Making Sense of Problems & Persevering in Solving Them for 1st Grade

Learn how to make sense of math problems and persevere through challenges with visual aids, step-by-step instructions, and practice exercises.

Problem-Solving Exercises & Solutions
1 Understanding Word Problems
Exercise 1
Tom has 5 apples. His mom gives him 3 more apples. How many apples does Tom have now?
Definition:

Making sense of problems: Understanding what the problem is asking before solving

Method:
  1. Read the problem carefully
  2. Identify what you know
  3. Determine what you need to find
  4. Choose the operation
  5. Solve step by step
Problem Analysis
What we know: Tom has 5 apples, mom gives 3 more
What we need: Total number of apples
Operation: Addition (combining amounts)
Solution: 5 + 3 = 8
5
+
3
=
8
1
Read problem
2
Identify parts
3
Choose operation
4
Solve
Step 1: Read carefully

Tom has 5 apples. His mom gives him 3 more apples.

Step 2: Identify information

We know: 5 apples + 3 more apples

Step 3: Determine operation

Getting more means adding: 5 + 3

Step 4: Solve

5 + 3 = 8

Tom has 8 apples
Final answer:

Tom has 8 apples in total.

Applied rules:

• Comprehension: Understand the problem before solving

• Analysis: Identify known and unknown information

• Operation selection: Choose the right operation

• Perseverance: Work through the problem step by step

2 Persevering Through Challenges
Exercise 2
Sarah had 10 cookies. She ate 4 cookies. How many cookies does she have left?
Definition:

Perseverance: Continuing to work on a problem even when it seems difficult

Problem Analysis
What we know: Sarah started with 10 cookies, ate 4
What we need: How many are left
Operation: Subtraction (taking away)
Solution: 10 - 4 = 6
10
-
4
=
6
Step 1: Read carefully

Sarah had 10 cookies. She ate 4 cookies.

Step 2: Identify information

We know: 10 cookies - 4 eaten

Step 3: Determine operation

Eating means taking away: 10 - 4

Step 4: Solve

10 - 4 = 6

1
Read problem
2
Identify parts
3
Choose operation
4
Solve
Sarah has 6 cookies left
Final answer:

Sarah has 6 cookies left.

Applied rules:

• Comprehension: Understand the problem before solving

• Analysis: Identify known and unknown information

• Operation selection: Choose the right operation

• Perseverance: Work through the problem step by step

3 Multi-Step Problem Solving
Exercise 3
There were 8 birds on a tree. 3 flew away. Then 2 more birds came. How many birds are on the tree now?
Definition:

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

Problem Analysis
What happens: Start with 8, take away 3, then add 2
Operations: Subtraction first, then addition
Solution: 8 - 3 + 2 = 7
8
-
3
+
2
=
7
Step 1: Read carefully

There were 8 birds on a tree. 3 flew away. Then 2 more birds came.

Step 2: Identify information

Start: 8 birds, subtract 3, then add 2

Step 3: Plan operations

First: 8 - 3 = 5, then: 5 + 2 = 7

Step 4: Solve

8 - 3 + 2 = 7

1
Read problem
2
Identify steps
3
Plan solution
4
Solve
7 birds on the tree
Final answer:

There are 7 birds on the tree now.

Applied rules:

• Comprehension: Understand the sequence of events

• Analysis: Break problem into smaller steps

• Operation sequence: Perform operations in the right order

• Perseverance: Work through each step methodically

Problem-Solving Strategy Overview
Step 1: Understand the Problem
Read carefully and identify what information is given and what you need to find
Step 2: Plan Your Solution
Decide what operations to use and in what order
Step 3: Execute Your Plan
Carry out the calculations step by step
Step 4: Check Your Answer
Verify that your answer makes sense and solves the problem
🤔
Understand
What do I know? What do I need?
📋
Plan
How will I solve this?
⚙️
Execute
Do the calculations
✅
Check
Does this make sense?
8
-
3
+
2
=
7
Key benefits:

Problem solving: Develops critical thinking skills

Perseverance: Builds resilience and determination

Confidence: Increases mathematical self-assurance

When to persevere:
  1. When confused: Take a deep breath and read again
  2. When stuck: Try a different approach
  3. When frustrated: Ask for help or take a break
  4. When uncertain: Check your work carefully
Tip 1: Draw pictures or use manipulatives to visualize the problem.
Tip 2: Break complex problems into smaller parts.
Tip 3: Always check if your answer makes sense.
Problem-Solving Concepts & Properties
Problem Solving = Understanding + Planning + Execution + Verification
Mathematical Reasoning Process
Definition:

Problem solving: The process of understanding and solving mathematical problems systematically

Comprehension: Understanding what the problem is asking.
Analysis: Identifying known and unknown information.
Perseverance: Continuing despite challenges.
Verification: Checking the reasonableness of answers.
Teaching strategies:
  1. Modeling: Demonstrate problem-solving steps
  2. Guided practice: Work through examples together
  3. Independent practice: Let students solve problems alone
  4. Reflection: Discuss problem-solving approaches
Key principles:

• Understanding: Always comprehend the problem first

• Planning: Think about how to approach the solution

• Execution: Carry out calculations carefully

• Verification: Always check your work

Common mistake: Rushing to calculate without understanding.
Practice tip: Use manipulatives to visualize problems.
Practice Activities & Tips
Practice Builds Fluency!
Problem-Solving Skill Development
Practice activities:

Word problems: Solve real-life scenarios

Picture problems: Interpret visual information

Multi-step problems: Work through complex scenarios

Learning progression:
  1. Simple problems: One-step addition/subtraction
  2. Two-step problems: Problems requiring multiple operations
  3. Complex problems: Multi-step with extra information
  4. Verification: Check reasonableness of answers
Tip 1: Practice 5-10 minutes daily for consistent improvement.
Tip 2: Use manipulatives to visualize problems.
Tip 3: Always verify your answers make sense.
Tip 4: Ask yourself: "Does this answer make sense?"
Assessment: Students should solve problems systematically.
Connection: Problem-solving supports all mathematical operations.
Common core alignment:

• 1.OA.1: Use addition and subtraction within 20 to solve word problems.

• 1.OA.2: Solve word problems that call for addition of three whole numbers.

• MP.1: Make sense of problems and persevere in solving them.

Detailed Summary & Key Takeaways
Key Concepts:

Problem comprehension: Understanding what the problem is asking

Information analysis: Identifying known and unknown information

Operation selection: Choosing the right mathematical operation

Verification: Checking if answers make sense

Core Rules & Principles:
  1. Understand first: Read and comprehend the problem completely
  2. Plan next: Think about how to approach the solution
  3. Solve systematically: Carry out calculations step by step
  4. Verify: Always check if the answer is reasonable
Examples (simple → advanced): Start with 5+3=?, then "Sarah has 5 apples...", then multi-step problems
Memorization tip: Use the U-P-E-V method (Understand, Plan, Execute, Verify)
Common pitfall: Calculating without understanding the problem
Application: Problem-solving skills support all mathematical operations
Long-term benefits:

• Thinking skills: Develops logical reasoning abilities

• Confidence: Increases mathematical self-assurance

• Perseverance: Builds resilience when facing challenges

• Foundation: Supports all future math learning

Questions & Answers

Question: How can I help my child develop problem-solving skills at home?

Answer: Here are effective home practice strategies:

  • Real-world problems: Use everyday situations for practice
  • Encourage thinking: Ask "What do you think?" before calculating
  • Model problem-solving: Show your own thinking process
  • Be patient: Allow time for children to work through problems

Encourage your child to explain their thinking process.

Question: Why is perseverance important in math problem solving?

Answer: Perseverance is important because:

  • Builds resilience: Students learn to keep trying
  • Develops confidence: Success comes from persistence
  • Encourages growth: Mistakes become learning opportunities
  • Supports independence: Students learn to solve problems alone

Perseverance is a key mathematical practice standard.

Question: What if a student gives up easily when facing challenging problems?

Answer: For students who give up easily:

  • Break problems down: Make them more manageable
  • Provide scaffolding: Offer support as needed
  • Celebrate effort: Praise persistence over perfection
  • Use positive language: Focus on "not yet" instead of "can't"

Building confidence through small successes helps develop perseverance.