NS.7c - Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.
WARM-UP
MINI LESSON - INDEPENDENT WORK/SHARE OUT/DISCUSSION
1) On a number line, how far is each of the following numbers from zero?
(a) 45
(b) −7
(c) x
(d) x+2
(e) 0
2) Mr. Pole is leading a submarine expedition to photograph the wreckage of the Titanic. When the submarine reaches the wreckage, Mr. Pole's elevation dial reads "-800 meters." Write an absolute value equation to represent how far Mr. Pole is below sea level.
3) Roger and Sal are roommates in Washington DC. Roger pays rent and utilities and emails Sal each month with a bill. In July, Sal gets an email from Roger with a list of charges for the month. At the bottom, it says, "Total: -724." Write an absolute value equation to represent how much Sal owes Roger.
4) Write two equations without absolute value symbols that, in combination, are equivalent to
|3x+5|=12. Solve each of these two equations.
(a) 45
(b) −7
(c) x
(d) x+2
(e) 0
2) Mr. Pole is leading a submarine expedition to photograph the wreckage of the Titanic. When the submarine reaches the wreckage, Mr. Pole's elevation dial reads "-800 meters." Write an absolute value equation to represent how far Mr. Pole is below sea level.
3) Roger and Sal are roommates in Washington DC. Roger pays rent and utilities and emails Sal each month with a bill. In July, Sal gets an email from Roger with a list of charges for the month. At the bottom, it says, "Total: -724." Write an absolute value equation to represent how much Sal owes Roger.
4) Write two equations without absolute value symbols that, in combination, are equivalent to
|3x+5|=12. Solve each of these two equations.
TEAM CHALLENGE
Jumping Flea
A flea is jumping around on the number line.
a. If he starts at 1 and jumps 3 units to the right, then where is he on the number line? How far away from 0 is he?
b. If he starts at 1 and jumps 3 units to the left, then where is he on the number line? How far away from 0 is he?
c. If the flea starts at 0 and jumps 5 units away, where might he have landed?
d. If the flea jumps 2 units and lands at 0, where might he have started?
e. The absolute value of a number is the distance it is from 0. The absolute value of the flea’s location is 4 and he is to the left of 0. Where is he on the number line?
A flea is jumping around on the number line.
a. If he starts at 1 and jumps 3 units to the right, then where is he on the number line? How far away from 0 is he?
b. If he starts at 1 and jumps 3 units to the left, then where is he on the number line? How far away from 0 is he?
c. If the flea starts at 0 and jumps 5 units away, where might he have landed?
d. If the flea jumps 2 units and lands at 0, where might he have started?
e. The absolute value of a number is the distance it is from 0. The absolute value of the flea’s location is 4 and he is to the left of 0. Where is he on the number line?