Intro to Solutions | Solved Exercises

Solution: Exercises 1 to 3

1 Addition solution

Exercise 1

If you have 3 apples 🍎🍎🍎 and get 2 more apples 🍎🍎, how many apples do you have? Show how you found the solution.

Definition:

Solution: The answer to a math problem that shows how you solved it

Addition: Combining groups to find the total amount

🍎

First, I counted the starting apples: 3 apples

Then, I counted the apples I got: 2 more apples

I combined both groups: 3 + 2 = 5

I counted all apples to check: 1, 2, 3, 4, 5

Step 1: Identify the problem

I have 3 apples and get 2 more apples

Step 2: Choose the operation

This is addition because I'm getting more apples

Step 3: Perform the calculation

3 + 2 = 5

Step 4: State the solution

I have 5 apples altogether

Solution: 3 + 2 = 5 apples

Final answer:

I have 5 apples. I solved this by adding 3 + 2 = 5.

Applied rules:

• Process: Identify → Choose → Calculate → State

• Operation: Use addition when getting more

• Verification: Count to check the answer

2 Subtraction solution

Exercise 2

You have 7 cookies 🍪🍪🍪🍪🍪🍪🍪. You eat 3 cookies. How many cookies are left? Show your solution process.

Definition:

Subtraction: Taking away part of a group to find what remains

Solution process: The steps you take to solve a problem

🍪

❌

🍪

I started with 7 cookies

I ate 3 cookies (took them away)

I subtracted: 7 - 3 = 4

I have 4 cookies left

Step 1: Identify the original amount

I started with 7 cookies

Step 2: Identify what's taken away

I ate 3 cookies

Step 3: Choose the operation

This is subtraction because I'm taking away

Step 4: Perform the calculation

7 - 3 = 4

Solution: 7 - 3 = 4 cookies

Final answer:

I have 4 cookies left. I solved this by subtracting 7 - 3 = 4.

Applied rules:

• Process: Original → Taken away → Operation → Result

• Operation: Use subtraction when taking away

• Verification: 4 + 3 = 7, so the answer is correct

3 Comparison solution

Exercise 3

Sarah has 6 stickers, Tom has 4 stickers. Who has more stickers? Show how you solved this.

Definition:

Comparison: Looking at two amounts to see which is greater

Greater than (>): Symbol meaning "more than"

Sarah

⭐

6 stickers

Tom

⭐

4 stickers

I counted Sarah's stickers: 6

I counted Tom's stickers: 4

I compared: 6 is greater than 4

Sarah has more stickers

Step 1: Count Sarah's stickers

Sarah has 6 stickers

Step 2: Count Tom's stickers

Tom has 4 stickers

Step 3: Compare the amounts

6 is greater than 4

Step 4: State who has more

Sarah has more stickers

Solution: 6 > 4, Sarah has more

Final answer:

Sarah has more stickers because 6 > 4.

Applied rules:

• Process: Count → Compare → State

• Comparison: Use > for "greater than"

• Verification: 6 is indeed more than 4

Solution Methods and Strategies

\text{Solution} = \text{Problem} + \text{Process} + \text{Answer}

Solution Formula

Read the problem carefully

Identify what you need to find

Choose the right operation

Solve the problem

Check your answer

Key definitions:

Solution: The answer to a math problem that includes the steps to solve it.

Problem: A mathematical question that needs to be solved.

Process: The steps you take to find the answer.

Verification: Checking that your answer is correct.

Operation: Addition, subtraction, or other mathematical actions.

Solution method:

Read: Understand what the problem is asking
Identify: Determine what information is given
Choose: Select the correct operation
Solve: Perform the calculation
Check: Verify your answer makes sense

Tip 1: Always read the problem carefully before solving.

Tip 2: Draw pictures to help visualize the problem.

Tip 3: Count objects to verify your answer.

Tip 4: Ask yourself if your answer makes sense.

Solution: Exercises 4 to 5

4 Multi-step solution

Exercise 4

You have 5 toys. Your mom gives you 2 more toys. Then you give 1 toy to your friend. How many toys do you have now?

Definition:

Multi-step problem: A problem that requires more than one calculation

Sequential operations: Doing operations in the correct order

Start: 5 toys

🧸

Get 2 more

🧸

Give 1 away

❌

Final: 6 toys

🧸

Start with 5 toys

Add 2 more: 5 + 2 = 7

Subtract 1: 7 - 1 = 6

Final answer: 6 toys

Step 1: Start with original amount

I have 5 toys

Step 2: Add the new toys

5 + 2 = 7 toys

Step 3: Subtract the toy given away

7 - 1 = 6 toys

Step 4: State the final answer

I have 6 toys now

Solution: 5 + 2 - 1 = 6 toys

Final answer:

I have 6 toys now. I solved this by doing 5 + 2 - 1 = 6.

Applied rules:

• Order: Work from left to right

• Multi-step: Solve one operation at a time

• Verification: Check each step

5 Verification solution

Exercise 5

You solved 4 + 3 = 7. How can you check if your answer is correct? Show your verification method.

Definition:

Verification: Checking that your answer is correct

Reverse operation: Using the opposite operation to check

4 + 3 = 7

🔴

My answer was 4 + 3 = 7

To check, I subtract: 7 - 3 = 4

Or I subtract: 7 - 4 = 3

Since I get back to the original numbers, my answer is correct

Step 1: Start with your answer

4 + 3 = 7

Step 2: Use reverse operation

Take away one of the original numbers: 7 - 3 = 4

Step 3: Check if you get the other number

Yes, 7 - 3 = 4, which was one of the original numbers

Step 4: Verify with the other number

Also, 7 - 4 = 3, which was the other original number

Verification: 7 - 3 = 4 ✓
7 - 4 = 3 ✓

Final answer:

To check if 4 + 3 = 7 is correct, I subtract: 7 - 3 = 4 and 7 - 4 = 3. Since I get back the original numbers, my answer is correct.

Applied rules:

• Verification: Use the reverse operation to check

• Subtraction: Is the reverse of addition

• Validation: If you get back to original numbers, answer is correct

Complete Summary: Intro to Solutions

Key Concepts and Definitions

Solution: The answer to a math problem that includes the steps to solve it.

Problem: A mathematical question that needs to be solved.

Process: The steps you take to find the answer.

Verification: Checking that your answer is correct.

Operation: Addition, subtraction, or other mathematical actions.

Multi-step problem: A problem that requires more than one calculation.

Reverse operation: Using the opposite operation to check answers.

Sequential operations: Doing operations in the correct order.

Core Rules and Principles

Rule 1: Always read the problem carefully before solving.

Rule 2: Identify what operation to use (addition, subtraction).

Rule 3: Show your work so others can follow your thinking.

Rule 4: Verify your answer by checking if it makes sense.

Rule 5: In multi-step problems, solve one step at a time.

Rule 6: Use reverse operations to verify your solutions.

Step-by-Step Methods

Method 1 - Single Operation Solution:

Read the problem carefully
Identify the numbers involved
Choose the correct operation
Perform the calculation
State the final answer

Method 2 - Multi-Step Solution:

Identify each step in the problem
Solve the first operation
Use the result for the next operation
Continue until all steps are completed
State the final answer

Method 3 - Verification:

Take your final answer
Use the reverse operation
Check if you get back to original numbers
If yes, your answer is correct
If no, review your work

Examples: Simple to Advanced

Simple Example: 2 + 3 = 5 (single operation)

Moderate Example: 6 - 2 = 4 (single operation with subtraction)

Advanced Example: 5 + 3 - 2 = 6 (multi-step operation)

Complex Example: 4 + 2 = 6, verify with 6 - 2 = 4 (verification)

Application Example: Word problems requiring multiple steps and verification

Tips, Tricks, and Common Pitfalls

Tips:

Always read the entire problem before starting
Draw pictures to help visualize the problem
Show your work step by step
Verify your answer by checking it
Ask yourself if the answer makes sense
Practice regularly to improve skills

Common Mistakes:

Rushing through the problem without reading carefully
Choosing the wrong operation
Not showing work clearly
Forgetting to verify the answer
Making calculation errors

Key Notes for Memorization

Memory Aid: "R.I.C.H." - Read, Identify, Calculate, Verify

Formula: Solution = Problem + Process + Answer

Strategy: Always follow the solution method systematically

Principle: Verification ensures accuracy in mathematical solutions

Goal: Develop logical thinking and problem-solving skills

Questions & Answers

StudentSolver

Elementary Level

Question: Why do I need to show my work? Isn't the answer enough?

TeachingExpert

Educational Specialist - Elementary Mathematics

Answer: Showing your work is very important for several reasons:

Thinking process: It shows how you arrived at your answer
Checking: You can find mistakes if something goes wrong
Learning: It helps you remember how to solve similar problems
Communication: Others can follow your thinking
Building skills: It develops good problem-solving habits

Even if you know the answer quickly, showing work builds strong mathematical foundations!

ParentHelper

Home Educator

Question: My child often makes calculation errors. How can I help them verify their answers?

MathMentor

Certified Elementary Mathematics Teacher

Answer: Here are effective verification strategies:

Counting: Have them count objects to check addition/subtraction
Reverse operation: For 5 + 3 = 8, check with 8 - 3 = 5
Estimation: Ask if the answer seems reasonable
Double-checking: Repeat the calculation
Visual aids: Use fingers or manipulatives to verify

Practice verification regularly - it builds accuracy and confidence!

QuestionSolver

Grade 1 Student

Question: Sometimes I don't know if I should add or subtract. How do I decide?

EducationPro

Early Childhood Education Specialist

Answer: Look for clue words in the problem:

Addition clues: "more," "get," "altogether," "total," "in all"
Subtraction clues: "eat," "take away," "left," "remain," "less"
Visualize: Picture what's happening in your mind
Ask: Am I getting more or am I taking away?

Practice identifying these clue words - it will help you choose the right operation!

Solved Exercises on Intro to Solutions in Grade 1

Questions & Answers