MidSchoolMath 1

Challenging problems involving addition and subtraction of rational numbers can often be made a bit easier to handle by rear-ranging the terms. During Bad Accounting, Cora Malone goes to Mr. Skinner, the gold exchange banker, to deposit a bit of gold and asks what she currently has in her account. Mr. Skinner goes through a list of all the things for which Cora owes him and tells her she owes him $105. She questions his integrity, so she asks to see his books so she can check his calculations. The data provided is Mr. Skinner’s ledger for Miss Malone’s account.

LESSON: BAD ACCOUNTINGIs the gold exchange banker swindling Miss Malone?

Bad Accounting

Apply properties of operations as strategies to add and subtract rational numbers.

The Math SimulatorTM

ImmersionPlay Bad Accounting Immersion video, whole-class. Restate the question: Is the gold exchange banker swindling Miss Malone?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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Download the Detailed Lesson PlanAvailable on the Teacher Dashboard

3 ResolutionPlay Bad Accounting Resolution video, whole-class. Prepare and give brief lecture (Teacher Instruction).

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+ 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.)

7.NS.A.1dThe Number System

MidSchoolMath Bad Accounting

Clicker QuizLaunch the Clicker Quiz, whole-class.

7.NS.A.1dThe Number System

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Gladys: Students will benefit from a refer-ence sheet listing the various properties of operations.

Kevin: Give students opportunities to explore using the properties of operations with varying expressions involving addition and subtraction of rational numbers. Let them discover for themselves which prop-erties they find helpful.

Megan: Ask that students indicate which property they use at each step, as some properties are so subtle they may not even realize they are using a property. Help stu-dents recognize this.

KevinSimpson

GladysGraham

MeganLeBleu

Ex. Clicker Quiz #5Standard Math Procedures

Instruction at a Glance

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Add the additive inverse.

Apply the commutative property.

Simplify and find the common denominator.

Apply the associative property.

Add.

- + 4 + 8 + (- )

4 + 8 + (- ) + (- )

12 + (- ) + (- )

12 + (- )

12 + (-1 ) = 10

34

13

23

34

712

712

712

912

1612

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BAD ACCOUNTINGIs Mr. Skinner swindling Miss Malone?Cora Malone and her family have had issues with Mr. Skinner’s banking practices for as long as she can remember. She makes it a point to check Mr. Skinner’s calculations each time she goes to do business at the bank. He almost always has the incorrect balance.

Determine if Mr. Skinner is swindling Miss Malone. If so, calculate Miss Malone’s actual account balance.

7.NS.A.1d

Apply properties of operations as strategies to add and subtract rational numbers.

About this standard

Date PeriodName

MidSchoolMath Bad Accounting 1 of 2

Is Mr. Skinner swindling Malone?YES NO

If YES, what is Miss Malone’s actual account balance?

APPLYING THE STANDARD

Evaluate each expression. Indicate the properties of operations where appropriate.1)

-5 + 6 + (-2) – 4a) 22 – 8 + (-3) + 10b)

MidSchoolMath Bad Accounting 2 of 2

Date PeriodName

How might this standard appear on a test?

Evaluate for x = :

-x + 2 – (-x)

4) Evaluate for x = -2.4 :

-3x + 6 + 2x

5)78

Write an “X” in the box beside each expression that is equivalent to .Select all that apply.

3) -5 + 1 35

15

-5 + (- ) + 1 + 35

15

5 + + (-1) + (- ) 35

15

-5 + + 1 + 35

15

-5 + 1 + (- ) + 35

15

Write an “X” in the box beside each expression that is equivalent to -6 – (1.25 + 3.5).Select all that apply.

2)

(-6 – 1.25) + 3.5

(-6 – 1.25) – 3.5

-(6 + 1.25) + 3.5

-(6 + 1.25) – 3.5

-3.5 + (-6 – 1.25)

3.5 + (-6 – 1.25)

-(3.5 – 6) – 1.25

60 + (-75) + 33 – 87 – (-15)c) 11.6 – (-12.4) + 15.3 – 9d)

32 + (-12 ) + f)– – (- ) +e) 23

512

16

12

78

12

Check out my worked example #1a

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