Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 57023
Graphing Points in the Plane
Students are asked to graph points given their coordinates and describe the coordinates of graphed points.
Subject(s): Mathematics
Grade Level(s): 6
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, coordinates, ordered pair, x-axis, y-axis, quadrants
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_GraphingPointsInThePlane_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problems on the Graphing Points in the Plane worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student is unable to effectively work with rational coordinates in the coordinate plane.
Examples of Student Work at this Level
The student makes multiple errors such as:
Interchanging x- and y-coordinates [e.g., describes the coordinates of point J as (2, 5)].
Treating negative coordinates as if they are positive.
Rounding fractional coordinates to whole numbers.
page 1 of 4 Questions Eliciting Thinking
How are coordinates related to the location of the point they describe?
Which axis is the x-axis, and which is the y-axis?
How did you determine the coordinates of these points? Can you use rational numbers so that the coordinates are more precise?
Can you show me how you graphed these points?
Instructional Implications
If necessary, review graphing fractions on the number line (3.NF.2) and graphing negative integers on the number line. Expose the student to number lines oriented both
horizontally and vertically. Review graphing points in the first quadrant (5.G.1). Next, provide explicit instruction on graphing points with rational coordinates in the
coordinate plane. Relate the x- and y-axes to basic number lines and explain the conventions for graphing [e.g., the x-axis is usually horizontal and the y-axis is vertical, and
when this is the case, ordered pairs are given in the form (x, y)]. Be sure the student understands basic terminology related to graphing in the coordinate plane: x-axis, yaxis, coordinates, ordered pair, points, origin, and quadrants. Discuss the signs of the coordinates of points in each quadrant. Provide abundant experience with both
graphing points given their coordinates and describing the coordinates of graphed points. Be sure to include points with rational coordinates.
Provide instruction on the conventions for writing the coordinates of a point: write the name of the point followed by its coordinates written as an ordered pair of numbers
enclosed in parentheses [e.g., A(-4, 2.5)]. Be sure the student understands that when graphing points, a point is shown on the graph at the location described by its
coordinates, and the name of the point is given nearby.
Moving Forward
Misconception/Error
The student correctly graphs points with rational coordinates but makes some errors in describing coordinates of graphed points with rational coordinates.
Examples of Student Work at this Level
The student graphs all points correctly in the second problem but errs in describing the coordinates of some of the points in the first problem. For example, the student:
Does not correctly describe the coordinates of points on axes.
Errs in describing some negative or rational coordinates of points.
Questions Eliciting Thinking
If a point is on the x-axis, what is its y-coordinate? If a point is on the y-axis, what is its x-coordinate?
Can you show me how you determined the coordinates of this point (referring to one the student described incorrectly)?
Instructional Implications
Provide feedback to the student concerning any errors made. Model describing the coordinates of points more precisely using rational numbers. Provide additional
opportunities to describe the coordinates of graphed points with rational coordinates.
Almost There
Misconception/Error
The student makes a minor error in either describing coordinates or graphing.
Examples of Student Work at this Level
All work is correct with one exception. For example, the student:
Omits the y-coordinate of a point.
page 2 of 4 Rounds the x-coordinate of a point rather than giving it more precisely as a rational number.
Graphs Q at (8.5, 0) instead of at (-8.5, 0).
Graphs Q at (-7.5, 0) instead of at (-8.5, 0).
Questions Eliciting Thinking
Can you show me how you determined the coordinates of this point (referring to one the student described incorrectly)?
Can you show me how you graphed this point (referring to one the student graphed incorrectly)?
Instructional Implications
Provide feedback to the student regarding any error made and allow the student to revise his or her work. Provide additional opportunities to graph points given their
coordinates and describe the coordinates of graphed points. Be sure to include points with rational coordinates.
Ask the student to describe, in general terms, the coordinates of points in each quadrant and on each axis by saying something like, “Points in the first quadrant are of the
form (x, y) where both x and y are positive.”
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student identifies the coordinates of the graphed points as J(5, 2) K(-4.5, 1.5) or K(
), L(
) or L(1.25, 0), and M(0,-4). The student correctly graphs
points N, P, Q, and R.
Questions Eliciting Thinking
Can you explain how the graph of (-8.5, 0) is different from the graph of (8.5, 0)?
Can you tell what quadrant a point is in by looking at its coordinates?
Instructional Implications
Ask the student to describe, in general terms, the coordinates of points in each quadrant and on each axis by saying something like, “Points in the first quadrant are of the
form (x, y) where both x and y are positive.”
Introduce the student to the concept of reflections and ask the student to describe the relationship between A(-5, 8) and B(5, 8) or A(-5, 8) and C(-5, -8) in terms of
reflections.
ACCOMMODATIONS & RECOMMENDATIONS
page 3 of 4 Special Materials Needed:
Graphing Points in the Plane worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.6.NS.3.6:
Description
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar
from previous grades to represent points on the line and in the plane with negative number coordinates.
a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize
that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.
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.
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.
page 4 of 4