Illustrative Math Alignment: Grade 6 Unit 1

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

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

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

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

Topic

Polygons

Description

This example showcases a pentagon with all sides labeled as 5. It demonstrates a regular pentagon, characterized by five sides of equal length. This visual representation helps students understand the concept of regular polygons and their defining characteristics.

The topic of polygon classification is crucial in geometry. This collection of examples provides a comprehensive look at various types of pentagons, both regular and irregular. By examining different configurations of sides and angles, students can develop a deeper understanding of polygon properties and classification criteria.

Topic

Polygons

Description

This example showcases a pentagon labeled with vertices A, B, C, D, E, where the angles are marked as 110°, 95°, 120°, 107°, and 108°. It demonstrates an irregular pentagon based on the variation in angle measures, highlighting that regularity depends on both side lengths and angle measures.

Understanding polygon classification is essential in geometry as it helps students recognize and categorize shapes based on their properties. This collection of examples emphasizes the importance of both side lengths and angle measures in determining the regularity of pentagons.

Topic

Polygons

Description

This example presents a pentagon labeled with vertices A, B, C, D, E, where the sides are marked with variables w, x, y, z, and v. It illustrates an irregular pentagon by using different variables to represent potentially different side lengths, emphasizing that side length variation 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, highlighting the importance of side length equality in determining regularity.

Topic

Polygons

Description

This example features a pentagon labeled with vertices A, B, C, D, E, where the angles are marked as 108°, x, y, z, and 107°. It demonstrates an irregular pentagon based on the variation in angle measures, highlighting that regularity depends on all angles being equal.

Understanding polygon classification is essential in geometry as it helps students recognize and categorize shapes based on their properties. This collection of examples emphasizes the importance of angle measures in determining the regularity of pentagons, showing that even one different angle makes the polygon irregular.

Topic

Polygons

Description

This example showcases a hexagon with all sides labeled as 5, indicating equal length. It demonstrates a regular hexagon, characterized by six sides of equal length. This visual representation helps students understand the concept of regular polygons and their defining characteristics.

The topic of polygon classification is crucial in geometry. This collection of examples provides a comprehensive look at various types of hexagons, both regular and irregular. By examining different configurations of sides and angles, students can develop a deeper understanding of polygon properties and classification criteria.

Topic

Polygons

Description

This example presents a hexagon with all sides labeled as x, indicating equal length. It illustrates another instance of a regular hexagon, reinforcing the concept that a regular polygon has all sides of equal length, even when represented by a variable.

Polygon classification is a fundamental topic in geometry that helps students understand the properties and characteristics of different shapes. This collection of examples provides a comprehensive overview of various hexagon types, allowing students to distinguish between regular and irregular polygons based on their side lengths and angle measures.

Topic

Polygons

Description

This example features a hexagon with sides labeled y, x, and 5, showing that x = y = 5, making all sides equal in length. It demonstrates a regular hexagon by using a combination of variables and numeric values to represent equal side lengths.

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 ways to represent regular hexagons, emphasizing the importance of side length equality in classification.

Topic

Polygons

Description

This example showcases a hexagon with all interior angles labeled as 120 degrees, indicating equal angles. It demonstrates that a regular hexagon can be identified not only by equal side lengths but also by equal angle measures, reinforcing the dual criteria for regularity in polygons.

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 aspects of regular hexagons, emphasizing both side length and angle measure as defining characteristics.

Topic

Polygons

Description

This example presents a hexagon with six equal sides labeled as x and equal angles, indicating a regular hexagon. It reinforces the concept of a regular polygon by visually representing both the equality of all sides and angles.

Understanding polygon classification is essential in geometry as it helps students recognize and categorize shapes based on their properties. This collection of examples provides various representations of regular hexagons, emphasizing the importance of both side length and angle measure equality in classification.

Topic

Polygons

Description

This example features a hexagon with two angles labeled as 120 degrees and sides labeled x and y, where x = y. It demonstrates how to determine if a hexagon is regular by solving for the unknown angle measures and confirming equal side lengths.

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 hexagons, highlighting the importance of both angle measures and side lengths in determining regularity.

Topic

Polygons

Description

This example showcases a hexagon with sides labeled with varying lengths: AB = 6, BC = 4, CD = 6, DE = 3, EF = 6, and FA = 5. It demonstrates an irregular hexagon, 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 hexagons, focusing on side length as a key determining factor.

Topic

Polygons

Description

This example presents a pentagon with all sides labeled as x, indicating equal length. It illustrates another instance of a regular pentagon, reinforcing the concept that a regular polygon has all sides of equal length.

Polygon classification is a fundamental topic in geometry that helps students understand the properties and characteristics of different shapes. This collection of examples provides a comprehensive overview of various pentagon types, allowing students to distinguish between regular and irregular polygons based on their side lengths and angle measures.

Topic

Polygons

Description

This example presents a hexagon with sides labeled as x, y, and z, indicating varying lengths. It illustrates another case of an irregular hexagon, demonstrating that the presence of different variables for side lengths suggests 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 hexagons, emphasizing the importance of side length equality in determining regularity.

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

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

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

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

Topic

Polygons

Description

This example showcases an octagon with all sides labeled as 5, indicating equal length. It demonstrates a regular octagon, characterized by eight sides of equal length. This visual representation helps students understand the concept of regular polygons and their defining characteristics.

The topic of polygon classification is crucial in geometry. This collection of examples provides a comprehensive look at various types of octagons, both regular and irregular. By examining different configurations of sides and angles, students can develop a deeper understanding of polygon properties and classification criteria.

Topic

Polygons

Description

This example presents an octagon with all sides labeled as x, indicating equal length. It illustrates another instance of a regular octagon, reinforcing the concept that a regular polygon has all sides of equal length, even when represented by a variable.

Understanding polygon classification is essential in geometry as it helps students recognize and categorize shapes based on their properties. This collection of examples provides various representations of regular octagons, emphasizing the importance of side length equality in classification.

Topic

Polygons

Description

This example features an octagon with sides labeled as x, z, and 5, showing that x = z = 5, indicating equal length for all sides. It demonstrates a regular octagon by using a combination of variables and numeric values to represent equal side lengths.

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 aspects of regular octagons, emphasizing the importance of side length equality in classification.

Topic

Polygons

Description

This example showcases an octagon with all angles labeled as 135 degrees, indicating congruent angles. It demonstrates that a regular octagon can be identified not only by equal side lengths but also by equal angle measures, reinforcing the dual criteria for regularity in polygons.

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 octagons, emphasizing both side length and angle measure as defining characteristics.

Topic

Polygons

Description

This example presents an octagon with all angles labeled as "x," indicating a regular polygon. It illustrates a regular octagon by visually representing the equality of all angles using a single variable. This reinforces the concept that a regular polygon has all angles of equal measure.

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 aspects of regular octagons, emphasizing the importance of side length equality in classification.

Topic

Polygons

Description

This example features a pentagon with sides labeled x and two sides labeled as 5, with x = 5, demonstrating that all sides are equal. It reinforces the concept of a regular pentagon by showing how different notations can represent the same length.

The study of polygon classification helps students develop critical thinking skills in geometry. This collection of examples illustrates various ways to represent and identify regular pentagons, emphasizing the importance of side length equality in classification.

Topic

Polygons

Description

This example features an octagon with angles labeled as 135° and angles labeled as "u" and "x." It demonstrates how to determine if an octagon is regular by solving for the unknown angle measures and confirming equal side lengths.

Understanding polygon classification is essential in geometry as it helps students recognize and categorize shapes based on their properties. This collection of examples provides insights into how partial information about angle measures and side lengths can be used to determine the regularity of octagons.

Topic

Polygons

Description

This example showcases an irregular octagon with sides of varying lengths labeled as 4, 5, 6, and 3. It demonstrates that not all eight-sided figures are regular, emphasizing the importance of equal side lengths in the classification of regular polygons.

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 differences between regular and irregular polygons based on side lengths.

Topic

Polygons

Description

This example presents an irregular octagon with sides labeled as w, x, y, z, and u, indicating varying lengths. It illustrates another case of an irregular octagon, demonstrating that the presence of different variables for side lengths suggests 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 importance of considering side lengths when determining the regularity of octagons.

Topic

Polygons

Description

This example features an octagon with sides labeled as x, y, 5, and 3. The sides are of varying lengths, indicating it is irregular. It demonstrates how a combination of variables and specific numeric values can be used to show irregularity in polygons.

Polygon classification is a fundamental concept in geometry that helps students analyze and categorize shapes based on their properties. This collection of examples provides insights into how partial information about side lengths can be used to determine the irregularity of octagons.

Topic

Polygons

Description

This example showcases an octagon with angles labeled as 150°, 140°, 115°, 145°, 155°, 115°, 125°, and 135°. The angles vary, indicating it is irregular. It demonstrates that irregularity in polygons can be determined by examining angle measures alone.

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 if side lengths are not given, angle information can be sufficient for classification.

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 is the transcript for the video entitled, Desmos Geometry Exploration: Polygons. In this video tutorial the polygons are explored. Students are then shown how to construct polygons using the Desmos geometry tools. The Desmos geometry tools can be found at www.desmos.com/geometry.

This is the transcript for the video entitled, Desmos Geometry Exploration: Regular Polygons 1. In this video tutorial regular polygons are explored. The focus of this video is on triangles and quadrilaterals. Students are then shown how to construct regular polygons using the Desmos geometry tools. The Desmos geometry tools can be found at www.desmos.com/geometry.

This is the transcript for the video entitled, Desmos Geometry Exploration: Regular Polygons 2. In this video tutorial regular polygons are explored. The focus of this video is on pentagons and hexagons. Students are then shown how to construct regular polygons using the Desmos geometry tools. The Desmos geometry tools can be found at www.desmos.com/geometry.

This is part of a collection of video tutorials on the topic of using the Desmos Geometry tools to explore geometric concepts.

This is part of a collection of video tutorials on the topic of using the Desmos Geometry tools to explore geometric concepts.

This is part of a collection of video tutorials on the topic of using the Desmos Geometry tools to explore geometric concepts.

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.