Looking at the process, describe why you choose to do what you did in the particular order and what connections are made between each step?
List the steps that you complete first in the blank.
- Table ___3____
- Equation ___1____
- Scenario (contextual situation) ___2__
What was your reasoning for doing the _______________ (table, equation, or scenario) first? Looking at the graph, I made a equation. From forming the equation, I knew exactly what the line represented. I knew that in blue line, you are losing something, and in the green you are gaining something. I also knew the y-intercept.
How did what you did first, help you with what you did second? Describe the connections from the first to the second thing that you did.I chose to do the scenario second because it made it clear what the x and y axis were. Without those, you can’t possibly make sense of the problem. You need to make sense of the problem first before you solve it. It gives you an example and it gives meaning to the numbers. By doing the equation first, I was able to decide for the blue line that every three months a person is losing 2 pounds. Without the equation I wouldn’t have been able to decide the numbers. Likewise, in the green line, every three months, you gain 2 pounds.
What did you fill out next? How did this help you with your last step? Describe the connections from the first to the second thing that you did.
After doing the scenario, I knew that every month you lose 2 pounds for the blue line, and gain 2 pounds for the green line. With knowing this from the scenario, I was able to make the table. I knew that the line was growing/decreasing at a constant rate, therefore I was able to check my work through the table. If I hadn’t made the scenario or equation, I could not have formed the table. Also the table asks what the axis represents, so you have to decide first what the scenario is.
Overall, compare and contrast the two lines:
- The axis represent the same things
- They have the same x-intercept
- They have same scale
- The absolute value is a me for the y-intercept
- One is a positive slope, one is negative
- You gain in one, lose in the other
- They have different y axis units
- The y-intercepts are different