Illustrative Math Alignment: Grade 8 Unit 2

Dilations, Similarity, and Introducing Slope

Lesson 1: Projecting and Scaling

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Topic
Math Example--Geometric Transformation--Transformations: Example 46	Math Example--Geometric Transformation--Transformations: Example 46 Topic Transformations Description This example demonstrates a single rotation in geometric transformations. The image presents two figures labeled "Before" and "After." The left figure shows a shape on a grid, while the right one displays the same shape after a rotation around a specified point marked with a pushpin. This illustrates how an object can change its orientation without altering its size or shape.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 47	Math Example--Geometric Transformation--Transformations: Example 47 Topic Transformations Description This example illustrates a combination of rotation and reflection in geometric transformations. Two figures are presented, labeled "Before" and "After." The left figure shows the original shape on a grid, while the right figure depicts the shape after undergoing a combination of transformations: first, a rotation around a point indicated by a pushpin, followed by a reflection across a dashed red line.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 48	Math Example--Geometric Transformation--Transformations: Example 48 Topic Transformations Description This example demonstrates a single reflection in geometric transformations. The image shows two figures labeled as "Before" and "After." The left figure includes a shape positioned within a grid, and the right figure illustrates the transformed shape after reflecting across a dashed red line. This showcases how an object can be flipped over a line while maintaining its size and shape but changing its orientation.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 49	Math Example--Geometric Transformation--Transformations: Example 49 Topic Transformations Description This example demonstrates a complex combination of transformations: translation, rotation, and reflection. The image shows two house-shaped figures on a grid. The "Before" figure is on the left, and the "After" figure is on the right. The transformation involves three steps: first, a translation moves the shape, then a rotation turns it around an axis marked by a pushpin, and finally, a reflection flips it across a dashed red line representing the axis of reflection.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 5	Math Example--Geometric Transformation--Transformations: Example 5 Topic Transformations Description This example illustrates a combination of rotation and reflection in geometric transformations. Two grids labeled "Before" and "After" show a black "T" shape in different orientations. The shape first undergoes a rotation, indicated by a pushpin showing the axis of rotation, and then a reflection, shown by a red dashed line representing the axis of reflection. This demonstrates how multiple transformations can be applied sequentially to create more complex changes in orientation and position.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 50	Math Example--Geometric Transformation--Transformations: Example 50 Topic Transformations Description This example demonstrates a simple translation in geometric transformations. The image shows two star-shaped figures on a grid. The "Before" figure is on the left, and the "After" figure is on the right. The transformation consists of a simple translation from left to right, showcasing how an object can move position without changing its size or orientation.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 51	Math Example--Geometric Transformation--Transformations: Example 51 Topic Transformations Description This example illustrates a combination of translation and rotation in geometric transformations. The image shows two star-shaped figures on a grid. The "Before" figure is on the left, and the "After" figure is on the right. There are two transformations: first, a translation moves the shape, then a rotation turns it around an axis marked by a pushpin. This demonstrates how multiple transformations can be applied sequentially to create more complex changes in position and orientation.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 52	Math Example--Geometric Transformation--Transformations: Example 52 Topic Transformations Description This example demonstrates a combination of reflection and translation in geometric transformations. The image shows two star-shaped figures on a grid. The "Before" figure is on the left, and the "After" figure is on the right, located lower and to the right. There are two transformations: first, a reflection across an axis shown by a red dashed line, followed by a translation to move the shape to its final position. This illustrates how multiple transformations can be applied sequentially to create more complex changes in position and orientation.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 53	Math Example--Geometric Transformation--Transformations: Example 53 Topic Transformations Description This example demonstrates a single rotation in geometric transformations. The image shows a star on a grid labeled "Before" and "After." The star has been rotated to a new position on the grid, as indicated by a pushpin that marks the axis of rotation. This illustrates how an object can change its orientation without altering its size or shape.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 54	Math Example--Geometric Transformation--Transformations: Example 54 Topic Transformations Description This example illustrates a combination of rotation and reflection in geometric transformations. The image displays a star on a grid with "Before" and "After" labels. The transformation involves two steps: first, a rotation around an axis marked by a pushpin, and second, a reflection across a vertical axis shown by a red dashed line. This demonstrates how multiple transformations can be applied sequentially to create more complex changes in orientation and position.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 55	Math Example--Geometric Transformation--Transformations: Example 55 Topic Transformations Description This example demonstrates a single reflection in geometric transformations. In this image, a star is shown before and after undergoing a reflection. The red dashed line represents the axis of reflection, which is horizontal in this case. This showcases how an object can be flipped over a line while maintaining its size and shape but changing its orientation.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 56	Math Example--Geometric Transformation--Transformations: Example 56 Topic Transformations Description This example demonstrates a complex combination of transformations: translation, rotation, and reflection. The image shows three transformations applied to the star: first, a translation moves the star to another position, then a rotation turns it around an axis indicated by a pushpin, and finally a reflection flips it across a vertical axis shown by a red dashed line. This illustrates how multiple transformations can be applied sequentially to create more complex changes in position and orientation.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 6	Math Example--Geometric Transformation--Transformations: Example 6 Topic Transformations Description This example demonstrates a single reflection in geometric transformations. Two grids labeled "Before" and "After" show a black "T" shape in different orientations. The solution diagram below illustrates a reflection of the shape across a red dashed line, which represents the axis of reflection. This transformation showcases how an object can be flipped over a line while maintaining its size and shape.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 7	Math Example--Geometric Transformation--Transformations: Example 7 Topic Transformations Description This example illustrates a complex combination of transformations: translation, rotation, and reflection. Two grids labeled "Before" and "After" show a black "T" shape in different orientations. The solution diagram below demonstrates three sequential transformations: first, a translation moves the shape, then a rotation turns it (indicated by a pushpin showing the axis of rotation), and finally, a reflection flips it across a red dashed line representing the axis of reflection.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 8	Math Example--Geometric Transformation--Transformations: Example 8 Topic Transformations Description This example demonstrates a simple translation in geometric transformations. Two grids labeled "Before" and "After" show an "O" shape slightly shifted between the grids. The solution diagram below illustrates a translation of the shape from one position to another, showcasing how an object can move position without changing its size or orientation.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 9	Math Example--Geometric Transformation--Transformations: Example 9 Topic Transformations Description This example illustrates a combination of transformations: translation and rotation. Two circular "O" shapes are shown on a grid, one labeled "Before" and the other "After". The solution involves a translation (movement) and a rotation, with a pushpin indicating the axis of rotation. This demonstrates how multiple transformations can be applied sequentially to a shape.	Definition of Transformations
Math Example--Polygons--Polygon Classification: Example 1	Math Example--Polygons--Polygon Classification: Example 1 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 1	Math Example--Polygons--Polygon Classification: Example 1 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 10	Math Example--Polygons--Polygon Classification: Example 10 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 10	Math Example--Polygons--Polygon Classification: Example 10 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 11	Math Example--Polygons--Polygon Classification: Example 11 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 11	Math Example--Polygons--Polygon Classification: Example 11 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 12	Math Example--Polygons--Polygon Classification: Example 12 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 12	Math Example--Polygons--Polygon Classification: Example 12 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 13	Math Example--Polygons--Polygon Classification: Example 13 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 13	Math Example--Polygons--Polygon Classification: Example 13 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 14	Math Example--Polygons--Polygon Classification: Example 14 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 14	Math Example--Polygons--Polygon Classification: Example 14 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 15	Math Example--Polygons--Polygon Classification: Example 15 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 15	Math Example--Polygons--Polygon Classification: Example 15 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 16	Math Example--Polygons--Polygon Classification: Example 16 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 16	Math Example--Polygons--Polygon Classification: Example 16 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 17	Math Example--Polygons--Polygon Classification: Example 17 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 17	Math Example--Polygons--Polygon Classification: Example 17 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 18	Math Example--Polygons--Polygon Classification: Example 18 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 18	Math Example--Polygons--Polygon Classification: Example 18 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 19	Math Example--Polygons--Polygon Classification: Example 19 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 19	Math Example--Polygons--Polygon Classification: Example 19 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 2	Math Example--Polygons--Polygon Classification: Example 2 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 2	Math Example--Polygons--Polygon Classification: Example 2 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.	Definition of a Polygon

Illustrative Math Alignment: Grade 8 Unit 2

Dilations, Similarity, and Introducing Slope

Lesson 1: Projecting and Scaling

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