Solved Exercises on Multi-Step Word Problems for Grade 3

Master multi-step word problems: addition, subtraction, multiplication, and division with real-world scenarios through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Shopping scenario
Exercise 1
Sarah bought 3 packs of pencils. Each pack has 12 pencils. She gave 5 pencils to her brother and 3 pencils to her sister. How many pencils does Sarah have left?
Definition:

Multi-step word problem: A problem that requires more than one mathematical operation to solve, often involving multiple pieces of information.

Multi-step problem-solving method:
  1. Read the problem carefully and identify what is being asked
  2. Find and list all the important information
  3. Determine the operations needed (multiplication, addition, subtraction)
  4. Solve step by step in the correct order
  5. Check your answer
Step 1
3 × 12 = 36
Step 2
5 + 3 = 8
Step 3
36 - 8 = 28
Step 1: Find total pencils

Sarah bought 3 packs with 12 pencils each

3 × 12 = 36 pencils total

Step 2: Find total given away

She gave 5 pencils to her brother and 3 to her sister

5 + 3 = 8 pencils given away

Step 3: Find pencils remaining

Total pencils - given away = remaining

36 - 8 = 28 pencils left

Sarah has 28 pencils left
Final answer:

Sarah has 28 pencils left

Check: 3×12=36, 36-(5+3)=36-8=28 ✓

Applied rules:

• Order of Operations: Complete each operation in logical sequence

• Grouping: Combine similar actions (giving pencils) before subtracting

• Verification: Check that the answer makes sense in context

2 School event scenario
Exercise 2
A school has 4 classrooms. Each classroom has 25 students. 15 students from each classroom went on a field trip. How many students stayed at school?
Definition:

Comparison problem: A problem that involves comparing quantities across different groups or situations.

Step 1
4 × 25 = 100
Step 2
4 × 15 = 60
Step 3
100 - 60 = 40
Step 1: Find total students

4 classrooms with 25 students each

4 × 25 = 100 students total

Step 2: Find total students on trip

15 students from each of 4 classrooms went on trip

4 × 15 = 60 students on field trip

Step 3: Find students at school

Total students - students on trip = students at school

100 - 60 = 40 students stayed at school

40 students stayed at school
Final answer:

40 students stayed at school

Alternative: Per classroom: 25-15=10, 4×10=40 ✓

Applied rules:

• Equal Groups: Use multiplication when dealing with equal-sized groups

• Comparison: Find differences between groups

• Alternative Methods: Multiple approaches can lead to the same answer

3 Time and planning scenario
Exercise 3
Emma practiced piano for 20 minutes on Monday, 25 minutes on Tuesday, and 30 minutes on Wednesday. On Thursday, she practiced twice as long as on Monday. How many minutes did Emma practice in total during these four days?
Definition:

Time accumulation problem: A problem that involves adding amounts of time across different periods.

Monday
20 min
Tuesday
25 min
Wednesday
30 min
Thursday
2×20=40 min
Total
115 min
Step 1: Find Thursday's practice time

Twice as long as Monday means 2 × 20 = 40 minutes

Step 2: Add all practice times

Monday: 20 minutes

Tuesday: 25 minutes

Wednesday: 30 minutes

Thursday: 40 minutes

Step 3: Calculate total

20 + 25 + 30 + 40 = 115 minutes

Emma practiced 115 minutes total
Final answer:

Emma practiced 115 minutes in total

Check: 20+25+30+(2×20)=20+25+30+40=115 ✓

Applied rules:

• Relationships: "Twice as long" means multiply by 2

• Sequential Addition: Add items in a logical order

• Organization: Keep track of different days separately

Multi-Step Word Problems: Complete Guide
\(\text{Total Steps} = \sum_{i=1}^{n} \text{Operation}_i\)
Multi-Step Process
Read Carefully
Understand the problem
What is asked?
Identify Info
Find important numbers
What do you know?
Plan Steps
Decide operations
How to solve?
Key definitions:

Multi-step Problem: A problem requiring two or more mathematical operations to reach the solution

Word Problem: A mathematical problem presented in sentence form

Operation: Addition, subtraction, multiplication, or division

Unknown: The quantity being sought in the problem

Given Information: The numbers and facts provided in the problem

Five-Step Problem-Solving Process:
  1. Read: Carefully read the entire problem
  2. Identify: Circle or underline key information and the question
  3. Plan: Decide which operations to use and in what order
  4. Solve: Carry out the calculations step by step
  5. Check: Verify your answer makes sense in the context
Tip 1: Draw a picture or diagram to visualize the problem.
Tip 2: Write down what you know and what you need to find.
Tip 3: Break complex problems into smaller, easier steps.
Tip 4: Estimate your answer first to check if your final answer is reasonable.
Tip 5: Always answer the specific question that was asked.
Common errors: Reading too quickly, missing key information, doing operations in wrong order, not answering the question asked.
Success strategies: Careful reading, organizing information, checking work, using estimation.
Common Keywords and Operations:

• Addition: total, sum, altogether, combined, increased by, more than

• Subtraction: difference, less than, fewer, decreased by, left, remained

• Multiplication: times, product, each, per, of, double, twice

• Division: quotient, divided by, per, each, shared equally, split

Solution: Exercises 4 to 5
4 Movie theater scenario
Exercise 4
A movie theater has 8 rows of seats. Each row has 15 seats. During a movie, 25 seats were empty in the first 3 rows, and 10 seats were empty in the remaining rows. How many people were watching the movie?
Definition:

Area and distribution problem: A problem involving rectangular arrangements and distribution of items within that area.

Total seats
8×15=120
Empty seats
25+10=35
Occupied seats
120-35=85
Step 1: Find total number of seats

8 rows with 15 seats each

8 × 15 = 120 total seats

Step 2: Find total number of empty seats

25 empty seats in first 3 rows + 10 empty seats in remaining rows

25 + 10 = 35 empty seats

Step 3: Find number of occupied seats

Total seats - empty seats = occupied seats

120 - 35 = 85 occupied seats

85 people were watching the movie
Final answer:

85 people were watching the movie

Check: 120-35=85 ✓

Applied rules:

• Rectangular Arrays: Rows × columns gives total items

• Partitioning: Divide the problem into sections (first 3 rows vs. remaining)

• Complementary Thinking: Total - empty = occupied

5 Fruit distribution scenario
Exercise 5
A farmer picked 120 apples on Monday and 95 apples on Tuesday. He packed the apples into boxes that hold 15 apples each. He sold 8 boxes and kept the rest. How many apples did the farmer keep?
Definition:

Distribution and grouping problem: A problem involving grouping items into containers and distributing those containers.

Total apples
120+95=215
Boxes made
215÷15=14 R5
Apples kept
(14-8)×15+5=95
Step 1: Find total number of apples

120 apples on Monday + 95 apples on Tuesday

120 + 95 = 215 apples total

Step 2: Find number of full boxes

Each box holds 15 apples

215 ÷ 15 = 14 remainder 5

So 14 full boxes and 5 extra apples

Step 3: Find number of boxes kept

He made 14 boxes and sold 8

14 - 8 = 6 boxes kept

Step 4: Find total apples kept

6 boxes × 15 apples per box + 5 extra apples

6 × 15 + 5 = 90 + 5 = 95 apples

The farmer kept 95 apples
Final answer:

The farmer kept 95 apples

Check: 14 boxes total, 8 sold, 6 kept; 6×15=90, 90+5=95 ✓

Applied rules:

• Division with Remainders: Understand what the remainder represents

• Grouping: Items distributed into equal-sized containers

• Multistep Calculations: Combine multiple operations in sequence

Advanced Multi-Step Problem Strategies
\(\text{Solution} = f(\text{Operations}, \text{Order}, \text{Context})\)
Solution Function
Advanced definitions:

Compound Problems: Problems with multiple interconnected questions

Rate Problems: Problems involving rates (per hour, per day, etc.)

Ratio Problems: Problems comparing quantities using ratios

Time Conversion Problems: Problems requiring conversion between units of time

Money Problems: Problems involving currency calculations

Advanced Multi-Step Methodology:
  1. Problem Decomposition: Break complex problems into simpler sub-problems
  2. Information Organization: Use tables, diagrams, or lists to organize data
  3. Operation Planning: Determine the sequence of operations needed
  4. Intermediate Checks: Verify each step before proceeding
  5. Final Verification: Check that the answer addresses the original question
  6. Alternative Methods: Consider different approaches to validate results
Tip 1: For complex problems, create a visual model or diagram.
Tip 2: When dealing with remainders, think about what they represent in the context.
Tip 3: Look for opportunities to group operations for efficiency.
Tip 4: Practice mental math for intermediate calculations.
Tip 5: Always state your final answer in the context of the problem.
Advanced errors: Misinterpreting remainders, not accounting for partial groups, overlooking units, incorrect order of operations.
Advanced strategies: Working backwards, using variables for unknowns, systematic organization, checking reasonableness.
Problem Structure Patterns:

• Sequential: Each step depends on the previous result

• Parallel: Multiple operations occur simultaneously, then combined

• Hierarchical: Sub-problems within larger problems

• Iterative: Similar operations repeated with different inputs

• Comparative: Multiple scenarios compared side by side

Questions & Answers

Question: Sometimes I don't know which operation to do first in a multi-step problem. How do I figure that out?

Answer: Great question! Here's how to determine the order:

  • Look for words that indicate relationships: "twice as much" means multiply, "left over" means subtract
  • Think about what makes sense: you usually need to find totals before you can divide them
  • Follow the story: if someone buys something first, then gives some away, do the buying before the giving
  • Group similar actions: if you're adding multiple things together, do that first

Example: "Sarah has 3 boxes of 10 cookies each, then eats 5." First find total cookies (3×10=30), then subtract eaten ones (30-5=25).

Question: My child gets overwhelmed by word problems with lots of information. How can I help them stay organized?

Answer: Organization is key for complex word problems! Try these strategies:

  • Have them underline or highlight important numbers and words
  • Encourage them to write down what they know in a list or table
  • Draw simple diagrams to visualize the problem
  • Read the problem twice: once for understanding, once for details
  • Ask "What do I need to find?" before starting calculations

Create a simple template: "Given: ___ Need to find: ___ Plan: ___"

Question: What should I do when I get a remainder in a word problem? Does it matter?

Answer: Yes, remainders are very important in word problems! The context determines what to do with them:

  • If making groups: the remainder represents leftover items that don't fill a complete group
  • If sharing equally: the remainder shows how many items can't be distributed evenly
  • If calculating resources: you might need to round up to ensure you have enough
  • Always consider what the remainder means in the problem's context

Example: If you have 25 apples and boxes hold 6 apples each, 25÷6=4 R1. You can fill 4 boxes completely and have 1 apple left over. Depending on the question, you might need 5 boxes total or you might have 1 apple remaining.