Illustrative Math Alignment: Grade 8 Unit 1

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.

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.

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

Topic

Geometry Concepts

Description

This image illustrates the concept of bilateral symmetry using the capital letter A. Bilateral symmetry occurs when an object can be divided into two identical halves by a single line, creating mirror images on either side.

In this case, the letter A demonstrates perfect bilateral symmetry along a vertical axis drawn through its center. The left side of the letter is an exact mirror image of the right side. This symmetry is evident in the equal angles of the letter's legs and the centered position of the crossbar.

Topic

Geometry Concepts

Description

This image showcases the bilateral symmetry of the capital letter H. Bilateral symmetry is present when an object can be divided into two identical halves by a single line, creating mirror images on each side.

The letter H exhibits bilateral symmetry along both vertical and horizontal axes. A vertical line through the center of the H divides it into identical left and right halves, while a horizontal line through its center creates identical top and bottom halves. This dual symmetry makes H one of the most symmetrical letters in the alphabet. This image shows the vertical line of symmetry.

Topic

Geometry Concepts

Description

This image demonstrates the bilateral symmetry of the capital letter I. Bilateral symmetry occurs when an object can be divided into two identical halves by a single line, creating mirror images on either side.

The letter I displays bilateral symmetry along both vertical and horizontal axes. A vertical line through its center creates identical left and right halves, while a horizontal line produces identical top and bottom halves. This makes I, like H, one of the most symmetrical letters in the alphabet. This image shows the vertical line of symmetry.

Topic

Geometry Concepts

Description

This image illustrates the bilateral symmetry of the capital letter M. Bilateral symmetry is present when an object can be divided into two identical halves by a single line, creating mirror images on each side.

The letter M demonstrates bilateral symmetry along a vertical axis drawn through its center. The left half of the M is a perfect mirror image of the right half, with the central peak serving as the axis of symmetry. This symmetry is evident in the equal angles and lengths of the letter's diagonal strokes.

Topic

Geometry Concepts

Description

This image showcases the bilateral symmetry of the capital letter O. Bilateral symmetry occurs when an object can be divided into two identical halves by a single line, creating mirror images on either side.

The letter O is unique among alphabet letters as it possesses infinite lines of symmetry if drawn as a perfect circle. Any straight line passing through the center of the O will divide it into two identical halves, demonstrating both vertical and horizontal bilateral symmetry, as well as diagonal symmetry.

Topic

Geometry Concepts

Description

This image illustrates the bilateral symmetry of the capital letter T. Bilateral symmetry occurs when an object can be divided into two identical halves by a single line, creating mirror images on either side.

The letter T demonstrates perfect bilateral symmetry along a vertical axis drawn through its center. The left side of the vertical stem is an exact mirror image of the right side, and the horizontal bar is equally divided by this axis. This symmetry is evident in the equal length of the horizontal bar on either side of the vertical stem.

Topic

Geometry Concepts

Description

This image showcases the bilateral symmetry of the capital letter U. Bilateral symmetry is present when an object can be divided into two identical halves by a single line, creating mirror images on each side.

The letter U exhibits bilateral symmetry along a vertical axis drawn through its center. The left side of the U is a perfect mirror image of the right side, with both vertical strokes being of equal length and the curved bottom perfectly symmetrical. This symmetry is evident in the equal distance between the vertical strokes and the center line at any given height.

Topic

Geometry Concepts

Description

This image demonstrates the bilateral symmetry of the capital letter V. Bilateral symmetry occurs when an object can be divided into two identical halves by a single line, creating mirror images on either side.

The letter V displays perfect bilateral symmetry along a vertical axis drawn through its center. The left diagonal stroke is an exact mirror image of the right diagonal stroke, with both meeting at a point at the bottom. This symmetry is evident in the equal angles formed by each stroke with the vertical axis.

Topic

Geometry Concepts

Description

This image illustrates the bilateral symmetry of the capital letter W. Bilateral symmetry is present when an object can be divided into two identical halves by a single line, creating mirror images on each side.

The letter W demonstrates bilateral symmetry along a vertical axis drawn through its center. The left half of the W is a perfect mirror image of the right half, with the central peak serving as the axis of symmetry. This symmetry is evident in the equal angles and lengths of the letter's diagonal strokes on either side of the central axis.

Topic

Geometry Concepts

Description

This image showcases the bilateral symmetry of the capital letter X. Bilateral symmetry occurs when an object can be divided into two identical halves by a single line, creating mirror images on either side.

The letter X is unique in that it exhibits bilateral symmetry along both vertical and horizontal axes. A vertical line through the center of the X divides it into identical left and right halves, while a horizontal line creates identical top and bottom halves. This dual symmetry makes X one of the most symmetrical letters in the alphabet. This image shows the vertical line of symmetry.

Topic

Geometry Concepts

Description

This image illustrates the bilateral symmetry of the capital letter Y. Bilateral symmetry is present when an object can be divided into two identical halves by a single line, creating mirror images on each side.

The letter Y demonstrates bilateral symmetry along a vertical axis drawn through its center. The upper arms of the Y are mirror images of each other, with the vertical stem extending down from their point of convergence. This symmetry is evident in the equal angles formed by the upper arms with the vertical axis and their equal length.

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.