Solved Exercises on Two Step Word Problems with Four Operations in Grade 3

Master two-step word problems: addition, subtraction, multiplication, and division through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Addition & Multiplication
Exercise 1
Sarah has 3 bags of marbles. Each bag contains 8 marbles. She gives 5 marbles to her friend. How many marbles does Sarah have left?
Definition:

Two-step problem: A problem requiring two different operations to solve

Problem-solving steps:
  1. Read the problem carefully and identify what is being asked
  2. Find the important numbers and operations needed
  3. Decide the order of operations (what to do first)
  4. Solve the first step, then the second step
  5. Check if the answer makes sense
Step 1
3 × 8 = 24
Step 2
24 - 5 = 19
Step 1: Find total marbles

Sarah has 3 bags with 8 marbles each

Total marbles = 3 × 8 = 24 marbles

Step 2: Subtract given marbles

Sarah gives 5 marbles to her friend

Marbles left = 24 - 5 = 19 marbles

Step 3: Verify the answer

Start with 3 bags of 8 marbles = 24

Give away 5 marbles = 24 - 5 = 19

Answer is reasonable

Sarah has 19 marbles left
Final answer:

Sarah has 19 marbles left

Applied rules:

• Order of operations: Multiplication before subtraction

• Problem breakdown: Separate into smaller steps

• Verification: Check answer makes logical sense

2 Subtraction & Division
Exercise 2
Tom had 25 stickers. He gave 5 stickers to his brother. Then he shared the remaining stickers equally among 4 friends. How many stickers did each friend get?
Definition:

Division: Splitting a number into equal groups

Step 1
25 - 5 = 20
Step 2
20 ÷ 4 = 5
Step 1: Find remaining stickers

Tom had 25 stickers, gave away 5

Remaining stickers = 25 - 5 = 20 stickers

Step 2: Share equally among friends

20 stickers shared among 4 friends

Stickers per friend = 20 ÷ 4 = 5 stickers

Step 3: Verify the answer

Start with 25 stickers

Give away 5 → 25 - 5 = 20

Share 20 among 4 → 20 ÷ 4 = 5 each

Answer is reasonable

Each friend gets 5 stickers
Final answer:

Each friend gets 5 stickers

Applied rules:

• Subtraction first: Find what remains after giving away

• Division second: Split remainder into equal parts

• Keywords: "shared equally" indicates division

3 Multiplication & Addition
Exercise 3
A bakery sells cupcakes in boxes of 6. Mrs. Johnson bought 4 boxes and then bought 3 more individual cupcakes. How many cupcakes did she buy in total?
Definition:

Multiplication: Repeated addition of equal groups

Step 1
4 × 6 = 24
Step 2
24 + 3 = 27
Step 1: Find cupcakes in boxes

4 boxes with 6 cupcakes each

Cupcakes in boxes = 4 × 6 = 24 cupcakes

Step 2: Add individual cupcakes

Mrs. Johnson also bought 3 more cupcakes

Total cupcakes = 24 + 3 = 27 cupcakes

Step 3: Verify the answer

4 boxes of 6 = 24 cupcakes

Plus 3 individual = 24 + 3 = 27

Answer is reasonable

Mrs. Johnson bought 27 cupcakes in total
Final answer:

Mrs. Johnson bought 27 cupcakes in total

Applied rules:

• Multiplication first: Calculate items in groups

• Addition second: Combine with additional items

• Keywords: "in boxes of" indicates multiplication

Operations and Problem-Solving Guide
Total = (Groups × Items per group) ± Extra
General Two-Step Pattern
Addition (+)
+
Combine quantities together
Subtraction (-)
−
Take away or find difference
Multiplication (×)
×
Repeated addition of equal groups
Division (÷)
÷
Split into equal groups
Multiply then Add
Find total in groups, then add extra
Multiply then Subtract
Find total in groups, then take away
Divide then Add
Split quantity, then add something
Subtract then Divide
Take away first, then share equally
Order: Multiply/Divide → Add/Subtract
Operation Priority
(Total ÷ Groups) = Items per group
Division Relationship
Solution: Exercises 4 to 5
4 Division & Subtraction
Exercise 4
There are 36 cookies to be shared equally among 6 children. After sharing, 4 cookies were eaten. How many cookies are left?
Definition:

Equal sharing: Dividing a total amount into equal parts

Step 1
36 ÷ 6 = 6
Step 2
36 - 4 = 32
Step 1: Share cookies equally

36 cookies divided among 6 children

Cookies per child = 36 ÷ 6 = 6 cookies each

Total distributed = 6 × 6 = 36 cookies

Step 2: Find remaining cookies

After sharing, 4 cookies were eaten

Wait - this needs correction. Let's re-read.

Actually: 36 cookies shared equally among 6 children = 6 each

Then 4 cookies were eaten from the original 36

Cookies left = 36 - 4 = 32 cookies

Step 3: Verify the answer

Original: 36 cookies

Eaten: 4 cookies

Left: 36 - 4 = 32 cookies

Answer is reasonable

32 cookies are left
Final answer:

32 cookies are left

Applied rules:

• Read carefully: Understand what happens to the total

• Division first: Share equally among groups

• Subtraction second: Take away from total

5 Mixed Operations
Exercise 5
A farmer has 5 baskets of apples. Each basket has 8 apples. He sells 12 apples and then puts the remaining apples equally into 4 new baskets. How many apples are in each new basket?
Definition:

Multi-step problem: Requires multiple operations in sequence

Step 1
5 × 8 = 40
Step 2
40 - 12 = 28
Step 3
28 ÷ 4 = 7
Step 1: Find total apples initially

5 baskets with 8 apples each

Total apples = 5 × 8 = 40 apples

Step 2: Find remaining apples after selling

Farmers sells 12 apples

Remaining apples = 40 - 12 = 28 apples

Step 3: Distribute remaining apples equally

28 apples put into 4 new baskets equally

Apples per new basket = 28 ÷ 4 = 7 apples

Step 4: Verify the answer

Start: 5 × 8 = 40 apples

Sell: 40 - 12 = 28 apples

Divide: 28 ÷ 4 = 7 apples per basket

Answer is reasonable

Each new basket has 7 apples
Final answer:

Each new basket has 7 apples

Applied rules:

• Follow sequence: Calculate in order of events

• Track quantities: Keep track of what remains

• Three-step process: Multiply, subtract, divide

Two-Step Word Problems Summary Guide
Problem = (Operation 1) → (Operation 2)
Two-Step Structure
Key definitions:

Two-step word problem: A mathematical problem that requires two different operations to solve completely

Keywords: Words that indicate which operation to use (more, total, altogether = addition; less, fewer, left = subtraction; each, per, groups of = multiplication; shared equally, split, divided = division)

Order of operations: In word problems, follow the sequence described in the problem

Five-step problem-solving method:
  1. Read: Carefully read the entire problem
  2. Identify: Find important numbers and what is being asked
  3. Plan: Decide which operations to use and in what order
  4. Solve: Work through each step systematically
  5. Check: Verify if the answer makes sense
Tip 1: Draw pictures or use objects to visualize the problem.
Tip 2: Look for clue words that indicate operations.
Tip 3: Always check if your answer is reasonable.
Tip 4: Write down each step to stay organized.
Common clue words: Addition: "total", "altogether", "combined", "more than". Subtraction: "left", "remaining", "less", "fewer". Multiplication: "each", "per", "groups of", "times". Division: "shared equally", "divided", "split", "per".
Memory aid: "Please Excuse My Dear Aunt Sally" (though for 3rd grade, focus on word context rather than PEMDAS).
Common two-step problem patterns:

• Multiply then Add: Find total in groups, then add extras

• Multiply then Subtract: Find total in groups, then take some away

• Divide then Add: Share equally, then add something extra

• Subtract then Divide: Take away first, then share what remains

• Add then Multiply: Combine amounts, then multiply by a factor

• Subtract then Multiply: Find difference, then multiply

Questions & Answers

Question: I always get confused about which operation to do first in two-step problems. How do I know?

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

  • Follow the story: Read the problem like a story and do the operations in the order they happen
  • Look for clue words: Words like "in all groups of" suggest multiplication first, then addition
  • Think logically: What makes sense? If you have groups first, multiply. If you need to share, divide last

Example: "Sarah has 3 boxes of 5 pencils each. She gives 2 away." - First: 3 boxes OF 5 pencils → multiply (3 × 5 = 15) - Second: gives 2 away → subtract (15 - 2 = 13)

The story tells you the order!

Question: How can I help my child practice two-step word problems at home?

Answer: Here are effective strategies for home practice:

  • Use real objects: Count toys, snacks, or household items to model problems
  • Create story problems: Make up problems about daily activities (shopping, cooking, games)
  • Draw pictures: Help visualize the problem with simple drawings
  • Practice regularly: Even 10 minutes daily helps build confidence

Example: "We have 3 bags of 4 cookies each. We eat 5 cookies. How many are left?" Use actual cookies or draw them to make it concrete.

Keep problems fun and connected to your child's interests!

Question: What if I don't understand the words in the problem? Some problems seem too hard to read.

Answer: That's completely normal! Here's what to do when words are tricky:

  • Ask for help: It's okay to ask a grown-up to read it aloud
  • Focus on numbers: Look for the important numbers first
  • Look for action words: "More," "less," "each," "shared" tell you what to do
  • Draw it out: Sketch what the problem is saying

Example: "Samantha purchased 4 packets of 6 stickers each" - even if "purchased" is unfamiliar, you see "4 packets of 6" which means 4 × 6.

The math is usually simpler than the vocabulary!