Curriculum  /  Math  /  6th Grade  /  Unit 4: Rational Numbers  /  Lesson 8

Rational Numbers

Lesson 8

Math

Unit 4

6th Grade

Lesson 8 of 13

Objective

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

Common Core Standards

Core Standards

  • 6.NS.C.7.A — Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret -3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right.
  • 6.NS.C.7.B — Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3 °C > -7 °C to express the fact that -3 °C is warmer than -7 °C.

Foundational Standards

  • 4.NF.A.2
  • 4.NF.C.7

Criteria for Success

  1. Understand that inequalities can be used to model the relationship between rational numbers in real-world contexts (MP.4).
  2. Understand that smaller numbers represent colder temperatures; the smaller the number or the farther left on the number line, the colder the temperature. 
  3. Understand that small numbers represent lower elevations; the smaller the number or the farther left on the number line, the lower the elevation and the farther from sea level. 
  4. Write inequalities to compare rational numbers.

Tips for Teachers

Students extend on their understanding of ordering fractions from fourth grade to include rational numbers.

Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems

25-30 minutes

Problem 1

Fill in each blank using a $${<}$$ or $${>}$$ inequality symbol

a.      $$5$$    _______    $$8$$

 

b.    $${11.3}$$    _______    $${11.13}$$

 

c.   $${\frac{2}{3}}$$    _______    $${\frac{3}{4}}$$

 

d.    $${-0.6}$$    _______    $${0.3}$$

 

e.    $$\frac{11}{8}$$    _______    $$-\frac{11}{8}$$

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

Problem 2

Here are the low temperatures (in Celsius) for one week in Juneau, Alaska:

Monday Tuesday Wednesday Thursday Friday Saturday Sunday
$$5$$ $$-1$$ $$-6$$ $$-2$$ $$3$$ $$7$$ $$0$$

a.   Arrange the temperatures in order from coldest to warmest temperature.

b.   On a winter day, the low temperature in Anchorage was $$23$$ degrees below $$0$$°C, and the low temperature in Minneapolis was $$14$$ degrees below $$0$$°C. Sophia wrote: “Minneapolis was colder because $$-14 < -23$$.” Is Sophia's statement correct? Explain your answer.

c.   The lowest temperature ever recorded on Earth was $$-89$$°C in Antarctica. The average temperature on Mars is about $$-55$$°C. Which is warmer, the coldest temperature on Earth or the average temperature on Mars? Write an inequality to support your answer.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

References

Illustrative Mathematics Comparing Temperatures

Comparing Temperatures, accessed on Aug. 11, 2017, 12:58 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem 3

The elevation of New Orleans, Louisiana, is $$7$$ feet below sea level. The elevation of Coachella, California, is $$-72$$ feet. Write an inequality to compare the elevations of the two cities.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

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

A number line is shown below.

a.   Find and label the numbers $${-3}$$ and $${-5}$$ on the number line.

b.   Which of the following are true inequalities? Use the number line diagram to help determine your answers.

  1. a.   $${-3}>{-5}$$

  2. b.   $${-5}>{-3}$$

  3. c.   $${-5}<{-3}$$

  4. d.   $${-3}<{-5}$$

Student Response

Upgrade to Fishtank Plus to view Sample Response.

References

Illustrative Mathematics Integers on the Number Line 1

Integers on the Number Line 1, accessed on Nov. 3, 2017, 3:30 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

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.

  • Always, sometimes, never for:
    • $${-a<a}$$
    • $${a<b}$$, when $$a$$ is to the right of $$0$$ and $$b$$ is to the left of $$0$$
    • $${a<b}$$, when $$a$$ is to the left of $$0$$ and $$b$$ is to the right of $$0$$
    • $${a<b}$$, when $$a$$ and $$b$$ are both to the left of $$0$$
  • Multiple-choice items where students must select a true comparison with reason
  • Multiple-select items with multiple correct answers similar to this SBAC item (adjust to include negatives)

Next

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

Lesson 9
icon/arrow/right/large

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

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

We Handle Materials So You Can Focus on Students

We Handle Materials So You Can Focus on Students

We've got you covered with rigorous, relevant, and adaptable math lesson plans for free