Curriculum  /  Math  /  7th Grade  /  Unit 2: Operations with Rational Numbers  /  Lesson 1

Operations with Rational Numbers

Lesson 1

Math

Unit 2

7th Grade

Lesson 1 of 18

Objective

Represent rational numbers on the number line. Define opposites, absolute value, and rational numbers.

Common Core Standards

Core Standards

  • 7.NS.A.1 — Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

Foundational Standards

  • 6.NS.C.5
  • 6.NS.C.6
  • 6.NS.C.7

Criteria for Success

  1. Understand that (by general convention) numbers on the number line increase from left to right (or bottom to top), and decrease from right to left (or top to bottom). 
  2. Represent positive and negative integers, fractions, and decimals on the number line.
  3. Define opposite numbers as numbers that are the same distance from 0 but on opposite sides on the number line.
  4. Define the absolute value of a number to be the distance from 0, which, as a measure of distance, is either positive or zero.
  5. Define rational numbers as numbers that can be written in the form $$\frac{a}{b}$$, where $$b \neq 0$$, and that can be located on the number line.  

Tips for Teachers

  • The first two lessons are approaching 7.NS.1 and review concepts and skills from sixth-grade standards in the number system domain. These standards are foundational to this seventh-grade unit and will support students in later lessons. Depending on the needs of your students, these lessons can be combined or left as separate lessons. The anchor problems can be used as part of whole-class instruction, diagnostically, or as part of independent practice.
  • A physical number line is a very helpful tool for students to have throughout the unit (MP.5). These can be printed out on cardstock or laminated so students can use them over time. A game piece or token to use as a place marker can make the idea of “moving on the number line” more tangible for students. If the number lines are laminated, then white board markers could also be used with them. This blog includes an example with some links to create some for your classroom.

Lesson Materials

  • Optional: Laminated number line (1 per student)
  • Optional: Dry erase marker (1 per student)
  • Optional: Game piece or token (1 per student)
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Anchor Problems

25-30 minutes

Problem 1

Darnell thinks that –4 is less than –6 because 4 is smaller than 6, and –4 is closer to 0 than –6 is. Draw a number line to show the numbers 0, –4, and –6. Then explain why Darnell is incorrect.

Guiding Questions

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Student Response

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Problem 2

In each situation, draw a number line and represent the two values as points on the number line. 

a.   deposit of $75 and withdrawal of $50

b.    $$5\frac{3}{4}$$ feet below sea level and 3 feet below sea level

c.   temperature of 25ËšC and 12 degrees below 0 on the Celsius scale

Guiding Questions

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Student Response

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Problem 3

Jessica says she’s thinking of two numbers. They are 24 units apart on the number line, and they are opposites. What are the two numbers?

Guiding Questions

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Student Response

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Problem 4

You and a friend are playing a game using a number line. You both place a game token on the number line at 2. You then roll a die and move your token that number of places on the number line. Your friend rolls the die and does the same. 

The two tokens end up at different locations on the number line, however the absolute value of each location is the same, 3. Where are the two tokens on the number line, and what did you and your friend roll on the die to get there?

Guiding Questions

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Student Response

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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

Point A is shown on the number line below.

a.   What number does point A represent?

b.   What is the absolute value of the number represented by point A?

c.   What is the opposite of the number represented by point A? Indicate this on the number line.

d.   What is the distance between point A and $$-1$$ on the number line?

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.

Next

Compare and order rational numbers. Write and interpret inequalities to describe the order of rational numbers.

Lesson 2
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Lesson Map

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Topic A: Adding and Subtracting Rational Numbers

Topic B: Multiplying and Dividing Rational Numbers

Topic C: Using all Four Operations with Rational Numbers

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