question: What should I do if I get confused about the steps in a multi-step problem?

Answer: Here are strategies to handle confusion:

  1. Read slowly: Take your time and read the problem at least twice
  2. Break it down: Identify what happens first, second, third, etc.
  3. Draw pictures: Visualize the situation
  4. Write steps: List what needs to be done in order
  5. Check as you go: Verify each step makes sense

It's okay to go slowly and make sure you understand each part before moving to the next step.

You can also try to solve a simpler version of the problem first to understand the pattern.

Question: How can I check if my answer to a multi-step problem is correct?

Answer: Here are several ways to check your answer:

  1. Reasonableness: Does the answer make sense? Is it too big or too small?
  2. Reverse calculation: Work backwards from your answer to see if you get the original numbers
  3. Estimation: Round numbers and see if your answer is close to the estimate
  4. Units: Do the units make sense in the context?

Example: If you got 200 stickers when starting with 45 and adding 23, that's unreasonable.

You can also solve the problem a different way to confirm your answer.