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of the problem, for example, they might decide to draw stage 2 or organize the data in a table (MP1).
(If you wish, share with students that this shape is known in mathematics as the Koch (pronounced “coke”) Snow ake.)
Launch
Draw an equilateral triangle for all to see, and then demonstrate how Stage 1 would be created by erasing the middle of each side and drawing two additional segments popping out of each side.
Ask students how many sides Stage 0 and Stage 1 has. This will help them tackle the rst question with a solid understanding of what it’s asking.
Student Task Statement
Here is a geometric shape built in stages.
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Stage 0 is an equilateral triangle.
To go from Stage 0 to Stage 1, take every edge of Stage 0 and replace its middle third with an outward-facing equilateral triangle.
To go from Stage 1 to Stage 2, take every edge of Stage 1 and replace its middle third with an outward-facing equilateral triangle.
This process can continue to create any stage of the design.
Find a rule for function , where is the number of sides in Stage . Use either a recursive or closed form de nition. What is ?
Consider a di erent function , where is the number of new triangles added when drawing stage . How many new triangles are there in stages 1, 2, and 3?
What is the total number of triangles used in building Stage 3?
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1. 2. 3.
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Teacher Guide
Algebra