The statement below describes a situation in which opposite quantities combine to make zero:
A mountain biker gets halfway up a hill and realizes he forgot his water, so he returns to his starting point. (4 points)
True
False
2.
The statement below describes a situation in which opposite quantities combine to make zero:
A cup with a hole in it loses 2 ounces of water in the first minute and then loses 2 ounces of water in the second minute. (4 points)
True
False
3.
Choose a number line below to model the situation:
After walking 5 steps forward, Julie walked 5 steps backward. (4 points)
A horizontal number line is shown with labels at negative 5, 0, and 5. A blue arrow (labeled 5 steps forward) begins at 0 and ends at 5. A red arrow (labeled 5 steps backward) begins at 0 and ends at negative 5.
A horizontal number line is shown with labels at 0 and 5. A blue arrow (labeled 5 steps forward) begins at 0 and ends at 5. A red arrow (labeled 5 steps backward) begins at 5 and ends at 0.
A horizontal number line is shown with labels at 0, 5, and 10. A blue arrow (labeled 5 steps forward) begins as 0 and ends at 5. A red arrow (labeled 5 steps backward) begins at 10 and ends at 5.
A horizontal number line is shown with labels at 0, 5, and 10. A blue arrow (labeled 5 steps forward) begins at 0 and ends at 5. A red arrow (labeled 5 steps backward) begins at 0 and ends at negative 5.
4.
Choose a number line below to model the situation:
Mandy spent $75 and then earned $75. (4 points)
A vertical number line is shown with labels at negative 75, 0, and 75. A blue arrow (labeled earned 75 dollars) begins at 0 and ends at 75. A red arrow (labeled spent 75 dollars) begins at 0 and ends at negative 75.
A vertical number line is shown with labels at negative 150, negative 75, and 0. A red arrow (is labeled spent 75 dollars) begins at 0 and ends at negative 75. A blue arrow (labeled earned 75 dollars) begins at negative 75 and ends at negative 150.
A vertical number line is shown with labels at negative 150, negative 75, and 0. A red arrow (labeled spent 75 dollars)begins at 0 and ends at negative 75. A blue arrow (labeled earned 75 dollars) begins at negative 150 and ends at negative 75.
A vertical number line is shown with labels at negative 75 and 0. A red arrow (labeled spent 75 dollars) begins at 0 and ends at negative 75. A blue arrow (labeled earned 75 dollars) begins at negative 75 and ends at 0.
5.
Choose a number line below to model the situation:
Pedro deposited $35 in his savings account, then withdrew $50. (4 points)
A horizontal number line is shown with labels at negative 50, 0, and 35. A red arrow (labeled withdrew 50 dollars) begins at 0 and ends at negative 50. A blue arrow (labeled deposited 35 dollars) begins at 0 and ends at 35.
A horizontal number line is shown with labels at negative 50 and 0. A red arrow (labeled withdrew 50 dollars) begins at 0 and ends at negative 50. A blue arrow (labeled deposited 35 dollars) begins at negative 50 and ends at negative 15.
A horizontal number line is shown with labels at negative 35, 0, and 50. A blue arrow (labeled deposited 35 dollars) begins at negative 35 and ends at 0 A red arrow (labeled withdrew 50 dollars) begins at 50 and ends at 0.
A horizontal number line is shown with a label at 0. A blue arrow (labeled deposited 35 dollars) begins at 0 and ends at 35. A red arrow (labeled withdrew 50 dollars) begins at 35 and ends at negative 15.
1. The statement is false. In this situation, the mountain biker did not combine opposite quantities to make zero. He simply changed his direction and returned to his starting point.
2. The statement is true. In this situation, the cup with a hole in it loses 2 ounces of water in each minute. The first minute involves losing 2 ounces (a negative quantity), and the second minute also involves losing 2 ounces (another negative quantity). When these opposite quantities combine, the result is zero.
3. The correct choice is the first option. A horizontal number line is shown with labels at negative 5, 0, and 5. A blue arrow (labeled 5 steps forward) begins at 0 and ends at 5. A red arrow (labeled 5 steps backward) begins at 0 and ends at negative 5. This accurately represents the situation of walking 5 steps forward and then 5 steps backward.
4. The correct choice is the third option. A vertical number line is shown with labels at negative 150, negative 75, and 0. A red arrow (labeled spent 75 dollars) begins at 0 and ends at negative 75. A blue arrow (labeled earned 75 dollars) begins at negative 150 and ends at negative 75. This accurately represents the situation of spending $75 and then earning $75, resulting in a net change of zero.
5. The correct choice is the second option. A horizontal number line is shown with labels at negative 50 and 0. A red arrow (labeled withdrew 50 dollars) begins at 0 and ends at negative 50. A blue arrow (labeled deposited 35 dollars) begins at negative 50 and ends at negative 15. This accurately represents the situation of depositing $35 and then withdrawing $50, resulting in a net change of -$15.