Illustrative Math Alignment: Grade 8 Unit 3

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.

Linear Expressions, Equations, and Functions

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: An overview of the key topics to be covered in the video.

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This is the transcript for the video of same title. Video contents: Why do rivers meander instead of traveling in a straight line? In going from point A to point B, why should a river take the circuitous route it does instead of a direct path? Furthermore, what information can the ratio of the river's length to its straight-line distance tell us? In this segment the geological forces that account for a river's motion are explained. In the process, the so-called Meander Ratio is explored. Students construct a mathematical model of a meandering river using the TI-Nspire. Having built the model, students then use it to generate data to find the average of many Meander Ratios. The results show that on average the Meander Ratio is equal to pi.

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?

This is the transcript for the video entitled, " Anatomy of an Equation: One-Step Addition Equations."

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This is the transcript for the video entitled, " Anatomy of an Equation: One-Step Addition Equations 2."

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This is the transcript for the video entitled, " Anatomy of an Equation: One-Step Division Equations."

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This is the transcript for the video entitled, " Anatomy of an Equation: One-Step Multiplication Equations."

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This is the transcript for the video entitled, " Anatomy of an Equation: One-Step Subtraction Equations."

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This is the transcript for the video entitled, " Anatomy of an Equation: One-Step Subtraction Equations 2."

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This is the transcript that goes with the video segment entitled Video Tutorial: One-Step Equations: Addition.

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This is the transcript that goes with the video segment entitled Video: One-Step Equations: Division.

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This is the transcript that goes with the video segment entitled Video Tutorial: One-Step Equations: Multiplication.

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This is the transcript that goes with the video segment entitled Video: One-Step Equations: Subtraction.

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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 that goes with the video segment entitled Video: Two-Step Equations: Division and Addition.

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This is the transcript that goes with the video segment entitled Video: Two-Step Equations: Division and Subtraction.

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This is the transcript that goes with the video segment entitled Video: Two-Step Equations: Multiplication and Addition.

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This is the transcript that goes with the video segment entitled Video: Two-Step Equations: Multiplication and Subtraction.

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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 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

The video discusses solving two-step equations like 2x + 2 = 4 using algebra tiles. It shows a multi-stage process for isolating variables, including handling subtraction as addition. Key vocabulary includes two-step equations, multi-stage process, and integer tiles.

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

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.

Topic

Expressions and Equations

Description

The video explains two-step equations involving combinations of operations like addition and division. Examples include 2x + 2 = 4 and x ÷ 2 - 4 = 10. It highlights rewriting subtraction as addition for modeling. Key vocabulary includes two-step equations, operations, integers, and variables.

Topic

Equations

Description

This tutorial explains solving one-step equations involving addition. Key math concepts include identifying the addition operation and isolating the variable to find the solution. Vocabulary includes terms like variable, isolate, and addition operation. The math application involves solving equations such as x + 2 = 5 by subtracting 2 from both sides to isolate the variable and find x = 3.

Topic

Equations

Description

This tutorial extends solving one-step equations involving addition with negative numbers. It focuses on isolating the variable and managing negative values. Vocabulary includes terms like variable, isolate, and negative number. The application includes equations like x + 4 = -9, solved by subtracting 4 from both sides to find x = -13.

Topic

Equations

Description

This tutorial explains solving one-step equations involving division. The key focus is on isolating the variable through multiplication. Vocabulary includes terms like variable, isolate, and division operation. For example, solving x / 5 = 4 involves multiplying both sides by 5 to find x = 20.

Topic

Equations

Description

This tutorial demonstrates solving one-step equations involving multiplication. Key concepts include identifying the multiplication operation and isolating the variable. Vocabulary includes terms like variable, isolate, and multiplication operation. The application involves equations like 2x = 10, solved by dividing both sides by 2 to find x = 5.

Topic

Equations

Description

This tutorial explores solving one-step equations involving subtraction. Key concepts include recognizing the subtraction operation and isolating the variable. Vocabulary includes terms like variable, isolate, and subtraction operation. The application demonstrates solving equations such as x - 3 = 5 by adding 3 to both sides to isolate the variable and find x = 8.

Topic

Equations

Description

This tutorial covers solving one-step equations involving subtraction with negative numbers. The focus is on isolating the variable while handling negative values. Vocabulary includes terms like variable, isolate, and negative number. An example involves solving x - 5 = -12 by adding 5 to both sides to find x = -7.

Topic

Solving Equations

Description

This video introduces one-step equations that require one mathematical operation to solve. The focus is on addition equations, indicated by the addition symbol. The solution process involves using subtraction to isolate the variable. Key math concepts include solving equations, inverse operations, and maintaining equation balance. Key vocabulary includes addition, subtraction, equation, and inverse operation. Practical applications involve basic algebraic problem-solving.

Topic

Solving Equations

Description

This video covers one-step division equations, identifiable by the division symbol or fraction notation. Multiplication is applied as the inverse operation to solve for the variable. Key concepts include solving equations, inverse operations, and keeping equations balanced. Vocabulary emphasized includes division, fraction, multiplication, inverse operation, and equation. These equations are practical for solving proportional problems and foundational algebraic expressions.

Topic

Solving Equations

Description

This tutorial demonstrates solving one-step multiplication equations. Such equations are characterized by a coefficient next to the variable. Division is used to isolate the variable. The key math concepts are solving equations, using inverse operations, and maintaining balance. Important vocabulary terms include multiplication, coefficient, variable, division, and inverse operation. Applications include foundational algebra skills for understanding more complex equations.

Topic

Solving Equations

Description

This video explains how to solve one-step subtraction equations. These equations are identified by the subtraction symbol, and solving them involves using addition to isolate the variable. Key concepts discussed are solving equations, inverse operations, and keeping equations balanced. Important vocabulary includes subtraction, addition, inverse operation, and equation. Applications include solving simple algebra problems encountered in everyday contexts.