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8-1 Objective: Students will be able to represent situations with integers Positive Numbers: Any numbers to the right of zero Negative Number: Any numbers to the left of zero Zero: The number zero is neither positive nor negative

Integers and Opposites Opposites: Two numbers that are the same distance from 0 on a number line but in opposite directions. Integers: The set of positive whole numbers, their opposites and zero

Integers and Opposites B C What are the opposites of points A, B and C?

5 degrees below zero 2) a gain of 3 yards 3) A loss of 6 dollars 4) 1 step backwards

Example Mt. Everest's elevation is 29,028 above sea level and the dead sea is 1,312 feet below sea level. Express each elevation as an integer.

Examples 1)What integer does point A represent? -What is the opposite of point A?

Example 9. Which situations could be represented by –104? Check all that apply. ❑ A. skiing 104 ft down a mountain ❑ B. a bird flying 104 ft above the ground ❑ C. spending $104 on vacation ❑ D. earning $104 at your summer job

Example 3) Which situation can the integer –10 represent? ❍ A. spending 10 dollars ❍ B. walking up 10 stairs ❍ C. gaining 10 yards ❍ D. earning 10 dollars 4) A point on the side of a mountain is 7,039 m above sea level. Express this elevation as an integer.

Example You and a friend are hiking up a mountain. At one point your friend is 54 ft higher up than you are. What integer represents your elevation relative to your friend’s? Your friend’s elevation relative to yours?

Example An airplane takes off from an airport that is 176 f above sea level. The airplane flies at 30000 ft. To avoid a storm, the airplane goes up 35,000 ft. Immediately after passing the storm, the airplane returns to its original altitude. Finally, the airplane lands at an airport that is 1920 ft above sea level. What integer represents the airplane’s change in altitude to avoid the storm? Immediately after passing the storm?

Example problems 1) Two people are scuba diving. One diver is 36 ft below the surface. The other is 44 ft below the surface. a) What integers represent where the divers are with respect to the surface? b) Which diver is deeper? 2) A contestant in a game show has 9,000 points. The contestant answers the next question incorrectly and loses 750 points. Does the word “lose” suggest a positive integer or a negative integer? b) What integer represents a loss of 750 points? 3)An airplane traveling at an altitude of 6,400 m changes its altitude by 1,400 m. Which situation describes the change in altitude? ❍ A. The altitude is 1,400 m higher after the change. ❍ B. The altitude is 1,400 m lower after the change. ❍ C. The altitude is 6,400 m higher after the change. ❍ D. The altitude is 6,400 m lower after the change.