Geometry 5-D-1: Exploring Dilations

Individually, I would have the students plot the original triangle on their graph, then multiply the coordinates by 2, plot the new points.   In partners, use the worksheet to talk about the similarities and differences of what they just did. Then I, or a student, could demonstrate what we should be seeing on an overhead for the class.   I would ask questions to compare how the coordinating points relate to the origin on the coordinate graph.  Then do the same thing with the pentagon, individually plot the points for the original figure, multiply each point by ½, then with a partner finish the questions on the worksheet.  As a class, have a different student or group present the graphing on an overhead. Again, look at how it correlates to the origin.

The following questions would be good classroom discussion and/or journal entries.  I would ask questions to compare the original coordinates to the coordinates to the dilated figures.  Did the shapes change?  How are they the same/different?     What would happen if we multiplied the original figure by 3, or ¼, will your figures enlarge or shrink?  Explain your reasoning.  How does if effect the relationship to the origin?  What do you notice about the distance from the origin to the 2 coordinating points of the figures?

At first, students might assume side length and angle measure will change in dilation.  But as you start comparing, you can explore the idea of similarity.  The students can cut out the figures to compare, side lengths change but the angle measure stays the same.  This is also a good way to confirm that no matter what size of triangle, pentagon, or any polygon, the angle sum of that particular figure will always be the same.  Students might also ask how small or large you can dilate a figure.  They can experiment with numbers with a partner until they come up with an answer, infinity both ways,  and be able to explain their reasoning.

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3 Responses to Geometry 5-D-1: Exploring Dilations

  1. rwhelchel says:

    I like how you have used journal entries to check for student understanding. Have you ever approached this concept with the idea of scale drawings in mind? I’m not sure what the curriculum is for different areas, but we start in 7th grade with scale and proportional relatioships which allows our student to make connections to dilations. Great ideas for this dilation lesson Julie!

    • juliestuff5 says:

      I have approached this on the idea of scale modeling. In honors geometry, we did an activity that would brought in proportions and scaling. The student worked in pairs and picked an everyday object to scale either bigger or smaller. They had to recreate it as a physical object and explain how they thought through their creation. My favorites that stand out were scaling a rubber ducky 3 times the original and a tv remote twice the original. They can be very creative and use math in a way that is fun to them.

  2. mathjoseph says:

    Hi Julie, I like your lesson presentation, I looks like a good one. Your questions about how the dilations move with respect to the origin are interesting. I also like the idea of cutting out the shape to make direct comparisons, this would serve the IEP students well. In Rachael’s commentary, the idea of using this lesson as a first step toward ratio, proportion and scale is a natural one. I think when we link one piece of content to another, it builds more solid understandings.

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