Solved Exercises on Two-Step Word Problems in Grade 3

Master two-step word problems: addition and subtraction, multiplication and division, mixed operations, and problem-solving strategies through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Addition and subtraction
Exercise 1
Sarah collected 24 seashells at the beach. On her way home, she found 15 more seashells. Then she gave 8 seashells to her friend. How many seashells does Sarah have now?
Definition:

Two-step word problem: A problem that requires two different mathematical operations to solve. Operations are performed in sequence following the order described in the problem.

Two-step method:
  1. Identify the first action and operation
  2. Solve the first step
  3. Use the result for the second operation
  4. Solve the second step
  5. State the final answer
Step 1
24 + 15 = 39
Step 2
39 - 8 = 31
Final
31 seashells
Step 1: Find total after collecting more

Sarah starts with 24 seashells and finds 15 more

24 + 15 = 39 seashells

Step 2: Subtract the seashells given away

From 39 seashells, Sarah gives 8 to her friend

39 - 8 = 31 seashells

Step 3: State the final answer

Sarah has 31 seashells now

Sarah has 31 seashells
Final answer:

Sarah has 31 seashells altogether

Applied rules:

• Sequence: Follow the order of actions in the problem

• Intermediate result: Use first answer for second calculation

• Verification: Work backwards to check: 31 + 8 = 39, 39 - 15 = 24 ✓

2 Multiplication and subtraction
Exercise 2
A teacher has 5 boxes of crayons. Each box contains 24 crayons. She gives 35 crayons to her students. How many crayons does she have left?
Definition:

Mixed operations: Problems that combine different mathematical operations (multiplication followed by subtraction, or other combinations).

Step 1
5 × 24 = 120
Step 2
120 - 35 = 85
Final
85 crayons
Step 1: Find total number of crayons

5 boxes with 24 crayons each

5 × 24 = 120 crayons

Step 2: Subtract the crayons given away

From 120 crayons, she gives 35 to students

120 - 35 = 85 crayons

Step 3: State the final answer

The teacher has 85 crayons left

Teacher has 85 crayons left
Final answer:

The teacher has 85 crayons remaining

Applied rules:

• Multiplication first: Find total from equal groups

• Subtraction second: Take away from the total

• Verification: 85 + 35 = 120, 120 ÷ 24 = 5 ✓

3 Division and addition
Exercise 3
There are 48 students going on a field trip. They will ride in buses that can hold 12 students each. Then, 3 teachers will join each bus. How many people will be on each bus?
Definition:

Grouping and adding: Problems that involve dividing a total into equal groups, then adding additional members to each group.

Step 1
48 ÷ 12 = 4
Step 2
12 + 3 = 15
Final
15 people per bus
Step 1: Find number of buses needed

48 students divided by 12 students per bus

48 ÷ 12 = 4 buses

Step 2: Find people per bus

Each bus has 12 students + 3 teachers

12 + 3 = 15 people per bus

Step 3: State the final answer

Each bus will have 15 people

Each bus has 15 people
Final answer:

There will be 15 people on each bus

Applied rules:

• Division first: Determine number of groups

• Addition second: Combine members per group

• Verification: 15 × 4 = 60 total people (48 students + 12 teachers)

Rules and methods, laws,...
Step 1 \rightarrow Result \rightarrow Step 2
Two-Step Process
Common Sequences
Add then Subtract
Add first, subtract second
Common Sequences
Multiply then Subtract
Multiply first, subtract second
Common Sequences
Divide then Add
Divide first, add second
Key definitions:

Two-step word problem: A mathematical problem that requires two different operations to solve, performed in the sequence described in the problem.

Intermediate result: The answer from the first step that becomes the starting number for the second step.

Order of operations: The sequence in which mathematical operations are performed (as described in the problem).

Problem decomposition: Breaking a complex problem into smaller, manageable steps.

Two-step problem-solving methodology:
  1. Read carefully: Understand the full problem and identify the sequence of events
  2. Identify steps: Determine what happens first, then second
  3. Find operations: Identify which operation to use for each step
  4. Solve first step: Calculate the result of the first operation
  5. Use intermediate result: Apply the first result to the second operation
  6. Solve second step: Calculate the final answer
  7. Check answer: Verify the answer makes sense in the context
Tip 1: Underline or circle the numbers and identify what happens to them in order.
Tip 2: Write down the first answer before moving to the second step.
Tip 3: Check that your answer is reasonable in the context of the problem.
Tip 4: Work backwards to verify your solution.
Common errors: Performing operations in wrong order, forgetting to use the intermediate result, calculation mistakes, not checking if answer makes sense.
Real-world applications: Shopping (buying items then receiving discount), cooking (measuring ingredients then adjusting), planning events (counting guests then adding staff), budgeting.
Problem-solving rules:

• Follow the sequence of events as described in the problem

• Use the result from Step 1 as input for Step 2

• Common sequences: Add then Subtract, Multiply then Subtract, Divide then Add

• Always verify your answer makes sense in the problem context

• Work backwards to check your solution

Solution: Exercises 4 to 5
4 Money problem
Exercise 4
Emma earned $3.50 from her allowance and $2.25 from doing chores. She spent $1.75 on a snack. How much money does Emma have left?
Definition:

Money calculations: Two-step problems involving earning or receiving money, then spending or giving some away.

Step 1
$3.50 + $2.25 = $5.75
Step 2
$5.75 - $1.75 = $4.00
Final
$4.00
Step 1: Calculate total money earned

Emma earned $3.50 + $2.25

$3.50 + $2.25 = $5.75

Step 2: Subtract money spent

From $5.75, Emma spent $1.75

$5.75 - $1.75 = $4.00

Step 3: State the final answer

Emma has $4.00 left

Step 4: Verify the answer

$4.00 + $1.75 = $5.75, and $5.75 - $2.25 = $3.50 ✓

Emma has $4.00 left
Final answer:

Emma has $4.00 remaining

Applied rules:

• Addition first: Combine all money received

• Subtraction second: Subtract money spent

• Verification: Work backwards to check calculations

5 Mixed operations problem
Exercise 5
A baker made 144 muffins. He packed them into boxes with 12 muffins in each box. Then he sold 8 boxes. How many muffins does he have left?
Definition:

Grouping and subtraction: Problems that involve dividing items into equal groups, then removing some of those groups.

Step 1
144 ÷ 12 = 12
Step 2
12 - 8 = 4
Boxes remaining
4 boxes
Muffins remaining
4 × 12 = 48
Step 1: Find number of boxes

144 muffins divided into boxes of 12

144 ÷ 12 = 12 boxes

Step 2: Find boxes remaining

From 12 boxes, he sold 8

12 - 8 = 4 boxes remaining

Step 3: Calculate muffins remaining

4 boxes × 12 muffins per box = 48 muffins

Step 4: State the final answer

The baker has 48 muffins left

Step 5: Verify the answer

48 + (8 × 12) = 48 + 96 = 144 ✓

Baker has 48 muffins left
Final answer:

The baker has 48 muffins remaining

Applied rules:

• Division first: Group items into equal sets

• Subtraction second: Remove some groups

• Multiplication final: Convert groups back to individual items

Complete Summary: Two-Step Word Problems
Step 1 \rightarrow Result \rightarrow Step 2
Two-Step Process
Key definitions:

Two-step word problem: A mathematical problem that requires two different operations to solve, performed in the sequence described in the problem. The result of the first operation becomes the input for the second operation.

Intermediate result: The answer obtained from the first step that serves as the starting number for the second step.

Order of operations: The sequence in which mathematical operations are performed, following the order of events described in the problem.

Problem decomposition: Breaking a complex problem into smaller, manageable steps that can be solved sequentially.

Common sequences: Add then Subtract, Multiply then Subtract, Divide then Add, Subtract then Add.

Complete two-step problem-solving methodology:
  1. Read carefully: Understand the full problem and identify the sequence of events
  2. Identify steps: Determine what happens first, then second
  3. Find operations: Identify which operation to use for each step
  4. Solve first step: Calculate the result of the first operation
  5. Use intermediate result: Apply the first result to the second operation
  6. Solve second step: Calculate the final answer
  7. Check answer: Verify the answer makes sense in the context
Tip 1: Underline or circle the numbers and identify what happens to them in order.
Tip 2: Write down the first answer before moving to the second step.
Tip 3: Check that your answer is reasonable in the context of the problem.
Tip 4: Work backwards to verify your solution.
Tip 5: Draw pictures or diagrams to visualize each step.
Common errors: Performing operations in wrong order, forgetting to use the intermediate result, calculation mistakes, not checking if answer makes sense, skipping steps or trying to do everything mentally.
Real-world applications: Shopping (buying items then receiving discount), cooking (measuring ingredients then adjusting), planning events (counting guests then adding staff), budgeting (earning money then spending), organizing items (grouping then redistributing).
Key problem-solving rules:

• Follow the sequence of events as described in the problem

• Use the result from Step 1 as input for Step 2

• Common sequences: Add then Subtract, Multiply then Subtract, Divide then Add, Subtract then Add

• Always verify your answer makes sense in the problem context

• Work backwards to check your solution

• Write down intermediate results to avoid mistakes

• Draw diagrams when visualizing helps

Visual Guide to Two-Step Word Problems

🔢
Step 1

Read the problem completely

Identify the first action

Example: 24 + 15 = 39

Calculate first result

Step 2

Use first result as input

Identify the second action

Example: 39 - 8 = 31

Calculate final answer

Common Patterns

Add then Subtract

Multiply then Subtract

Divide then Add

Subtract then Add

Group then Distribute

Verification

Check if answer is reasonable

Work backwards to verify

Re-read problem to confirm

Check calculations

Ensure units match

Questions & Answers

Question: How do I know which operation to do first in a two-step problem? Sometimes I get confused about the order.

Answer: Look at the problem in the order it happens:

  • What happens first? Do that operation first
  • What happens next? Do that operation second
  • Follow the story: Just like reading a book, do the math in the same order the events happen

Example: "Sarah had 24 seashells, found 15 more, then gave 8 away"

First: She had 24 (start)

Second: Found 15 more (addition: 24 + 15 = 39)

Third: Gave 8 away (subtraction: 39 - 8 = 31)

Always follow the sequence of events in the problem!

Question: After I finish the first step, I forget what my answer was when I need to do the second step. What should I do?

Answer: Here are some strategies to remember your first answer:

  • Write it down: Circle or box your first answer so you can easily find it
  • Label it: Write "Step 1 result:" next to your answer
  • Use scratch paper: Keep your work organized with each step clearly marked
  • Repeat it: Say the number out loud after calculating it

Example: If Step 1 is 24 + 15 = 39, write "39 seashells after finding more" so you remember to use 39 in Step 2.

Don't try to do everything in your head - writing helps you stay organized!

Question: How can I check if my answer is right? Sometimes I think I did everything correctly but my answer seems too big or too small.

Answer: Here are several ways to check your answer:

  • Is it reasonable? Does the answer make sense in the story?
  • Work backwards: Start with your answer and reverse the operations
  • Estimate: Make a rough guess to see if your answer is close
  • Re-read: Go back to the problem to make sure you answered the right question

Example: If you found that Sarah has 31 seashells, check: Did she start with 24, find 15 more (24+15=39), then give 8 away (39-8=31)? Yes, that matches!

Also ask: Is 31 more than 24? Yes, because she found more shells before giving some away.

Trust your reasoning, but always double-check!