Lesson 11 | Rational Numbers | 6th Grade Mathematics

Objective

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

Common Core Standards

Core Standards

The core standards covered in this lesson

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.

The Number System

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.

The Number System

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

The foundational standards covered in this lesson

5.G.A.1

Geometry

5.G.A.1 — Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

Criteria for Success

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

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.
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.
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

Suggestions for teachers to help them teach this lesson

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

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

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.

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

Guiding Questions

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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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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

A set of suggested resources or problem types that teachers can turn into a problem set

Fishtank Plus Content

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

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

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.

EngageNY Mathematics Grade 6 Mathematics > Module 3 > Topic C > Lesson 14 — Exercises 1-2, and Problem Set 1-2
EngageNY Mathematics Grade 6 Mathematics > Module 3 > Topic C > Lesson 15 — Exercises 1-3, and Problem Set
Illustrative Mathematics Plotting Points in the Coordinate Plane
Desmos Mini Golf Marbleslides — This activity requires computers. This is a fun and challenging activity where students change the placement of a slide using coordinates in order to guide marbles into a hole.

Lesson 10

Lesson 12

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

The Number System

Foundational Standards

Geometry

Criteria for Success

Tips for Teachers

Lesson Materials

Anchor Problems

Problem 1

Guiding Questions

Problem 2

Guiding Questions

References

Problem Set

Target Task

Student Response

Additional Practice

Lesson Map

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