Illustrative Math Alignment: Grade 8 Unit 9

Topic

Polygons

Description

This example presents an octagon with sides labeled as x, y, z, w, u, t, s, and v. The sides are of varying lengths and angles, indicating it is irregular. It illustrates how using different variables for both side lengths and angles can suggest irregularity in a polygon.

Polygon classification is a crucial topic in geometry that helps students distinguish between regular and irregular shapes. This collection of examples provides a comprehensive look at various types of octagons, highlighting the importance of considering both side lengths and angle measures in determining regularity.

Topic

Polygons

Description

This example features an octagon with angles labeled as 155° and 125°, and other angles labeled with variables t, v, w, x, y, and z. The angles vary, indicating it is irregular. It demonstrates how a combination of specific angle measures and variables can be used to show irregularity in polygons.

Understanding polygon classification is essential in geometry as it helps students recognize and categorize shapes based on their properties. This collection of examples highlights the importance of angle measures in determining the regularity of octagons, showing that even partial information can be sufficient for classification.

Topic

Polygons

Description

This example showcases a pentagon with each angle labeled as 108 degrees, indicating congruent angles. It demonstrates that a regular pentagon can be identified not only by equal side lengths but also by equal angle measures.

Understanding polygon classification is crucial in geometry as it helps students recognize and categorize shapes based on their properties. This collection of examples highlights different aspects of regular pentagons, emphasizing both side length and angle measure as defining characteristics.

Topic

Polygons

Description

This example presents a pentagon labeled with vertices A, B, C, D, and E, with each side marked with an "x" to indicate equal length. It reinforces the concept of a regular pentagon by visually representing the equality of all sides.

Polygon classification is a fundamental topic in geometry that helps students understand the properties and relationships of different shapes. This collection of examples provides various representations of regular pentagons, emphasizing the importance of side length equality in classification.

Topic

Polygons

Description

This example features a pentagon labeled with vertices A, B, C, D, and E, where two angles are marked as 108 degrees, and the other angles are marked as "x". It demonstrates how to determine if a pentagon is regular by solving for the unknown angle measures.

Understanding polygon classification is essential in geometry as it helps students analyze and categorize shapes based on their properties. This collection of examples highlights different aspects of regular pentagons, emphasizing both side length and angle measure as defining characteristics.

Topic

Polygons

Description

This example showcases a pentagon labeled with vertices A, B, C, D, and E, where the sides have different lengths: 5, 7, 7, 5, and 6 units. It illustrates an irregular pentagon, demonstrating that not all five-sided figures are regular.

Polygon classification is a crucial topic in geometry that helps students distinguish between regular and irregular shapes. This collection of examples provides a comprehensive look at various types of pentagons, highlighting the differences between regular and irregular polygons based on side lengths and angle measures.

Topic

Polygons

Description

This example presents a pentagon labeled with vertices A, B, C, D, and E, where the sides are marked with variables x, y, and z, indicating different lengths. It demonstrates another instance of an irregular pentagon, emphasizing that side length variation results in irregularity.

Understanding polygon classification is crucial in geometry as it helps students recognize and categorize shapes based on their properties. This collection of examples highlights the differences between regular and irregular pentagons, focusing on side length as a key determining factor.

Topic

Polygons

Description

This example features a pentagon labeled with vertices A, B, C, D, E, where the sides are labeled as y, z, 5, 4, and x. It illustrates another case of an irregular pentagon, demonstrating that the presence of different side lengths, including both numeric and variable representations, results in irregularity.

Polygon classification is a fundamental concept in geometry that helps students analyze and categorize shapes based on their properties. This collection of examples provides a comprehensive look at various types of pentagons, emphasizing the importance of side length equality in determining regularity.

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

Related Resources

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

This set of tutorials provides 56 examples of transformations of geometric figures on a graph.

Related Resources

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

This set of tutorials provides 56 examples of transformations of geometric figures on a graph. NOTE: The download is a PPT file.

Roller coasters provide an ideal opportunity to explore translations and rotations. Displacement vectors are also introduced. Note: The download for this resources is the Promethean Flipchart.

To access the full video [Geometry Applications: Transformations, Segment 1: Translations and Rotations]: https://www.media4math.com/library/geometry-applications-transformations-segment-1-translations-and-rotations

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-transformations-segment-1-translations-and-rotations

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. Note: The download for this resources is the Promethean Flipchart.

To access the full video [Geometry Applications: Transformations, Segment 2: 3D Translations]: https://www.media4math.com/library/geometry-applications-transformations-segment-2-3d-translations

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-transformations-segment-2-3d-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. Note: The download for this resources is the Promethean Flipchart.

The full video [Geometry Applications: Transformations, Segment 3: Rotations, Reflections, and Symmetry] can be found here: https://media4math.com/library/geometry-applications-transformations-segment-3-rotations-reflections-and-symmetry

This is the transcript for the video of same title. Video contents: 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.

This is the transcript for the video of same title. Video contents: 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.

This is the transcript for the video of same title. Video contents: 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.

This is the transcript for the video of same title. Video contents: The Petronas Towers in Indonesia provide an opportunity to explore the composite shapes used in the design of the towers.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript for the video of same title. Video contents: 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.

This is the transcript for the video of same title. Video contents: Roller coasters provide an ideal opportunity to explore translations and rotations. Displacement vectors are also introduced.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript for the video of same title. Video contents: 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.

This is the transcript for the video of same title. Video contents: 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

Area and Volume

Description

This segment focuses on surface area, using the Louvre Pyramid to highlight geometric tessellations and triangular net calculations. It explains the surface area formula for pyramids and how these calculations are applied in architectural design and material efficiency.

Topic

Polygons

Topic

Polygons

Description

This segment introduces polygons through the Pentagon's design. The building’s advantages include increased perimeter and accessibility due to its five-sided structure, illustrating how polygons solve real-world design challenges. Key concepts include perimeter, angles, and design versatility.

Relevance to Topic: This video explains and highlights various applications of polygons in real-life scenarios and mathematical contexts, providing valuable insights for understanding geometric concepts.

Topic

Polygons

Description

The segment explores Islamic art’s reliance on geometric patterns formed by regular polygons. It demonstrates how artisans used compasses and straightedges to create precise designs, highlighting properties like congruent sides and angles, and applications in tiling and architecture.

Relevance to Topic: This video explains and highlights various applications of polygons in real-life scenarios and mathematical contexts, providing valuable insights for understanding geometric concepts.

Topic

Polygons

Description

Composite figures in architecture, like the Petronas Towers, combine polygons to form complex shapes. This segment examines patterns like overlapping squares and calculates areas using properties of triangles and hexagons. Applications include architectural symmetry and efficiency.

Relevance to Topic: This video explains and highlights various applications of polygons in real-life scenarios and mathematical contexts, providing valuable insights for understanding geometric concepts.

Topic

Transformations

Topic

Transformations

Description

Explores translations and rotations in motion, using roller coasters as an example. Key concepts include displacement vectors, magnitude, and direction, modeled geometrically and computationally for practical applications in physics and engineering.

Topic

Transformations

Description

This segment applies 3D translations to logistics, focusing on container arrangement in shipping. Using coordinate systems, it demonstrates efficiency in loading/unloading cargo, leveraging geometric organization and data sorting methods for real-world impact.

Topic

Transformations

Description

Analyzes observatory designs and their use of rotational and reflective symmetry for astronomical viewing. The segment models celestial movements and applies rotational geometry concepts to optimize the structure’s functionality.

This is part of a collection of math worksheets that are crossword puzzles of math vocabulary.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of geometric shapes.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of geometric shapes.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of geometric shapes.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of geometric shapes.

Related Resources

Worksheet Library