Illustrative Math Alignment: Grade 8 Unit 3

Topic

Equations

Description

Congruent To signifies that two geometric shapes are congruent, meaning their corresponding sides and angles are equal. For example, triangles ABC and DEF are congruent, so side AB equals side DE. This term introduces geometric equality, tying equations to geometric properties and congruence criteria.

Topic

Equations

Description

Assigning Values to Variables involves assigning a numerical value to a variable for evaluating functions. For instance, let x = 3 in f(x) = 2x + 8 yields f(3) = 14. This term supports understanding how to evaluate equations and functions by substituting values, a key step in problem-solving.

Topic

Equations

Description

A Conditional Equation is true only for specific variable values. Examples include x + 1 = 4 (x = 3), x2 - 25 = 0 (x = ±5), and 2x - 5 = x + 9 (x = 14). This term supports solving equations by emphasizing that solutions depend on satisfying the given conditions.

Topic

Equations

Description

A Constant Term in an algebraic equation is a number without a variable. Examples include 2 in x2 + 3x + 2 = 0, -10 in x3 - 2x2 + 4x - 10 = 0, and 5 in x4 - 2x3 + 4x2 - x + 5 = 0. This term explains the role of constants in equations, crucial for identifying and isolating terms when solving equations.

Topic

Equations

Description

The Division Property of Equality allows division by the same non-zero quantity on both sides of an equation, maintaining equality. For example, if a = b, then a / c = b / c, where c ≠ 0. Solving 5x = 15 yields x = 3 by dividing both sides by 5. This term builds on equality principles, showing another method to isolate variables and solve equations.

Topic

Equations

Description

Equality refers to a mathematical statement where two expressions are equal. Examples include 1 + 2 = 3 and x + 3 = 7, where both sides represent the same value. This term defines the core concept of equations, ensuring all manipulations preserve equality to find solutions.

This is the transcript for the video of same title. Video contents: In this episode of Algebra Applications, two real-world explorations of inequalities are developed: Hybrid Cars. An examination of the equations and inequalities that involve miles per gallon (mpg) for city and highway traffic reveals important information about hybrid cars and those with gasoline-powered engines. Floods in Venice. Venice experiences a great deal of flooding, and with the expected rise of sea levels over the next century, this ancient city is in peril. Through a series of inequalities, students analyze the impact of flooding.

This is the transcript for the video of same title. Video contents: With the increasing demand worldwide for cars, the cost of gasoline continues to rise. The need for fuel-efficient cars makes hybrids a current favorite. An examination of the equations and inequalities that involve miles per gallon (mpg) for city and highway traffic reveals important information about hybrid cars and those with gasoline-powered engines. Students use the Graphs and Geometry features of the TI-Nspire.

This is the transcript for the video of same title. Video contents: The city of Venice is slowly sinking into the Adriatic Sea. So what does a city whose streets are full of water do about flooding? Venice experiences a great deal of flooding, and with the expected rise of sea levels over the next century, this ancient city is in peril. Through a series of inequalities, students analyze the impact of flooding, rising sea levels, and sinking have on this grand, ancient city. Students use the Lists and Spreadsheets and the Program Editor features of the TI-Nspire.

This is the transcript for the video of same title. Video contents: In this episode of Algebra Applications, students explore various scenarios that can be explained through the use of systems of equations. Such disparate phenomena as profit and loss, secret codes, and ballistic missile shields can be explored through systems of equations.

This is the transcript for the video of same title. Video contents: Profit and loss are the key measures in a business. A system of equations that includes an equation for income and one for expenses can be used to determine profit and loss. Students solve a system graphically.

This is the transcript for the video of same title. Video contents: Secret codes and encryption are ideal examples of a system of equations. In this activity, students encrypt and decrypt a message.

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This is the transcript for the video of same title. Video contents: A ballistic missile shield allows you to shoot incoming missiles out of the sky. Mathematically, this is an example of a linear-quadratic system. Students graph such a system and find the points of intersection between a line and a parabola.

This is the transcript for the video of same title. Video contents: Used in just about any industry, inequalities, like equations, are fundamental building blocks of algebra. Written and hosted by internationally acclaimed mathematics educator Dr. Monica Neagoy, this video explores inequalities -- concepts, properties, solutions, and notations -- connects them to real-world contexts, and uses the TI-Nspire to make the algebra meaningful. The focus of this program is on linear inequalities in one and two variables. Concepts explored: Equations, inequalities

This is the transcript for the video of same title. Video contents: In this Investigation we explore linear inequalities in one variable.

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This is the transcript for the video of same title. Video contents: In this Investigation we look at linear inequalities in two variables.

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This is the transcript for the video of same title. Video contents: Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video introduces students to systems of linear equations in two or three unknowns. To solve these systems, the host illustrates a variety of methods: four involve the TI-Nspire (spreadsheet, graphs and geometry, matrices and nSolve) and two are the classic algebraic methods known as substitution and elimination, also called the linear combinations method. The video ends with a summary of the three possible types of solutions. Concepts explored: equations, linear equations, linear systems

This is the transcript for the video of same title. Video contents: In this Investigation we solve a linear system.

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This is the transcript for the video of same title. Video contents: In this Investigation we use matrices and the elimination method to solve a linear system.

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What Are Algebra Tiles?

What Are Algebra Tiles?

What Are Algebra Tiles?

What Are Algebra Tiles?

What Are Algebra Tiles?

What Are Algebra Tiles?

What Are Algebra Tiles?

What Are Algebra Tiles?

What Are Algebra Tiles?

What Are Algebra Tiles?

What Are Algebra Tiles?

What Are Algebra Tiles?

What Are Algebra Tiles?

What Are Algebra Tiles?

What Are Algebra Tiles?

What Are Algebra Tiles?

What Are Algebra Tiles?

This is the transcript for the TI-Nspire Mini-Tutorial entitled, Solving a System of Two Linear Equations.

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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.

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

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

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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.