Solved Exercises on Two Step Word Problems in Grade 3

Master two step word problems: mathematical reasoning, problem solving strategies, addition and subtraction applications through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Shopping Problem
Exercise 1
Sarah had 25 apples. She bought 15 more apples. Then she gave 8 apples to her friend. How many apples does Sarah have now?
Definition:

Two step word problem: A problem that requires two operations to find the solution. In this case: addition then subtraction.

Problem solving method:
  1. Read carefully: Identify what is known and what is being asked
  2. Identify operations: Determine which operations are needed
  3. Solve step by step: Perform one operation at a time
  4. Check answer: Verify if the answer makes sense
Context: Sarah starts with some apples, gets more, then gives some away.
Step 1:
Sarah had 25 apples and bought 15 more apples. So we add: 25 + 15 = 40 apples total.
Step 2:
Then she gave 8 apples to her friend. So we subtract: 40 - 8 = 32 apples left.
25 + 15 = 40
40 - 8 = 32
Solution:

Sarah has 32 apples now.

Final answer:

Sarah has 32 apples now.

Applied rules:

• Order of operations: Solve problems step by step as described

• Addition: Combine quantities when items are added

• Subtraction: Remove quantities when items are taken away

2 Fish Tank Problem
Exercise 2
There were 42 fish in a tank. The pet store owner added 18 more fish. Later, 15 fish were sold. How many fish are left in the tank?
Definition:

Two step word problem: A problem that requires two operations to find the solution. In this case: addition then subtraction.

Context: Starting with fish, adding more, then removing some.
Step 1:
There were 42 fish and 18 more were added. So we add: 42 + 18 = 60 fish total.
Step 2:
Then 15 fish were sold. So we subtract: 60 - 15 = 45 fish left.
42 + 18 = 60
60 - 15 = 45
Solution:

There are 45 fish left in the tank.

Final answer:

There are 45 fish left in the tank.

Applied rules:

• Order of operations: Follow the sequence of events in the problem

• Addition: Combine quantities when items are added

• Subtraction: Remove quantities when items are taken away

3 Library Books Problem
Exercise 3
The school library had 85 books. They received 23 new books. Then 32 books were borrowed by students. How many books are left in the library?
Definition:

Two step word problem: A problem that requires two operations to find the solution. In this case: addition then subtraction.

Context: Starting with books, getting more, then lending some out.
Step 1:
The library had 85 books and received 23 more. So we add: 85 + 23 = 108 books total.
Step 2:
Then 32 books were borrowed. So we subtract: 108 - 32 = 76 books left.
85 + 23 = 108
108 - 32 = 76
Solution:

There are 76 books left in the library.

Final answer:

There are 76 books left in the library.

Applied rules:

• Order of operations: Follow the sequence of events in the problem

• Addition: Combine quantities when items are added

• Subtraction: Remove quantities when items are taken away

Problem Solving Strategies
Problem Solving Steps
Understand, Plan, Solve, Check
🔍
Understand
Read the problem carefully and identify what is being asked
📝
Plan
Decide which operations to use and in what order
🧮
Solve
Perform the calculations step by step
✅
Check
Verify if the answer makes sense
Keywords for Addition: total, altogether, combined, increased by, more than, sum
Keywords for Subtraction: difference, less than, fewer, decreased by, take away, left over
Two Step Problems: Require TWO different operations to solve (usually addition and subtraction)
Tip 1: Draw pictures or use objects to visualize the problem.
Tip 2: Write down the numbers and operations as you read the problem.
Tip 3: Always solve step by step - don't try to do everything at once.
Common Mistakes to Avoid:

• Not reading the problem completely

• Using the wrong operation (addition vs subtraction)

• Forgetting to complete both steps

• Not checking if the answer makes sense

Additional Examples & Visual Models
Visual Representation
Bar Models and Number Lines
Example Pattern
Pattern: Start with a number → Add something → Subtract something → Get final answer
Initial amount + Added amount = Total after addition
Total after addition - Removed amount = Final amount
Balance Concept
Think of it as: Starting quantity changes through two operations
➕
Addition
Makes the total bigger
➖
Subtraction
Makes the total smaller
Key concepts:

Two-step problems: Require exactly two different operations to solve

Mathematical reasoning: Thinking through the logical steps needed

Problem solving: Applying math skills to real-world situations

Advanced strategy:
  1. Circle key numbers in the problem
  2. Underline action words (gave, got, spent, etc.)
  3. Draw a model showing the changes
  4. Solve one step at a time
  5. Check by working backwards
Tip 4: Practice with different scenarios (money, toys, animals, etc.)
Tip 5: Always reread the question to make sure you answered correctly
Questions & Answers

Student Questions

Question: I get confused about whether to add or subtract first in two step problems. How do I know which operation to do first?

Answer: Great question Jake! You should follow the order that the story happens in the problem:

  • If the problem says "Sarah had 10 apples, then she bought 5 more", you ADD first because buying adds to what she already has.
  • Then if it says "she gave 3 to her friend", you SUBTRACT because giving takes away from what she has.

Always read the problem from beginning to end and do the operations in the same order they happen in the story. Don't worry about what comes first in math - just follow the story!

Question: How can I check if my answer is right after solving a two step word problem?

Answer: There are several ways to check your answer:

  • Does it make sense? If your answer seems too big or too small, check your work.
  • Work backwards: Take your final answer and reverse the operations to see if you get back to where you started.
  • Estimate: Round the numbers and see if your answer is close to your estimate.

For example, if you started with 20 items, added 10, then subtracted 5, your answer should be around 25 (20+10-5=25).

Question: Sometimes I see problems that have more than two steps. Are those still two step problems?

Answer: Good observation Lucy! Two step problems specifically require exactly two operations to solve. If a problem needs three or four operations, it would be called a multi-step problem.

For example:

  • Two step: "I had 10, got 5 more, then gave away 3" (add then subtract)
  • Multi-step: "I had 10, got 5 more, gave 3 away, then found 2 more" (add, subtract, add)

In 3rd grade, focus on mastering two step problems first before moving to more complex ones.