1. Lesson 14: Ordered Pairs
Date: 2/9/15 138
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•3Lesson 14
Lesson 14: Ordered Pairs
Student Outcomes
 Students use ordered pairs to name points in a grid and to locate points on a map.
 Students identify the firstnumber in an ordered pair as the first coordinate and the second number as the
second coordinate.
Lesson Notes
Students will understand the use of ordered pairs of numbers as describingthe locations of points on a planein various
situations. They will recognizethe significanceof the order of numbers in ordered pairs by lookingatthe different
interpretations.
Classwork
OpeningExercise (5 minutes)
Before students arrive,arrangetheir desks into straightrows. Assign a number (1, 2, 3, …) to each row, and also to the
seats in each row startingatthe front with seat 1. As students enter the room, give them a sticky note containing a pair
of numbers correspondingwith the seatinglocations in theroom. Instructstudents to find the seatdescribed by their
sticky note, apply the sticky note to the desk, and be seated.
Most students will be confused as only those with matching numbers will be ableto find their seats. Monitor
conversations takingplacebetween students as they agree upon a convention (e.g., that the firstnumber will represent
the row, and the second number will representthe seat).
 How did you find your seat in the classroom?
 Did the order of the numbers matter? Why or why not?
 The order mattered since there are two different seats that involve the numbers 2 and 3. For instance,
row 2, seat 3 and row 3, seat 2.
Example 1 (5 minutes): The Order in OrderedPairs
Instructstudents to rotate their desks 90 degrees in one direction. This changes the orientation of the rows, so that
students can better see the meanings of each of the coordinates. Students understand that the coordinates of their
location fromthe opening exercise (in most cases) aredifferent in Example 1. For example, the student sittingin row 1,
seat 3 for the Opening Exercise, is now sittingin row 3, seat 1.
Example 1
The first number ofan ordered pair iscalledthe first coordinate .
The second number ofan orderedpair iscalled the second coordinate .

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NYS COMMON CORE MATHEMATICS CURRICULUM 6•3Lesson 14
Define the firstand second coordinates in this exampleas (row #, seat #). Ask all students in the classroomto stand.
Call outan appropriateordered pair and ask for the student in that location to raise his or her hand, briefly explain why
the ordered pair of numbers describes that student’s position in the room, then be seated. Now have that student call
out a different ordered pair that corresponds with the location of another student. Continue this process until all
students have participated.
Example 2 (10 minutes): UsingOrderedPairs to Name Locations
Task: Dividestudents into small groups and provideeach group with one of the ordered
pair scenariosbelow. Students will read their scenario and describehowthe ordered pair
is beingused, indicatingwhatdefines the firstcoordinateand what defines the second
coordinate. Allow groups 5 minutes to read and discuss thescenario and preparea
responseto report out to the class.
Example 2: Using Ordered Pairsto Name Locations
Describe how theorderedpair isbeing used in yourscenario. Indicatewhat definesthe first
coordinate and what definesthesecond coordinate inyour scenario.
Ordered pairs arelikea set of directions;they indicatewhere to go in one direction, and then indicatewhere to go in the
second direction.
 Scenario 1: The seats in a collegefootball stadiumarearranged into 210 sections,with 144 seats in each
section. Your ticket to the game indicates thelocation of your seat using the ordered pair of numbers
(123, 37). Describethe meaning of each number in the ordered pair and how you would use them to find
your seat.
 Scenario 2: Airlinepilots usemeasurements of longitude and latitudeto determine their location and to find
airports around the world. Longitude is measured as 0–180ᵒ east, or 0–180ᵒ west of a linestretchingfrom
the North Pole to the South Pole through Greenwich, England called the prime meridian. Latitude is measured
as 0–90ᵒ north or 0–90ᵒ south of the Earth’s Equator. A pilothas the ordered pair (90ᵒ west, 30ᵒ north).
What does each number in the ordered pair describe? How would the pilotlocatethe airporton a map?
Would there be any confusion if a pilotwere given the ordered pair (90°, 30°)? Explain.
 Scenario 3: Each room in a school buildingisnamed by an ordered pair of numbers that indicates thenumber
of the floor on which the room lies, followed by the sequential number of the room on the floor from the main
staircase. A new student at the school is tryingto get to scienceclass in room 4–13. Describeto the student
what each number means and how she should usethe number to find her classroom. Suppose there are
classrooms belowthe main floor. How might these rooms be described?
Ask student groups to report their answers to the scenarios aloud to the class.
Scaffolding:
Provideextra practicein
naminglocations usingordered
pairs by playinga game on the
coordinateplanewhere
students try to guess the
locations of their opponent’s
points.
MP.3

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NYS COMMON CORE MATHEMATICS CURRICULUM 6•3Lesson 14
Exercises1–2 (12 minutes)
Students use the gridded maps in the student materials to name points that correspond with the given ordered pairs
(and vice-versa). The firstcoordinates represent numbers on the linelabeled 𝑥, and the second coordinates represent
numbers on the linelabeled 𝑦.
Exercises1–2
For Exercises 1 and 2, the first coordinatesofthe orderedpairsrepresent thenumberson theline labeled 𝒙 and the
second coordinatesrepresent the numberson the linelabeled 𝒚.
1. Name the letter from the gridthat correspondswith each ordered pair ofnumbersbelow.
a. (𝟏,𝟒)
Point F
b. (𝟒,𝟏)
Point B
c. (𝟓,−𝟐)
Point G
d. (𝟐,−𝟏)
Point C
e. (𝟎,𝟓)
Point A
f. (𝟖.𝟓,𝟖)
Point L
g. (𝟓,𝟒.𝟐)
Point H
h. (𝟎,𝟗)
Point E
2. List the orderedpair ofnumbersthat correspondswith each letter from thegrid below.
a. Point M
(𝟓,𝟕)
b. Point N
(𝟔,𝟎)
c. Point P
(𝟎,𝟔)
d. Point Q
(𝟐,𝟑)
Scaffolding:
If students do not understand
the negative numbers on the
vertical axis,reviewwith
students how the floors below
ground level might be
described in Scenario 3 from
Example 2.

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NYS COMMON CORE MATHEMATICS CURRICULUM 6•3Lesson 14
e. Point R
(𝟎,𝟑)
f. Point S
(−𝟐,𝟑)
g. Point T
(−𝟑,𝟐)
h. Point U
(𝟕,𝟓)
i. Point V
(−𝟏,𝟔)
Have students provide the correct answers to the exercises.
Closing(5 minutes)
 Why does order matter when using ordered pairs of numbers?
 Alayna says the order in which the values aregiven in an ordered pair doesn’t always matter. Give an example
of when the order does matter and an example of when the order does not matter.
 Explain howto locatepoints when pairs of integers areused.
Exit Ticket (8 minutes)
Lesson Summary
 The order ofnumbersin an ordered pairisimportant because the ordered pair should describe one
location in the coordinateplane.
 The first number (called the first coordinate)describesalocation using the horizontal direction.
 The second number (calledthe second coordinate)describesalocationusing thevertical direction.

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NYS COMMON CORE MATHEMATICS CURRICULUM 6•3Lesson 14
Name ___________________________________________________ Date____________________
Lesson 14: Ordered Pairs
Exit Ticket
1. On the map below, the firedepartment and the hospital have one matching coordinate. Determine the proper
order of the ordered pairs in themap, and write the correct ordered pairs for the locations of the firedepartment
and hospital. Indicatewhich of their coordinates arethe same.
2. On the map above, locateand label the locations of each description below:
a. The local bank has the same firstcoordinateas the Fire Department, but its second coordinateis half of the
firedepartment’s second coordinate. What ordered pair describes the location of the bank? Locate and label
the bank on the map usingpoint 𝐵.
b. The VillagePoliceDepartment has the same second coordinateas the bank,but its firstcoordinateis −2.
What ordered pair describes the location of the VillagePoliceDepartment? Locate and label the VillagePolice
Department on the map usingpoint 𝑃.

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NYS COMMON CORE MATHEMATICS CURRICULUM 6•3Lesson 14
.B.P
Exit Ticket Sample Solutions
1. On the map below, the fire department and thehospital haveone matching coordinate. Determine theproper
order ofthe ordered pairsin themap, and writethecorrect ordered pairsfor thelocationsofthe firedepartment
and hospital. Indicate which oftheir coordinates are thesame.
The order ofthenumbers is (𝒙,𝒚); FireDepartment: (𝟔,𝟕)and Hospital: (𝟏𝟎,𝟕); they havethesamesecond
coordinate.
2. On the map above, locate and labelthe location ofeach description below:
a. The local bank hasthe same first coordinateasthe Fire Department and itssecond coordinateishalfofthe
fire department’ssecondcoordinate. What ordered pair describesthe location ofthe bank? Locateand label
the bank on the map using point 𝑩.
(𝟔,𝟑.𝟓); See themap imagefor thecorrect locationofpoint 𝑩.
b. The Village Police Department hasthe same second coordinateasthe bank, but itsfirst coordinate is −𝟐.
What ordered pair describesthelocation oftheVillage Police Department? Locate and label theVillage
Police Department on themap using point 𝑷.
(−𝟐,𝟑.𝟓); See themap imagefor thecorrectlocation ofpoint 𝑷.
Problem Set Sample Solutions
1. Use the set ofordered pairsbelow to answer each question:
{(𝟒,𝟐𝟎),(𝟖,𝟒),(𝟐,𝟑),(𝟏𝟓,𝟑),(𝟔,𝟏𝟓),(𝟔,𝟑𝟎),(𝟏,𝟓),(𝟔,𝟏𝟖),(𝟎,𝟑)}
a. Write the orderedpair(s)whose first and secondcoordinatehave agreatestcommon factor of 𝟑.
(𝟏𝟓,𝟑)and (𝟔,𝟏𝟓)
b. Write the orderedpair(s)whose first coordinateisa factor ofitssecond coordinate.
(𝟒,𝟐𝟎),(𝟔,𝟑𝟎),(𝟏,𝟓),(𝟔,𝟏𝟖)

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NYS COMMON CORE MATHEMATICS CURRICULUM 6•3Lesson 14
c. Write the orderedpair(s)whose second coordinate isaprimenumber.
(𝟐,𝟑),(𝟏𝟓,𝟑),(𝟏,𝟓),𝒂𝒏𝒅 (𝟎,𝟑)
2. Write ordered pairsthat represent the location ofpoints 𝑨, 𝑩, 𝑪, and 𝑫, where the
first coordinate representsthe horizontal direction, and thesecond coordinate
representsthe vertical direction.
𝑨 (𝟒,𝟏); 𝑩 (𝟏,−𝟑); 𝑪 (𝟔,𝟎); 𝑫 (𝟏,𝟒)
3. Extension:
Write ordered pairsofintegersthat satisfy the criteriain each part below. Rememberthat theoriginisthe point
whose coordinatesare ( 𝟎,𝟎). When possible,give ordered pairs suchthat: (i)both coordinatesare positive; (ii)
both coordinatesare negative; and (iii)thecoordinateshave oppositesignsin eitherorder.
a. These points’ vertical distance from theorigin istwice theirhorizontal distance.
Answers will vary; examples (𝟓,𝟏𝟎),( −𝟐,𝟒),(−𝟓,−𝟏𝟎),(𝟐,−𝟒)
b. These points’ horizontal distancefrom theoriginistwo unitsmore than the vertical distance.
Answers will vary; examples (𝟑,𝟏),(−𝟑,𝟏),(−𝟑,−𝟏),(𝟑,−𝟏)
c. These points’ horizontal and vertical distances from theorigin are equal but only onecoordinate ispositive.
Answers will vary; examples ( 𝟑,−𝟑), (−𝟖,𝟖)