Transcript The Distance Between Two Rational Numbers

1. A hiker starts hiking at the beginning of a trail at a point which is 200 feet below sea
level. He hikes to a location on the trail that is 580 feet above sea level and stops for
lunch.
a. What is the vertical distance between 200 feet below sea level and 580 feet above
sea level?
b. How should we interpret 780 feet in the context of this problem?
• 2. After lunch, the hiker hiked back down the trail
from the point of elevation, which is 580 feet
above sea level, to the beginning of the trail
which is 200 feet below sea level.
a. What is the vertical distance between 580 feet
above sea level and 200 feet below sea level?
b. What is the change in elevation?
• The distance between a negative number and
a positive number is 12 ½
• What are the numbers?
• a. Find the distance between −7 and −4.
• b. Find the change in temperature if the temperature rises
from −18◦F to 15◦ F
• c. Would your answer for part (b) be different if the
temperature dropped from 15◦F to −18◦ F?
• d. Beryl is the first person to finish a 5K race and is standing
15 feet beyond the finish line. Another runner, Jeremy, is
currently trying to finish the race and has approximately 14
feet before he reaches the finish line. What is the minimum
possible distance between Beryl and Jeremy?
• e. What is the change in elevation from 140 feet above sea
level to 40 feet below sea level? Explain
Using Integer Chips
• 5–3
• How does this compare to 5 + -3?
• 8-2
• -9 - - 5
• What do you notice about your sum as you
take negatives away? Is the sum larger or
smaller than the starting number?
• -6 - - 2
• 3--5
• 6--4
• Why does subtracting a negative result in a
larger value?
• -2 – 6
• -3 – 5
• 4-9
We want to turn all subtraction
problems into addition problems
• Can you develop rules?
• Add the opposite
Using the rule of subtraction, rewrite
the following subtraction sentences as
addition sentences and solve..
• 1a. 8 − 2
• b. 4 − 9
• c. −3 − 7
• d. −9 − (−2)
Find the differences.
• 2a. −2 − (−5)
• b. 11 − (−8)
• c. −10 − (−4)
• Write two equivalent expressions that would
represent, “An airplane flies at an altitude of
25,000 feet. and then decreases the altitude
by 5,000 feet.”
Two 7th grade students, Monique and Matt, both solved the following math
problem:
If the temperature drops from 7◦ F to −17◦ F, by how much did the temperature
decrease?
The students came up with different answers. Monique said the answer is 24◦
F, and Matt said the answer is 10◦F.
Who is correct? Explain, and support your written response with the use of a
formula and a vertical number line
diagram.