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The Scale of a Lion

Authors: Allison Manley

Grade: 9th 

Subjects: Honors Geometry

Timeline: 8 weeks

Essential Question

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How can we use similarity to scale up a geometric mural?

Project Description​

 

Students applied skills of dilation and explored the characteristics of similar figures to co-create a geometric mural. Students all created an original design, voted on one to create, divided up the mural into panels, and then each scaled up their portion. Students practiced measuring with precision by using protractors and rulers, developed collaborative and communication skills as they worked to make each side of the mural line up with the next, and utilized painting and construction techniques to create the finished product. In their presentation to the community at exhibition, students emphasized how much perseverance and patience this project required.

Products and Exhibition

 

8 x 10 foot 4 panel Geometric Mural

Reflections (student and teacher)

 

“In math class, my peers and I worked diligently and with commitment to complete a geometric mural. The first thing we did was come up with a beginning design on paper. Once we had decided on a mural outline and design, we cut the board we would eventually use to draw our final mural on into four sections, each piece for a student. We then began to dilate our section of the drawing onto the board using a scale factor. This was the hardest part because it was tedious and involved lots of math. It was very easy to mess up and if you did, the rest of the mural would be wonky and not fit the way it was supposed to. It took a very long time because it wasn’t too much fun and we made a lot of errors that we later had to fix. I overcame this by not giving up and making small goals for myself along the way, such as being determined to finish two grid boxes per day. We then moved onto taping, so that our lines would be neat and clean, and painting our mural. This part was the most fun for me, especially mixing fun colors and using them in the mural. I learned so much in the process of this project. I learned a lot about using scale factors to create similar shapes and I get a lot better at using a protractor to measure angles. I also got better at measuring with a ruler. Other skills I improved in were painting, cutting wood, measuring, and sanding. This project demonstrates the concept of similarity because each shape from the original drawing was scaled up by a factor of 4.77, making the shape on the board similar to the first. This process is dilation. Our sides changed but the angles stayed the same and the sides grew by a scale factor. I also observed that the area and the perimeter of the original and dilated shapes had relationships! This project was so much fun and I learned a lot.” - Rylan Ascher

Standards Addressed:

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CCSS.MATH.CONTENT.HSG.SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. CCSS.MATH.CONTENT.HSG.SRT.A.1 Verify experimentally the properties of dilations given by a center and a scale factor. CCSS.MATH.CONTENT.HSG.SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.

CCSS.MATH.PRACTICE.MP6 Attend to precision.

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