Illustrative Math Alignment: Grade 8 Unit 3

Topic

Geometric Models

Topic

Geometric Models

Topic

Geometric Models

In this Algebra Application, students develop a linear mathematical model based on the maximum heart rate during exercise based on age. Using this model, students investigate heart rate for moderate and vigorous workouts. The math topics covered include: Mathematical modeling, Linear functions, Families of functions, Computational thinking. The culminating activity is for students to create a simple program (using either a spreadsheet or a programming language like Python) to develop an exercise chart. This is a great back-to-school activity for middle school or high school students. A relevant real-world application allows them to review math concepts.

In this Algebra Application, students study the direction between diameter and circumference of a circle. Through measurement and data gathering students analyze the line of best fit and explore ways of calculating pi. The math topics covered include: Mathematical modeling, Linear functions, Data gathering and analysis, Ratios, Direct variation. This is a great back-to-school activity for middle school or high school students. This is also a great crossover activity that ties algebra and geometry.

This slide show provides 8 examples of quadratic functions in factored form and analyzes their graphs.

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This slide show provides 18 examples of quadratic functions in standard form and analyzes their graphs.

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This slide show provides 8 examples of quadratic functions in vertex form and analyzes their graphs.

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In this Slide Show, apply concepts of linear functions to the context of circumference vs. diameter.

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In this Slide Show, apply concepts of linear functions to the context of cost vs. time data and graphs.

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In this Slide Show, apply concepts of linear functions to the context of cricket chirps.

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In this Slide Show, apply concepts of linear functions to the context of distance vs. time data and graphs.

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In this Slide Show, apply concepts of linear functions to the context of Hooke's law.

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In this Slide Show, apply concepts of linear functions to the context of momentum and impulse.

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In this Slide Show, apply concepts of linear functions to the context of rectangular perimeter.

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In this Slide Show, apply concepts of linear functions to the context of saving money.

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In this Slide Show, apply concepts of linear functions to the context of speed and acceleration.

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In this Slide Show, apply concepts of linear functions to the context of converting Celsius and Fahrenheit temperatures.

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In this Slide Show, use the Desmos graphing calculator to explore absolute value functions. To see the complete collection of Desmos Resources click on this link.

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In this Slide Show, use the Desmos graphing calculator to explore linear functions. To see the complete collection of Desmos Resources click on this link.

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In this Slide Show, learn about graphs of linear functions.

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In this Slide Show, learn about linear function models.

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The complete set of 32 examples that make up this set of tutorials.

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This set of tutorials provides 32examples that involve finding the equation of a line parallel or perpendicular to a given line and through a given point.

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This set of tutorials provides an overview of the 24 worked-out examples that show how to calculate the surface area of different three-dimensional figures.

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This set of tutorials provides 40 examples of absolute value functions in tabular and graph form. NOTE: The download is a PPT file.

In this Slide Show, absolute value functions are graphed, including graphs centered at the origin, graphs displaced along the x-axis, and graphs displaced along the y-axis. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

In this Slide Show, the Graph Window is used to graph linear inequalities. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

In this Slide Show, the Graph Window is used to graph inequalities using sliders. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

In this Slide Show, linear functions are graphed. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

In this Slide Show, explore the properties of parallel and perpendicular lines. Use a slider to define the slope and then graph parallel and perpendicular lines linked to this slider.

In this Slide Show, we show how to construct the perpendicular bisectors of the three sides of a triangle to show they intersect at a single point. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

In this TI-Nspire Activity, use the Geometry and Graphing Tools to explore the ratio of Circumference to Radius as a linear function. 

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This interactive crossword puzzle tests knowledge of key terms on the topic of the graphs of Parallel and Perpendicular Lines.

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Use this Jeopardy-style math game to review linear functions. This Jeopardy game has a bank of hundreds of questions for thousands of unique game experiences. To see the complete set of Math Games and Puzzles, click on this link.

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In this drag-and-drop game, match the linear equation with the equation of a parallel line through a given point. This game generates thousands of different equation combinations, offering an ideal opportunity for skill review in a game format.

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In this drag-and-drop game, match the linear equation with the equation of a perpendicular line through a given point. This game generates thousands of different equation combinations, offering an ideal opportunity for skill review in a game format.

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In this drag-and-drop game, match f(x) with f(a) for a given value of a. This game generates thousands of different equation combinations, offering an ideal opportunity for skill review in a game format.

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In this drag-and-drop game, match f(x) with f(a) for a given value of a. This game generates thousands of different equation combinations, offering an ideal opportunity for skill review in a game format.

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In this drag-and-drop game, match the linear function in standard form with its slope-intercept counterpart. This game generates thousands of different equation combinations, offering an ideal opportunity for skill review in a game format.

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Use this math game to review linear functions in slope-intercept form.

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Use this math game to review 3D figures. This is a Memory-style game in which students must remember the location of pairs of identical images.

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In this Math Riddles Game, have your students review vocabulary around the topic of 3D Geometry. The Math Riddles games are useful for practicing: Math Vocabulary, Key Concepts, Critical Thinking.

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Lesson Plan: Linear Functions and Applications

This is the fifth and final lesson in a five-part series on linear equations and inequalities designed for middle school students. In this lesson, students explore linear functions in-depth, learning how to represent them using equations, tables, and graphs. They will analyze key function properties, including slope, y-intercept, domain, and range, to develop a complete understanding of how linear functions behave.

The lesson focuses on real-world applications, demonstrating how linear functions are used in various fields such as finance, physics, and business. Students will solve problems involving rates of change, cost analysis, and motion, reinforcing the practical significance of linear functions. Through guided practice and hands-on activities, they will interpret linear relationships and predict outcomes using function models.

In this lesson, students will explore direct variation, a special type of proportional relationship where one variable is a constant multiple of another. They will learn how to identify direct variation in tables, graphs, and equations, determine the constant of variation (\( k \)), and understand how direct variation relates to linear functions.

Key concepts covered in this lesson include:

In this lesson, students explore the properties of parallel and perpendicular lines in coordinate geometry. They will learn how to identify these lines based on their slopes, determine equations for parallel and perpendicular lines, and apply these concepts to solve real-world and mathematical problems.

Key concepts covered in this lesson include:

This lesson is the third installment in Media4Math's comprehensive six-part series on understanding slope in mathematics. It focuses on helping students visualize and comprehend slope by engaging in hands-on activities that involve plotting points on a coordinate plane and analyzing the resulting lines.

This lesson is the sixth and final installment in Media4Math's comprehensive six-part series on understanding slope in mathematics. It focuses on interpreting slope as a rate of change between two quantities, enabling students to apply this concept to real-world scenarios and mathematical problems.

In this engaging math lesson, students explore cross-sections of cubes, cylinders, and cones through interactive activities, real-world examples, and animated visuals. They will learn how slicing three-dimensional shapes in different ways produces a variety of two-dimensional figures, helping to develop spatial reasoning and geometric understanding.

The lesson begins with a conceptual introduction to cross-sections, followed by hands-on practice with everyday objects such as gift boxes, paper towel rolls, and ice cream cones. Students will investigate how horizontal, vertical, and diagonal slices impact the resulting shapes. Animated GIFs illustrate these concepts, reinforcing learning through dynamic visual representations.

In this engaging geometry lesson, students will explore how rectangular prisms, spheres, and pyramids are affected by different slicing planes. Using visual aids, real-world examples, and hands-on activities, students will identify the cross-sections created by horizontal, vertical, and diagonal cuts.

Through interactive exploration, students will learn that a rectangular prism produces rectangular or parallelogram cross-sections, a sphere always results in a circular cross-section regardless of the slicing direction, and a pyramid creates triangles, trapezoids, or smaller versions of its base. The lesson also introduces the volume formula for a rectangular prism, reinforcing the connection between cross-sections and three-dimensional measurements.