Math Three-Tier Activity by Cesar Hernandez-Perez

Tier 1 Task: Plant Growth

hernandezperezcesar40 — 2024-07-29 18:58:28 UTC

You have recently collected data that shows the height of a plant (in centimeters). It increases by 2 centimeters for every 1 gram of fertilizer used. The initial height of the plant with no fertilizer was 10 centimeters.

Create a linear equation that represents the height of the plant f(x) as a function of the amount of fertilizer used (x) in grams.

Graph the function f(x) and predict the plant's height if 8 grams of fertilizer are used.

Questions:

What does the y-intercept of the function f(x) represent in terms of the plant's growth?
How would you explain the slope of the function f(x) in this given context?
How might different growth rates or different initial height affect your graph? Explain.

Information

hernandezperezcesar40 — 2024-07-29 19:55:02 UTC

Grade level: 9th and 10th grade

Standard: A.F-IF.B.4 Interpret functions that arise in applications in terms of the context.

Essential Question: How can we use linear functions to understand and improve the relationship between fertilizer use and plant growth in a sustainable way?

Tier 2 Task: Comparing Growth Rates

hernandezperezcesar40 — 2024-07-29 20:14:20 UTC

A different plant species has a different growth rate. It had an initial height of 15 centimeters with no fertilizer and grows by 1.5 centimeter for every 1 gram of fertilizer used.

Create a linear equation that represents the height of this second plant g(x) as a function of the amount of fertilizer used (x) in grams.

Graph the function g(x) on the same graph of the function f(x)

Determine at what amount of fertilizer both plants will have to reach the same height.

Questions:

What strategies did you use to find the point of intersection where both plants reached the same height? Are there more than 1 strategy?
Are there any additional factors that impact the growth of the plants? If so, how does it impact the linear equations and graphs you created?

Tier 3 Task: External Factors

hernandezperezcesar40 — 2024-07-29 20:30:04 UTC

Due to the environmental concerns, you will need to minimize the amount of fertilizer used. However you still need to achieve the plant height of 25 centimeters.

Determine the minimum amount of fertilizer needed to reach this height.

Construct an argument on which plant is more efficient for the environment based on your calculations.

Questions:

How would you convince people to buy the more environmentally efficient plant if the plant is not to their liking?
Are there other factors such as water availability that might affect your recommendations? If so, how will you address this in your argument?