PhET: Integer Operations on a Number Line

Real-Life Integer Situations

Display:

Situation                                  Integer
Deposit $20                                 +20
Withdraw $15                               -15
Rise 8 floors                                 +8
Descend 3 floors                           -3

Ask:

• What do positive numbers represent?
• What do negative numbers represent?
• If you start at 0 and move +5, where do you end?
• If you then move -2, where are you now?

Co-Use Activity

Partners discuss the scenarios and create one additional real-life example involving positive and negative numbers.

Integers as Movement

Draw a number line.

Model:

• Start at 0.
• Move right 4 spaces.
• Move left 2 spaces.

Ask:

• What operation is represented?
• Where do you end?

Introduce:

• Positive movement = right
• Negative movement = left
• Addition = move according to the sign
• Subtraction = remove or reverse movement

Co-Use Activity

Student A chooses an integer.

Student B demonstrates where it belongs on the number line.

Switch roles.

Exploring the PhET Simulation

Students open the Number Line: Operations simulation.

Teacher demonstrates:

Example 1

Start at 3

Add 4

Observe movement:

3 + 4 = 7

Example 2

Start at 5

Add -3

Observe movement:

5 + (-3) = 2

Example 3

Start at -2

Add 5

Observe movement:

-2 + 5 = 3

Discuss:

• What direction did the arrow move?
• How does the sign affect movement?

Co-Use Activity
Partners predict the answer before using the simulation.

Integer Investigation

Students work in pairs.

Activity 1: Predict and Test

Complete the chart:

Expression                           Prediction                         Simulation Result
4 + 3

5 + (-2)

-3 + 6

-4 + (-3)

Discuss patterns.

 
Activity 2: Subtraction Exploration

Use the simulation to solve:

1. 8 - 3
2. 4 - 7
3. -2 - 4
4. -5 - (-3)

Record:

• Starting point
• Movement
• Ending point

 
Activity 3: Create a Challenge

Each pair creates two integer problems.

Another pair solves them using the simulation.

Team Discussion

What patterns did you notice?

Students should discover:

• Adding a positive moves right.
• Adding a negative moves left.
• Subtracting a positive moves left.
• Subtracting a negative moves right.

Exit Ticket

Solve and explain:

1. -4 + 7
2. 6 + (-9)
3. -2 - 5
4. -3 - (-4)

Short Response:

How does a number line help you understand integer operations?

Success Criteria

Students can:

✓ Add integers.

✓ Subtract integers.

✓ Explain movement on a number line.

✓ Use the simulation to justify answers

Co-Use Activity

Partners compare solutions before submitting individual answers.

Real-World Integer Stories

Students choose one situation:

Banking

You deposit $30 and then withdraw $45.

What is your balance change?

Temperature

The temperature is 2°F and drops 7 degrees.

What is the new temperature?

Elevator

An elevator starts on Floor 3 and goes down 8 floors.

Where does it end?

Co-Use Activity

Partners create a real-world scenario involving integer addition or subtraction and exchange it with another pair.