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The Hexagon Train Task

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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  1. The Hexagon Train Task

  2. 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.

  3. 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.

  4. 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.

  5. 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

  6. 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.

  7. 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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