Rational Numbers

Lesson 1

Math

Unit 4

6th Grade

Lesson 1 of 13

Objective


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

Common Core Standards


Core Standards

  • 6.NS.C.6 — Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
  • 6.NS.C.6.C — Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

Foundational Standards

  • 3.NF.A.2

Criteria for Success


  1. Understand that the number line can be extended to the left (or below zero) to include values that are negative or less than zero. 
  2. Know that numbers increase from left to right (or from bottom to top) and decrease from right to left (or top to bottom) on a number line. 
  3. Define integers as a set of numbers that includes whole numbers, their opposites (negative values of whole numbers), and zero.

Tips for Teachers


  • The number line will be a critical tool throughout this unit. We recommend giving students their own individual number line to have and use when they see fit (MP.5), including one blank number line so they can change the scale or practice labeling, and one that is pre-labeled with a scale of -10 to 10 (or similar). These can be laminated or put in a sheet protector so students can draw on them with a dry-erase marker. 
  • This Number Line Generator from HelpingWithMath.com is a good website for generating number lines.
  • Note that the reference to number lines in this unit assume the convention of labeling with the smaller numbers to the left or to the bottom of the number line.

Lesson Materials

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


Problem 1

The number line below shows labels for integers $$0-6$$

a.   Make three observations about the number line. 

b.   What labels would you use for the integer marks to the left of 0 on the number line? 

Guiding Questions

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Problem 2

A number line is shown below with points $$A$$, $$B$$, and $$C$$ marked. The scale on the number line is 1.

a.    If point $$A$$ is at 0, then what are the values of points $$B$$ and $$C$$?

b.   If point $$B$$ is at 0, then what are the values of points $$A$$ and $$C$$?

c.   If point $$C$$ is at 0, then what are the values of points $$A$$ and $$B$$?

Guiding Questions

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Problem 3

Andrea thinks that $$-5$$ is less than $$-7$$ because $$5$$ is smaller than $$7$$. Draw a number line to show the numbers $$0$$, $$-5$$, and $$-7$$. Then use it to explain why Andrea's reasoning is incorrect. 

Guiding Questions

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Problem Set

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Target Task


Problem 1

On the number line below, $$b$$ is a negative integer and $$d$$ is a positive integer.

Name one set of values for $$a$$, $$b$$, $$c$$, and $$d$$.

Problem 2

Explain the error in the number line below. 

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.

  • Include examples similar to the Anchor Problems but on vertical number lines.
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Lesson 2

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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