MidSchoolMath 1

The concept of absolute value can be confusing for students, especially when relating it to numerical order. In Coffee Accounting, Victor is a barista in a coffee shop who has a misunderstanding with a customer. He tells the customer that he has a "negative debt" on his account balance. Victor’s sister, Analisa, who is a CPA, overhears the conversation and offers to clarify Victor’s under-standing of absolute value and numerical order. The data provided are the coffee shop’s account balance ledger and a set of seven statements that Analisa writes about those balances.

LESSON: COFFEE ACCOUNTINGWhich statements are true based on the account balances?

Coffee Accounting

Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than -30 dollars represents a debt greater than 30 dollars.

The Math SimulatorTM

ImmersionPlay Coffee Accounting Immersion video, whole-class. Restate the question: Which statements are true based on the account balances?Facilitate classroom discussion; ask students: "What are your ideas?"

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2 Data & ComputationPrint the Data Artifact, cut into halves, 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 Coffee Accounting 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.)

6.NS.C.7dThe Number System

MidSchoolMath 2Coffee Accounting

Clicker QuizLaunch the Clicker Quiz, whole-class.

6.NS.C.7dThe Number System

Gladys: Remind students that absolute value doesn't "make a number positive." It states the distance a number is from zero.

Kevin: Help students see that the order of absolute values of positive numbers is the same as the order of the numbers them-selves.

Megan: Help students see that the order of absolute values of negative numbers is the opposite of the order of the numbers themselves.

KevinSimpson

GladysGraham

MeganLeBleu

Ex. Clicker Quiz #3Standard Math Procedures

Instruction at a Glance

1 Analyze number line.

a is negative; b is positive.

a is further away from 0 than b.

A: a > b

B: |a| > |b |

C: Both are true. False.

True.D: Neither are true.

False; negative numbers are less than positive numbers.

False; a's distance from 0 is greater than b's distance from 0.

2 Determine if each statement is true.

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COFFEE ACCOUNTINGWhich statements are true based on the account balances?

Victor works at The Big Friendly Java coff ee shop and is often confused about how to express account balances in the house account log. Recently his sister, Analisa, helped him by creating some true/false statements about the listings in the house account log. She has added two more statements to the list.

1) Ryan O’Connell’s debt is less than Elena Maestas’ debt.

2) Kim Wing has a debt greater than 25 dollars.

Use the house account balances, shown in the log below, to determine whether these statements are true or false. Explain your answer.

6.NS.C.7d

Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than -30 dollars represents a debt greater than 30 dollars.

About this standard

Date PeriodName

MidSchoolMath Coff ee Accounting 1 of 2

COFFEE ACCOUNTINGWhich statements are true based on the account balances?

Victor works at The Big Friendly Java coff ee shop and is often confused about how to express account balances in the house account log. Recently his sister, Analisa, helped him by creating some true/false statements about the listings in the house account log. She has added two more statements to the list.

1) Ryan O’Connell’s debt is less than Elena Maestas’ debt.

2) Kim Wing has a debt greater than 25 dollars.

Use the house account balances, shown in the log below, to determine whether these statements are true or false. Explain your answer.

6.NS.C.7d

Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than -30 dollars represents a debt greater than 30 dollars.

About this standard

Date PeriodName

MidSchoolMath Coff ee Accounting 1 of 2

APPLYING THE STANDARD

MidSchoolMath 2 of 2

Date PeriodName

How might this standard appear on a test?

Coff ee Accounting

The manager of The Big Friendly Java coff ee shop wants to know who has a debt greater than $20. Use the house account balances on the previous page to tell who would be included.Explain why.

1)

Lars Gusterson, a customer at The Big Friendly Java, also owes 24 dollars to the pastry shop. To which store does he owe more? Explain your answer.

2)

Sonar detects fi ve artifacts underwater in the area of an ancient sunken city. The artifacts are measured at depths of 82 meters, 106 meters, 251 meters, 317 meters, and 394 meters. Divers can only go -330 meters. How many artifacts can they retrieve? Use the idea of absolute value to explain your answer.

5)

A person began walking every day to lose weight. This chart shows the change in weight each month, in pounds.

3)

Tomo owes $5 to her friend Madison and $7.50 to her friend Anika. Her friend Kyra owes her $6.75, and her friend Elena owes her $4.50. Which is greater: the amount that Tomo owes to her friends or the amount her friends owe her?

4)

Write an integer to represent the weight change each month. Put the integers in order from least to greatest.

Now put the values in order from the least amount of change to the greatest amount of change.

Why are the two lists diff erent? (Use the idea of absolute value in your answer.)

a)

b)

c)

Check out my worked example #4

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