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8th Grade Task: Hexagon Puzzle

Standards & Objectives

Essential and guiding questions:

The key understandings that students should come to in the discussion of this task and questions you can ask in the whole group setting to support arrival at these key understandings.
Key understanding:

Are all of these expressions equivalent? How do we know? What would be the perimeter of the 9th figure? 100th figure?
Discuss different students’ approaches to solving the different models.
There may be several paths to form a relationship but if they all simplify to the same equation then they must be equal.
What property can we use to justify our findings? Reflexive property of equality y=y 4n+2=4n+2

Activity/Task Variations

Blooms taxonomy level:

Understanding

Differentiation suggestions:

If students can’t get started….

Could you write a table of values of number of shapes compared to the perimeter of the figure? This may give you insight into the equation.
How does equation A relate to the linear model of y=mx+b?

Extension suggestions:

If students finish early….

If I added a fifth shape would any of the equations model that relationship.
What if I put together triangles with each side being one unit. How many different equations could you write to model that relationship?

Originator:

Tennessee Department of Education