Illustrative Math Alignment: Grade 8 Unit 3

This is part of a series of video animations of three-dimensional figures. These animations show different views of these figures: top, side, and bottom. Many of these figures are a standard part of the geometry curriculum and being able to recognize them is important.

Study these animations to learn the basic properties of these 3D figures. In particular, make a note of their sides, edges, and vertices. Look for any symmetries they have. Look for polygon shapes that are familiar. Finally, think of real-world examples that use these  figures.

Below we also include information about Platonic solids and 2D nets of these 3D figures. To get a better understanding of these 3D figures, study these basic forms.

This is part of a series of video animations of three-dimensional figures. These animations show different views of these figures: top, side, and bottom. Many of these figures are a standard part of the geometry curriculum and being able to recognize them is important.

Study these animations to learn the basic properties of these 3D figures. In particular, make a note of their sides, edges, and vertices. Look for any symmetries they have. Look for polygon shapes that are familiar. Finally, think of real-world examples that use these  figures.

Below we also include information about Platonic solids and 2D nets of these 3D figures. To get a better understanding of these 3D figures, study these basic forms.

This is part of a series of video animations of three-dimensional figures. These animations show different views of these figures: top, side, and bottom. Many of these figures are a standard part of the geometry curriculum and being able to recognize them is important.

Study these animations to learn the basic properties of these 3D figures. In particular, make a note of their sides, edges, and vertices. Look for any symmetries they have. Look for polygon shapes that are familiar. Finally, think of real-world examples that use these  figures.

Below we also include information about Platonic solids and 2D nets of these 3D figures. To get a better understanding of these 3D figures, study these basic forms.

This is the Teacher's Guide that accompanies Algebra Applications: Linear Functions.

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This is the Teacher's Guide that accompanies Algebra Nspirations: Inequalities.

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In this program, internationally acclaimed mathematics educator Dr. Monica Neagoy, explores the nature of linear functions through the use TI graphing calculators. Examples ranging from air travel, construction, engineering, and space travel provide real-world examples for discovering algebraic concepts. All examples are solved algebraically and then reinforced through the use of the TI-Nspire. Algebra teachers looking to integrate hand-held technology and visual media into their instruction will benefit greatly from this series. Concepts explored: Standard form, slope-intercept form, point-slope form, solving linear equations.

Topic

3D Geometry

Description

This animation demonstrates how rotating a circle around its diameter creates a sphere. It's a powerful visualization of how 2D shapes can generate 3D objects through rotation, illustrating a fundamental concept in solid geometry and calculus.

Using animated math clip art like this helps students understand the relationship between 2D and 3D shapes, as well as the concept of solids of revolution. It bridges the gap between abstract mathematical concepts and visual representations, making complex ideas more accessible and engaging for learners.

Teachers can use this animation to introduce or reinforce various mathematical concepts:

In this presentation we show how to convert a linear equation in Standard Form to a linear function in Slope Intercept Form. We go over the reason for such a conversion and applications that give rise to these equations. Note: The download is a PPT.

Linear Expressions, Equations, and Functions

Linear Expressions, Equations, and Functions

Linear Expressions, Equations, and Functions

Linear Expressions, Equations, and Functions

Linear Expressions, Equations, and Functions

In this program, internationally acclaimed mathematics educator Dr. Monica Neagoy, explores the nature of linear functions through the use TI graphing calculators. Examples ranging from air travel, construction, engineering, and space travel provide real-world examples for discovering algebraic concepts. All examples are solved algebraically and then reinforced through the use of the TI-Nspire. Algebra teachers looking to integrate hand-held technology and visual media into their instruction will benefit greatly from this series. Concepts explored: Standard form, slope-intercept form, point-slope form, solving linear equations.

In this Investigation we look at linear models for objects moving at a constant speed. This video is Segment 1 of a 4 segment series related to Algebra Nspirations: Linear Functions. Segments 1 and 2 are grouped together.

In this Investigation we look at a linear regression for carbon dioxide emission data. This video is Segment 3 of a 4 segment series related to Algebra Nspirations: Linear Functions. Segments 3 and 4 are grouped together.

In this program we explore the properties of three-dimensional figures. We do this in the context of two real-world applications. In the first, we look at the three-dimensional structure of Mayan pyramids. These stair-step structures provide a unique opportunity to also explore sequences and series. In the second application we look at the Shanghai Tower as an example of cylindrically shaped structures.

Study these animations to learn the basic properties of these 3D figures. In particular, make a note of their sides, edges, and vertices. Look for any symmetries they have. Look for polygon shapes that are familiar. Finally, think of real-world examples that use these  figures.

We visit ancient Greece to learn about the Platonic Solids. This provides an introduction to the more general topic of three-dimensional figures.

Study these animations to learn the basic properties of these 3D figures. In particular, make a note of their sides, edges, and vertices. Look for any symmetries they have. Look for polygon shapes that are familiar. Finally, think of real-world examples that use these  figures.

Below we also include information about Platonic solids and 2D nets of these 3D figures. To get a better understanding of these 3D figures, study these basic forms.

Rectangular Prisms. Mayan pyramids are essentially stacks of rectangular prisms. The volume of each successive level is a percentage decrease of its lower neighbor. This introduces the notion of a geometric sequence and series, including an infinite series.

Study these animations to learn the basic properties of these 3D figures. In particular, make a note of their sides, edges, and vertices. Look for any symmetries they have. Look for polygon shapes that are familiar. Finally, think of real-world examples that use these  figures.

Below we also include information about Platonic solids and 2D nets of these 3D figures. To get a better understanding of these 3D figures, study these basic forms.

The Shanghai Tower in China is a stack of cylindrical shapes, where each successive layer is a percentage decrease of its lower neighbor. As with the previous section, this introduces the notion of a geometric sequence and series.

Study these animations to learn the basic properties of these 3D figures. In particular, make a note of their sides, edges, and vertices. Look for any symmetries they have. Look for polygon shapes that are familiar. Finally, think of real-world examples that use these  figures.

Below we also include information about Platonic solids and 2D nets of these 3D figures. To get a better understanding of these 3D figures, study these basic forms.

Video Tutorial: Linear Functions: Negative Slope, Negative y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a negative slope and a negative y-intercept.

Video Tutorial: Linear Functions: Negative Slope, Positive y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a negative slope and a positive y-intercept.

Video Tutorial: Linear Functions: Negative Slope, Zero y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a negative slope and a zero y-intercept.

Video Tutorial: Linear Functions: Positive Slope, Negative y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a positive slope and a negative y-intercept.

Video Tutorial: Linear Functions: Positive Slope, Positive y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a positive slope and a positive y-intercept.

Video Tutorial: Linear Functions: Positive Slope, Zero y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a positive slope and a zero y-intercept.

Explore Fahrenheit-vs-Celsius graphs using this Desmos graphing calculator activity. In this activity explore linear functions of the form y = mx + b. There is a companion worksheet for this activity, which subscribers can download. The worksheet is a PDF file. Related Resources

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Explore Cost-vs-Time graphs using this Desmos graphing calculator activity. In this activity explore linear functions of the form y = mx. There is a companion worksheet for this activity, which subscribers can download. The worksheet is a PDF file. Related Resources

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

Desmos Collection

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Explore Cost-vs-Time graphs using this Desmos graphing calculator activity. In this activity explore linear functions of the form y = mx + b. There is a companion worksheet for this activity, which subscribers can download. The worksheet is a PDF file. Related Resources

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

Desmos Collection

To see the complete collection of Desmos Resources click on this link.

Explore Cricket Chirps-vs-Temperature graphs using this Desmos graphing calculator activity. In this activity explore linear functions of the form y = mx + b. There is a companion worksheet for this activity, which subscribers can download. The worksheet is a PDF file. Related Resources

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

Desmos Collection

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Explore Distance-vs-Time graphs using this Desmos graphing calculator activity. This activity explores linear functions of the form y = mx. There is a companion worksheet for this activity, which subscribers can download. The worksheet is a PDF file.

Related Resources

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Desmos Collection

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Explore Distance-vs-Time graphs using this Desmos graphing calculator activity. This activity explores linear functions of the form y = mx + b. There is a companion worksheet for this activity, which subscribers can download. The worksheet is a PDF file. Related Resources

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

Desmos Collection

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Explore Hooke's Law using this Desmos graphing calculator activity. In this activity explore linear functions of the form y = mx. There is a companion worksheet for this activity, which subscribers can download. The worksheet is a PDF file. Related Resources To see additional resources on this topic click on the Related Resources tab above. Desmos Collection To see the complete collection of Desmos Resources click on this link.

In this graphing calculator activity, have your students explore linear functions of the form y = mx + b. This Desmos template allows students to explore the effect of changes in the slope (m) and the y-intercept (b) have on the graph of the line. A companion downloadable worksheet uses the graphing calculator template to explore the properties of these linear functions. Note: The download is a PDF worksheet. Related Resources To see additional resources on this topic click on the Related Resources tab above. Desmos Collection To see the complete collection of Desmos Resources click on this link.

The formula for the Surface Area of a Sphere.

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The formula for the Volume of a Sphere.

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This is the Teacher's Guide that accompanies Geometry Applications: 3D Geometry.

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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.

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

Note: The download is a PPT file.

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

Note: The download is a PPT file.

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

Note: The download is a PPT file.

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

Note: The download is a PPT file.

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

Note: The download is a PPT file.

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

Note: The download is a PPT file.

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

Note: The download is a PPT file.

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

Note: The download is a PPT file.

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

Note: The download is a PPT file.

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

Note: The download is a PPT file.

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In this Slide Show, use the Desmos graphing calculator to explore linear equations in slope intercept form. To see the complete collection of Desmos Resources click on this link.

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