8th Grade  Lesson 30 minutes

"Goal Line Geometry: Dilations in Football!"

Zachary I
CCSS.Math.Content.8.G.A.3
CCSS.Math.Content.8.G.A.4
8.G.A.3
8.G.A.4
Self Directed Learning
+ 2 more
1-pager

Purpose

The purpose of this learning experience is to deepen your understanding of geometric transformations, specifically dilations, through a real-world application involving football field design. You will use mathematical concepts to collaboratively create scale models, fostering critical thinking and problem-solving skills. This project encourages self-directed learning as you reflect on your process and challenges, while also building a sense of identity and belonging within your group. Through hands-on activities, you will explore the importance of maintaining proportions and congruence in design, connecting math to practical scenarios.

Learning goals

Develop an understanding of how dilations affect two-dimensional figures using coordinates and apply this knowledge to create scale models of football fields. Collaborate effectively in small groups to design a football field that meets specific size requirements while maintaining proportional accuracy. Reflect on your learning process, identifying challenges and successes in applying mathematical concepts to real-world scenarios. Engage in critical thinking and problem-solving by considering innovative approaches to meet the project's goals.
Standards
  • [Common Core] CCSS.Math.Content.8.G.A.3 - Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
  • [Common Core] CCSS.Math.Content.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

Build a scaled model of a football field using graph paper and coordinate grids, applying dilations to ensure accurate proportions. Collaborate in small groups to design and construct the model, demonstrating your understanding of dilations and congruence. Facilitate a gallery walk to showcase your models and provide feedback on the accuracy and creativity of each design.

Launch

Begin the lesson with a short video clip of a football game, focusing on the field's dimensions and layout. Discuss how the field's proportions are crucial for gameplay and strategy. Then, challenge yourself to think about how you would adjust the field's size using dilations while maintaining these proportions. Use this discussion to set the stage for the hands-on activity of creating scale models of football fields.

Exhibition

Facilitate a gallery walk where you can display your scale models of football fields. Invite peers and teachers to view your work and provide constructive feedback on the accuracy and creativity of your designs. Use this opportunity to discuss the mathematical concepts of dilations and congruence applied in your models, highlighting the challenges you faced and the solutions you developed.