Illustrative Math Alignment: Grade 7 Unit 7

This is the Teacher's Guide that accompanies Algebra Applications: Equations.

Related Resources

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

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 part of a collection of videos from the Algebra Applications video series on the topic of Systems of Equations.

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 part of a collection of videos from the Algebra Applications video series on the topic of Variables and Equations.

This is the Teacher's Guide that accompanies Algebra Nspirations: Variables and Equations.

Related Resources

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

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.

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.

Topic

Equations

Description

This animated clip art illustrates the process of solving one-step addition equations. The animation visually demonstrates how to isolate the variable by subtracting the constant term from both sides of the equation, reinforcing the concept of maintaining balance in equations.

Topic

Equations

Description

This animated clip art illustrates the process of solving one-step addition equations. The animation visually demonstrates how to isolate the variable by subtracting the constant term from both sides of the equation, reinforcing the concept of maintaining balance in equations.

Topic

Equations

Description

This animated clip art illustrates the process of solving one-step addition equations. The animation visually demonstrates how to isolate the variable by subtracting the constant term from both sides of the equation, reinforcing the concept of maintaining balance in equations.

Topic

Equations

Description

This animated clip art illustrates the process of solving one-step addition equations. The animation visually demonstrates how to isolate the variable by subtracting the constant term from both sides of the equation, reinforcing the concept of maintaining balance in equations.

Topic

Equations

Description

This animated clip art demonstrates solving one-step subtraction equations. The animation shows adding a constant to both sides of the equation to isolate the variable, emphasizing the importance of maintaining balance.

This visual tool is effective in teaching students the concept of solving equations. It helps students visualize the abstract process of balancing equations through a clear, step-by-step example. This clip art can be used in lessons to reinforce understanding of subtraction equations.

Topic

Equations

Description

This animated clip art demonstrates solving one-step subtraction equations. The animation shows adding the same value to both sides of the equation to isolate the variable, emphasizing the importance of maintaining balance.

This visual tool is effective in teaching students the concept of solving equations. It helps students visualize the abstract process of balancing equations through a clear, step-by-step example. This clip art can be used in lessons to reinforce understanding of subtraction equations.

Topic

Equations

Description

This animated clip art demonstrates solving one-step subtraction equations. The animation shows adding the same value to both sides of the equation to isolate the variable, emphasizing the importance of maintaining balance.

This visual tool is effective in teaching students the concept of solving equations. It helps students visualize the abstract process of balancing equations through a clear, step-by-step example. This clip art can be used in lessons to reinforce understanding of subtraction equations.

Topic

Equations

Description

This animated clip art demonstrates solving one-step subtraction equations. The animation shows adding the same value to both sides of the equation to isolate the variable, emphasizing the importance of maintaining balance.

This visual tool is effective in teaching students the concept of solving equations. It helps students visualize the abstract process of balancing equations through a clear, step-by-step example. This clip art can be used in lessons to reinforce understanding of subtraction equations.

Topic

Equations

Description

This animated clip art shows the process of solving one-step multiplication equations. The animation demonstrates dividing both sides of the equation, or multiplying by the reciprocal, to isolate the variable, highlighting the concept of maintaining equation balance.

This visual resource is effective for teaching the concept of solving equations. It helps students visualize the abstract process of balancing equations through a clear, step-by-step example. This clip art can be used in lessons to provide multiple perspectives on solving equations, enhancing understanding.

Topic

Equations

Description

This animated clip art illustrates the process of solving one-step multiplication equations. The animation demonstrates dividing both sides of the equation by the same number to isolate the variable, highlighting the concept of maintaining equation balance.

This visual resource is effective for teaching the concept of solving equations. It helps students visualize the abstract process of balancing equations through a clear, step-by-step example. This clip art can be used in lessons to provide multiple perspectives on solving equations, enhancing understanding.

Topic

Equations

Description

This animated clip art illustrates the process of solving one-step multiplication equations. The animation demonstrates dividing both sides of the equation by the same value to isolate the variable, highlighting the concept of maintaining equation balance.

This visual resource is effective for teaching the concept of solving equations. It helps students visualize the abstract process of balancing equations through a clear, step-by-step example. This clip art can be used in lessons to provide multiple perspectives on solving equations, enhancing understanding.

Topic

Equations

Description

This animated clip art illustrates the process of solving one-step multiplication equations. The animation demonstrates dividing both sides of the equation by the same value to isolate the variable, highlighting the concept of maintaining equation balance.

This visual resource is effective for teaching the concept of solving equations. It helps students visualize the abstract process of balancing equations through a clear, step-by-step example. This clip art can be used in lessons to provide multiple perspectives on solving equations, enhancing understanding.

Topic

Equations

Description

This animated clip art demonstrates solving one-step division equations. The animation shows multiplying both sides of the equation by the same number to isolate the variable, emphasizing the principle of maintaining equation balance.

This visual tool is valuable for teaching students the concept of solving equations. It helps students visualize the abstract process of balancing equations by providing a clear, step-by-step example. This clip art can be part of a comprehensive lesson plan that uses multiple animations to reinforce understanding.

Topic

Equations

Description

This animated clip art demonstrates solving one-step division equations. The animation shows multiplying both sides of the equation by the same number to isolate the variable, emphasizing the principle of maintaining equation balance.

This visual tool is valuable for teaching students the concept of solving equations. It helps students visualize the abstract process of balancing equations by providing a clear, step-by-step example. This clip art can be part of a comprehensive lesson plan that uses multiple animations to reinforce understanding.

Topic

Equations

Description

This animated clip art demonstrates solving one-step division equations. The animation shows multplying both sides of the equation by the same number to isolate the variable, emphasizing the principle of maintaining equation balance.

This visual tool is valuable for teaching students the concept of solving equations. It helps students visualize the abstract process of balancing equations by providing a clear, step-by-step example. This clip art can be part of a comprehensive lesson plan that uses multiple animations to reinforce understanding.

Topic

Equations

Description

This animated clip art demonstrates solving one-step division equations. The animation shows multiplying both sides of the equation by the same number to isolate the variable, emphasizing the principle of maintaining equation balance.

This visual tool is valuable for teaching students the concept of solving equations. It helps students visualize the abstract process of balancing equations by providing a clear, step-by-step example. This clip art can be part of a comprehensive lesson plan that uses multiple animations to reinforce understanding.

In this presentation we show how to convert a linear equation in Standard Form to a linear function in Slope Intercept Form. We go over the reason for such a conversion and applications that give rise to these equations. Note: The download is a PPT.

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.

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.

Secret codes and encryption are ideal examples of a system of equations. In this activity, students encrypt and decrypt a message.

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.

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.

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

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.

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.

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.

In this Investigation we solve a linear system. This video is Segment 1 of a 4 segment series related to Algebra Nspirations: Solving Systems of Equations. Segments 1 and 2 are grouped together.

In this Investigation we use matrices and the elimination method to solve a linear system. This video is Segment 3 of a 4 segment series related to Algebra Nspirations: Solving Systems of Equations. Segments 3 and 4 are grouped together.

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.

In this Investigation we get a historical overview of equations. This video is Segment 1 of a 2 segment series related to Variables and Equations.

In this Investigation we solve linear and quadratic equations. This video is Segment 3 of a 4 segment series related to Variables and Equations. Segments 3 and 4 are grouped together.

Description

Video Tutorial: Algebra Tiles: Modeling Equations Using Algebra Tiles. In this tutorial, review the basic definition of what algebra tiles are and how they are used. Then the video focuses on how to model equations using algebra tiles.

This is part of a collection of video tutorials the topic of Algebra Tiles.This series of videos describes what algebra tiles are and how they can be used to model numbers, operations, expressions, and equations. Use this series if you are incorporating the use of algebra tiles in your instruction.

Description

Video Tutorial: Algebra Tiles: Modeling Multi-Step Equations Using Algebra Tiles. In this tutorial, students review the basics of how to use algebra tiles to model equations. Then the video focuses on how to model multi-step equations using algebra tiles.

This is part of a collection of video tutorials the topic of Algebra Tiles.This series of videos describes what algebra tiles are and how they can be used to model numbers, operations, expressions, and equations. Use this series if you are incorporating the use of algebra tiles in your instruction.

Description

Video Tutorial: Algebra Tiles: Modeling One-Step Equations Using Algebra Tiles. In this tutorial, review the basics of how to use algebra tiles to model equations. Then the video focuses on how to model one-step equations using algebra tiles.

The following section reviews the basics of algebra tiles. Use this material as background material, and also as a supplement to the video series.

Video Tutorial: Algebra Tiles: Modeling Quadratic Equations Using Algebra Tiles. In this tutorial, review the basics of how to use algebra tiles to model equations. Then the video focuses on how to model quadratic equations using algebra tiles.

Description

Video Tutorial: Algebra Tiles: Dividing Integers Using Algebra Tiles. In this tutorial, review the basic definition of what algebra tiles are and how they are used. Then the video focuses on how to divide integers using algebra tiles.

This is part of a collection of video tutorials the topic of Algebra Tiles.This series of videos describes what algebra tiles are and how they can be used to model numbers, operations, expressions, and equations. Use this series if you are incorporating the use of algebra tiles in your instruction.

Description

Video Tutorial: Algebra Tiles: Modeling Two-Step Equations Using Algebra Tiles. In this tutorial, students review the basics of how to use algebra tiles to model equations. Then the video focuses on how to model two-step equations using algebra tiles.

This is part of a collection of video tutorials the topic of Algebra Tiles.This series of videos describes what algebra tiles are and how they can be used to model numbers, operations, expressions, and equations. Use this series if you are incorporating the use of algebra tiles in your instruction.

Video Tutorial: Algebra Tiles: Solving Multi-Step Equations Using Algebra Tiles. In this tutorial, students review how to model equations with algebra tiles. Then the video focuses on how to solve multi-step equations with algebra tiles.

Description

This is part of a collection of video tutorials the topic of Algebra Tiles.This series of videos describes what algebra tiles are and how they can be used to model numbers, operations, expressions, and equations. Use this series if you are incorporating the use of algebra tiles in your instruction.

Description

This is part of a collection of video tutorials the topic of Algebra Tiles.This series of videos describes what algebra tiles are and how they can be used to model numbers, operations, expressions, and equations. Use this series if you are incorporating the use of algebra tiles in your instruction.

The following section reviews the basics of algebra tiles. Use this material as background material, and also as a supplement to the video series.

Description

This is part of a collection of video tutorials the topic of Algebra Tiles.This series of videos describes what algebra tiles are and how they can be used to model numbers, operations, expressions, and equations. Use this series if you are incorporating the use of algebra tiles in your instruction.

The following section reviews the basics of algebra tiles. Use this material as background material, and also as a supplement to the video series.

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. . .

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. . .

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. . .

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. . .

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. .