The Pythagoras Tree

8.G.7     8.EE.2

Act 1

Watch the video:

Suggested question(s):  How big are each of the squares?  How many (grid) squares were cut (area) for each color of the tree?  How much area for the whole tree?

Estimate the number of grid squares for the whole tree.  Now make estimates that you know are too high and too low.

Draw and fill in the number line with your “too low” and “too high” estimates.  Then find the approximate location of your estimate.

Act 2

As students ask questions about the task, provide them with the following:

Grid paper used:

multiwidth (5)

plain (6)

Note:  Green square lengths needed to be rounded to the nearest hundredth.  Green square cuts were estimated.  Accuracy of these cuts was facilitated through the use of inch grid paper subdivided and benchmarked into tenths.


Act 3

Students share strategies and solutions, using precise mathematical language and calculations.  Students should discuss various strategies and look for efficiency and flexibility in other students’ thinking.

Validate student thinking.

Pythagoras Tree Act 3

How close was your estimate?

What patterns did you notice?

How can you explain these patterns?




  1. I really like this activity. You could really extend your GATE kids with the ideas of how far can the branches keep going? But also engage all levels in the activity.

    1. Thanks Rachael. You’re right. With fractal patterns like this, the branches could really go on forever – if we could cut the paper small enough. One thing I realized after putting this task together is that you don’t have to know the Pythagorean theorem to solve it, which makes it more accessible to a larger population. Thanks for sharing your thoughts.

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