Illustrative Math Alignment: Grade 8 Unit 9

Overview

Overview

The glass-paneled pyramid at the Louvre Museum in Paris is a tessellation of rhombus-shaped glass panels. Students create a model of the pyramid to calculate the number of panels used to cover the surface area of the pyramid.

In this program we explore the properties of polygons. We do this in the context of two real-world applications. In the first, we look at Islamic tile patterns as examples of regular polygons. We explore how such intricate patterns were created using a compass and straight edge. In the second application we look at composite figures, specifically in the context of the design of the Petronas Towers in Indonesia.

The Pentagon is one of the most famous polygon-shaped buildings in the world. But why was this shape chosen over a more straightforward quadrilateral shape? We briefly explore the properties of pentagons and use this as a way of introducing the key concepts throughout the program.

In the ancient city of Marrakesh polygons are on display. As part of the Islamic tile work prevalent throughout the Middle Ages, Marrakesh provides an opportunity to explore the properties of polygons, and how these properties are taken advantage of in the intricate designs found throughout this fascinating city.

The Petronas Towers in Indonesia provide an opportunity to explore the composite shapes used in the design of the towers.

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.

In this Slide Show, apply concepts of linear functions to the context of the interior angles of a polygon. Note: The download is a PPT file.

This set of tutorials provides 36 examples of how to classify polygons based on side and angle characteristics.

Library of Instructional Resources

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

In this TI-Nspire Activity, use the Geometry Tools to construct a regular polygon and measure its area using the apothem-perimeter formula. 

Note: The Preview is a Google Slide Show and the download is a PPT. Subscribers to Media4Math can download resources.

This interactive crossword puzzle tests knowledge of key terms on the topic of quadrilaterals.

Related Resources

Topic

Geometry Basics

Description

This image is part of a series designed to teach fundamental concepts about polygons. It serves as a title card, prominently displaying the words "Polygon Basics" to introduce students to the topic. The use of clear, bold text on a simple background helps focus attention and set the stage for the lessons to follow.

Topic

Geometry Basics

Description

This image is part of a series designed to teach fundamental concepts about polygons. It presents a table that correlates the number of sides with the names of different polygons. The caption emphasizes that the number of sides determines the type of polygon, providing a clear, visual representation of this important concept.

Topic

Geometry Basics

Description

This image is part of a series designed to teach fundamental concepts about polygons. It features an illustration of a regular pentagon, accompanied by a caption explaining that a regular polygon has congruent sides and congruent angles. This visual representation helps students understand the defining characteristics of regular polygons.

Topic

Geometry Basics

Description

This image is part of a series designed to teach fundamental concepts about polygons. It presents a side-by-side comparison of an irregular triangle and a regular triangle, with a caption stating that polygons can be either regular or irregular. This visual juxtaposition effectively illustrates the difference between these two types of polygons.

Topic

Geometry Basics

Description

This image is part of a series designed to teach fundamental concepts about polygons. It showcases an irregular quadrilateral alongside a regular quadrilateral, reinforcing the concept that polygons can be either regular or irregular. This visual comparison helps students understand the distinction between these two categories of quadrilaterals.

Topic

Geometry Basics

Description

This image is part of a series designed to teach fundamental concepts about polygons. It presents a comparison between an irregular pentagon and a regular pentagon, further reinforcing the concept that polygons can be either regular or irregular. This visual representation helps students understand how these classifications apply to more complex polygons.

Topic

Geometry Basics

Description

This image is part of a series designed to teach fundamental concepts about polygons. It showcases an irregular hexagon alongside a regular hexagon, further emphasizing the concept that polygons can be either regular or irregular. This visual comparison helps students extend their understanding of polygon classifications to shapes with even more sides.

Topic

Geometry Basics

Description

This image is part of a series designed to teach fundamental concepts about polygons. It illustrates a polygon with its interior angles labeled, demonstrating that the sum of these angles relates to the number of sides. This visual representation helps students understand the relationship between a polygon's structure and its angular properties.

Topic

Geometry Basics

Description

This image is part of a series designed to teach fundamental concepts about polygons. It presents a table that illustrates the relationship between the number of sides in a polygon, the number of triangles that can be formed within it, and the sum of its interior angles. The caption emphasizes that the sum of interior angles depends on the number of sides, reinforcing this crucial geometric principle.

Topic

Geometry Basics

Description

This image is part of a series designed to teach fundamental concepts about polygons. It features an illustration of a polygon with its exterior angles highlighted, accompanied by a caption stating that the sum of the interior angles of a polygon is based on the number of triangles that can be formed. This visual representation helps students understand a key property of polygons that remains constant regardless of the number of sides.

Topic

Geometry Basics

Description

This math clip art image serves as the introductory title card for a series on regular polygons. The simple yet effective design features the words "Regular Polygons" prominently displayed, setting the stage for the educational content to follow. This image is crucial in capturing students' attention and clearly establishing the topic of study.

Topic

Geometry Basics

Description

This math clip art image is the second in a series about regular polygons, focusing on the fundamental definition of a polygon. The illustration showcases a general polygon shape, accompanied by a clear, concise caption that defines a polygon as a closed figure with a distinct number of straight sides.

Topic

Geometry Basics

Description

This math clip art image is the third in a series about regular polygons, introducing the specific definition of a regular polygon. The illustration features a regular pentagon, accompanied by a caption explaining that a regular polygon has congruent sides and congruent angles.

Topic

Geometry Basics

Description

This math clip art image is the fourth in a series about regular polygons, focusing on the equilateral triangle. The illustration presents a clear example of an equilateral triangle, accompanied by a caption highlighting its key properties: 60° angles and three congruent sides.

Topic

Geometry Basics

Description

This math clip art image serves as a title card for the process of constructing a regular triangle. It introduces a new section in the series on regular polygons, shifting focus from definitions and properties to the practical application of geometric principles.

Topic

Geometry Basics

Description

This math clip art image is the sixth in the series about regular polygons and the first step in constructing a regular triangle. It illustrates the initial stage of the construction process, showing a compass being used to draw a circle. The caption clearly states that this is Step 1 in constructing a regular triangle.

Topic

Geometry Basics

Description

This math clip art image is the seventh in the series about regular polygons and represents Step 2 in constructing a regular triangle. The illustration shows a line drawn through the center of the circle created in the previous step. This step is crucial in establishing the base for the equilateral triangle.

Topic

Geometry Basics

Description

This math clip art image is the eighth in the series about regular polygons and illustrates Step 3 in constructing a regular triangle. The image shows the construction of a semi-circle using the compass, building upon the previous steps of drawing a full circle and a line through its center.

Topic

Geometry Basics

Description

This math clip art image is the ninth in the series about regular polygons and represents Step 4 in constructing a regular triangle. The illustration highlights the centers used in the previous construction steps, emphasizing their importance in the process.

Topic

Geometry Basics

Description

This math clip art image is part of a series on regular polygons, focusing on the construction of an equilateral triangle. The illustration shows Step 5 of the process, where key points are highlighted in red. This visual aid is crucial in guiding students through the precise steps of geometric construction.

Using math clip art like this in geometry lessons helps students visualize abstract concepts and follow complex procedures. It bridges the gap between theoretical knowledge and practical application, making the learning process more engaging and effective.

Topic

Geometry Basics

Description

This math clip art image continues the series on regular polygons, illustrating Step 6 in constructing an equilateral triangle. The image shows the actual construction of the triangle based on the points and arcs established in previous steps. This visual representation is essential in demonstrating how geometric principles come together to form regular shapes.

Topic

Geometry Basics

Description

This math clip art image is part of the series on regular polygons, focusing on Step 7 of constructing an equilateral triangle. The illustration emphasizes the congruent sides of the newly constructed triangle, a key characteristic of equilateral triangles. This visual aid is crucial in helping students understand the defining properties of regular polygons.

Topic

Geometry Basics

Description

This math clip art image is part of the series on regular polygons, illustrating Step 8 in the construction of an equilateral triangle. The image emphasizes the completed equilateral triangle, showcasing the result of the step-by-step construction process. This visual representation is crucial in reinforcing the concept of regular polygons and their properties.

Topic

Geometry Basics

Description

This math clip art image continues the series on regular polygons, focusing on Step 9 of constructing an equilateral triangle. The illustration points out another equilateral triangle formed during the construction process. This visual aid is essential in demonstrating how geometric constructions can yield multiple regular shapes simultaneously.

Topic

Geometry Basics

Description

This math clip art image is part of the series on regular polygons, illustrating Step 10 in the construction of an equilateral triangle. The image highlights the central angle and its intercepted arc within the construction. This visual aid is crucial in demonstrating the relationship between central angles and regular polygons.

Topic

Geometry Basics

Description

This math clip art image continues the series on regular polygons, focusing on Step 11 of constructing an equilateral triangle. The illustration highlights the resulting 60° inscribed angle within the construction. This visual aid is essential in demonstrating the relationship between inscribed angles and central angles in a circle.

Topic

Geometry Basics

Description

This math clip art image is part of the series on regular polygons, illustrating Step 12 in the construction of an equilateral triangle. The image emphasizes that the inscribed triangle within the circle is equilateral. This visual representation is crucial in demonstrating how circular properties guarantee the formation of a regular polygon.

Topic

Geometry Basics

Description

This math clip art image concludes the series on constructing a regular triangle, showcasing the final result of the step-by-step process. The illustration presents the completed equilateral triangle as the simplest regular polygon. This visual representation is essential in summarizing the construction process and reinforcing the concept of regular polygons.

Topic

Geometry Concepts

Description

This image features a kite shape, in this case a circular one. Ordinarily a kite is a quadrilateral with two pairs of adjacent equal-length sides. The diagonals intersect at right angles, and one diagonal bisects the other, creating a symmetrical shape.

Kite shapes are important in geometry for understanding properties like symmetry, area, and perimeter. They are used in various mathematical applications, including tiling and design.

Teacher's Script: "Examine this kite. What makes it a kite in the everyday understanding of it? Is it a kite in geometric terms?"

Topic

Geometry Concepts

Description

This image features a kite shape, a quadrilateral with two pairs of adjacent equal-length sides and diagonals that intersect at right angles. The symmetry and unique properties of kite shapes make them interesting geometric figures.

Kite shapes are used to explore properties such as symmetry, area, and perimeter. They are applicable in various mathematical contexts, including geometry and design.

Topic

Geometry Concepts

Description

This image depicts a kite shape, characterized by two pairs of adjacent equal-length sides and diagonals that intersect at right angles. This geometric configuration is symmetrical and unique.

Kite shapes are used to explore geometric properties such as symmetry, area, and perimeter. They are applicable in various fields, including mathematics, design, and architecture.

Teacher's Script: "Look at this kite shape. How do its symmetrical properties and intersecting diagonals help us understand its geometry? What are some mathematical concepts you can explore using kite shapes?"

Topic

Geometry Concepts

Description

This image illustrates a kite shape, a quadrilateral with two pairs of adjacent equal-length sides and diagonals that intersect at right angles. The symmetry and unique properties of kite shapes make them interesting geometric figures.

Kite shapes are used to explore properties such as symmetry, area, and perimeter. They are applicable in various mathematical contexts, including geometry and design.

Topic

Geometry Concepts

Description

This image illustrates a triangular-shaped kite. Geometrically, a kite is a quadrilateral with two pairs of adjacent equal-length sides and diagonals that intersect at right angles. The symmetry and unique properties of kite shapes make them interesting geometric figures.

Kite shapes are used to explore properties such as symmetry, area, and perimeter. They are applicable in various mathematical contexts, including geometry and design.

Teacher's Script: "Observe this kite. How is this a kite in the everyday sense? Is this a kite in the geometric sense?"

Topic

Geometry Concepts

Description

This image features a triangular-shaped kite. Geometrically, a kite is a quadrilateral with two pairs of adjacent equal-length sides and diagonals that intersect at right angles. The symmetry and unique properties of kite shapes make them interesting geometric figures.

Kite shapes are used to explore properties such as symmetry, area, and perimeter. They are applicable in various mathematical contexts, including geometry and design.

Teacher's Script: "Examine this kite. How is it a kite in the everyday sense? Is it geometrically a kite?"

Topic

Geometry Concepts

Description

This image depicts a triangular-shaped kite. Geometrically, a kite is characterized by two pairs of adjacent equal-length sides and diagonals that intersect at right angles. This geometric configuration is symmetrical and unique.

Kite shapes are used to explore geometric properties such as symmetry, area, and perimeter. They are applicable in various fields, including mathematics, design, and architecture.

Teacher's Script: "Look at this kite. How is this a kite in the everyday sense? Is this a kite in the geometric sense?"