Understanding Addition of Integers Lesson 3 for Grade 1

Complete lesson on addition of integers with visual models, step-by-step exercises, and interactive learning approaches.

Lesson 3 Solutions: Exercises 1 to 3
1 Positive + Positive
Exercise 1
Add 3 + 2 using positive objects to show your thinking.
Learning Objective:

Students will understand that adding positive numbers results in a larger positive number.

Definition:

Positive integer: A whole number greater than zero (1, 2, 3, ...). Adding positive numbers means combining more items.

3
3
3
First number: 3
+
2
2
Second number: 2
=
5
5
5
5
5
Total: 5
First Number
3
Operation
+
Second Number
2
Result
5
Step 1: Understand the problem

We need to add 3 and 2, which are both positive numbers

Step 2: Visualize with objects

Draw 3 circles and then 2 more circles

Step 3: Count all objects

Count: 1, 2, 3, 4, 5

3 + 2 = 5
Final answer:

3 + 2 = 5

Applied rules:

• Positive + Positive: Always results in a larger positive number

• Counting: Combine all objects to find the total

• Visual representation: Helps understand the concept

2 Positive + Zero
Exercise 2
What is 4 + 0? Use objects to show why adding zero doesn't change the number.
Learning Objective:

Students will understand the identity property of addition (adding zero).

Definition:

Identity property: Adding zero to any number gives the same number. Zero is called the "identity element" for addition.

4
4
4
4
First number: 4
+
Zero: no objects
=
4
4
4
4
Result: 4
Step 1: Start with 4 objects

○ ○ ○ ○ (4 objects)

Step 2: Add 0 objects

No additional objects are added

Step 3: Count the result

Still have 4 objects

4 + 0 = 4
Final answer:

4 + 0 = 4

Applied rules:

• Identity property: n + 0 = n

• Zero concept: Adding nothing doesn't change the amount

• Conservation: The original number is preserved

3 Commutative Property
Exercise 3
Show that 2 + 3 = 3 + 2 using objects. Are the answers the same?
Learning Objective:

Students will understand that the order of numbers doesn't change the sum (commutative property).

Definition:

Commutative property: The order of numbers in addition doesn't change the sum. a + b = b + a

2
2
2
+
3
3
3
3
=
5
5
5
5
5
5
3
3
3
3
+
2
2
2
=
5
5
5
5
5
5
Order 1
2 + 3 = 5
Order 2
3 + 2 = 5
Step 1: Add 2 + 3

Start with 2 objects, add 3 more

Step 2: Add 3 + 2

Start with 3 objects, add 2 more

Step 3: Compare results

Both equal 5, so order doesn't matter

2 + 3 = 3 + 2 = 5
Final answer:

Yes, both equations equal 5. The order doesn't change the sum.

Applied rules:

• Commutative property: a + b = b + a

• Order independence: Numbers can be added in any order

• Consistent result: The sum remains the same

Lesson 3 Solutions: Exercises 4 to 5
4 Counting Strategy
Exercise 4
Use the counting-on strategy to solve 5 + 3. Start with 5 and count 3 more.
Learning Objective:

Students will use the counting-on strategy to add efficiently.

Definition:

Counting-on strategy: Starting with the first number and counting forward the number of steps equal to the second number.

1
2
3
4
5
6
7
8
Step 1: Start at the first number

Begin counting at 5

Step 2: Count forward

Count 3 more numbers: 6, 7, 8

Step 3: Find the result

After counting 3 from 5, we reach 8

5 + 3 = 8
Final answer:

5 + 3 = 8

Applied rules:

• Counting-on: More efficient than counting all objects

• Sequential counting: Numbers follow in order

• Number line visualization: Shows the process visually

5 Making 10
Exercise 5
What number do you add to 7 to make 10? Complete: 7 + ___ = 10
Learning Objective:

Students will find the missing addend to make 10, a key benchmark number.

Definition:

Missing addend: Finding the unknown number that completes an addition equation.

7
7
7
7
7
7
7
7 objects
+
?
?
?
? more objects
=
10
10
10
10
10
10
10
10
10
10
10 total
Step 1: Start with 7

We have 7 objects

Step 2: Need to reach 10

Count from 7 to 10: 8, 9, 10

Step 3: Count the difference

From 7 to 10 is 3 more

Step 4: Verify the answer

7 + 3 = 10 ✓

7 + 3 = 10
Final answer:

7 + 3 = 10

Applied rules:

• Missing addend: Find what number completes the equation

• Counting strategy: Count from known number to target

• Benchmark numbers: 10 is an important reference point

Integer Addition Concepts - Lesson 3
+
Positive + Positive
= Positive
0
Identity Property
n + 0 = n
🔄
Commutative
a + b = b + a
🎯
Making 10
Benchmark
a + b = b + a
Commutative Property
n + 0 = n
Identity Property
Property 1
Commutative
Order doesn't matter
Property 2
Identity
Adding zero doesn't change the number
Property 3
Associative
Grouping doesn't matter
Key Concept: Addition has special properties that make it easier to use.
Memory Aid: "Switch the order, still the same!" for commutative property.
Comprehensive Addition Summary - Lesson 3
Key Concepts & Definitions
  • Integer
    A whole number that can be positive, negative, or zero (...-3, -2, -1, 0, 1, 2, 3...)
  • Commutative Property
    The order of numbers in addition doesn't change the sum (a + b = b + a)
  • Identity Property
    Adding zero to any number gives the same number (n + 0 = n)
  • Counting-On Strategy
    Starting with the first number and counting forward the second number
  • Missing Addend
    Finding the unknown number that completes an addition equation
Core Rules & Properties
Commutative Property: a + b = b + a
The order of numbers doesn't change the sum
Example: 2 + 3 = 3 + 2 = 5
Identity Property: n + 0 = n
Adding zero to any number gives the same number
Example: 5 + 0 = 5, 0 + 7 = 7
Associative Property: (a + b) + c = a + (b + c)
Grouping doesn't affect the sum
Example: (2 + 3) + 4 = 2 + (3 + 4) = 9
Step-by-Step Methods
Method 1: Counting-On Strategy
1. Start with the first number
2. Count forward the number of steps equal to the second number
3. The number you land on is the answer
Method 2: Finding Missing Addends
1. Identify the known number and the target sum
2. Count from the known number to the target
3. The number of steps is the missing addend
Method 3: Using Properties
1. Recognize when you can use the commutative property
2. Rearrange numbers to make the problem easier
3. Solve using the easier arrangement
Examples (Simple → Advanced)
Simple: 1 + 2 = 3
Basic combination of small numbers
Moderate: 4 + 3 = 3 + 4 = 7
Using commutative property
Advanced: 6 + 4 = 10
Recognizing benchmark number combinations
Complex: 8 + 2 = 2 + 8 = 10
Using commutative property with benchmark numbers
Tips, Tricks & Common Pitfalls
Tip 1: Use the commutative property to make addition easier (start with the larger number).
Tip 2: Remember that adding zero never changes the original number.
Pitfall 1: Forgetting that order doesn't matter in addition.
Pitfall 2: Not recognizing when adding zero leaves the number unchanged.
Key Notes for Memorization
  • Memory Phrase
    "Switch the order, still the same!" for commutative property.
  • Visual Strategy
    Always draw objects or use manipulatives when starting out.
  • Practice Pattern
    Focus on making 10 combinations (1+9, 2+8, 3+7, 4+6, 5+5).
  • Check Method
    Always verify your answer by using a different method.

Questions & Answers

Question: How do I explain the commutative property of addition to first graders?

Answer: Explain the commutative property using concrete examples:

  • Object demonstration: "If you have 2 red blocks and 3 blue blocks, you have 5 blocks. If you have 3 blue blocks and 2 red blocks, you still have 5 blocks!"
  • Physical activity: Have students hold 2 pencils in one hand and 3 in the other, then switch hands - they still have 5 pencils total
  • Visual models: Draw the same groups in different orders but show the total remains the same

Use the phrase "switch the order, still the same" to help them remember this important property.

Question: My child struggles with finding missing addends. What strategies work best?

Answer: Effective strategies for missing addends include:

  • Counting strategy: Start with the known number and count up to the target
  • Using manipulatives: Give the child objects to physically add until reaching the target
  • Number line: Show the jump from the known number to the target
  • Fact families: Connect addition and subtraction facts (if 7 + 3 = 10, then 10 - 7 = 3)
  • Visual models: Draw the known part and see what's needed to complete the whole

Start with benchmark numbers like 10, as these are easier for children to visualize.

Question: What's the importance of learning the identity property in first grade?

Answer: The identity property is important because:

  • Foundation for algebra: It establishes that zero is the additive identity
  • Computational efficiency: Children learn they can ignore zeros in addition
  • Conceptual understanding: Reinforces that adding nothing doesn't change the original amount
  • Problem-solving: Helps with missing addend problems involving zero
  • Future learning: Essential for understanding place value and regrouping

This property also builds confidence as children see that some addition problems are very easy to solve.