Illustrative Math Alignment: Grade 8 Unit 3

What Are Algebra Tiles?

This is the transcript for the video of same title. Video contents: 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.

This is the transcript for the video of same title. Video contents: We visit ancient Greece to learn about the Platonic Solids. This provides an introduction to the more general topic of three-dimensional figures.

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This is the transcript for the video of same title. Video contents: 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.

This is the transcript for the video of same title. Video contents: 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.

This is the transcript for the TI-Nspire Mini-Tutorial entitled, Exploring the Slope-Intercept form Using Sliders.

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This is the transcript for the TI-Nspire Mini-Tutorial entitled, Finding the Slope of a Line Connecting Two Points.

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This is the transcript for the TI-Nspire Mini-Tutorial entitled, Graphing a Linear Inequality.

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This is the transcript for the TI-Nspire Mini-Tutorial entitled, Graphing a Linear Inequality Using Sliders.

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This is the transcript for the TI-Nspire Mini-Tutorial entitled, Graphing a Quadratic Function.

To see the complete collection of video transcriptsy, click on this link.

Topic

Expressions and Equations

Description

The video introduces algebra tiles as tactile and visual models used to represent integers, variables, variable expressions, and equations. It describes six types of tiles, including yellow tiles for positive integers, green tiles for variables and their squares, and red tiles for their negative counterparts. Key vocabulary includes positive integers, variables, x-squared, and negative quantities. The video explains how to use combinations of tiles to model algebraic numbers and expressions.

Topic

Expressions and Equations

Description

This video covers multi-step equations with multiple operations and variables on both sides. Examples include equations like 2x - 2 = x + 4 and 2x + 4 = x - 5. It demonstrates simplifying equations and isolating variables. Key vocabulary includes multi-step equations, operations, simplification, and variables.

Topic

Expressions and Equations

Description

This video explains how to model quadratic equations, such as x2 + 2x + 1 = 0, using algebra tiles. It demonstrates how x-squared tiles, x tiles, and integer tiles represent the equation visually. Key vocabulary includes quadratic equations, x-squared, and zero pairs.

Topic

Expressions and Equations

Description

The video covers the addition of integers using algebra tiles, including examples like 4 + 5 and 4 + (-5). It highlights concepts like zero pairs for simplifying expressions and arranging tiles to model sums. Key vocabulary includes addition, zero pairs, and integers.

Topic

Expressions and Equations

Description

This video demonstrates subtracting integers with algebra tiles, using methods like the take-away model and rewriting subtraction as addition. Examples include 6 - 3 and 3 - 6. Key vocabulary includes subtraction, zero pairs, and take-away model.

Topic

Expressions and Equations

Description

The video explains integer division using algebra tiles with examples like 6 ÷ 3 and -6 ÷ 3. It also covers scenarios with remainders, such as 7 ÷ 3. Key vocabulary includes division, remainders, and integers.

Relevance: This video ties into the topic of Expressions and Equations by providing students with a hands-on approach to understanding the concepts of algebra. Algebra tiles serve as a visual and tactile way to model mathematical operations, helping students internalize these ideas effectively.

Topic

Expressions and Equations

Description

This video focuses on modeling integer multiplication with algebra tiles. Examples include 6 • 3, -6 • 3, and -6 • -3. Rectangular arrays of tiles are used to visualize products. Key vocabulary includes multiplication, rectangular arrays, and integers.

Topic

Expressions and Equations

Description

The video explains how to simplify variable expressions like (x + 3) + (x + 1) using algebra tiles. It demonstrates combining like terms and using zero pairs for simplification. Key vocabulary includes simplifying, variable expressions, and zero pairs.

Topic

Expressions and Equations

Description

This video explains solving one-step equations like x + 2 = 4 and x ÷ 2 = 4 with algebra tiles. It covers addition, subtraction, multiplication, and division operations. Key vocabulary includes one-step equations, zero pairs, and operations.

Topic

Expressions and Equations

Description

This video covers multi-step equations, such as 3x + 2 = x + 4, using algebra tiles. It demonstrates how to isolate variables through a multi-stage process involving addition and subtraction. Key vocabulary includes multi-step equations, isolation, and operations.

Topic

Expressions and Equations

Description

This video explains modeling positive integers using algebra tiles, focusing on the yellow tiles representing positive integers. Examples demonstrate different tile arrangements modeling integers like 6 and 8, emphasizing that arrangement does not affect the value represented. Key vocabulary includes positive integers, tiles, and arrangements.

Topic

Expressions and Equations

Description

This video covers the use of red tiles to model negative integers. It demonstrates counting tiles to represent integers like -10 and -8 and shows that arrangement does not alter the integer modeled. Key vocabulary includes negative integers, tiles, and arrangement.

Topic

Expressions and Equations

Description

This video introduces the concept of zero pairs, where opposite tiles, like +1 and -1, cancel each other out. It explains how to simplify tile groups using zero pairs and provides examples with both integers and variables. Key vocabulary includes zero pairs, integers, and simplification.

Topic

Expressions and Equations

Description

The video demonstrates using green tiles to model variables and their squares. Examples include expressions like 2x and 3x2. Negative variables and squares are also modeled using red tiles. Key vocabulary includes variables, x2, positive tiles, and negative tiles.

Topic

Expressions and Equations

Description

This video explains how to model expressions like 2x + 3 or -3x + 5 using algebra tiles. Examples include both positive and negative tiles for variables and integers, as well as more complex expressions with x-squared. Key vocabulary includes variable expressions, integers, x-squared, and tiles.

Topic

Expressions and Equations

Description

The video demonstrates modeling equations with algebra tiles, using a vertical bar to represent the equals sign. Examples include linear equations like x + 2 = -2 and quadratic equations like x-squared + x + 2 = 2. Key vocabulary includes equations, quadratic, integers, and variables.

Topic

Expressions and Equations

Description

This video focuses on modeling one-step equations using algebra tiles. Examples include equations involving addition, subtraction, multiplication, and division, such as x + 2 = 4 or x ÷ 9 = 10. Key vocabulary includes one-step equations, operations, integers, and variables.

In this video, learn about the properties of equality that are the core of the equation-solving process. They'll learn about true properties for each of the four operations. Only subscribers to Media4Math Library can download these resources.

In this video, students expand their knowledge of properties of equations with a focus on identities. Students will see how to use identities to solve equations, in particular certain quadratic equations.

In this video, students the basics of equations. They'll learn about true equations, false equations, and conditional equations.

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.

Topic

Topic: Inequalities

Topic

Topic: Inequalities

Description

This video models an inequality to explain how floodgates in Venice prevent flooding during storms. The key concept is the activation threshold, where the water level exceeds a critical value. Vocabulary includes inequality, threshold, variable, and model. Using a TI-Nspire, the video demonstrates creating a random variable for water levels and a function to evaluate if floodgates should activate. It illustrates real-world applications in engineering and environmental management.

Topic

Inequalities

Description

This video introduces inequalities, contrasting them with equations, and discusses their properties and solution methods. Key concepts include graphing solutions, interval notation, and inequality symbols. Applications are contextualized through scenarios like semester grades and fitness ranges. Key terms include inequality, interval notation, and solution set.

Topic

Inequalities

Description

In this Math Lab explore compound inequalities on a number line.

This video highlights key concepts in inequalities, offering practical examples that make abstract math principles more accessible. Through a comprehensive approach, students can connect theoretical knowledge to real-world applications.

Relevance: This video directly supports the topic by illustrating inequalities in a clear and engaging way, making it easier for students to understand complex ideas.

Topic

Inequalities

Description

Building on Part 1, this video explores systems of inequalities and their geometric representations. Applications include business profit modeling using linear inequalities. Key vocabulary includes half-planes, slope-intercept form, and solution regions. Real-world examples, like yoga studio budgeting, highlight practical uses of inequalities.

Topic

Inequalities

Description

In this Math Lab explore graphical solutions to linear inequalities.

This video highlights key concepts in inequalities, offering practical examples that make abstract math principles more accessible. Through a comprehensive approach, students can connect theoretical knowledge to real-world applications.

Relevance: This video directly supports the topic by illustrating inequalities in a clear and engaging way, making it easier for students to understand complex ideas.

Topic

3D Geometry

Topic

3D Geometry

Description

This segment introduces Platonic solids, including tetrahedron, cube, and dodecahedron, emphasizing their congruent edges, vertices, and angles. It connects these geometric figures to both natural and man-made structures, setting the stage for exploring 3D geometry applications.

This video offers a comprehensive look at the mathematical concepts behind 3D Geometry. Students will gain insights into practical applications and theoretical understanding of the topic, enhancing their ability to visualize and apply these concepts.

Topic

3D Geometry

Description

This segment explores pyramids, particularly Mayan and Egyptian structures, to distinguish rectangular and square bases. It discusses the volume of truncated pyramids using proportional relationships and introduces the concept of tiered volume reduction through geometric sequences.

This video offers a comprehensive look at the mathematical concepts behind 3D Geometry. Students will gain insights into practical applications and theoretical understanding of the topic, enhancing their ability to visualize and apply these concepts.

Topic

3D Geometry

Description

This segment examines cylinders, using the Shanghai Tower as a case study. It highlights how adjustments to height and radius affect volume and surface area, demonstrating these principles with geometric calculations and their architectural applications in energy efficiency.

This video offers a comprehensive look at the mathematical concepts behind 3D Geometry. Students will gain insights into practical applications and theoretical understanding of the topic, enhancing their ability to visualize and apply these concepts.

In this TI Nspire tutorial, the Graph window is used to create a slider-based graph of a linear function in slope-intercept form. This video supports the TI-Nspire Clickpad and Touchpad.

In this TI Nspire tutorial, the Graph window is to find the slope of two points connected by a line. This video supports the TI-Nspire Clickpad and Touchpad.

In this TI Nspire tutorial, the Graph window is used to graph a linear inequality. This video supports the TI-Nspire Clickpad and Touchpad.

In this TI Nspire tutorial, the Graph window is used to graph a linear inequality in slope-intercept form using sliders. This video supports the TI-Nspire Clickpad and Touchpad.

In this TI Nspire tutorial for the TI-Nspire CAS, the Graph Window is used to graph quadratic inequalities. This video supports the TI-Nspire Clickpad and Touchpad.

This is part of a collection of math worksheets on the topic of solving two-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving two-step equations.

Related Resources

Worksheet Library