Algebra I Task: Will and Latisha Tiles

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?