This lesson teaches students about locating ordered pairs on the coordinate plane: - It reviews extending the x-axis and y-axis to include negative numbers, dividing the plane into four quadrants. - Students learn to identify the origin and locate points on the axes or in the quadrants by their ordered pair coordinates. - Exercises have students graph points, identify quadrants, and note properties of points based on their coordinates.

1. Lesson 15: Locating OrderedPairs ontheCoordinatePlane
Date: 2/9/15 145
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•3Lesson 15
Lesson 15: Locating Ordered Pairs on the Coordinate Plane
Student Outcomes
 Students extend their understandingof the coordinateplaneto includeall four quadrants ,and recognizethat
the axes (identified as the 𝑥-axis and 𝑦-axis) of the coordinateplanedividethe planeinto four regions called
quadrants (that arelabeled from first to fourth and are denoted by Roman Numerals).
 Students identify the origin,and locate points other than the origin,which lieon an axis.
 Students locatepoints in the coordinateplanethat correspond to given ordered pairs of integers and other
rational numbers.
Classwork
OpeningExercise (5 minutes)
Hang posters on the wall,each containingoneof the followingterms: 𝑥-axis, 𝑦-axis, 𝑥-coordinate, 𝑦-coordinate,origin,
and coordinatepair. Pair students up and have them discuss thesevocabulary terms and what they remember about
the terms from Grade 5. Student pairs will then write what they discussed on the posters with the appropriate
vocabulary term. Some importantaspects for students to remember include:
 The 𝑥-axis is a horizontal number line; the 𝑦-axis is a vertical number line.
 The axes meet forminga 90° angleat the point (0,0) called the origin.
Example 1 (6 minutes): Extendingthe AxesBeyondZero
Students recognize that the axes arenumber lines and usingstraightedges, extend the axes on the coordinateplane to
includenegative numbers revealing the second, third,and fourth quadrants.
 Describethe 𝑥-axis. Considering whatwe have seen in this module, what types of numbers should itinclude?
Why?
 The 𝑥-axis is a horizontal number line that includes positive and negative numbers. The axis extends in
both directions (left and right of zero) because signed numbers represent values or quantities that have
opposite directions.
Example 1: Extending the AxesBeyond Zero
The point below representszeroon the number line. Draw anumber lineto therightstarting at zero. Then follow
directionsasprovided by the teacher.
Students use straightedges to extend the 𝑥-axis to the left of zero to represent the real number linehorizontally and
complete the number lineusingthe same scale as on the right sideof zero.
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2. Lesson 15: Locating OrderedPairs ontheCoordinatePlane
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•3Lesson 15
(𝟑,𝟎)
(𝟔,𝟎)
(−𝟓,𝟎)
(−𝟏,𝟎)(−𝟖,𝟎)
(𝟎,𝟖)
(𝟎,−𝟖)
(𝟎,𝟓)
(𝟎,𝟑)
(𝟎,−𝟒)
 Describethe 𝑦-axis. Whattypes of numbers should itinclude?
 The 𝑦-axis is a vertical number line that includes numbers on both sides of zero (above and below), and
so it includes both positive and negative numbers.
Students use straightedges to extend the 𝑦-axis belowzero to represent the real number linevertically and complete
the number lineusingthe same scaleas thatshown above zero.
Example 2 (4 minutes): Componentsof the Coordinate Plane
Students examine how to use the axes and the origin of the coordinateplaneto determine
other locations in theplane.
Example 2: Componentsofthe CoordinatePlane
All pointson the coordinate plane are described withreferenceto the origin. What isthe origin,
and what are itscoordinates?
The origin is thepointwherethe 𝒙-and 𝒚-axes intersect. Thecoordinates oftheorigin are (𝟎,𝟎).
 The axes of the coordinateplane intersectat their zero coordinates,which is a
point called the origin. The origin is the reference point from which all points in thecoordinateplaneare
described.
To describe locationsofpoints in thecoordinate plane weuse ordered pairs ofnumbers. Order isimportant, so on
the coordinateplane we use theform ( 𝒙, 𝒚 ). The first coordinate representsthe point’slocation from zeroon the
𝒙 -axis, and the second coordinate representsthe point’slocation from zeroon the 𝒚 -axis.
Exercises1–3 (8 minutes)
Students locateand label points thatlieon the axes of the coordinateplane.
Exercises1–3
1. Use the coordinateplanebelow to answer parts (a)–(c):
a. Graph at least five pointson the 𝒙-axisand label their
coordinates.
Points will vary.
b. What do the coordinatesofyour pointshave in common?
Each point has a 𝒚-coordinateof 𝟎.
c. What must be true about any point that lieson the 𝒙-axis?
Explain.
If a point lies on the 𝒙-axis, its 𝒚-coordinatemust be 𝟎
becausethepoint is located 𝟎units aboveor below the 𝒙-axis.
The 𝒙-axis intersects the 𝒚-axis at 𝟎.
Scaffolding:
 The term origin means
startingpoint.
 A person’s country of
origin is the country from
which he or she came.
 When usinga global
positioningunit(GPS)
when travelling,your
origin is where your trip
began.
MP.7
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3. Lesson 15: Locating OrderedPairs ontheCoordinatePlane
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•3Lesson 15
2. Use the coordinateplaneto answer parts (a)–(c):
a. Graph at least five pointson the 𝒚-axisand label their coordinates.
Points will vary.
b. What do the coordinatesofyour pointshave in common?
Each point has an 𝒙-coordinateof 𝟎.
c. What must be true about any point that lieson the 𝒚-axis? Explain.
If a point lies on the 𝒚-axis, its 𝒙-coordinatemustbe 𝟎becausethepoint is located 𝟎 units left or right ofthe
𝒚-axis. The 𝒚-axis intersects 𝟎on the 𝒙-axis.
3. If the origin isthe only pointwith 𝟎for both coordinates, what must be true aboutthe origin?
The origin is theonly point that is on both the 𝒙-axis and the 𝒚-axis.
Example 3 (6 minutes): Quadrants of the Coordinate Plane
Students examine the four regions of the coordinateplanecut by the intersectingaxes.
Example 3: Quadrantsofthe Coordinate Plane
 The 𝑥- and 𝑦-axes dividethe coordinateplaneinto regions called Quadrants. Why are the regions called
quadrants?
 The axes cut the plane into four regions. The prefix “quad” means four.
 Which of the four regions did you work with most in Grade 5, and why was it the only region you used?
 The region on the top right of the coordinate plane. We only used this region because we had not
learned about negative numbers yet.
 The four quadrants arenumbered one through four usingRoman Numerals. The upper right quadrantis
QuadrantI and the remainingquadrants arenumbered moving counter-clockwisefrom QuadrantI; Quadrant
II,QuadrantIII,and QuadrantIV. What was the firstaxis thatwe extended in Example 1 and what did it
reveal?
 We extended the 𝑥-axis to the left beyond zero and it revealed another region of the coordinate plane.
Scaffolding:
 Remind students that the
prefix quad means four
and site some other
examples where the prefix
is used.
 Some students may not
have knowledge of Roman
numerals. Create a table
in which students can
compare the standard
symbols 1–8 and the
Roman numerals 1–8.
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4. Lesson 15: Locating OrderedPairs ontheCoordinatePlane
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•3Lesson 15
 This top left region is called QuadrantII. Label QuadrantII in your student materials. These regions only make
up half of the coordinateplane. Where does the remaininghalf of the coordinateplanecome from? Explain.
 We need to extend the 𝑦-axis down below zero to show its negative values. This reveals two other
regions on the plane; one to the left of the 𝑦-axis and one to the right of the 𝑦-axis.
 The quadrants of the coordinateplanearein a counter-clockwisedirection startingwith QuadrantI. Label the
remainingquadrants in your student materials.
Exercise 4–6 (5 minutes)
Students locateand label points thatlieon the coordinateplaneand indicate in which of the four quadrants the points
lie.
Exercises4–6
4. Locate and label eachpointdescribed by theordered pairsbelow. Indicate whichofthe quadrantsthe pointsliein.
a. (𝟕,𝟐)
Quadrant I.
b. (𝟑,−𝟒)
Quadrant IV.
c. (𝟏,−𝟓)
Quadrant IV.
d. (−𝟑,𝟖)
Quadrant II.
e. (−𝟐,−𝟏)
Quadrant III.
5. Write the coordinatesofat least one other point ineach ofthe four quadrants.
a. Quadrant I
Answers will vary.
b. Quadrant II
Answers will vary.
c. Quadrant III
Answers will vary.
d. Quadrant IV
Answers will vary.
MP.7
(𝟕,𝟐)
(−𝟑,𝟖)
(𝟑,−𝟒)
(𝟏,−𝟓)
(−𝟐,−𝟏)

5. Lesson 15: Locating OrderedPairs ontheCoordinatePlane
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•3Lesson 15
6. Do you see any similaritiesin thepoints within eachquadrant? Explainyour reasoning.
The ordered pairs describingthepoints in QuadrantI contain both positivevalues. Theordered pairs describing the
points in QuadrantIII contain both negativevalues. Thefirst coordinateoftheordered pairs describing thepoints in
Quadrant II are negative values but their second coordinates are positive values. Thefirst coordinateoftheordered
pairs describing thepoints in QuadrantIV are positive values, but theirsecondcoordinates are negativevalues.
Closing(4 minutes)
 If a pointlies on an axis,whatmust be true about its coordinates? Specifically,whatis true for a pointthat lies
on the 𝑥-axis? 𝑦-axis?
 What do you know aboutthe location of a pointon the coordinateplaneif:
 Both coordinates arepositive?
 Only one coordinateis positive?
 Both coordinates arenegative?
 One coordinateis zero?
 Both coordinates arezero?
Exit Ticket (4 minutes)
Lesson Summary
 The 𝒙-axis and 𝒚-axisof the coordinateplaneare number linesthat intersect at zero on each number
line.
 The axescreate four quadrantsin the coordinateplane.
 Pointsin the coordinateplanelieeitheron an axisor in one ofthe four quadrants.
MP.7

6. Lesson 15: Locating OrderedPairs ontheCoordinatePlane
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•3Lesson 15
Name ___________________________________________________ Date____________________
Lesson 15: Locating Ordered Pairs on the Coordinate Plane
Exit Ticket
1. Label the second quadranton the coordinateplanethen answer
the followingquestions:
a. Write the coordinates of one pointthat lies in the second
quadrantof the coordinateplane.
b. What must be true about the coordinates of any point that
lies in the second quadrant?
2. Label the third quadranton the coordinateplanethen answer
the followingquestions:
a. Write the coordinates of one pointthat lies in the third quadrantof the coordinateplane.
b. What must be true aboutthe coordinates of any point that lies in the third quadrant?
3.
a. An ordered pair has coordinates thathave the same sign. In which quadrant(s) could the pointlie? Explain.
b. Another ordered pair has coordinates thatareopposites. In which quadrant(s) could the point lie? Explain.

7. Lesson 15: Locating OrderedPairs ontheCoordinatePlane
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•3Lesson 15
Quadrant II
Quadrant III
Exit Ticket Sample Solutions
1. Label the secondquadrant on the coordinateplane then
answer the following questions:
a. Write the coordinatesofone point that liesin the
second quadrant ofthe coordinateplane.
Answers will vary.
b. What must be true about thecoordinatesofany point
that liesin the secondquadrant?
The 𝒙-coordinatemust bea negativevalueand they-
coordinatemust bea positivevalue.
2. Label the third quadrant on thecoordinate plane then
answer the following questions:
a. Write the coordinatesofone point that liesin thethird quadrantofthe coordinate plane.
Answers will vary.
b. What must be true about thecoordinatesofany point that liesin the third quadrant?
The 𝒙-and 𝒚-coordinates ofany point inthethird quadrant must bothbenegativevalues.
3.
a. An ordered pair hascoordinatesthat have thesame sign. In which quadrant(s)couldthe point lie? Explain.
The point would haveto belocated either in QuadrantI whereboth coordinates arepositivevalues, or in
Quadrant III whereboth coordinates arenegativevalues.
b. Another orderedpair hascoordinatesthat areopposites. In which quadrant(s)could thepoint lie? Explain.
The point would haveto belocated in either QuadrantII or Quadrant IVbecausethosearethetwo quadrants
wherethecoordinates haveoppositesigns.
Problem Set Sample Solutions
1. Name the quadrant in which each ofthe pointslies. Ifthe point doesnot liein aquadrant, specify which axisthe
point lieson.
a. (−𝟐,𝟓)
Quadrant II
b. (𝟗.𝟐,𝟕)
Quadrant I
c. (𝟎,−𝟒)
None; thepoint is not in a quadrant becauseit lies on the 𝒚-axis.

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NYS COMMON CORE MATHEMATICS CURRICULUM 6•3Lesson 15
d. (𝟖,−𝟒)
Quadrant IV
e. (−𝟏,−𝟖)
Quadrant III
2. Jackie claimsthat pointswith thesame 𝒙-and 𝒚-coordinatesmust liein Quadrant I or Quadrant III. Do you agreeor
disagree? Explain your answer.
Disagree; most points with thesame 𝒙-and 𝒚-coordinates liein QuadrantI or Quadrant III,but theorigin (𝟎,𝟎)is on
the 𝒙- and 𝒚-axes, not in any quadrant.
3. Locate and label eachset ofpointson thecoordinate plane. Describe similaritiesofthe ordered pairsin eachset
and describe the pointson theplane.
a. {(−𝟐,𝟓),(−𝟐,𝟐),(−𝟐,𝟕),(−𝟐,−𝟑),(−𝟐,𝟎. 𝟖)}
The ordered pairs all have 𝒙-coordinates of – 𝟐
and thepoints liealonga vertical lineaboveand
below – 𝟐on the 𝒙-axis.
b. {(−𝟗,𝟗),(−𝟒,𝟒),(−𝟐,𝟐),(𝟏,−𝟏),(𝟑,−𝟑),(𝟎,𝟎)}
The ordered pairs each haveoppositevalues for
their 𝒙-and 𝒚-coordinates. Thepoints in the
planelineup diagonally through QuadrantII, the
origin, and Quadrant IV.
c. {(−𝟕,−𝟖),(𝟓,−𝟖),(𝟎,−𝟖),(𝟏𝟎,−𝟖),(−𝟑,−𝟖)}
The ordered pairs all have 𝒚-coordinates of −𝟖
and thepoints liealonga horizontal lineto the
left and right of −𝟖 on the 𝒚-axis.
4. Locate and label at least five pointson the
coordinate planethat have an 𝒙-coordinateof 𝟔.
a. What istrue ofthe 𝒚-coordinatesbelow
the 𝒙-axis?
The 𝒚-coordinates areall negativevalues.
b. What istrue ofthe 𝒚-coordinatesabove
the 𝒙-axis?
The 𝒚-coordinates areall positive values.
c. What must be true ofthe 𝒚-coordinateson
the 𝒙-axis?
The 𝒚-coordinates on the 𝒙-axis must be 𝟎.
(𝟔,𝟑)
(𝟔,𝟔)
(𝟔,−𝟏)
(𝟔,−𝟐)
(𝟔,−𝟑)
(𝟔,−𝟒)
(𝟔,−𝟓)
(𝟔,−𝟕)
(𝟔,−𝟖)
(𝟔,𝟏)
(𝟔,𝟐)
(𝟔,𝟒)
(𝟔,𝟓)
(𝟔,𝟕)
(𝟔,𝟖)