Activity
Graphing concepts activity 1: Attributes and coordinates
Is your student prepared to use digital math tools such as Desmos? Try these tactile activities!
Introduction
The concepts practiced in this set of activities are prerequisite skills for using a graphing calculator, such as the Orion TI-84 Plus Talking Graphing Calculator or the Desmos online graphing calculator for graphing equations.
Typically, students are introduced to the coordinate plane in 5th grade. Instruction focuses on key attributes of the coordinate plane (axes, origin, x-, y-coordinates) and graphing ordered pairs in the first quadrant. This set of activities includes skills that will go beyond that level and may be helpful for students as a review going into Algebra I.
TSVIs (and students) should communicate with a student’s classroom math teacher to determine the outline of the math class, the sequence of the curriculum. Knowing when the content will be introduced in the class may help a TSVI time the introduction of these tools and strategies. Introducing graphing concepts prior to the class can help a student better understand the instruction in class. It may help to have the student’s math teacher join you and your student for a review session after math class to help reinforce the concept.
This set of activities can be used (and re-used) as an assessment tool and an instructional tool.
If you would like to review coordinate plane concepts, I would recommend:
- Basic Geometry – Coordinate Plane (Khan Academy)
- Algebra Basics – Graphing Lines and Slope (Khan Academy)
- Cartesian Coordinates (Math is Fun)
- Equation of a Straight Line (Math is Fun)
Materials
- APH Graphic Aid for Mathematics (graph board), set-up instructions are below
- Pushpins for plotting points
- Rubber bands for connecting the points. Thin, stretchy rubber bands work well. Rubber bands that are too strong can pull the pushpins out of the board.
- String and bendable copper wire work well, also. Experiment with options that seem safe and effective for your student.
- A list of the points to plot (Activity 2) and the equation to be used (Activity 3), both in your student’s preferred medium. Students may also benefit from an example of a data table (see Activity 3).
- Preferred writing medium for each student, so they can create a data table (Activity 3).
- Pegboard alternatives to the graph board:
- Graph paper and art supplies (e.g., sticky dots, art tape, Wikki Stix)
A note on alternatives
The APH graph board is considered an outstanding tool for graphing on a coordinate plane. There may be circumstances when one of the alternatives is required or preferred. Any of the tools can be used to practice the concepts in this set of activities; the APH graph board is not required.
Graph board set-up
Lengths of thin elastic beading cord work well for axes. You can find it at most fabric or craft stores or order it online.
Tie one end into a simple loop and pin it down with a thumbtack. Then put a little stretch in the elastic to see how long to make the axis, add an inch, cut it, tie a simple loop 1″ back from the cut end, and pin that down as well. Do this for each axis. Pin the Origin down with a thumbtack, too.
If you are afraid that the loops will come undone, leave a 1″ piece past the loop at each end, and twist that extra bit of elastic around the thumbtack and tuck it out of sight.
Instead of elastic cord, you can use long, thin rubber bands, looping 2 or 3 together to make them long enough to reach from edge to edge, and pin them down.
Activities
Since these activities can be used as an assessment tool or as an instructional tool, each part of the activity will begin with the assessment question or task followed by instructional delivery details. Each activity builds upon the previous, so in most cases it is best to begin instruction at the point where a student is unable to answer the assessment question. If the student demonstrates understanding or partial understanding of a concept in later activities or in a later part of an activity, make note of that pre-assessment knowledge.
Activity 1 – Attributes and Coordinates
Step 1:
Show me the Origin. The student should be able to put their finger on the spot where the two lines cross without any uncertainty.
It is not required at this point that the student know or be able to tell the coordinates of the Origin, (0,0), just the location.
Instruction
The Origin is the point where the two axes cross, or intersect. Teach and reinforce the location of the Origin without using terms like “middle” or “center.” The Origin can appear in a variety of locations on the coordinate plane, so if a student is introduced to the concept using these terms, it can be confusing later. The key to the Origin is that it is the location where the x- and y-axes cross or intersect.
Step 2:
Name the axes. Which is the x-axis? Which is the y-axis?
- The student should be able to use a finger to trace the full length of each axis from edge to edge.
Instruction
And, the location where the axes cross is called the… ?
- The Origin. Again, this is that spot where the two axes intersect. This is a good opportunity to reinforce the location of the Origin.
Step 3:
Where are Quadrants 1, 2, 3, and 4?
Instruction
The quadrants are generally written using the Roman numerals, I, II, III, and IV. Students will likely see them written that way in textbooks.
- Quadrant I is at the top right, above the x-axis and to the right of the y-axis.
- Quadrant II is at the top left, above the x-axis and to the left of the y-axis.
- Quadrant III is at the bottom left, below the x-axis and to the left of the y-axis.
- Quadrant IV is at the bottom right, below the x-axis and to the right of the y-axis.
Starting in Quadrant I, students should be able to read the quadrants in order (1, 2, 3, 4) moving counterclockwise on the graph board.
Once students are introduced to the location of each quadrant, it is fun to play a game of “Show me…” (i.e., “Show me Quadrant III”). This is good practice until students have learned the quadrants.
The majority of graphs presented in 5th through 8th grades, and many of the real-world problems presented in Algebra I, are Quadrant I graphs.
Step 4:
Show the positive and negative tick marks indicating scale on the x– and y-axis. Count the positive and negative values of each tick mark. (Tick marks are also known as hash marks or hatch marks.)
- The student should start at the origin and count lines accurately in both directions along both axes.
- The Origin is “0,” not “1.”
- Ensure that students understand the positive and negative values. It may help to ask them to say “positive” and “negative” (e.g., “positive one, positive two, …” and “negative one, negative two, …”) as they count along the axis.
- Ensure students are touching the tick marks (the grid lines on the graph board) when they count, not the spaces between the tick marks.
Instruction
By 5th grade, students should have seen a variety of horizontal and vertical number lines, but they may need reinforcement with the skill of reading, adding, subtracting and rounding using number lines.
The x-axis is a horizontal number line. If students have an understanding of number lines but have not seen them on the coordinate plane, begin with the x-axis.
- Begin at the origin. Count by ones to the right on the x-axis. These are positive values to the right of the origin (positive one, positive two, etc.). Return to the origin.
- Count by ones to the left on the x-axis. These are negative values to the left of the origin (negative one, negative two, etc.). Return to the origin.
- Count by twos, fives, and tens on the x-axis in both positive and negative directions. Students should have seen similar number lines, and this introduces the concept of scale on the coordinate plane.
The y-axis is a vertical number line. Positive values are above the origin. Negative values are below the origin. Introduce and practice the above three counting skills on the y-axis.
Step 5:
What are the coordinates of the Origin? Or, what is the ordered pair at the Origin?
The coordinates of the Origin are (0, 0). A student can answer, “zero, zero.”
Instruction
If a student is not familiar with the terms “ordered pair” and “coordinates” they can be introduced as the x-value and the y-value at a point on the coordinate plane.
- At the Origin, the x-value is zero, and the y-value is zero.
- A student may be introduced to representing ordered pairs in Nemeth Code at this point, using the symbols for open parentheses, mathematical comma, and close parentheses.
Step 6:
What are the positive and negative attributes of the coordinates, or ordered pairs, in each quadrant?
A student should be able to indicate the positive and/or negative values of the ordered pairs in each quadrant.
Instruction
Ordered pairs, or coordinates, are written in parentheses with the written first and then the y-value, (x,y).
The values of the ordered pairs are based on the values on the x- and y-axes. For example:
- (4,4) is in Quadrant I. The x-value is positive four, and the y-value is positive four.
- (-4,4) is in Quadrant II. The x-value is negative four, and the y-value is positive four.
- (-4,-4) is in Quadrant III. The x-value is negative four, and the y-value is negative four.
- (4,-4) is in Quadrant IV. The x-value is positive four, and the y-value is negative four.
Next Steps
Whether a student has made it successfully through question 7 of this activity as an assessment or as an instructional activity, they are ready to move on to Activity 2, Plotting Points.
Resources
Here is an accessible version of this post as a Word document. Graphing concepts activities 1: Attributes and coordinates introduction
Next in Graphing Concepts series:
Graph Board to Desmos series:
- Post 1: Setting up Jaws for Desmos
- Post 2: Plotting points and navigating Audio Trace
- Post 3: Representing functions in Desmos
- Input functions into the expression list
- Create tables from functions
- Navigate tables
- Editing expressions
- Sharing a graph
Additional math resources by TEAM Initiative:
- Digital math: Introducing skill level checklists
- Digital math: Workflows from teacher to student and student to teacher
Pegboard post:
This post was created as part of the TEAM Initiative to assist Teachers of Students with Visual Impairments (TSVIs) in teaching foundational tactile skills, which are essential before introducing students to digital math concepts. Written by John Rose. If you would like more information about the TEAM Initiative, contact Leslie Thatcher at [email protected].
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