Curriculum  /  Math  /  6th Grade  /  Unit 4: Rational Numbers  /  Lesson 11

Rational Numbers

Lesson 11

Math

Unit 4

6th Grade

Lesson 11 of 13

Objective

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

Common Core Standards

Core Standards

  • 6.NS.C.6.B — Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
  • 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

  • 5.G.A.1

Criteria for Success

  1. Extend the $${{{{x-}}}}$$ and $${{{{y-}}}}$$axes of the first quadrant of the coordinate plane to create a four quadrant grid; understand a four quadrant grid is created when two perpendicular number lines intersect at zero.
  2. Represent a location in a coordinate plane using an ordered pair, where the $${{{{x-}}}}$$coordinate indicates distance and direction along the $${{{{x-}}}}$$axis, and the $${{{{y-}}}}$$coordinate indicates distance and direction along the $${{{{y-}}}}$$axis.
  3. Understand that the signs of ordered pairs indicate in which quadrant a point is located (i.e., an ordered pair $${(-a,b)}$$ will be located in quadrant 2 because you travel left along the $${{{{x-}}}}$$axis and up along the $${{{{y-}}}}$$axis).

Tips for Teachers

  • Students may need to review concepts and skills associated with the first quadrant (standard 5.G.1) before they are able to fully access this lesson. 
  • A common misconception students may have prior to extending beyond the first quadrant is that an $${x-}$$coordinate indicates how far to move right, and a $${y-}$$coordinate indicates how far to move up. Discuss how the addition of negative values in an ordered pair creates the need for a more precise way to describe movement in the coordinate plane (MP.6).

Lesson Materials

  • Graph Paper (2-3 sheets per student)
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Anchor Problems

25-30 minutes

Problem 1

Plot each point described by the ordered pairs below. Label each point with its letter. Indicate in which quadrant each point is located. 

  1. $$(5, 2)$$
  2. $$(3, -6)$$
  3. $$(2, -8)$$
  4. $$(-5, 8)$$
  5. $$(-5, -1)$$

 

Guiding Questions

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Student Response

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Problem 2

Some points are shown in the coordinate grid below. (Note: $$x$$ and $$y$$ are on the same scale. The scale is 1 unit.)

a.   Choose any two points. Consider their locations in the plane. How are they the same? How are they different? Write down at least three things you notice.

b.   Name the coordinates for each point.

c.   Make some observations relating coordinates to locations in the plane. (Here is an example: "When the first coordinate is positive, that point is located to the right of the $$y-$$axis.") Write down at least three things you notice.

d.   Consider the rule, "When the first coordinate is positive, that point is located to the right of the $$y-$$axis." Will that always be true or only happen sometimes? Explain your reasoning. 

e.   Choose one of the things you noticed from part (c) and explain why it will always be true or only happen sometimes.

Guiding Questions

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Student Response

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References

Illustrative Mathematics Locations in the Coordinate Plane

Locations in the Coordinate Plane, accessed on Nov. 3, 2017, 3:47 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.

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

Label the second quadrant on the coordinate plane, and then answer the following questions.

a.   Write the coordinates of one point that lies in the second quadrant of the coordinate plane.

b.    What must be true about the coordinates of any point that lies in the second quadrant?

c.    Plot and label the following points:

$${A: (-4, 6)}$$

$${B: (6, -4)}$$

$${C: (0, -2)}$$

$${D: (2, 0)}$$

$${E: (-5, -3)}$$

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

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

Lesson 12
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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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