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.

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.

Topic

Circles

Definition

Circular composite figures are shapes that include circles or parts of circles combined with other geometric figures.

Topic

Polygons

Definition

A compound figure is a geometric shape that is composed of two or more simple polygons combined to form a more complex figure.

Description

In geometry, a compound figure is a shape that is formed by combining two or more polygons. These figures are significant because they allow for the exploration of more complex shapes and their properties, which can be broken down into simpler, more manageable components. Understanding compound figures is essential for solving problems related to area, perimeter, and other geometric properties.

Topic

Polygons

Definition

A polygon is a closed two-dimensional shape with straight line segments, while a compound figure is a shape formed by combining two or more geometric figures.

Topic

Polygons

Definition

A compound figure, also known as a composite figure, is a shape that is made up of two or more simple geometric figures such as triangles, rectangles, squares, parallelograms, trapezoids, and circles.

Topic

Geometry

Description

This holiday-themed math clip art features a festive candy box, offering a delightful blend of seasonal cheer and geometric concepts. The image can be broken down into its fundamental geometric components, showcasing both 2D and 3D elements.

In 2D, the candy box presents a cardioid shape, resembling a heart or rounded triangle. This unique curve can be explored in terms of its properties and equations. The box's decorative elements, such as bows or patterns, may incorporate additional 2D shapes like circles, ovals, or polygons.

Topic

Geometry

Description

This holiday-themed math clip art showcases a classic candy cane, a perfect subject for exploring various geometric concepts. The candy cane's distinctive shape offers rich opportunities for analyzing both 2D and 3D geometric elements.

In 2D, the candy cane can be broken down into rectangles and semicircles. The straight part of the cane forms a rectangle, while the curved hook at the top creates a semicircle. This allows for discussions about properties of these shapes, such as area calculations and the relationship between a semicircle's diameter and its arc length.

This is part of a collection of math clip art images that take holiday images and render them as two- and three-dimensional geometric objects.

Math Clip Art Library

To see the complete Math Clip Art Library, click on this link.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

This is part of a collection of math clip art images that take holiday images and render them as two- and three-dimensional geometric objects.

Math Clip Art Library

To see the complete Math Clip Art Library, click on this link.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

Topic

Geometry

Description

This holiday-themed math clip art features chocolate candy, providing an excellent opportunity to explore geometric concepts in both 2D and 3D contexts. The simplicity of the candy's shape belies the rich mathematical discussions it can inspire.

In 2D, the chocolate candy presents as a perfect circle. This allows for exploration of circular properties such as diameter, radius, circumference, and area. The candy's surface design, which may include patterns or decorations, can introduce concepts like symmetry, geometric transformations, or even basic trigonometry if the designs include angular elements.

Topic

Geometry

Description

This holiday-themed math clip art showcases a Christmas tree, offering a festive way to explore various geometric concepts in both 2D and 3D contexts. The tree's distinctive shape provides rich opportunities for mathematical analysis and discussion.

In 2D, the Christmas tree can be broken down into a triangle for the main body and a rectangle for the trunk. This allows for exploration of properties such as angles, base, height, area, and perimeter. The decorations on the tree can introduce concepts of symmetry, patterns, and even coordinate geometry if we imagine the ornaments as points on a plane.

Topic

Geometry

Description

This holiday-themed math clip art features a dreidel, a traditional Hanukkah toy that offers a unique opportunity to explore geometric concepts in both 2D and 3D contexts. The dreidel's distinctive shape provides a rich foundation for various mathematical discussions.

In 2D, the dreidel can be broken down into several shapes. The body presents as a square or rectangle, the top as a smaller rectangle, and the point at the bottom as a triangle. This allows for exploration of properties such as angles, sides, area, and perimeter. The Hebrew letters on each face introduce concepts of symmetry and rotational transformations.

Topic

Geometry

Description

This holiday-themed math clip art features a festive drum, offering an excellent opportunity to explore geometric concepts in both 2D and 3D contexts. The drum's simple yet distinctive shape provides a rich foundation for various mathematical discussions.

In 2D, the drum can be broken down into basic shapes. The top and bottom of the drum present as circles, while the side forms a rectangle. This allows for exploration of properties such as diameter, radius, circumference, and area for circles, as well as length, width, and perimeter for rectangles. The decorative elements on the drum's surface can introduce concepts of symmetry and patterns.

This is part of a collection of math clip art images that take holiday images and render them as two- and three-dimensional geometric objects.

Math Clip Art Library

To see the complete Math Clip Art Library, click on this link.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

Topic

Geometry

Description

This holiday-themed math clip art features a gingerbread house, offering a delightful way to explore geometric concepts in both 2D and 3D contexts. The gingerbread house's structure provides a rich foundation for various mathematical discussions, combining architectural elements with festive design.

Topic

Geometry

Description

This holiday-themed math clip art showcases a gingerbread man, offering a festive way to explore geometric concepts in both 2D and 3D contexts. The gingerbread man's shape provides a unique opportunity to discuss various geometric forms and their combinations.

Topic

Geometry

Description

This Halloween-themed math clip art features candy corn, offering a seasonal way to explore geometric concepts in both 2D and 3D contexts. The distinctive shape of candy corn provides an excellent opportunity to discuss various geometric forms and their properties.

In 2D, candy corn is typically represented as a triangle. This allows for exploration of properties such as angles, base, height, area, and perimeter. The three-color design of candy corn also introduces the concept of dividing a triangle into smaller triangles, which can lead to discussions about similarity and proportions.

Topic

Geometry

Description

This holiday-themed math clip art showcases a chocolate bar, offering a delightful way to explore geometric concepts in both 2D and 3D contexts. The chocolate bar's simple yet structured shape provides an excellent foundation for various mathematical discussions.

In 2D, the chocolate bar presents as a rectangle. This allows for exploration of properties such as length, width, perimeter, and area. The individual chocolate squares within the bar create a grid, introducing concepts of arrays, rows, and columns. This grid structure can also be used to discuss fractions and ratios.

Topic

Geometry

Description

This Halloween-themed math clip art features a lollipop, offering a sweet way to explore geometric concepts in both 2D and 3D contexts. The lollipop's simple yet distinctive shape provides a rich foundation for various mathematical discussions.

Topic

Geometry

Description

This holiday-themed math clip art features a festive candy mint, providing an excellent opportunity to explore geometric concepts in both 2D and 3D contexts. The simplicity of the mint's shape belies the rich mathematical discussions it can inspire.

In 2D, the candy mint presents as a perfect circle. This allows for exploration of circular properties such as diameter, radius, circumference, and area. The mint's surface design, often featuring spirals or radial patterns, can introduce concepts like rotational symmetry and geometric transformations.

Topic

Geometry

Description

This Halloween-themed math clip art features a moon, offering a celestial way to explore geometric concepts in both 2D and 3D contexts. The moon's simple yet evocative shape provides a rich foundation for various mathematical discussions, particularly fitting for the spooky atmosphere of Halloween.

Topic

Geometry

Description

This Halloween-themed math clip art showcases a pumpkin, offering a festive way to explore geometric concepts in both 2D and 3D contexts. The pumpkin's distinctive shape provides a rich foundation for various mathematical discussions.

Topic

Geometry

Description

This Halloween-themed math clip art features a title page, offering a spooky introduction to explore geometric concepts in both 2D and 3D contexts. While a title page might not immediately suggest geometric analysis, it provides an opportunity to discuss layout, design, and the geometric principles underlying visual communication.

Topic

Geometry

Description

This Halloween-themed math clip art features a vampire coffin, offering a spooky way to explore geometric concepts in both 2D and 3D contexts. The coffin's unique shape provides an excellent opportunity to discuss various geometric forms and their properties.

Topic

Geometry

Description

This Halloween-themed math clip art features a witch's hat, offering a spooky way to explore geometric concepts in both 2D and 3D contexts. The distinctive shape of the witch's hat provides an excellent opportunity to discuss various geometric forms and their properties.

Topic

Geometry

Description

This holiday-themed math clip art features festive lights, offering a bright way to explore geometric concepts in both 2D and 3D contexts. The string of lights provides a unique opportunity to discuss various geometric forms and their combinations.

This is part of a collection of math clip art images that take holiday images and render them as two- and three-dimensional geometric objects.

Math Clip Art Library

To see the complete Math Clip Art Library, click on this link.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

Topic

Geometry

Description

This holiday-themed math clip art features another representation of a lollipop, offering a different perspective on blending sweet imagery with mathematical precision. The image demonstrates how basic geometric shapes can be combined in various ways to create recognizable objects, reinforcing the connection between abstract geometry and everyday items.

Topic

Geometry

Description

This holiday-themed math clip art features a North Pole sign, offering a festive way to explore geometric concepts in both 2D and 3D contexts. The North Pole sign provides a unique opportunity to discuss various geometric forms and their combinations.

In 2D, the North Pole sign can be broken down into basic shapes. The pole itself is represented by a rectangle, while the the top is represented by a circle. This composition allows for exploration of properties such as length, width, area, and perimeter for rectangles, as well as diameter and circumference for circles.

Topic

Geometry

Description

This holiday-themed math clip art features a Christmas ornament, offering a festive way to explore geometric concepts in both 2D and 3D contexts. The ornament's simple yet distinctive shape provides a rich foundation for various mathematical discussions.

Topic

Geometry

Description

This holiday-themed math clip art showcases a gift box, offering a festive way to explore geometric concepts in both 2D and 3D contexts. The gift box's simple yet distinctive shape provides a rich foundation for various mathematical discussions.

In 2D, the gift box can be broken down into basic shapes. The main body of the box is likely represented by a square or rectangle, while the ribbon and bow might be depicted using additional rectangles or curved shapes. This allows for exploration of properties such as length, width, area, and perimeter. The symmetry of the gift box design can also be a point of discussion.

Topic

Geometry

Description

This holiday-themed math clip art features a snow globe, offering a magical way to explore geometric concepts in both 2D and 3D contexts. The snow globe's unique shape provides an excellent opportunity to discuss various geometric forms and their combinations.

Topic

Geometry

Description

This holiday-themed math clip art showcases a snowman, offering a delightful way to explore geometric concepts in both 2D and 3D contexts. The snowman's simple yet distinctive shape provides a rich foundation for various mathematical discussions.

Topic

Geometry

Description

This holiday-themed math clip art features a snowflake, offering a beautiful way to explore geometric concepts primarily in 2D contexts. The snowflake's intricate and symmetrical shape provides a rich foundation for various mathematical discussions.

Topic

Geometry

Description

This holiday-themed math clip art showcases a star, offering a brilliant way to explore geometric concepts primarily in 2D contexts, with some interesting 3D applications. The star's distinctive shape provides a rich foundation for various mathematical discussions.

Topic

Geometry

Description

This holiday-themed math clip art features a Christmas stocking, offering a festive way to explore geometric concepts in both 2D and 3D contexts. The stocking's unique shape provides an excellent opportunity to discuss various geometric forms and their combinations.

Topic

Geometry

Description

This holiday-themed math clip art showcases a toy soldier, offering a festive way to explore geometric concepts in both 2D and 3D contexts. The toy soldier's complex shape provides a rich foundation for various mathematical discussions, combining multiple geometric forms.

Topic

Geometry

Description

This holiday-themed math clip art features a wreath, offering a festive way to explore geometric concepts in both 2D and 3D contexts. The wreath's circular shape with its intricate details provides a rich foundation for various mathematical discussions.

Topic

Geometry Concepts

Description

This image depicts a composite shape made up of a square and an equilateral triangle. This combination of shapes is commonly seen in architectural designs and various decorative patterns.

To calculate the total area of this composite figure, we would add the area of the square (s²) to the area of the equilateral triangle (A = (√3/4)s², where s is the side length). The perimeter would involve summing the lengths of all outer sides, excluding any shared edges.

Topic

Geometry Concepts

Description

This image illustrates a composite shape made up of a square and a semicircle. This configuration is often seen in architectural elements such as arches and decorative motifs.

To calculate the total area of this composite figure, we would add the area of the square (s²) to the area of the semicircle (½πr², where r is the radius of the semicircle). The perimeter would involve summing the lengths of the square's sides and the curved edge of the semicircle.

Topic

Geometry Concepts

Description

This image shows a composite shape consisting of an equilateral triangle and a semicircle. This combination is often found in architectural designs and artistic patterns.

To calculate the total area of this composite figure, we would add the area of the equilateral triangle (A = (√3/4)s²) to the area of the semicircle (½πr²). The perimeter would involve summing the lengths of the triangle's sides and the curved edge of the semicircle.

Topic

Geometry Concepts

Description

This image depicts a composite shape made up of a regular hexagon and two equilateral triangles. This configuration is often seen in tessellation patterns and architectural designs.

To calculate the total area of this composite figure, we would add the area of the hexagon (A = (3√3/2)s²) to the areas of the two equilateral triangles (A = (√3/4)s² for each). The perimeter would involve summing the lengths of all outer sides, excluding any shared edges.

Topic

Geometry Concepts

Description

This image illustrates a "rocket ship" composite shape made up of a rectangle, two congruent right triangles, and an equilateral triangle. This playful configuration is often used in educational and design contexts to engage students.

To calculate the total area of this composite figure, we would add the area of the rectangle (l * w), the areas of the two right triangles (½bh for each), and the area of the equilateral triangle (A = (√3/4)s²). The perimeter would involve summing the lengths of all outer sides, excluding any shared edges.

Topic

Geometry Concepts

Description

This image shows a composite shape consisting of a regular hexagon with two semicircles. This configuration is often found in decorative patterns and architectural elements.

To calculate the total area of this composite figure, we would add the area of the hexagon (A = (3√3/2)s²) to the areas of the two semicircles (½πr² for each). The perimeter would involve summing the lengths of the hexagon's sides and the curved edges of the semicircles.

Topic

Geometry Concepts

Description

This image depicts a composite shape made up of a rectangle and two parallelograms. This configuration is often used in architectural designs and various structural layouts.

To calculate the total area of this composite figure, we would add the area of the rectangle (l * w) to the areas of the two parallelograms (bh for each). The perimeter would involve summing the lengths of all outer sides, excluding any shared edges.