8th Grade  Lesson 30 minutes

"Building Blocks: Dilations & Measurements"

Daniela M
CCSS.Math.Content.8.G.A.3
CCSS.Math.Content.8.G.A.4
Self Directed Learning
Academic Mindset
Critical Thinking & Problem Solving
1-pager

Purpose

The purpose of this learning experience is to engage you in a practical exploration of geometric transformations, particularly dilations, through the creation of scale models of famous buildings or bridges. By constructing these models, you will deepen your understanding of the mathematical concepts of similarity and congruence, as well as the real-world application of these principles in architecture. This project encourages you to develop critical thinking and problem-solving skills as you reflect on the transformation processes and the challenges encountered during the model-building activity.

Learning goals

Explore how dilations can be used to create accurate scale models of famous buildings or bridges, and understand the relationship between the original structure and its model. Apply transformations such as dilations, rotations, and reflections to demonstrate how two-dimensional blueprints are transformed into three-dimensional structures. Identify and describe sequences of transformations that illustrate the concept of similarity between two-dimensional figures in architectural designs.
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.
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

Design and build a scale model of a famous building using graph paper and cardboard, applying dilations to accurately represent the dimensions. Present your model in a classroom exhibition, highlighting the transformations used to achieve similarity between the original and the model. Facilitate a gallery walk where you can view and provide feedback on each other's models, focusing on the use of dilations and other transformations.

Launch

Begin by exploring a virtual tour of a famous building or bridge, such as the Eiffel Tower or the Golden Gate Bridge. As you navigate the structure, take note of its dimensions and unique features. Discuss with peers how these elements might transform if you were to create a scale model. Use this exploration to spark curiosity and set the stage for your hands-on project involving dilations and transformations.

Exhibition

Organize a classroom exhibition where you display your scale models of famous buildings and bridges. Set up a gallery walk, allowing peers and teachers to view your work and provide constructive feedback. Use this opportunity to explain the transformation processes you applied, such as dilations, rotations, and reflections, and how these relate to the original structures. Capture your reflections on the challenges and successes encountered during the project in a journal entry, focusing on the concept of congruence and similarity.