Part A
Ashley dives in increments of 10 feet. What rational number represents diving 10 feet below sea level?
Response: The rational number that represents diving 10 feet below sea level is -10.
Part B
Write a numerical expression that represents the number of increments it will take Ashley to reach -60 feet.
Response: The numerical expression is -60 / -10.
Part C
Is the number of increments in part B positive or negative?
Response: The number of increments is positive.
Part D
Rewrite the expression from part B by distributing -1 from each of the negative numbers.
Response: The expression from part B can be rewritten as -(60 / 10).
Part E
If you divide any number by itself, what is the result? How can you apply this result to the expression in part D?
Response: The result of dividing any number by itself is 1 (as long as the number is not zero). In the expression from part D, you can apply this result by stating that (60 / 10) = 6, so the expression becomes -6.
Part F
Based on your work so far, how many increments of -10 feet are in -60 feet?
Response: There are 6 increments of -10 feet in -60 feet.
Part G
Copy and paste this image into the space below the correct number of times to show an elevation of -60 feet.
A down arrow implying 10 feet.
Response: ⬇️⬇️⬇️⬇️⬇️⬇️
Part H
Suppose that Ashley’s brother, Alex, makes the same dive in 4 increments instead of 6. Write a numerical expression to represent Alex’s elevation change in feet per increment.
Response: The numerical expression is -60 / 4.
Part I
How many negative numbers are in the expression in part H? What will the sign of the solution be? How do you know?
Response: There is 1 negative number in the expression in part H. The sign of the solution will be negative because dividing a negative number by a positive number results in a negative number.
Part J
What was Alex’s elevation change in feet per increment?
Response: Alex’s elevation change in feet per increment is -15 feet.
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.
Response: I would rate my work a 5. I feel confident that I accurately answered each part of the activity. I learned how to represent descent in terms of rational numbers and the importance of understanding the signs of the results in such situations. The challenge was ensuring I correctly distributed and interpreted the expressions throughout, but I feel I effectively managed that.
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