The Similarity Ratio

26 Jan

The Similarity Ratio

How would your students solve the following problem? (After they discuss their love or hatred of clowns, that is.) A clown’s face on a balloon is 4 in. high when the balloon holds 108 in.3 of air. How much air must the balloon hold for the face to be 8 in. high?

My students try to take the given measurements and make a proportion out of them. For several years now, I have tried to figure out a way to help students not just understand that the areas and volumes of two similar figures are not proportional to their side lengths (or perimeters) but know how to apply that concept to solve problems.

This year we started with the Soccer Ball Inflation video on 101 Questions.

Then we explored what happened with similar rectangles – their similarity ratios, perimeters, and areas.

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Screen Shot 2014-01-26 at 5.35.56 PM

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Screen Shot 2014-01-26 at 5.36.03 PM

We summarized the results:

Screen Shot 2014-01-26 at 5.36.32 PM

And then moved to right triangles.

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Screen Shot 2014-01-26 at 5.38.38 PM

And then we worked problems similar to the clown problem, uncovering misconceptions, figuring out the incorrect thinking that occurred for incorrect responses.

Screen Shot 2014-01-26 at 5.43.32 PM

And the results on the summative assessment were better than usual. Last year, on a problem like the clown problem, less than 50% of students answered it correctly. This year, 72% answered it correctly.

And so, the journey continues, where some years the results are better than others …


Posted by on January 26, 2014 in Dilations, Geometry


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2 responses to “The Similarity Ratio

  1. Amy Zimmer

    December 30, 2015 at 7:01 pm

    Hi Jennifer,
    I am looking for a great lesson to start dilation and similarity for the new semester.
    I am really excited about the soccer ball modeling project. I noticed that on one of your posts you mentioned that you completed lesson 6A, 6B, 6C, etc…
    Can you please tell me what these reference?
    We have covered congruence, but now I see that next year we may need to look at congruence as a special circumstance of similarity.

    Thank you for all the good information.



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