Videos to help Grade 6 students understand ordered pairs and how to locate ordered pairs on the coordinate plane.

New York State Common Core Math Grade 6, Module 3, Lesson 15

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Common Core For Grade 6

Lesson 15 Student Outcomes

• Students extend their understanding of the coordinate plane to include all four quadrants, and recognize that the axes (identified as the -axis and -axis) of the coordinate plane divide the plane into four regions called quadrants (that are labeled from first to fourth and are denoted by Roman Numerals).

• Students identify the origin, and locate points other than the origin, which lie on an axis.

• Students locate points in the coordinate plane that correspond to given ordered pairs of integers and other rational numbers.

Lesson 15 Summary

• The x-axis and y-axis of the coordinate plane are number lines that intersect at zero on each number line.

• The axes create four quadrants in the coordinate plane.

• Points in the coordinate plane lie either on an axis or in one of the four quadrants.

Lesson 15 Opening Exercise

Example 1: Extending the Axes Beyond Zero

The point below represents zero on the number line. Draw a number line to the right starting at zero. Then follow directions as provided by the teacher.

Example 2: Components of the Coordinate Plane

All points on the coordinate plane are described with reference to the origin. What is the origin, and what are its coordinates?

Exercises 1-3

1. Use the coordinate plane below to answer parts (a)-(c):

a. Graph at least five points on the -axis and label their coordinates.

b. What do the coordinates of your points have in common?

c. What must be true about any point that lies on the y-axis?

Explain.

2. Use the coordinate plane to answer parts (a)-(c):

a. Graph at least five points on the -axis and label their coordinates.

b. What do the coordinates of your points have in common?

c. What must be true about any point that lies on the -axis? Explain.

3. If the origin is the only point with for both coordinates, what must be true about the origin?

Exercises 4-6

4. Locate and label each point described by the ordered pairs below. Indicate which of the quadrants the points lie in.

a. (7, 2)

b. (3, -4)

c. (1, -5)

d. (-3, 8)

e. (-2, -1)

5. Write the coordinates of at least one other point in each of the four quadrants.

a. Quadrant I

b. Quadrant II

c. Quadrant III

d. Quadrant IV

6. Do you see any similarities in the points within each quadrant? Explain your reasoning.

1. Name the quadrant in which each of the points lies. If the point does not lie in a quadrant, specify which axis the point lies on.

a. (-2,5)

b. (8,-4)

c. (-1,-8)

d. (9.2,7)

e. (0,-4)

2. Jackie claims that points with the same x- and y-coordinates must lie in Quadrant I or Quadrant III. Do you agree or disagree? Explain your answer.

3. Locate and label each set of points on the coordinate plane. Describe similarities of the ordered pairs in each set, and describe the points on the plane.

a. {(-2,5),(-2,2),(-2,7),(-2,-3),(-2,-0.8)}

b. {(-9,9),(-4,4),(-2,2),(1,-1),(3,-3),(0,0)}

c. {(-7,-8),(5,-8),(0,-8),(10,-8),(-3,-8)}

4. Locate and label at least five points on the coordinate plane that have an x-coordinate of 6.

a. What is true of the y-coordinates below the x-axis?

b. What is true of the y-coordinates above the x-axis?

c. What must be true of the y-coordinates on the x-axis?

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