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?