In this lesson:
By the end of this lesson, you should be able to:
A bank account tells a clear story about opposites:
Football: gain 8 yards, lose 8 yards → net gain: 0.
Every rational number has an additive inverse :
What is the additive inverse of each?
Verify: Sum each pair — does it equal ?
Think through each one before the next slide.
Additive inverses exist for every rational number:
means "opposite of " — if , then
To compute : start at , then move units.
The sign gives direction. The absolute value gives distance.
Start at , move 4 units right — land at
Start at , move 5 units left — land at
Start at , move 3 units left — land at
Use the number line model to predict the result:
Reason through the movement before computing numerically.
Same signs → that sign, larger absolute value:
Different signs → sign of the larger :
A scuba diver at ft ascends ft.
Start at , move 20 units up on a vertical number line — land at .
She is 5 feet above sea level.
Temperature at noon: . Drops another by midnight.
Start at , move 8 units left — land at .
Midnight temperature:
Verify using the number line model:
Start at , move 6 units right — land at exactly .
Additive inverses: equal distance, opposite direction → always land at .
Compute each sum using the number line model.
For each: identify start, direction, distance, and landing point.
Try all three before the next slide.
1, 2: different signs → larger wins. 3: same sign → more negative.
In Lesson 2, we extend the number line model to subtraction: