Illustrative Math Alignment: Grade 8 Unit 3

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

This is part of a collection of math examples that show how to solve one-step equations that include addition, subtraction, multiplication, or division.

What Are Algebra Tiles?

Numerical Models

This Teacher's Guide provides an overview of the 12 worked-out examples that show how to graph a linear inequality.

Related Resources

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

This Teacher's Guide provides an overview of the 13 worked-out examples that solve a variety of one-variable equations with fractions.

Related Resources

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

What Are Percents?

This Teacher's Guide provides an overview of the 27 worked-out examples that solve a variety of one-variable equations.

Related Resources

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

This Teacher's Guide provides an overview of the 24 worked-out examples that show how to calculate the surface area of different three-dimensional figures.

Related Resources

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

This set of tutorials provides 24 examples of how to find the volume of various 3-dimensional geometric figures.

Related Resources

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

This set of tutorials provides 24 examples of how to find the volume of various 3-dimensional geometric figures. NOTE: The download is a PPT file.

September 2016. In this issue of Math in the News, we look at back-to-school purchases and the impact that different tax rates have on the total cost.

Related Resources

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

6/13/11. In this issue we explore the volcanic eruption in Chile that resulted in a huge plume of smoke and ash that was miles high. We explore the viscosity of lava that makes such eruptions possible.

Related Resources

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

6/27/11. In this issue we look at the technology of hydraulic fracking. In particular, we estimate the amount of drilling required for such wells.

Related Resources

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

9/19/11. To commemorate the 10-year anniversary of the 911, we look at the geometry and architecture of the Freedom Tower, currently under construction.

Related Resources

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

11/14/11. In this issue we commemorate the 125th anniversary of the Statue of Liberty. We also look at the geometry and architecture of this monument.

Related Resources

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

11/28/11. In this issue we look at the geometry of parade balloons.

Related Resources

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

12/7/11. In this issue we look at the heroic work of salvaging and retrofitting many of the ships sunk during the attack on Pearl Harbor.

Related Resources

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

12/12/11. In this issue we look at the MLK Memorial and the special properties of granite that presented some design challenges in the construction of the statue.

Related Resources

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

January 2012. In this issue of Math in the News we analyze how the Costa Concordia sank.

Related Resources

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

April 2012. In this issue of Math in the News we analyze the sinking of the Titanic. It has been a hundred years, yet the story of the sinkin g of the Titanic still fascinates.

Related Resources

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

May 2012. In this issue of Math in the News we look at the architecture of the Freedom Tower, now that it has become the tallest building in NYC.

Related Resources

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

August 2013. In this issue we look at the geometry of funnel cakes. You'll like the sweet results.

Related Resources

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

5/9/11. In this issue we look at tornado season. In particular we study why the swirling winds of a tornado are so damaging.

Related Resources

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

November 2013. In this issue of Math in the News we look at the arrival of Comet ISON, scheduled for arrival in late November 2013. We model the trajectory of the comet using a parabolic model.

Related Resources

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

5/16/11. In this issue we look at the flooding along the Mississippi. In particular we analyze the flooding along Memphis, Tennessee. We develop a model for predicting the amount of flooding.

Related Resources

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

This is part of a collection of math quizzes on the topic of algebra tiles.

Related Resources

Quiz Library

ary">click on this link.

This is part of a collection of math quizzes on the topic of algebra tiles.

Related Resources

Quiz Library

ary">click on this link.

This is part of a collection of math quizzes on the topic of algebra tiles.

Related Resources

Quiz Library

ary">click on this link.

This is part of a collection of math quizzes on the topic of the Graphing Inequalities.

Related Resources

Quiz Library

ary">click on this link.

This is part of a collection of math quizzes on the topic of the Graphing Inequalities.

Related Resources

Quiz Library

ary">click on this link.

This is part of a collection of math quizzes on the topic of the Graphing Inequalities.

Related Resources

Quiz Library

ary">click on this link.

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. Note: The download for this resources is the Promethean Flipchart.

For access to the full video [Geometry Applications: 3D Geometry, Segment 2: Pyramids]: https://media4math.com/library/geometry-applications-3d-geometry-segment-2-pyramids

This video includes a Video Transcript [Video Transcript: Geometry Applications: 3D Geometry, Segment 2: Pyramids]: https://www.media4math.com/library/video-transcript-geometry-applications-3d-geometry-segment-2-pyramids

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. Note: The download for this resources is the Promethean Flipchart.

To access the full video [Geometry Applications: 3D Geometry, Segment 3: Cylinders]: https://media4math.com/library/geometry-applications-3d-geometry-segment-3-cylinders

This video includes a Video Transcript [Video Transcript: Geometry Applications: 3D Geometry, Segment 3: Cylinders]: https://www.media4math.com/library/video-transcript-geometry-applications-3d-geometry-segment-3-cylinders

In this tutorial, students are shown the process of solving equations. In particular, they look at the properties of equality that allow for the manipulation of equations in order to arrive at a solution.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link. 

In this hands-on game using readily available materials in your class or (in the case of virtual learning) home, students learn to model equations. They'll use this model to explore properties of equality and get a concrete grounding in the properties of equations.

Related Resources

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

Topic

Equations

Description

The Not Equal To Sign (≠) indicates two expressions are not equal, forming an inequation. For example, 2 + 1 ≠ 4 and x + 3 ≠ x are inequations. This term builds on equality concepts by introducing inequalities, critical for exploring a broader range of mathematical statements.

Topic

Equations

Description

An Equation is a mathematical statement that says two expressions are equal to each other. Equations can be true or false, as shown in examples like 1 + 1 = 2 (true) and 1 + 2 = 4 (false). This term introduces the concept of equality and sets the foundation for understanding other types of equations.

Topic

Equations

Description

An Equation in One Variable has an unknown represented by a single variable. Examples include 2 + 3x = 5 and (x + 2)^2 = 25. This term focuses on single-variable equations, forming a basis for solving and understanding algebraic structures.

Topic

Equations

Description

Equations in Two Variables. A two-variable equation shows a relationship between two variables. Examples include y = 3x + 5, x2 + y2 = 25, and xy = 5, highlighting equations that can be graphed in a coordinate system. This builds on the idea of variables in equations and introduces the concept of relationships between variables, applicable in graphing and real-world modeling.

Topic

Equations

Description

Equivalent Equations result from changing an equation while maintaining equality, often by performing the same operation on both sides. For example, x - 3 = 5 becomes x = 8 after adding 3 to both sides. This term demonstrates how equations can be manipulated without altering their solution, a key concept in solving equations.

Topic

Equations

Description

A False Equation is mathematically inaccurate. For example, 2 + 1 = 4 is false, and x + 3 = x has no solution, as no value of x satisfies the equation. This term contrasts true equations and emphasizes the need to verify solutions, highlighting logical consistency in mathematics.

Topic

Equations

Description

An Identity Equation is always true for all variable values. Examples include x = x and (x + 1)2 = x2 + 2x + 1. Identity equations often use the symbol ≡ to indicate their universal truth. This term introduces a special class of equations, linking algebraic manipulation and properties of equivalence.

Topic

Equations

Description

An Inequation is a mathematical statement that shows two expressions are not equal, as in 2 + 1 ≠ 4 or x + 3 ≥ 0, which includes inequalities. This term broadens the discussion to include inequalities, expanding the types of relationships between expressions.

Topic

Equations

Description

Isolating the Variable refers to the process of solving an equation by focusing on and isolating the variable of interest. For example, x + 3 = 5 becomes x = 2 by subtracting 3 from both sides. This term highlights a key step in solving equations, emphasizing strategies for simplifying equations to find solutions.

Topic

Equations

Description

The Left Side of the Equation is the expression on the left of the equals sign. For example, in 2x + 3 = x - 5, the left side is 2x + 3. This term provides clarity in identifying components of equations, aiding in understanding structure and solving strategies.