MidSchoolMath 1

Students must become aware that although there are many times in math where there is exactly one answer, there are also times in which there are no answers or many answers. During The Business Guru in YOU!, Tony Ram Scott, a financial expert, addresses the audience and congratulates them on "taking the first step toward financial nirvana!" He continues his presentation, focusing on the importance of knowing the breakeven point for any business. He walks through an example, then asks the audience to simplify the equations to find the breakeven point and to try to describe the business model. The data provided is Tony Ram Scott’s presentation slide, showing the expenses = revenue equation for three businesses.

LESSON: THE BUSINESS GURU IN YOU!What is the breakeven point for each business model?

Describe what is happening in each business.

The Business Guru in YOU!

Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

The Math SimulatorTM

ImmersionPlay The Business Guru in YOU! Immersion video, whole-class. Restate the question: What is the breakeven point for each business model? Describe what is happening in each business.Facilitate classroom discussion; ask students: "What do we need to know?"

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2 Data & ComputationPrint the Data Artifact and distribute to students. Allow students work time. Ask students: "Does your answer make sense?"Consider using a sharing protocol leading to mathematical insights and/or highlighting misconceptions. Allow students to revise their work.

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3 ResolutionPlay The Business Guru in YOU! Resolution video, whole-class. Prepare and give brief lecture (Teacher Instruction).

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Download the Detailed Lesson PlanAvailable on the Teacher Dashboard

+ Simulation TrainerAssign the Simulation Trainer.Use protocols that encourage students to help each other.Use Progress Monitoring to access real-time data for the classroom.Provide individual help for students who are not making progress.

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(Use student headphones.)

8.EE.C.7aExpressions & Equations

MidSchoolMath The Business Guru in YOU!

Clicker QuizLaunch the Clicker Quiz, whole-class.

8.EE.C.7aExpressions & Equations

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Gladys: Remind students of the many properties they can use to help them solve more complex equations.

Kevin: Make sure students understand the meaning behind solutions. If an equation has one solution, there is only one number that makes the equation true. If an equation has no solutions, there is no number anywhere that will make that equation true. If an equation has infinite solutions, all real numbers will make it true. The reasons for this will become apparent in subsequent standards that connect the equations to lines on a graph.

Megan: Help students discover the similar structure of equations with no solution, one solution, and infinite solutions. Consider providing them with a list of equations along with an indication of the number of solutions it has. Ask students to analyze the equations for patterns and structure for each type.

KevinSimpson

GladysGraham

MeganLeBleu

Ex. Clicker Quiz #6Standard Math Procedures

Instruction at a Glance

1 Convert the fraction to a common denominator.

x ÷ = 7 ÷

x = 56

x – x = 3 + 4

(56) – 4 = (56) + 3

21 – 4 = 14 – 317 = 17

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3

Isolate the variable by using inverse operations.

Check the solution by substitution.

x – 4 = x + 338

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38

28

38

18

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THE BUSINESS GURU IN YOU!What is the breakeven point for eachbusiness model?Financial expert Tony Ram Scott believes that anyone who wishes to be fi nancially independent must understand the importance of the breakeven point–when money brought in (revenue) equals money spent (expenses).

Look at the “expenses = revenue” equations for the three businesses shown in Tony Ram Scott’s presentation slide. Find the breakeven point for each business.

8.EE.C.7a

Give examples of linear equations in one variable with one solution, infi nitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are diff erent numbers).

About this standard

Date PeriodName

MidSchoolMath The Business Guru in YOU! 1 of 2

What is the breakeven point for each business?

Business 1: __________ Business 2: __________ Business 3: __________

APPLYING THE STANDARD

Observe each equation and determine the number of solutions. In the blank, write one solution, infi nite solutions, or no solution.

1)

8x – 9 = -4x + 15a)

6 – 2h = -2h – 4b)

0.72 – 3w = 5w + 0.28d)

n + = + nc)

MidSchoolMath The Business Guru in YOU! 2 of 2

Date PeriodName

How might this standard appear on a test?

Determine values of P and Q so that the equation has infi nite solutions.

Determine values of P and Q so that the equation has no solution.

-14x + P = Qx + 18 Px – 17 = 22 + Qx

P = _________ Q = _________ P = _________ Q = _________

An equation (in simplest form) has no solution when ___________________________________

______________________________________________________________________________.

Complete each statement.

2) 3)

10)

An equation (in simplest form) has infi nite solutions when ______________________________

______________________________________________________________________________

11)

-2c + 16 = 16 + 7c4)

7(y + 3) = 5y + 87)

3x + 21 = -11 – 5x5)

4(3r + 5) = -8(2r + 1)8)

4b + 8 = 7b + 8 – 3b6)

9)

12

35

35

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Solve for the given variable.

– a = - a +194

7 2

14

32

Check out my worked example #1b

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