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Algebra I Task: Pool Patio Problem

Standards & Objectives

Essential and guiding questions:

Why did you decide to partition your drawing this way?
How does your equation relate to your drawing?
How does each of the equations relate to each other?
Why did you decide to use your method to solve the problem? What advantages/disadvantages did your method have?
Your equation had two answers. How did you determine which answer to use?
Did the owner use all of the leftover material in Part B? Justify.

Activity/Task Variations

Differentiation suggestions:

If students can’t get started….
Assessing Questions:

What is the question asking?
Draw and label a picture that represents the scenario. Where is the pool in your picture? Where is the patio?
How did you determine what labels to use?

Advancing Questions:

What would be the area of each partition of your drawing? How did you determine that area?
How could you use each individual area to determine the area of the frame?

Extension suggestions:

If students finish early….
Assessing Questions:

Show me how your equation relates to your drawing.
Why did you decide to partition your drawing this way?
Why did you decide to use this method to solve the problem?
Why are there two potential solutions to this problem?
Given the scenario, which value of x would make sense? Why?

Advancing Questions:

Group or pair students who are finished – How are your methods similar and different? How are all of your equations related?
What if the owner wanted to plant small gardens in the four square corners of the patio. How would this change the problem scenario? What type of function would this create?
Is there a case where the owner’s claim will hold true?
Mathematically justify your answer.

Originator:

Tennessee Department of Education