PA – MDC GRADE 5
COORDINATES
This lesson is intended to help you assess how well students use
directions to locate a point on the coordinate plane within
quadrant one, and to correctly identify the x-coordinate and ycoordinate.
This lesson is adapted from the web address;
http://www.cpalms.org/Public/PreviewResourceAssessment/Prev
iew/70458 and revised by PA-MDC Writing Committee.
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Concept
Development
Formative
Assessment
Lesson
With Sincere thanks and appreciation for the effort and work of the Members of the PA- MDC Writing
Committee and for the unwavering support from their home districts: Camp Hill School District,
Cumberland Valley School District, Lower Dauphin School District and Shippensburg School District.
Joan Gillis, State Lead MDC
Dan Richards, Co- Lead MDC
PA –MDC Writing Committee
Jason Baker
Heather Borrell Susan Davis Carrie Tafoya
Richard Biggs Carrie Budman
Miranda Shipp
Review Committee
Katherine Remillard, Saint Francis University
Renee Yates, MDC Specialist, Kentucky
Carol Buckley, Messiah University
Josh Hoyt, Berks IU
Dr. Karla Carlucci, NEIU
Kate Lange, CCIU
Lori Rogers, CAIU
If you have any questions please contact Joan Gillis at [email protected]
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COORDINATES
This Formative Assessment Lesson is designed to be part of an instructional unit. This task should be
implemented approximately two-thirds of the way through the instructional unit. The results of this task
should then be used to inform the instruction that will take place for the remainder of your unit.
Mathematical goals: This lesson is intended to help you assess how well students use directions
to locate a point on the coordinate plane within quadrant one. In addition, it will identify students
that correctly identify the x-coordinate and y-coordinate.
Common Core State Standards This lesson involves a range of mathematical practices from
the standards, with emphasis on:
Geometry
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5.G.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).
This lesson involves a range of Standards for Mathematical Practice, with emphasis on:
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
6. Attend to precision.
PA Core Standards:
CC.2.3.5.A.1 Graph points in the first quadrant on the coordinate plane and interpret these points
when solving real world and mathematical problems
Introduction: This lesson unit is structured in the following way:
 Before the lesson, students work individually on a pre-assessment task that is designed to
reveal their current understandings and difficulties. You then review their work and
create questions for students to answer in order to improve their solutions and
misconceptions.
 Students work in small groups (partners/pairs) on collaborative discussion tasks to
correctly graph order pairs. Throughout their work, students justify and explain their
decisions to their peers.
 Students return to their original assessment tasks, and try to improve their own responses.
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Time Needed: estimated 70 – 80 minutes
Timings given are only approximate. Exact timings will depend on the needs of the class. All
students need not finish all card sets to complete the lesson.
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Pre-assessment: 15 minutes
Whole Class Lesson Introduction: 10 minutes
Collaborative Activity: 30 minutes
Whole Class Discussion: 10 minutes
Post – Assessment: 15 minutes
Materials required:
All students will need:
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White board or graph paper in transparency sleeves
dry-erase markers/eraser
ruler
pencils
a copy of the Pre-Assessment, Coordinates
Each pair of students will need:
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Coordinate Point Cards
Coordinate Plane Activity Worksheet
Quadrant Graph
Before the Lesson
Pre-Assessment Task: Coordinates (15 minutes)
Have students do this task individually in class a day or more before the
formative assessment lesson. This will give you an opportunity to assess
the work, and to find out the kinds of difficulties students have. You will
be able to target your help more effectively in the follow-up lesson.
Framing the Task:
Today we will work on a task to see how well you are able
determine the coordinates of a point.
First, you will write the ordered pair of the point and correctly
identify both the x-coordinate and y-coordinate. You will have 15
minutes to work independently on the task pre-assessment task.
After 15 minutes, I will collect your papers and see how you explained your problems.
Give each student a copy of the pre-assessment. Students should use their understanding of
coordinates of an ordered pair and explain their thinking.
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Students should not worry too much if they do not understand or do everything, because in the
next lesson they will engage in a similar task, which should help them. Explain to students that
by the end of the next lesson, they should expect to answer questions such as these confidently.
This is their goal.
Assessing Students’ Responses
Collect students’ responses to the task. Make some notes about what their work reveals about
their current levels of understanding, and their different problem solving approaches.
We suggest that you do no score students’ work. The research shows that this will be
counterproductive, as it will encourage students to compare their scores, and will distract their
attention from what they can do to improve their mathematics.
Instead, help students to make further progress by summarizing their difficulties as a series of
questions. Some questions below may serve as examples. These questions have been drawn
from commonly identified student misconceptions. These can be written on the board (or
projected) at the end of the lesson before the students revisit the initial task.
We suggest that you write a list of your own questions, based on your students’ work, using the
ideas that follow. You may choose to write questions on each students’ work. If you do not
have time to do this, select a few questions that will be helpful to the majority of students. These
can be written on the board at the end of the lesson.
Below is a list of common issues and questions/prompts that may be written on individual initial
tasks or during the collaborative activity to help students clarify and extend their thinking.
Common Issues:
Suggested Questions and Prompts:
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The student does not start at the origin when
locating a point on the coordinate plane.
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The student interprets the coordinates as
individual numbers each associate with a
point instead of an ordered pair associated
with one point (i.e., the student says that the
coordinates indicate that one should put two
points on a coordinate plane, one at four and
one at five).
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What are you being asked to do?
Which point on the coordinate plane is the
origin? What are its coordinates?
Can you identify the axes on this
coordinate plane?
Which is the x-axis?
Which is the y-axis?
How many points does each ordered pair
describe?
How can the ordered pair be used to locate
a point?
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The student confuses the x-coordinate and the
y-coordinate when moving on a coordinate
plane and when writing an ordered pair.
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What is the difference between a point
that has coordinates (4, 5) and a point that
has coordinates (5, 4)?
If you are moving to the right of the
origin, which axis are you traveling? If
you are moving to up from the origin,
which axis are you traveling?
Please use the blanks to add your class misconceptions and directed questions.
Suggested Lesson Outline
Whole Class Introduction (10 minutes)
Explain to the class that in this lesson they will be working on graphing points/ordered pairs.
Before beginning this activity we will do a quick review using the questions below.
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Can you name some real life situations where knowing how to read and apply the use of
coordinate pairs would be valuable? …for the teacher, examples could include:
airplane/hiking/tour guide/military/surveyor/architect/city or highway engineer…
Which is the x-axis? Which is the y-axis?
Which point of the coordinate plane is the origin? (Allow some time for discussion with
this question, but if students have not clearly stated where the origin is located.)
Pre-Assessment Review
Return your students’ work on the Coordinate – Pre-Assessment task. If you have not added
questions to the students’ work, write (or project) a short-list of your most common questions on
the board for them to consider in review of their work. Use these questions to guide a discussion
prior to the students completing the activity with a partner. Draw students’ attention to the
questions you have written (or projected), to think about as they complete the activity.
(NOTE: Listed below are example questions to ask, but either use questions listed above or
others that fit the needs of your students.)
Collaborative Activity: Coordinate – Points (30 minutes)
Homogeneously group students based on the results of the pre-assessment. Groups should
consist of two or four students. Within groups of four, students will need to work in pairs. With
larger groups, some students may not fully engage in the task.
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Framing the Collaborative Activity:
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Each pair of students should receive a copy of the Coordinate Plane Activity Worksheet
and a set of Coordinate Point Cards.
NOTE: you may also use transparency sleeves over the Coordinate Plane Activity
Worksheet and use dry erase makers to note point placement
Students will look at the first cards and follow the directions given to place the coordinate
point onto the coordinate plane. Remind students that they should identify each point
with the card’s letter (i.e. A, B, C, D, E, F, G, or H). Take turns flipping over a card and
placing the point onto the coordinate plane. NOTE: the first four cards give the students
direction similar to the pre-assessment and the last four cards give the students an ordered
pair, in both cases they place a point onto the coordinate plane. The next 4 cards will
extend their thinking.
As a coordinate coint is being placed onto the coordinate plane, the student must explain
why they are placing the point at that particular location. If the partner agrees with the
explanation, another card is flipped and the students continue. If the partner does not
agree, they get a turn to explain where they think it goes. Both students must agree on
where the coordinate point is to be placed. If the pair cannot agree, they can return to that
Coordinate Point Card later.
Repeat until all the cards have been placed.
As the students do the activity, the teacher should:
 Circulate around the room to observe the students work. Listen to students reasoning as
they place the point onto the coordinate plane. Ask a student to re-explain why the point
is being placed in the location they chose.
 If there is a card that is not agreed upon, listen to both arguments, and guide students
(ask leading questions) to help them make a final decision. Try not to make suggestions
that move students toward a particular approach. Instead, ask questions to help students
clarify their thinking. Encourage students to use each other as a resource for learning
 Make a note of student approaches to the task. You can then use this information to
focus a whole-class discussion towards the end of the lesson. In particular, notice any
common mistakes. Partners should be engaged in checking their partner, asking for
clarification, and taking turns. When calling on students make sure you allow the
struggling groups to share first.
NOTE: If you notice a group struggling on the same issue, allow a student to travel to another
working pair to ask them for a brief explanation.
Points A, G, and F are three vertices of a rectangle. What are the coordinates of the fourth
vertex? Justify your answer.
Upon completion of the collaborative activity, students can create three polygons from a list of
the following ordered pairs:
Triangle (4,5) (4,4) (3,5) (4,5)
Rectangle (4,4) (2,2) (1,3) (3,5) (4,4)
Trapezoid (2,1) (2,2) (1,3) (0,3) (2,1)
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NOTE: Students graph the first ordered pair and then draw a line to the next until you have a
polygon. What shape did it make?
Whole-class discussion (10 minutes)
Summarize/conclude the lesson by discussing and generalizing what has been learned.
Students sharing the strategies they used aloud will be valuable to the learning of the group. The
generalization involves extending what has been learned to new examples.
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What have you learned today?
Can you describe your method to us?
Explain how it works?
What advice would you give to someone learning how to graph ordered pairs ?
How did you improve on your understanding of coordinates? Explain.
Improving individual solutions to the assessment task (15 minutes)
Return the initial task to students as well as the post-assessment task.
Look at your original responses and think about what you have learned during this
lesson. Using what you have learned, try to improve your work.
If you have not added feedback questions to individual pieces of work then write (or project)
your list of questions on the board.
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Coordinates: Pre-Assessment Task
Name ____________________________
1. Suppose you start at the origin and move four units to the right of the origin and then five units
up. Use the graph above. What are the coordinates of the point where you end? _____________
 Which is the x-coordinate? _____________
 Which is the y-coordinate? _____________
2. Suppose you start at the origin and move zero units to the right of the origin and then six units up.
Use the graph above. What are the coordinates of the point where you end? _____________
 Which is the x-coordinate? _____________
 Which is the y-coordinate? _____________
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Coordinates: Activity
Names __________________________
Use the coordinate planes below to graph the eight different points (ordered pairs)
from each card. Be sure to place the correct identifying letter next to each point.
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Coordinate Point Cards – page 1 of 2
Point A – Starting at the
origin, move one unit to
the right of the origin and
then move two units up.
Point B – Starting at the
origin, move two units to
the right of the origin and
up zero units.
Point C – Starting at the
origin, move three units to
the right fo the origin and
then move three units up.
Point D – Starting at the
origin, move five units to
the right of the origin and
then move one unit up.
Point E – (1, 7)
Point F – (4, 5)
Point G – (1, 5)
Point H – (6, 2)
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Coordinate Point Cards – page 2 of 2
Triangle
Points A, G, and F are three
vertices of a rectangle.
(4, 5)
(4, 4)
(3, 5)
(4, 5)
What are the coordinates of the
fourth vertex?
Justify your answer.
Rectangle
Trapezoid
(4, 4)
(2, 2)
(1, 3)
(3, 5)
(4, 4)
(2, 1)
(2, 2)
(1, 3)
(0, 3)
(2, 1)
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Coordinate Activity – Answer Key
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Additional Resource
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Tear-Off Sheet with Suggestions for Helping Students Access Information
Barrier to Learning
Suggested Strategy
Student lacks understanding of
math language
Review domain specific vocabulary; create a picture
dictionary with student.
Student lacks basic perimeter/area
knowledge
Review prior lessons in perimeter and area; use
manipulatives to explore perimeter/area concepts.
Use key words and "picture stories" to help students
identify the appropriate operation.
Students have problems in
understanding math word
problems (reading comprehension)
Build vocabulary through repeated classroom use and
picture dictionary.
Work on reading and understanding problems through
modeling in small groups and peer-to- peer situations.
Student struggles with multi-step
problems
Break the problem into smaller tasks, an understandable
sequence.
Student struggles with writing
explanations and math reasoning
Continued use of Math Journaling and Share Time in
which classmates critique each other can help strengthen
this. Explain to the student that written explanation
takes the place of verbal communication and the reader
needs to understand how you solve the problem.
Student struggles with creating a
rectangle with a given perimeter.
Identify the perimeter of objects by measuring with a
ruler. Develop skill through use of geoboard. Have
student count each line drawn creating a rectangle.
Student struggles with identifying
the area of a rectangle.
Provide multiple methods of find area: counting
squares, repeated addition, composite units, multiplying
the length and width.
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