Illustrative Math Alignment: Grade 7 Unit 7

Topic

Equations

Description

Proportional To indicates a linear relationship between two variables. For example, distance (d) is proportional to time (t), written as d ∝ t. This term links linear equations to real-world relationships, reinforcing practical applications of mathematical concepts.

Topic

Equations

Description

Similar To. When two geometric shapes are similar, corresponding sides are proportional. ΔABC ~ ΔDEF; AB ∝ DE

The topic of this video is closely tied to Equations, providing an essential understanding of its fundamental concepts. This video explores the mathematics behind this topic by delving into how key principles are applied in practical contexts.

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

Quadratics

Description

Quadratic Equation: A quadratic function set equal to zero, from which the roots of the quadratic can be found. This is foundational in solving quadratic problems algebraically. Introduces the mathematical setup for finding solutions to quadratic functions.

Relevance to Topic: This video series provides a deep dive into the topic of Quadratics. It explores mathematical concepts and demonstrates real-world applications to help solidify understanding.

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.

Topic

Linear Functions

Description

The term is "The Equation of a Line from Two Coordinates," defined as deriving the equation of a line in slope-intercept form from two given points. The slope is calculated as m = (y2 - y1) / (x2 - x1), and the equation is written as y - y1 = m(x - x1). This term builds the connection between points on a graph and their corresponding linear equation, demonstrating practical derivations.

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: In this episode of Algebra Applications, two real-world explorations are developed: Biology. Analyzing statistics from honey bee production allows for a mathematical analysis of the so-called Colony Collapse Disorder. Geology. Why do rivers meander instead of traveling in a straight line? In this segment the geological forces that account for a river??s motion are explained.

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: Honey bees not only produce a tasty treat, they also help pollinate flowering plants that provide much of the food throughout the world. So, when in 2006 bee colonies started dying out, scientists recognized a serious problem. Analyzing statistics from honey bee production allows for a mathematical analysis of the so-called Colony Collapse Disorder.

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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This is the transcript for the video of same title. Video contents: Ever since the mathematics of the Babylonians, equations have played a central role in the development of algebra. Written and hosted by internationally acclaimed mathematics educator Dr. Monica Neagoy, this video traces the history and evolution of equations. It explores the two principal equations encountered in an introductory algebra course -- linear and quadratic -- in an engaging way. The foundations of algebra are explored and fundamental questions about the nature of algebra are answered. In addition, problems involving linear and quadratic equations are solved using the TI-Nspire graphing calculator. Algebra teachers looking to integrate hand-held technology and visual media into their instruction will benefit greatly from this series.

This is the transcript for the video of same title. Video contents: In this Investigation we get a historical overview of equations.

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This is the transcript for the video of same title. Video contents: In this Investigation we solve linear and quadratic equations.

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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?

This is the transcript for the video entitled, Anatomy of an Equation: Linear Equations in Standard Form to Slope-Intercept Form 1: AX + By = C. In this video tutorial, analyze the steps in converting a linear equation in Standard Form to a linear function in Slope-Intercept Form. In this video we work with this version of the Standard Form: AX + By = C. 

The corresponding video is at this Link.

Note: The download is a PDF file.

This is the transcript for the video entitled, Anatomy of an Equation: Linear Equations in Standard Form to Slope-Intercept Form 2: AX + By = -C. In this video tutorial, analyze the steps in converting a linear equation in Standard Form to a linear function in Slope-Intercept Form. In this video we work with this version of the Standard Form: AX + By = -C. 

The corresponding video is at this Link.

Note: The download is a PDF file.

This is the transcript for the video entitled, Anatomy of an Equation: Linear Equations in Standard Form to Slope-Intercept Form 3: Ax - By = C. In this video tutorial, analyze the steps in converting a linear equation in Standard Form to a linear function in Slope-Intercept Form. In this video we work with this version of the Standard Form: AX - By = C. 

The corresponding video is at this Link.

Note: The download is a PDF file.

This is the transcript for the video entitled, Anatomy of an Equation: Linear Equations in Standard Form to Slope-Intercept Form 4: -Ax + By = C. In this video tutorial, analyze the steps in converting a linear equation in Standard Form to a linear function in Slope-Intercept Form. In this video we work with this version of the Standard Form: -Ax + By = C.

This is the transcript for the video entitled, Anatomy of an Equation: Linear Equations in Standard Form to Slope-Intercept Form 5: Ax - By = -C. In this video tutorial, analyze the steps in converting a linear equation in Standard Form to a linear function in Slope-Intercept Form. In this video we work with this version of the Standard Form: Ax - By = -C. 

The corresponding video is at this Link.

Note: The download is a PDF file.

This is the transcript for the video entitled, Anatomy of an Equation: Linear Equations in Standard Form to Slope-Intercept Form 6: -Ax + By = -C. In this video tutorial, analyze the steps in converting a linear equation in Standard Form to a linear function in Slope-Intercept Form. In this video we work with this version of the Standard Form: -Ax + By = -C.

This is the transcript for the video entitled, Anatomy of an Equation: Linear Equations in Standard Form to Slope-Intercept Form 7: -Ax - By = C. In this video tutorial, analyze the steps in converting a linear equation in Standard Form to a linear function in Slope-Intercept Form. In this video we work with this version of the Standard Form: -Ax - By = C.

This is the transcript for the video entitled, Anatomy of an Equation: Linear Equations in Standard Form to Slope-Intercept Form 8:-Ax - By = -C. In this video tutorial, analyze the steps in converting a linear equation in Standard Form to a linear function in Slope-Intercept Form. In this video we work with this version of the Standard Form: -Ax - By = -C.

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 a video transcript for the video on solving quadratic equations. In this video, we work with this version of the quadratic equation: ax^2 + bx + c = 0.

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This is a video transcript for the video on solving quadratic equations. In this video, we work with this version of the quadratic equation: ax^2 + bx - c = 0.

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This is a video transcript for the video on solving quadratic equations. In this video, we work with this version of the quadratic equation: ax^2 - bx + c = 0.

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This is a video transcript for the video on solving quadratic equations. In this video, we work with this version of the quadratic equation: -ax^2 + bx + c = 0.

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