Vivian is at a fair in Coachella Valley, California. Much of the valley lies below sea level. Vivian has brought along an altimeter to measure her elevation at different places in the valley. Vivian’s first ride was on the Ferris wheel. When she sat on the wheel at its lowest point, her altimeter read -9.6 feet. When she reached the top of the wheel, her altimeter read 12.3 feet.

Question

Complete the following steps to calculate the change in Vivian's elevation from the bottom of the Ferris wheel to the top.

Part A
Is the change in Vivian's elevation from the bottom of the Ferris wheel to the top a positive number or a negative number? Why?
Part B
Write an expression to represent Vivian's change in elevation from -9.6 feet at the bottom of the Ferris wheel to 12.3 feet at the top.
Part C
Subtracting a number is the same as adding its additive inverse. For which elevation do we need to find the additive inverse? What is the additive inverse of that elevation?
Part D
Now, rewrite the expression from part B using the additive inverse that you identified in part C.
Part E
Simplify the expression that you wrote in part D, and explain what the number means with regard to the problem.
Self-Evaluation
How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score. Then write a brief evaluation of your work below. Note what you learned and what challenged you.

Answer 1

Part A
The change in Vivian's elevation from the bottom of the Ferris wheel to the top is a positive number. This is because she is moving from a lower elevation (below sea level) at -9.6 feet to a higher elevation at 12.3 feet, which is above sea level.

Part B
To represent Vivian's change in elevation from -9.6 feet at the bottom to 12.3 feet at the top, we can write the expression: \[ \text{Change in elevation} = 12.3 - (-9.6) \]

Part C
We need to find the additive inverse of the elevation at the bottom of the Ferris wheel, which is -9.6 feet. The additive inverse of -9.6 feet is 9.6 feet because adding 9.6 feet to -9.6 feet results in 0.

Part D
Now, we rewrite the expression from Part B using the additive inverse we identified: \[ \text{Change in elevation} = 12.3 - (-9.6) = 12.3 + 9.6 \]

Part E
Now, let's simplify the expression: \[ 12.3 + 9.6 = 21.9 \]

This means that the change in Vivian's elevation from the bottom of the Ferris wheel to the top is 21.9 feet. The positive result indicates that she rose 21.9 feet in elevation from the lowest point to the highest point of the Ferris wheel.

Self-Evaluation
I would rate my work a 5. I clearly analyzed each part of the problem, demonstrated the steps logically, and arrived at a correct conclusion. I learned how to think about changes in elevation using both positive and negative values and how to apply the concept of additive inverses to simplify my calculations. The challenge was ensuring that I correctly understood how to interpret elevation readings relative to sea level.