Using Effective Questions | Solved Exercises | Mathematics Grade 3 Addition, Subtraction, and Estimation

Solution: Exercises 1 to 3

1 Problem-Solving Strategy

Exercise 1

Sarah has 24 apples. She gives 8 to her friend. How many does she have left?
Effective Question: What is the starting amount? What is being taken away?

Definition:

Effective Question: A question that helps break down a problem into manageable parts

Problem-solving method:

Identify the starting amount (24 apples)
Identify what is happening (giving away 8)
Choose the operation (subtraction)
Solve and check the answer

Starting Amount

Amount Given Away

Operation

Subtraction

Step 1: Identify the problem parts

Starting amount = 24 apples, Amount given away = 8 apples

Step 2: Choose the operation

Since Sarah is giving away apples, we subtract: 24 - 8

Step 3: Solve the problem

24 - 8 = 16

Sarah has 16 apples left

Final answer:

Sarah has 16 apples left

Applied rules:

• Problem identification: Break down the word problem into parts

• Operation selection: Determine the correct mathematical operation

• Verification: Check that the answer makes sense

2 Estimation Strategy

Exercise 2

There are 47 students in one class and 32 in another. About how many students are there total?
Effective Question: Should I estimate or find the exact answer?

Definition:

Estimation: Finding an approximate answer by rounding numbers

Original Numbers

47 + 32

Rounded Numbers

50 + 30

Estimated Sum

Step 1: Round to the nearest ten

47 rounds to 50, 32 rounds to 30

Step 2: Add the rounded numbers

50 + 30 = 80

Step 3: Compare with exact answer

Exact: 47 + 32 = 79, Estimate: 80 (very close!)

About 80 students total

Final answer:

About 80 students total

Applied rules:

• Rounding: Round to the nearest ten for easier calculation

• Estimation: Use rounded numbers to get an approximate answer

• Verification: Check that estimate is reasonable compared to exact answer

3 Addition with Regrouping

Exercise 3

Tom collected 56 seashells. His sister collected 28 more. How many did they collect together?
Effective Question: Do I need to regroup in ones or tens?

Definition:

Regrouping: Moving values from one place value to another when adding or subtracting

Numbers to Add

56 + 28

Regrouping Needed

Yes (6+8=14)

Final Answer

Step 1: Identify the need for regrouping

Ones place: 6 + 8 = 14 (more than 10, so regroup)

Step 2: Perform the addition with regrouping

Ones: 6 + 8 = 14 → Write 4, carry 1 to tens

Tens: 5 + 2 + 1 (carried) = 8

Step 3: Combine the results

8 tens and 4 ones = 84

56 + 28 = 84

Final answer:

They collected 84 seashells together

Applied rules:

• Regrouping rule: When sum in a place value is 10 or more, carry to next higher place

• Place value: Keep digits in correct columns

• Addition algorithm: Add from right to left, carrying when needed

Solution: Exercises 4 to 5

4 Subtraction with Borrowing

Exercise 4

Lisa had 72 stickers. She gave 35 to her friends. How many does she have now?
Effective Question: Do I need to borrow from the tens place?

Definition:

Borrowing: Taking from a higher place value when the top number is smaller than the bottom number

Numbers to Subtract

72 - 35

Borrowing Needed

Yes (2 < 5)

Final Answer

Step 1: Identify the need for borrowing

Ones place: 2 < 5, so we need to borrow from tens

Step 2: Borrow from tens place

72 becomes 6 tens and 12 ones (72 = 60 + 12)

Step 3: Perform the subtraction

Ones: 12 - 5 = 7

Tens: 6 - 3 = 3

72 - 35 = 37

Final answer:

Lisa has 37 stickers left

Applied rules:

• Borrowing rule: When top digit is smaller, borrow from next higher place

• Value preservation: Borrowing doesn't change the overall value

• Subtraction algorithm: Subtract from right to left, borrowing when needed

5 Multi-Step Problem

Exercise 5

A store sold 45 books on Monday and 28 on Tuesday. They started with 120 books. How many are left?
Effective Question: What is the first step? Then what?

Definition:

Multi-step problem: A problem requiring more than one operation to solve

Books Sold Total

45 + 28 = 73

Books Remaining

120 - 73 = 47

Final Answer

Step 1: Find total books sold

Monday + Tuesday = 45 + 28 = 73 books

Step 2: Subtract from starting amount

Started with - Sold = 120 - 73 = 47 books left

Step 3: Verify the answer

47 + 73 = 120 ✓

47 books are left

Final answer:

There are 47 books left in the store

Applied rules:

• Order of operations: Solve problems step by step in logical order

• Verification: Check that the final answer makes sense

• Multi-step planning: Break complex problems into simpler parts

Rules and methods, laws,...

Effective Questions

Asking the Right Questions

Question Type 1

What is known?

Identify given information

Question Type 2

What is unknown?

Find what needs to be solved

Question Type 3

What operation?

Choose addition, subtraction, etc.

Question Type 4

Does it make sense?

Check if answer is reasonable

Question Type 5

How to solve?

Determine the strategy

Question Type 6

How to verify?

Check your work

Key Tip: Ask "Does this answer make sense?" after solving any problem.

Strategy: Break complex problems into smaller, manageable questions.

Effective Questions in Math Problem Solving

Problem Solving Process

Understanding Through Questions

Key definitions:

Effective Questions: Questions that guide mathematical thinking and problem-solving

Mathematical Reasoning: Logical thinking used to solve math problems

Estimation: Approximating answers to check reasonableness

Problem-solving methodology:

Understand: Read the problem carefully and identify what is asked
Plan: Ask effective questions to determine the solution path
Solve: Carry out the mathematical operations
Check: Verify the answer makes sense

Tip 1: Always ask "What do I know?" and "What do I need to find?"

Tip 2: Look for clue words like "total," "left," "more," "less" to determine operations.

Tip 3: Estimate first to predict a reasonable answer range.

Tip 4: Always check your work by asking "Does this answer make sense?"

Common errors: Misreading the question, choosing wrong operation, forgetting to check answer.

Success strategies: Ask effective questions, draw pictures when helpful, verify your work.

Essential questioning strategies:

• What information is given? Identify all numbers and facts

• What is the question asking? Understand what needs to be found

• What operation should I use? Addition, subtraction, multiplication, or division?

• Should I estimate first? To predict a reasonable answer

• How can I check my answer? Use inverse operations or estimation

Additional Exercises 6-8

6 Money Problem

Exercise 6

Emma had $5.25. She spent $2.75 on a book. How much money does she have left?
Effective Question: How do I handle dollars and cents?

Definition:

Money subtraction: Subtracting amounts with dollars and cents

Starting Amount

$5.25

Amount Spent

$2.75

Amount Left

$2.50

Step 1: Align decimal points

Line up the decimals when subtracting: $5.25 - $2.75

Step 2: Subtract cents first

25¢ - 75¢ requires borrowing: 125¢ - 75¢ = 50¢

Step 3: Subtract dollars

$4 - $2 = $2 (after borrowing)

$5.25 - $2.75 = $2.50

Final answer:

Emma has $2.50 left

7 Time Problem

Exercise 7

A movie starts at 2:45 PM and lasts for 1 hour and 30 minutes. What time does it end?
Effective Question: Should I add hours first or minutes first?

Definition:

Time calculation: Adding hours and minutes separately

Start Time

2:45 PM

Duration

1h 30m

End Time

4:15 PM

Step 1: Add the minutes first

45 min + 30 min = 75 min = 1 hour and 15 minutes

Step 2: Add the hours

2 PM + 1 hour (from duration) + 1 hour (from extra minutes) = 4 PM

Step 3: Combine hours and minutes

4 PM + 15 minutes = 4:15 PM

Movie ends at 4:15 PM

Final answer:

The movie ends at 4:15 PM

8 Comparison Problem

Exercise 8

Jake read 125 pages of a book. Emma read 98 pages of the same book. How many more pages did Jake read?
Effective Question: Am I finding a total or a difference?

Definition:

Comparison subtraction: Finding the difference between two quantities

Jake's Pages

125

Emma's Pages

Difference

Step 1: Identify the larger number

Jake read more pages (125) than Emma (98)

Step 2: Set up the subtraction

To find how many more: 125 - 98

Step 3: Solve the subtraction

125 - 98 = 27

Jake read 27 more pages

Final answer:

Jake read 27 more pages than Emma

Solution: Exercises 9 to 10

9 Growth Pattern

Exercise 9

A plant was 12 cm tall. It grew 8 cm in the first week and 5 cm in the second week. How tall is it now?
Effective Question: Do I add all the growth amounts together?

Definition:

Cumulative addition: Adding multiple amounts to an initial value

Initial Height

12 cm

Week 1 Growth

8 cm

Week 2 Growth

5 cm

Final Height

25 cm

Step 1: Identify all values to add

Starting height + Week 1 growth + Week 2 growth = 12 + 8 + 5

Step 2: Add the values sequentially

12 + 8 = 20, then 20 + 5 = 25

Step 3: State the final answer

The plant is now 25 cm tall

12 + 8 + 5 = 25 cm

Final answer:

The plant is now 25 cm tall

10 Multi-Step Word Problem

Exercise 10

A school has 245 students. 89 students went on a field trip. Then 35 more students joined the school. How many students are there now?
Effective Question: What happens first? Then what?

Definition:

Sequential operations: Performing multiple operations in the correct order

Initial Students

245

Students Gone

-89

Students Added

+35

Final Count

191

Step 1: Subtract students who left

245 - 89 = 156 students remaining

Step 2: Add new students

156 + 35 = 191 students now

Step 3: Verify the answer

245 - 89 + 35 = 191 ✓

245 - 89 + 35 = 191

Final answer:

There are now 191 students at the school

Visual Infographic: Using Effective Questions

Effective Questions Flowchart

Step 1: Understand the Problem

📖 Read carefully
❓ What do I know?
❓ What do I need to find?
🏷️ Circle important numbers

Step 2: Plan the Solution

🔍 Look for clue words
➕ ➖ Decide operation
🤔 Ask: "What strategy?"
📐 Draw a picture if helpful

Step 3: Solve

✏️ Show all work
👁️ Check for accuracy
⏱️ Take your time
📝 Write answer clearly

Step 4: Check Work

❓ Does answer make sense?
🔢 Estimate to verify
🔄 Use inverse operation
✅ Match units to question

Problem-Solving Cycle

Read

Think

Solve

Check

Effective Questions Mind Map

🧠 What do I know?
🎯 What do I need to find?
🤔 How can I solve this?
✅ Does my answer make sense?

Remember: Good questions lead to good solutions!

Questions & Answers

ThirdGradeTeacher

Elementary Educator

Question: How do I teach my students to ask effective questions when solving math problems? What are some specific strategies that work well for 3rd graders?

MathEducationExpert

PhD in Elementary Mathematics Education

Answer: Teaching effective questioning to 3rd graders requires simple, memorable strategies:

Create a "Question Wall" with prompts like "What do I know?" and "What do I need to find?"
Use the "READ" method: R - Read carefully, E - Examine the question, A - Ask yourself key questions, D - Do the math
Practice with sentence frames: "I need to find..." "I know that..." "This means I should..."
Model thinking aloud: "Hmm, the question asks for the total. That makes me think I need to add."

Make it visual with question cards, color-coding, or question wheels. Students remember better when questions are presented visually and practiced regularly.

ParentHelpingKid

Parent of 3rd Grader

Question: My child struggles with word problems. How can I help them identify which operation to use by asking the right questions?

StudentSupportCoach

Educational Specialist

Answer: Help your child develop a systematic approach with these key questions:

"Am I putting things together or taking them apart?" (Addition vs Subtraction)
"Are there equal groups?" (Multiplication)
"Am I sharing equally?" (Division)
"Will the answer be bigger or smaller than the starting number?"

Teach them to look for clue words: "total," "altogether," "sum" suggest addition; "difference," "how many more," "left" suggest subtraction. Practice these questions regularly until they become automatic.

Also encourage drawing pictures or using manipulatives to visualize the problem.

Solved Exercises on Using Effective Questions in Grade 3

Effective Questions Flowchart

Questions & Answers