8th Grade  Lesson 30 minutes

"Dilation Drills: Sports Geometry Challenge!"

Allison R
8.G.A.3
8.G.A.4
8.G.A.3
8.G.A.4
Self Directed Learning
+ 2 more
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Purpose

Engage in a hands-on exploration of geometric transformations by designing a scaled model of a sports field. This project challenges you to apply your understanding of dilations, translations, rotations, and reflections to create an accurate and visually appealing representation. Through collaboration and feedback, refine your model while developing critical thinking and problem-solving skills. This experience fosters self-directed learning and strengthens your academic mindset by connecting mathematical concepts to real-world applications in sports.

Learning goals

Explore how dilations and congruence can be applied to real-world scenarios, such as designing sports fields. Investigate the sequence of transformations needed to create scaled models, and analyze how these transformations affect the design and functionality of the field. Develop critical thinking skills by considering innovative solutions to design challenges, while fostering self-directed learning through reflection and feedback.
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.
  • [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.
Competencies
  • Self Directed Learning - Students use teacher and peer feedback and self-reflection to monitor and direct their own learning while building self knowledge both in and out of the classroom.
  • Academic Mindset - Students establish a sense of place, identity, and belonging to increase self-efficacy while engaging in critical reflection and action.
  • Critical Thinking & Problem Solving - Students consider a variety of innovative approaches to address and understand complex questions that are authentic and important to their communities.

Products

Create a scaled model of a sports field using graph paper and coordinate geometry to demonstrate dilations and congruence. Develop a presentation that outlines the sequence of transformations applied to achieve similarity between the original and scaled models. Facilitate a gallery walk where you can view and provide feedback on each other's models and presentations, reflecting on the effectiveness of the transformations used.

Launch

Begin by examining images of various sports fields, such as soccer, basketball, and baseball, focusing on their dimensions and layout. Use a digital tool to plot the coordinates of key points on one of these fields. Then, collaboratively discuss how you might transform these points using dilations, rotations, reflections, and translations to create a scaled model of the field. Consider how these transformations impact the design and functionality of the field, and share your initial thoughts with peers.

Exhibition

Facilitate a gallery walk where you display your scaled sports field models, highlighting the transformations used to achieve similarity. Invite peers and teachers to provide feedback on the accuracy and creativity of your transformations. Use this opportunity to reflect on your learning process and discuss how the mathematical concepts apply to real-world sports field design.