Answer Key for Two Step Word Problems in Grade 3

Complete answer key with detailed solutions: sequential operations, mathematical reasoning, and problem-solving verification.

Answer Key: Exercises 1 to 3
1 Addition then Subtraction
Exercise 1
Sarah had 15 stickers. Her mom gave her 8 more stickers. Then she gave 6 stickers to her friend. How many stickers does Sarah have now?
Definition:

Two step word problem: A problem that requires two separate calculations to reach the final answer.

Problem-solving method:
  1. Read the problem carefully
  2. Identify the operations needed
  3. Solve the first step
  4. Use the result for the second step
15
+
8
=
23
-
6
=
17
Step 1: Calculate how many stickers Sarah has after getting more

Sarah starts with 15 stickers
Her mom gives her 8 more
So: 15 + 8 = 23 stickers

Step 2: Calculate how many stickers she has after giving some away

Sarah now has 23 stickers
She gives 6 to her friend
So: 23 - 6 = 17 stickers

Step 3: State the final answer

Sarah has 17 stickers remaining

Answer: 17 stickers
Final answer:

Sarah has 17 stickers now.

Applied rules:

• Sequential operations: Solve one step at a time in order

• Carry forward results: Use the answer from step 1 in step 2

• Context awareness: Understand the meaning of each operation

2 Subtraction then Addition
Exercise 2
Tom had 24 marbles. He lost 9 marbles while playing. Then he found 5 more marbles later. How many marbles does Tom have now?
Definition:

Subtraction: Taking away or losing items
Addition: Getting or finding more items

24
-
9
=
15
+
5
=
20
Step 1: Calculate how many marbles Tom has after losing some

Tom starts with 24 marbles
He loses 9 marbles
So: 24 - 9 = 15 marbles

Step 2: Calculate how many marbles he has after finding more

Tom now has 15 marbles
He finds 5 more marbles
So: 15 + 5 = 20 marbles

Step 3: State the final answer

Tom has 20 marbles remaining

Answer: 20 marbles
Final answer:

Tom has 20 marbles now.

Applied rules:

• Operation identification: Recognize "lost" means subtraction and "found" means addition

• Sequential processing: Perform operations in the order they occur in the story

• Result tracking: Keep track of the running total after each step

3 Money Problem
Exercise 3
Emma had $30. She spent $12 on a book. Then she earned $8 doing chores. How much money does Emma have now?
Definition:

Money problems: Word problems involving dollars and cents, requiring careful tracking of amounts.

$30
-
$12
=
$18
+
$8
=
$26
Step 1: Calculate how much money Emma has after buying the book

Emma starts with $30
She spends $12 on a book
So: $30 - $12 = $18

Step 2: Calculate how much money she has after earning more

Emma now has $18
She earns $8 doing chores
So: $18 + $8 = $26

Step 3: State the final answer

Emma has $26 remaining

Answer: $26
Final answer:

Emma has $26 now.

Applied rules:

• Unit consistency: Keep track of currency units throughout

• Operation recognition: "Spent" means subtraction, "earned" means addition

• Financial literacy: Understand the impact of spending and earning

Answer Key: Exercises 4 to 5
4 Multiplication then Addition
Exercise 4
A farmer has 4 baskets. Each basket has 6 apples. Then he picks 8 more apples from the tree. How many apples does he have altogether?
Definition:

Multiplication: Repeated addition (groups of items)
Addition: Combining amounts together

4×6
=
24
+
8
=
32
Step 1: Calculate the total number of apples in the baskets

There are 4 baskets
Each basket has 6 apples
So: 4 × 6 = 24 apples

Step 2: Calculate the total number of apples including the newly picked ones

Apples in baskets: 24
Newly picked apples: 8
So: 24 + 8 = 32 apples

Step 3: State the final answer

The farmer has 32 apples altogether

Answer: 32 apples
Final answer:

The farmer has 32 apples altogether.

Applied rules:

• Group recognition: "Each basket has" indicates multiplication

• Combining totals: Add the grouped amount to the additional amount

• Problem interpretation: Understand the relationship between groups and individuals

5 Subtraction then Division
Exercise 5
There were 36 students in the gym. 12 students went back to their classrooms. The remaining students were divided equally into 4 groups. How many students are in each group?
Definition:

Division: Splitting a total into equal parts or groups.

36
-
12
=
24
÷
4
=
6
Step 1: Calculate how many students remain in the gym

Initial students: 36
Students who left: 12
So: 36 - 12 = 24 students

Step 2: Calculate how many students are in each group

Remaining students: 24
Number of groups: 4
So: 24 ÷ 4 = 6 students per group

Step 3: State the final answer

There are 6 students in each group

Answer: 6 students per group
Final answer:

There are 6 students in each group.

Applied rules:

• Sequential operations: Subtraction must be completed before division

• Equal grouping: "Divided equally" indicates division

• Context understanding: Know that division creates equal parts

Visual Infographic: Answer Key Guide
📖
Read Carefully
Understand what the problem is asking
📝
Identify Operations
Find keywords that indicate math operations
🔢
Solve Step by Step
Complete one calculation at a time
✅
Check Answer
Make sure your answer makes sense
Exercise Problem Type First Operation Second Operation Answer
1 Addition then Subtraction 15 + 8 = 23 23 - 6 = 17 17 stickers
2 Subtraction then Addition 24 - 9 = 15 15 + 5 = 20 20 marbles
3 Subtraction then Addition $30 - $12 = $18 $18 + $8 = $26 $26
4 Multiplication then Addition 4 × 6 = 24 24 + 8 = 32 32 apples
5 Subtraction then Division 36 - 12 = 24 24 ÷ 4 = 6 6 students
Two Step Problem = First Operation + Second Operation
Problem-Solving Formula
Keywords for Addition
more, total, altogether, increased by
Combine or add amounts
Keywords for Subtraction
less, fewer, left, decreased by
Take away or find difference
Keywords for Multiplication
each, per, times, groups of
Repeated addition or equal groups
Detailed Summary: Two Step Word Problems Answer Key
Definition and Core Concepts

Two step word problems are mathematical problems that require two separate calculations to find the answer. These problems involve reading a story situation, identifying the mathematical operations needed, and performing calculations in the correct order.

Answer key: A comprehensive guide providing correct solutions, step-by-step processes, and verification methods for two step word problems.

Problem = (Initial Amount ± Change₁) ± Change₂
General Formula
Key definitions:

Word problem: A mathematical question presented in narrative form

Two-step: Requiring two separate calculations to reach the solution

Answer key: A detailed solution guide showing the correct answer and solution process

Operations: Mathematical actions like addition, subtraction, multiplication, or division

Complete methodology:
  1. Read the entire problem: Understand the situation described
  2. Identify key information: Note numbers and what they represent
  3. Find operation keywords: Look for words indicating math operations
  4. Solve the first step: Perform the first calculation
  5. Use the result: Take the answer from step 1 to solve step 2
  6. State the final answer: Clearly answer the question asked
  7. Check your work: Verify if the answer makes sense
Tip 1: Circle or underline important numbers and keywords in the problem.
Tip 2: Draw a simple picture to visualize the problem situation.
Tip 3: Write down the first answer before moving to the second step.
Tip 4: Ask yourself: "Does my final answer make sense in the story?"
Common errors: Forgetting to carry forward the first result, mixing up the order of operations, misreading the question being asked.
Test preparation: Practice identifying keywords, work on sequential thinking, master basic arithmetic operations.
Key strategies to remember:

• Keyword identification: "More" means addition, "less" means subtraction

• Sequential processing: Always solve step 1 before step 2

• Result tracking: Keep the first answer handy for the second step

• Context awareness: Understand the real-world meaning of each operation

• Verification: Check if your answer fits logically in the problem context

Questions & Answers

Question: How can I use this answer key to improve my problem-solving skills?

Answer: The answer key is a powerful learning tool when used correctly:

  • Attempt first: Try solving the problem on your own before checking the answer
  • Compare process: Check if your steps match the solution process
  • Learn from differences: Identify where your approach differed from the correct one
  • Practice repeatedly: Work through problems multiple times until you understand the process

Focus on understanding why each step is taken, not just getting the right answer. This builds strong problem-solving foundations!

Question: My child gets frustrated when their answer doesn't match the key. How can I help them handle this?

Answer: Mistakes are valuable learning opportunities! Here's how to help:

  • Normalize errors: Explain that everyone makes mistakes while learning
  • Focus on process: Celebrate effort and logical thinking, not just correct answers
  • Review together: Go through the answer key step by step to find where the error occurred
  • Encourage persistence: Remind them that problem-solving is a skill that improves with practice

Emphasize that the answer key shows the correct path, and finding errors is part of learning. This builds resilience and growth mindset!

Question: Sometimes I get the right answer but my steps are different from the answer key. Is that okay?

Answer: In mathematics, there can sometimes be multiple valid approaches to solve a problem! However, for two-step word problems:

  • Check your logic: Does your alternative method make mathematical sense?
  • Verify consistency: Do your steps follow logically from the problem?
  • Confirm accuracy: Does your method work for similar problems?
  • Ask for feedback: Share your method with your teacher to validate it

While the answer key shows the standard approach, creative problem-solving is encouraged. Just make sure your method is reliable and produces consistent results!