The hexagon train task
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The Hexagon Train Task. Hexagon Train Task. Trains 1, 2, and 3 are the first 3 trains in the hexagon pattern. Compute the perimeters of the first 3 trains. Construct the 4 th train and find its perimeter. Determine the perimeter of the 10 th train without constructing it.

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The Hexagon Train Task

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The Hexagon Train Task


Hexagon Train Task

  • Trains 1, 2, and 3 are the first 3 trains in the hexagon pattern.

    • Compute the perimeters of the first 3 trains.

    • Construct the 4th train and find its perimeter.

    • Determine the perimeter of the 10th train without constructing it.

    • Write a description/expression that could be used to determine the perimeter of any train in the pattern.


Hexagon Train Task

  • Find as many different ways as you can to compute the perimeter for any train in the pattern and be prepared to justify each way.


More Hexagon Trains

  • Terri, Tim, Jerry and Linda each came up with a different expression to find the perimeter of the nth hexagon train.

  • Explain what each student was thinking to find the perimeter of the nth train.


More Hexagon Trains

  • Explain what each student was thinking to find the perimeter of the nth train.

  • Terri: 1 + 4n + 1

  • Tim: 1 + 2(2n) + 1


More Hexagon Trains

  • Explain what each student was thinking to find the perimeter of the nth train.

  • Jerry: 5 + 4(n – 2) + 5

  • Linda: Multiply n times 6, then subtract n – 1 times 2.


Hexagon Train Extension Q’s

  • Are all these expressions equivalent?

  • What is the most simplified expression for the perimeter of any hexagon train?

  • What is the rate of change of the perimeter of the hexagon trains? In what units would it be expressed?

  • How would the problem change if the train were made of octagons? Triangles?


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