Curriculum  /  Math  /  6th Grade  /  Unit 4: Rational Numbers  /  Lesson 2

Rational Numbers

Lesson 2

Math

Unit 4

6th Grade

Lesson 2 of 13

Objective

Use positive and negative numbers to represent real-world contexts, including money and temperature.

Common Core Standards

Core Standards

  • 6.NS.C.5 — Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

Criteria for Success

  1. Use positive and negative numbers to represent deposits, credits, withdrawals, charges, and other changes made to money accounts.
  2. Use positive and negative numbers to represent temperatures.
  3. Understand the meaning of zero in situations. 
  4. Find and use an appropriate scale for a number line in order for all relevant numbers to be located on the number line.

Tips for Teachers

  • Lessons 2 and 3 introduce students to various real-world applications that can be modeled with positive and negative values (MP.4). This lesson focuses on money and temperature, and Lesson 3 focuses on elevation. 
  • Students may need additional support or remediation around setting up appropriate scales for number lines, especially with the introduction of negative values.
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Anchor Problems

25-30 minutes

Problem 1

The number line below does not have a scale shown on it. 

What scale would you use if you wanted to plot each set of numbers below?

a.    $$0$$ and $$150$$

b.    $$8$$ and $$-12$$

c.    $$-50$$ and $$50$$

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 6 Mathematics > Module 3 > Topic A > Lesson 2 — Opening Exercise

Grade 6 Mathematics > Module 3 > Topic A > Lesson 2 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Read the story about Tim:

For Tim’s 13th birthday, he received $150 in cash from his relatives. His dad took him to the bank to open a savings account. Tim gave the cash to the banker to deposit into the account. The banker credited Tim’s new account $150 and gave Tim a receipt. One week later, Tim deposited another $25 that he earned from babysitting. The next month, Tim’s dad gave him permission to withdraw $35 to buy a soccer ball. Tim’s dad explained that the bank would charge a $2 fee for each withdrawal from the savings account and that each withdrawal and charge results in a debit to the account.

Write each individual description below as an integer. Model the integer on the number line using an appropriate scale.

Event Integer Number Line Model
Open a bank account with $0                                                                                                      
Make a $150 deposit.    
Make a deposit of $25.    
A bank makes a charge of $2.    
Tim withdraws $35.    

 

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 6 Mathematics > Module 3 > Topic A > Lesson 2 — Example 1 and 2

Grade 6 Mathematics > Module 3 > Topic A > Lesson 2 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

During winter break, Mr. Stadel went to Brian Head, Utah. He took several screenshots on his phone of the temperature throughout the day. The temperature at 4:13 AM is shown below.

a.   What do you notice? What do you wonder?

b.   Plot the temperature at 4:13 AM on a vertical number line. 

c.   Predict the temperature in Brian Head, Utah, at 6 AM, 7 AM, 9:30 AM, 2:30 PM, and 8 PM.

d.   Your teacher will share screenshots of the actual temperatures around those times. For each one, plot the temperature on your vertical number line and label with the time. 

e.   How much did the temperature change between each time interval?

Guiding Questions

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Student Response

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References

Divisible By 3 Integers [temperatures]

Integers [temperatures] is made available by Andrew Stadel on Divisible by 3 under the CC BY-NC-SA 3.0 license. Accessed Nov. 3, 2017, 3:15 p.m..

Modified by Fishtank Learning, Inc.

Problem Set

15-20 minutes

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes

Write the integer that describes each of the following situations. Then represent the integer on a horizontal or vertical number line. Include the value 0 on your number line and use an appropriate scale.

a.   A deposit made of $15

b.   A withdrawal of $75

c.   A credit of $110

d.   A temperature of 15 degrees below 0

Student Response

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Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Have students write their own stories about changes made to a bank account. Students can swap stories and write the integers to represent the numbers in the stories. 

Next

Use positive and negative numbers to represent real-world contexts, including elevation.

Lesson 3
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Understanding Positive and Negative Rational Numbers

Topic B: Order and Absolute Value

Topic C: Rational Numbers in the Coordinate Plane

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