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Algebra I Task: Will and Latisha Tiles

Standards & Objectives

Essential and guiding questions:

Why did you decide to partition your arrangement this way?
How does your function rule relate to your drawing? Where is each part of your expression in the arrangement?
How does each of the expressions relate to each other?
Why did you decide to use your method to solve the problem? What advantages/disadvantages did your method have?
Were any of the forms easier to solve? Why?
Your equation had two answers. How did you determine which answer to use?

Activity/Task Variations

Blooms taxonomy level:

Applying

Differentiation suggestions:

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

What is the question asking?
Have students draw or build the next few arrangements and describe how they determined the arrangement.
Describe how you are visualizing the partitions of the arrangements. Why did you decide to partition your drawing this way?
Have students mark/show what each part of the arrangement represents from their expression.

Advancing Questions:

Have students test their expression with the known (built) arrangements. Does your expression work? Why or why not?
How could you use what you know about the 5th and 10th arrangements to find the number of tiles for the 20th arrangement? 50th arrangement? 101st arrangement?
What do you notice is changing and what is staying the same about each arrangement?

Extension suggestions:

If students finish early….
Assessing Questions:

Show me how your function rule relates to the arrangement.
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?
Are any of the forms of the equations easier to solve than others? Why?

Originator:

Tennessee Department of Education