Lesson 2 | Rational Numbers | 6th Grade Mathematics

Objective

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

Common Core Standards

Core Standards

The core standards covered in this lesson

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.

The Number System

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

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Use positive and negative numbers to represent deposits, credits, withdrawals, charges, and other changes made to money accounts.
Use positive and negative numbers to represent temperatures.
Understand the meaning of zero in situations.
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

Suggestions for teachers to help them teach this lesson

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

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

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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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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References

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

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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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

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Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

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.

Illustrative Mathematics It's Warmer in Miami
EngageNY Mathematics Grade 6 Mathematics > Module 3 > Topic A > Lesson 2 — Example 2, Exercises 3-5, and Problem Set

Lesson 1

Lesson 3

Lesson Map

Topic A: Understanding Positive and Negative Rational Numbers

Extend the number line to include negative numbers. Define integers.

6.NS.C.6 6.NS.C.6.C

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

6.NS.C.5

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

6.NS.C.5

Define opposites and label opposites on a number line. Recognize that zero is its own opposite.

6.NS.C.6.A 6.NS.C.6.B

Find and position integers and rational numbers on the number line.

6.NS.C.6.C

Topic B: Order and Absolute Value

Order integers and rational numbers. Explain reasoning behind order using a number line.

6.NS.C.6.C 6.NS.C.7.A

Compare and interpret the order of rational numbers for real-word contexts.

6.NS.C.6.C 6.NS.C.7.A

Write and interpret inequalities to compare rational numbers in real-world and mathematical problems.

6.NS.C.7.A 6.NS.C.7.B

Define absolute value as the distance from zero on a number line.

6.NS.C.7.C

Model magnitude and distance in real-life situations using order and absolute value.

6.NS.C.7.C 6.NS.C.7.D

Topic C: Rational Numbers in the Coordinate Plane

Use ordered pairs to name locations on a coordinate plane. Understand the structure of the coordinate plane.

6.NS.C.6.B 6.NS.C.6.C

Reflect points across axes and determine the impact of reflections on the signs of ordered pairs.

6.NS.C.6.B

Calculate vertical and horizontal distances on a coordinate plane using absolute value in real-world and mathematical problems.

6.NS.C.7.C 6.NS.C.8

Rational Numbers

Objective

Common Core Standards

Core Standards

The Number System

Criteria for Success

Tips for Teachers

Anchor Problems

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

References

Problem Set

Target Task

Student Response

Additional Practice

Lesson Map

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