Illustrative Math Alignment: Grade 8 Unit 2

Overview

Overview

In this program we look at applications of transformations. We do this in the context of three real-world applications. In the first, we look at translations and rotations in the context of roller coaster rides. In the second example we look at translations in three-dimensional space in the context of cargo ships. In the third example, we look at the design of observatories to look at rotations, reflections, and symmetry.

Cargo ships transport tons of merchandise from one country to another and accounts for most of the global economy. Loading and unloading these ships requires a great deal of organization and provides an ideal example of three-dimensional translations.

Roller coasters provide an ideal opportunity to explore translations and rotations. Displacement vectors are also introduced.

The Gemini telescope in Hawaii is an example of architecture that moves. All observatories rotate in order to follow objects in the sky. This also provides an opportunity to explore rotations, reflections, and symmetry.

This hands-on activity is a companion to the video segment from the Geometry Applications: Angles and Planes video. In particular, it supports the segment on the architecture of Himeji Castle.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.

This hands-on activity is a companion to the video segment from the Geometry Applications: Angles and Planes video. In particular, it supports the segment on the architecture of Himeji Castle.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.

This hands-on activity is a companion to the video segment from the Geometry Applications: Angles and Planes video. In particular, it supports the segment on the architecture of Himeji Castle.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.

Topic

Geometry Concepts

Description

This image depicts a scale drawing of a square that has been scaled up by a factor of 1:2. This means that each side of the square in the drawing is twice the length of the corresponding side in the actual object. Scale drawings are essential for accurately representing objects in a manageable size while maintaining proportionality.

Teacher's Script: "Observe this scale drawing of a square. How does the 1:2 scale factor help us understand the relationship between the drawing and the actual square? What are some real-world applications of scaling up objects, such as in architecture or design?"

Topic

Geometry Concepts

Description

This image illustrates a scale drawing of a square that has been scaled up by a factor of 1:3. Each side of the square in the drawing is three times the length of the corresponding side in the actual object. This scaling helps in visualizing larger versions of objects while maintaining accurate proportions.

Teacher's Script: "Look at this scale drawing of a square. How does the 1:3 scale factor affect the dimensions of the drawing compared to the actual square? What are some mathematical concepts you can explore using scale drawings, such as ratios or proportions?"

Topic

Geometry Concepts

Description

This image shows a scale drawing of a rectangle that has been scaled up by a factor of 1:4. Each side of the rectangle in the drawing is four times the length of the corresponding side in the actual object. This scaling is useful for enlarging objects while maintaining their proportional dimensions.

Teacher's Script: "Examine this scale drawing of a rectangle. How does the 1:4 scale factor influence the size of the drawing compared to the actual rectangle? What are some real-world applications of scaling up objects, such as in engineering or construction?"

Topic

Geometry Concepts

Description

This image illustrates a scale drawing of a rectangle that has been scaled up by a factor of 1:5. Each side of the rectangle in the drawing is five times the length of the corresponding side in the actual object. Scale drawings like this are crucial for visualizing larger versions of objects while maintaining accurate proportions.

Teacher's Script: "Observe this scale drawing of a rectangle. How does the 1:5 scale factor affect the dimensions of the drawing compared to the actual rectangle? What are some mathematical concepts you can explore using scale drawings, such as ratios or proportions?"

Topic

Geometry Concepts

Description

This image depicts a scale drawing of a right triangle that has been scaled down by a factor of 5:1. This means each side of the triangle in the drawing is one-fifth the length of the corresponding side in the actual object. Scaling down is useful for creating manageable representations of larger objects.

Teacher's Script: "Examine this scale drawing of a right triangle. How does the 5:1 scale factor help us understand the relationship between the drawing and the actual triangle? What are some real-world applications of scaling down objects, such as in model making or map creation?"

Topic

Geometry Concepts

Description

This image illustrates a scale drawing of a right triangle that has been scaled down by a factor of 4:1. Each side of the triangle in the drawing is one-fourth the length of the corresponding side in the actual object. This scaling helps in visualizing smaller versions of objects while maintaining accurate proportions.

Teacher's Script: "Observe this scale drawing of a right triangle. How does the 4:1 scale factor affect the dimensions of the drawing compared to the actual triangle? What are some mathematical concepts you can explore using scale drawings, such as ratios or proportions?"

Topic

Geometry Concepts

Description

This image depicts a scale drawing of a right triangle that has been scaled down by a factor of 3:1. Each side of the triangle in the drawing is one-third the length of the corresponding side in the actual object. Scaling down is useful for creating manageable representations of larger objects.

Teacher's Script: "Examine this scale drawing of a right triangle. How does the 3:1 scale factor help us understand the relationship between the drawing and the actual triangle? What are some real-world applications of scaling down objects, such as in model making or map creation?"

Topic

Geometry Concepts

Description

This image illustrates a scale drawing of a right triangle that has been scaled down by a factor of 2:1. Each side of the triangle in the drawing is one-half the length of the corresponding side in the actual object. This scaling helps in visualizing smaller versions of objects while maintaining accurate proportions.

Teacher's Script: "Observe this scale drawing of a right triangle. How does the 2:1 scale factor affect the dimensions of the drawing compared to the actual triangle? What are some mathematical concepts you can explore using scale drawings, such as ratios or proportions?"

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.

This is part of a collection of math examples that focus on geometric transformations.