Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 8 Unit 3

Linear Equations and Linear Systems

Lesson 9: When Are They the Same?

Use the following Media4Math resources with this Illustrative Math lesson.

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Math in the News: Issue 6--The BP Oil Spill, a Year Later Math in the News: Issue 6--The BP Oil Spill, a Year Later Math in the News: Issue 6--The BP Oil Spill, a Year Later

4/25/11. In this issue we discuss the BP oil spill one year after the spill. In particular we look at how damaging oil spills are to marine life and to oxygen levels in the water.

This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.

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Data Analysis
VIDEO: Overview of Variables and Equations VIDEO: Overview of Variables and Equations VIDEO: Overview of Variables and Equations

What Is a Variable?

A variable is a symbol, usually a letter, that can stand for different things.

Variable Expressions, Applications of Equations and Inequalities and Variables and Unknowns
Paper-and-Pencil Quiz: Equations with Fractions (Easy) Paper-and-Pencil Quiz: Equations with Fractions (Easy) Paper-and-Pencil Quiz: Equations with Fractions (Easy)

This is part of a collection of math quizzes on the topic of Equations with Fractions.

To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).

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Quiz Library

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ary">click on this link.

Solving Fraction Equations
Paper-and-Pencil Quiz: Equations with Fractions (Hard) Paper-and-Pencil Quiz: Equations with Fractions (Hard) Paper-and-Pencil Quiz: Equations with Fractions (Hard)

This is part of a collection of math quizzes on the topic of Equations with Fractions.

To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).

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Quiz Library

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ary">click on this link.

Solving Fraction Equations
Paper-and-Pencil Quiz: Equations with Fractions (Medium) Paper-and-Pencil Quiz: Equations with Fractions (Medium) Paper-and-Pencil Quiz: Equations with Fractions (Medium)

This is part of a collection of math quizzes on the topic of Equations with Fractions.

To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).

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Quiz Library

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ary">click on this link.

Solving Fraction Equations
Paper-and-Pencil Quiz: Equations with Percents (Easy) Paper-and-Pencil Quiz: Equations with Percents (Easy) Paper-and-Pencil Quiz: Equations with Percents (Easy)

This is part of a collection of math quizzes on the topic of Equations with Percents.

To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).

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Quiz Library

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ary">click on this link.

Solving Percent Equations
Paper-and-Pencil Quiz: Equations with Percents (Hard) Paper-and-Pencil Quiz: Equations with Percents (Hard) Paper-and-Pencil Quiz: Equations with Percents (Hard)

This is part of a collection of math quizzes on the topic of Equations with Percents.

To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).

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Quiz Library

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ary">click on this link.

Solving Percent Equations
Paper-and-Pencil Quiz: Equations with Percents (Medium) Paper-and-Pencil Quiz: Equations with Percents (Medium) Paper-and-Pencil Quiz: Equations with Percents (Medium)

This is part of a collection of math quizzes on the topic of Equations with Percents.

To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).

Related Resources

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Quiz Library

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

ary">click on this link.

Solving Percent Equations
Promethean Flipchart: Algebra Nspirations: Systems of Equations

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

To access the full video [Algebra Nspirations: Solving Systems of Equations]: https://media4math.com/library/algebra-nspirations-solving-systems-equations

Applications of Linear Systems
Quizlet Flash Cards: Evaluating Quadratic Functions, Set 01 Quizlet Flash Cards: Evaluating Quadratic Functions, Set 01 Description

Evaluate quadratic functions of the form f(x) = ax^2 + bx + c in this 20-flash card set. The values of a and b are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

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Quizlet Library

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Applications of Quadratic Functions
Quizlet Flash Cards: Evaluating Quadratic Functions, Set 02 Quizlet Flash Cards: Evaluating Quadratic Functions, Set 02 Description

Evaluate quadratic functions of the form f(x) = ax^2 + bx + c in this 20-flash card set. The values of a and b are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

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Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Applications of Quadratic Functions
Quizlet Flash Cards: Evaluating Quadratic Functions, Set 03 Quizlet Flash Cards: Evaluating Quadratic Functions, Set 03 Description

Evaluate quadratic functions of the form f(x) = ax^2 + bx + c in this 20-flash card set. The values of a and b are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

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Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Applications of Quadratic Functions
Quizlet Flash Cards: Evaluating Quadratic Functions, Set 04 Quizlet Flash Cards: Evaluating Quadratic Functions, Set 04 Description

Evaluate quadratic functions of the form f(x) = ax^2 + bx + c in this 20-flash card set. The values of a and b are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

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

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Applications of Quadratic Functions
Quizlet Flash Cards: Evaluating Quadratic Functions, Set 05 Quizlet Flash Cards: Evaluating Quadratic Functions, Set 05 Description

Evaluate quadratic functions of the form f(x) = ax^2 + bx + c in this 20-flash card set. The values of a and b are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

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

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Applications of Quadratic Functions
Quizlet Flash Cards: Evaluating Quadratic Functions, Set 06 Quizlet Flash Cards: Evaluating Quadratic Functions, Set 06 Description

Evaluate quadratic functions of the form f(x) = ax^2 + bx + c in this 20-flash card set. The values of a and b are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

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

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Applications of Quadratic Functions
Quizlet Flash Cards: Evaluating Quadratic Functions, Set 07 Quizlet Flash Cards: Evaluating Quadratic Functions, Set 07 Description

Evaluate quadratic functions of the form f(x) = ax^2 + bx + c in this 20-flash card set. The values of a and b are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

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

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Applications of Quadratic Functions
Quizlet Flash Cards: Evaluating Quadratic Functions, Set 08 Quizlet Flash Cards: Evaluating Quadratic Functions, Set 08 Description

Evaluate quadratic functions of the form f(x) = ax^2 + bx + c in this 20-flash card set. The values of a and b are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

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

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Applications of Quadratic Functions
Quizlet Flash Cards: Evaluating Quadratic Functions, Set 09 Quizlet Flash Cards: Evaluating Quadratic Functions, Set 09 Description

Evaluate quadratic functions of the form f(x) = ax^2 + bx + c in this 20-flash card set. The values of a and b are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

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

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Applications of Quadratic Functions
Quizlet Flash Cards: Evaluating Quadratic Functions, Set 10 Quizlet Flash Cards: Evaluating Quadratic Functions, Set 10 Description

Evaluate quadratic functions of the form f(x) = ax^2 + bx + c in this 20-flash card set. The values of a and b are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

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

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Applications of Quadratic Functions
Quizlet Flash Cards: Non-linear Systems Quizlet Flash Cards: Non-linear Systems Description

In this set of Quizlet flash cards test understanding of nonlinear systems.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

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Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Solving Systems of Equations
QuizletFlashCards.jpg Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 01

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3cwZzXj
Factoring Quadratics and Quadratic Equations and Functions
QuizletFlashCards.jpg Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 02

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3cwZzXj
Factoring Quadratics and Quadratic Equations and Functions
QuizletFlashCards.jpg Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 03

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3cwZzXj
Factoring Quadratics and Quadratic Equations and Functions
QuizletFlashCards.jpg Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 04

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3cwZzXj
Factoring Quadratics and Quadratic Equations and Functions
QuizletFlashCards.jpg Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 05

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3cwZzXj
Factoring Quadratics and Quadratic Equations and Functions
QuizletFlashCards.jpg Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 06

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3cwZzXj
Factoring Quadratics and Quadratic Equations and Functions
QuizletFlashCards.jpg Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 07

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3cwZzXj
Factoring Quadratics and Quadratic Equations and Functions
QuizletFlashCards.jpg Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 08

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3cwZzXj
Factoring Quadratics and Quadratic Equations and Functions
QuizletFlashCards.jpg Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 09

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3cwZzXj
Factoring Quadratics and Quadratic Equations and Functions
QuizletFlashCards.jpg Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 10

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3cwZzXj
Factoring Quadratics and Quadratic Equations and Functions
QuizletFlashCards.jpg Quizlet Flash Cards: Solving Quadratic Equations Using the Quadratic Formula, Set 01

Solve quadratic equations by using the quadratic formula in this 20-flash card set. The values of the quadratic equation terms are in the range -15 to 15.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/2Ub2fn5
Quadratic Equations and Functions and Quadratic Formula
QuizletFlashCards.jpg Quizlet Flash Cards: Solving Quadratic Equations Using the Quadratic Formula, Set 02

Solve quadratic equations by using the quadratic formula in this 20-flash card set. The values of the quadratic equation terms are in the range -15 to 15.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/2Ub2fn5
Quadratic Equations and Functions and Quadratic Formula
QuizletFlashCards.jpg Quizlet Flash Cards: Solving Quadratic Equations Using the Quadratic Formula, Set 03

Solve quadratic equations by using the quadratic formula in this 20-flash card set. The values of the quadratic equation terms are in the range -15 to 15.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/2Ub2fn5
Quadratic Equations and Functions and Quadratic Formula
QuizletFlashCards.jpg Quizlet Flash Cards: Solving Quadratic Equations Using the Quadratic Formula, Set 04

Solve quadratic equations by using the quadratic formula in this 20-flash card set. The values of the quadratic equation terms are in the range -15 to 15.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/2Ub2fn5
Quadratic Equations and Functions and Quadratic Formula
QuizletFlashCards.jpg Quizlet Flash Cards: Solving Quadratic Equations Using the Quadratic Formula, Set 05

Solve quadratic equations by using the quadratic formula in this 20-flash card set. The values of the quadratic equation terms are in the range -15 to 15.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/2Ub2fn5
Quadratic Equations and Functions and Quadratic Formula
QuizletFlashCards.jpg Quizlet Flash Cards: Solving Quadratic Equations Using the Quadratic Formula, Set 06

Solve quadratic equations by using the quadratic formula in this 20-flash card set. The values of the quadratic equation terms are in the range -15 to 15.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/2Ub2fn5
Quadratic Equations and Functions and Quadratic Formula
QuizletFlashCards.jpg Quizlet Flash Cards: Solving Quadratic Equations Using the Quadratic Formula, Set 07

Solve quadratic equations by using the quadratic formula in this 20-flash card set. The values of the quadratic equation terms are in the range -15 to 15.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/2Ub2fn5
Quadratic Equations and Functions and Quadratic Formula
QuizletFlashCards.jpg Quizlet Flash Cards: Solving Quadratic Equations Using the Quadratic Formula, Set 08

Solve quadratic equations by using the quadratic formula in this 20-flash card set. The values of the quadratic equation terms are in the range -15 to 15.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/2Ub2fn5
Quadratic Equations and Functions and Quadratic Formula
QuizletFlashCards.jpg Quizlet Flash Cards: Solving Quadratic Equations Using the Quadratic Formula, Set 09

Solve quadratic equations by using the quadratic formula in this 20-flash card set. The values of the quadratic equation terms are in the range -15 to 15.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/2Ub2fn5
Quadratic Equations and Functions and Quadratic Formula
QuizletFlashCards.jpg Quizlet Flash Cards: Solving Quadratic Equations Using the Quadratic Formula, Set 10

Solve quadratic equations by using the quadratic formula in this 20-flash card set. The values of the quadratic equation terms are in the range -15 to 15.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/2Ub2fn5
Quadratic Equations and Functions and Quadratic Formula
QuizletFlashCards.jpg Quizlet Flash Cards: Solving Systems Using the Elimination Method

In this set of Quizlet flash cards test understanding of solving systems using the elimination method.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete Quizlet Flash Card Library, click on this link: https://media4math.com/Quizlet-Resources
Solving Systems of Equations
QuizletFlashCards.jpg Quizlet Flash Cards: Solving Systems Using the Substitution Method

In this set of Quizlet flash cards test understanding of solving systems using the substitution method.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete Quizlet Flash Card Library, click on this link: https://media4math.com/Quizlet-Resources
Solving Systems of Equations
QuizletFlashCards.jpg Quizlet Flash Cards: Systems of Linear Equations

In this set of Quizlet flash cards test understanding of linear systems.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete Quizlet Flash Card Library, click on this link: https://media4math.com/Quizlet-Resources
Solving Systems of Equations
QuizletFlashCards.jpg Quizlet Flash Cards: The Discriminant, Set 01

In this set of 10 interactive flash cards find the mean of four numbers. Press the Options button to decide how to display the flash cards. Press the Play button to auto-play the sequence of flash cards. Press Shuffle to change the order of the cards.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/2zRaRbH
Quadratic Formula
QuizletFlashCards.jpg Quizlet Flash Cards: The Discriminant, Set 02

In this set of 10 interactive flash cards find the mean of four numbers. Press the Options button to decide how to display the flash cards. Press the Play button to auto-play the sequence of flash cards. Press Shuffle to change the order of the cards.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/2zRaRbH
Quadratic Formula
QuizletFlashCards.jpg Quizlet Flash Cards: The Discriminant, Set 03

In this set of 10 interactive flash cards find the mean of four numbers. Press the Options button to decide how to display the flash cards. Press the Play button to auto-play the sequence of flash cards. Press Shuffle to change the order of the cards.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/2zRaRbH
Quadratic Formula
QuizletFlashCards.jpg Quizlet Flash Cards: The Discriminant, Set 04

In this set of 10 interactive flash cards find the mean of four numbers. Press the Options button to decide how to display the flash cards. Press the Play button to auto-play the sequence of flash cards. Press Shuffle to change the order of the cards.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/2zRaRbH
Quadratic Formula
QuizletFlashCards.jpg Quizlet Flash Cards: The Discriminant, Set 05

In this set of 10 interactive flash cards find the mean of four numbers. Press the Options button to decide how to display the flash cards. Press the Play button to auto-play the sequence of flash cards. Press Shuffle to change the order of the cards.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/2zRaRbH
Quadratic Formula
QuizletFlashCards.jpg Quizlet Flash Cards: The Discriminant, Set 06

Find the discriminant in this 20-flash card set. The values of the quadratic equation terms are in the range -15 to 15.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/2zRaRbH
Quadratic Formula
QuizletFlashCards.jpg Quizlet Flash Cards: The Discriminant, Set 07

Find the discriminant in this 20-flash card set. The values of the quadratic equation terms are in the range -15 to 15.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/2zRaRbH
Quadratic Formula