"Sports Geometry: Dilation & Congruence Play!"

8th Grade Lesson 30 minutes

"Sports Geometry: Dilation & Congruence Play!"

Sergio V

8.G.A.3

8.G.A.4

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Purpose

Explore how mathematical transformations can be applied to real-world contexts by designing a scaled sports field and creating a sports logo. Engage with concepts of dilation, congruence, and similarity to understand how shapes can be manipulated while maintaining their proportions. Develop skills in using graph paper to plot and transform figures, fostering a deeper understanding of geometry through practical application in sports design.

Learning goals

Understand and apply the concepts of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Demonstrate the ability to create and analyze scaled models and sports logos, ensuring proportionality is maintained through transformations. Collaborate effectively to design and present a project that showcases the sequence of transformations used to achieve similarity and congruence.

Standards

[California] 8.G.A.3 - Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
[California] 8.G.A.4 - Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

Products

Create a scaled model of a sports field on graph paper, applying dilations and transformations to demonstrate your understanding of congruence and similarity. Work with a partner to plot points and perform transformations, creating a series of drawings that replicate the dimensions of a sports field. Additionally, design a sports logo using transformations, ensuring it maintains its proportions when resized. Present your logo to the class, explaining how each transformation preserves the logo's proportions.

Launch

Begin by watching a short video clip of a sports game, focusing on the field and team logos. Discuss how the shapes and designs are consistent in size and proportion, no matter the camera angle or zoom level. Then, challenge yourself to think about how these logos maintain their proportions when resized, setting the stage for exploring dilations and transformations in your project.

Exhibition

Facilitate a gallery walk where you display your scaled sports field models and sports logos. Share your design process and explain the transformations used to maintain proportions. Engage with peers by providing feedback on their work and discussing different transformation sequences. Invite questions to deepen understanding of how transformations affect two-dimensional figures.

Rubric

Learning Journey

Project Activities

30 min over capacity (30 min available across 1 day)

Introduction to Transformations

Activity 5m

Introduction to Sports and Transformations

Activity 5m

Hands-On Practice with Transformations

Activity 15m

Hands-On Graph Paper Activity: Sports Field Model

Activity 15m

Sports Logo Design Challenge

Activity 10m

Designing a Scaled Sports Field

Activity 5m

Create a Sports Logo

Activity 5m

Plan

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"Sports Geometry: Dilation & Congruence Play!"

Purpose

Learning goals

Standards

Products

Launch

Exhibition

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