Illustrative Math Alignment: Grade 7 Unit 9

Putting it All Together

Lesson 9: Measurement Error (Part 2)

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Topic
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 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 20	Math Example--Polygons--Polygon Classification: Example 20 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 21	Math Example--Polygons--Polygon Classification: Example 21 This is part of a collection of math examples that focus on geometric shapes.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 22	Math Example--Polygons--Polygon Classification: Example 22 This is part of a collection of math examples that focus on geometric shapes.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 23	Math Example--Polygons--Polygon Classification: Example 23 This is part of a collection of math examples that focus on geometric shapes.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 24	Math Example--Polygons--Polygon Classification: Example 24 This is part of a collection of math examples that focus on geometric shapes.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 25	Math Example--Polygons--Polygon Classification: Example 25 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 26	Math Example--Polygons--Polygon Classification: Example 26 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 27	Math Example--Polygons--Polygon Classification: Example 27 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 28	Math Example--Polygons--Polygon Classification: Example 28 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 29	Math Example--Polygons--Polygon Classification: Example 29 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 3	Math Example--Polygons--Polygon Classification: Example 3 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 30	Math Example--Polygons--Polygon Classification: Example 30 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 31	Math Example--Polygons--Polygon Classification: Example 31 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 32	Math Example--Polygons--Polygon Classification: Example 32 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 33	Math Example--Polygons--Polygon Classification: Example 33 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 34	Math Example--Polygons--Polygon Classification: Example 34 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 35	Math Example--Polygons--Polygon Classification: Example 35 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 36	Math Example--Polygons--Polygon Classification: Example 36 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 4	Math Example--Polygons--Polygon Classification: Example 4 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 5	Math Example--Polygons--Polygon Classification: Example 5 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 6	Math Example--Polygons--Polygon Classification: Example 6 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 7	Math Example--Polygons--Polygon Classification: Example 7 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 8	Math Example--Polygons--Polygon Classification: Example 8 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.	Definition of a Polygon
Math Example--Polygons--Polygon Classification: Example 9	Math Example--Polygons--Polygon Classification: Example 9 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.	Definition of a Polygon
Math Example--Volume Concepts--Calculating Volume: Example 1	Math Example--Volume Concepts--Calculating Volume: Example 1 Topic Volume Description A rectangular prism with dimensions labeled: length = 30, width = 10, and height = 8. The image shows how to find the volume of the prism using the formula for volume of a rectangular prism. This image illustrates Example 1: The caption explains how to calculate the volume of the rectangular prism using the formula V = l * w * h. The given dimensions are substituted into the formula: V = 30 * 10 * 8 = 2400..	Volume
Math Example--Volume Concepts--Calculating Volume: Example 10	Math Example--Volume Concepts--Calculating Volume: Example 10 Topic Volume Description A green cylinder with a general radius y and height x. The radius is marked on the top surface, and the height is marked on the side. This image illustrates Example 10: The task is to find the volume of this cylinder. The volume formula V = πr2h is used, and substituting r = y and h = x, the volume is calculated as V = xy2π.	Volume
Math Example--Volume Concepts--Calculating Volume: Example 11	Math Example--Volume Concepts--Calculating Volume: Example 11 Topic Volume Description A hollow green cylinder with an outer radius of 10 units, an inner radius of 9 units, and a height of 15 units. The radii are marked on the top surface, and the height is marked on the side. This image illustrates Example 11: The task is to find the volume of this hollow cylinder. The volume formula for a hollow cylinder V = πr12h1 - πr22h2 is used. Substituting values, the result is V = 285π.	Volume
Math Example--Volume Concepts--Calculating Volume: Example 12	Math Example--Volume Concepts--Calculating Volume: Example 12 Topic Volume Description A hollow green cylinder with an outer radius y, an inner radius y - 1, and a height x. The radii are marked on the top surface, and the height is marked on the side. This image illustrates Example 12: The task is to find the volume of this hollow cylinder. Using V = π(r12h1 - r22h2), substituting values gives: V = πx(y2 - (y - 1)2= πx(2y - 1).	Volume
Math Example--Volume Concepts--Calculating Volume: Example 13	Math Example--Volume Concepts--Calculating Volume: Example 13 Topic Volume Description A rectangular-based pyramid is shown with dimensions: base length 10, base width 8, and height 30. The image demonstrates how to calculate the volume of this pyramid. This image illustrates Example 13: The caption provides a step-by-step solution for calculating the volume of a pyramid with a rectangular base using the formula V = (1/3) * Area of Base * h. Substituting values: V = (1/3) * 8 * 10 * 30 = 800.	Volume
Math Example--Volume Concepts--Calculating Volume: Example 14	Math Example--Volume Concepts--Calculating Volume: Example 14 Topic Volume Description A general rectangular-based pyramid is shown with variables x, y, and z representing the base dimensions and height. This example shows how to calculate the volume of a pyramid using variables instead of specific numbers. This image illustrates Example 14: The caption explains how to calculate the volume of a pyramid with a rectangular base using the formula V = (1/3) * Area of Base * h, which simplifies to V = (1/3) * x * y * z.	Volume
Math Example--Volume Concepts--Calculating Volume: Example 15	Math Example--Volume Concepts--Calculating Volume: Example 15 Topic Volume	Volume
Math Example--Volume Concepts--Calculating Volume: Example 16	Math Example--Volume Concepts--Calculating Volume: Example 16 Topic Volume Description A truncated rectangular-based pyramid is shown with variables x, y, and z representing dimensions. The smaller virtual pyramid has reduced dimensions by 3 units for both width and length and reduced height by z - 20. The image demonstrates how to calculate the volume in terms of variables. This image illustrates Example 16: The caption explains how to find the volume of a truncated pyramid using variables for both pyramids' dimensions. Formula: V = (1/3) * xy(z + 20) - (1/3) * (y - 3)(x - 3)(z), which simplifies to V = (1/3) * (xyz + 60x + 60y - 180).	Volume
Math Example--Volume Concepts--Calculating Volume: Example 17	Math Example--Volume Concepts--Calculating Volume: Example 17 Topic Volume Description A green sphere with a radius labeled as 3. The image is part of a math example showing how to calculate the volume of a sphere. This image illustrates Example 17: The text describes finding the volume of a sphere. The formula used is V = (4/3) * π * r3, where r = 3. After substituting, the result is V = 36π. Volume is a fundamental concept in geometry that helps students understand the space occupied by three-dimensional objects. In this collection, each example uses various geometric shapes to calculate volume, showcasing real-life applications of volume in different shapes.	Volume
Math Example--Volume Concepts--Calculating Volume: Example 18	Math Example--Volume Concepts--Calculating Volume: Example 18 Topic Volume Description A green sphere with a radius labeled as x. This image is part of a math example showing how to calculate the volume of a sphere using an unknown radius. This image illustrates Example 18: The text explains how to find the volume of a sphere with an unknown radius x. The formula used is V = (4/3) * π * r3, and substituting r = x gives V = (4/3) * x3 * π.	Volume
Math Example--Volume Concepts--Calculating Volume: Example 19	Math Example--Volume Concepts--Calculating Volume: Example 19 Topic Volume Description A green cube with side length labeled as 7. The image illustrates how to calculate the volume of a cube with known side length. This image illustrates Example 19: The text describes finding the volume of a cube. The formula used is V = s3, where s = 7. After substituting, the result is V = 343. Volume is a fundamental concept in geometry that helps students understand the space occupied by three-dimensional objects. In this collection, each example uses various geometric shapes to calculate volume, showcasing real-life applications of volume in different shapes.	Volume
Math Example--Volume Concepts--Calculating Volume: Example 2	Math Example--Volume Concepts--Calculating Volume: Example 2 Topic Volume Description A rectangular prism with dimensions labeled as x, y, and z. The image shows a general example of calculating the volume of a rectangular prism using variables instead of specific numbers. This image illustrates Example 2: The caption describes how to find the volume of a rectangular prism using variables for length (x), width (y), and height (z). The formula is given as V = x * y * z, but no specific values are provided.	Volume

Illustrative Math Alignment: Grade 7 Unit 9

Putting it All Together

Lesson 9: Measurement Error (Part 2)

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