Drawing in the Coordinate Plane

15 min

Teacher Prep
Required Preparation
For the digital version of the activity, acquire devices that can run the applet.

Narrative

In this activity, students identify the coordinates of points necessary to recreate an image. They write a list of ordered pairs that when connected by line segments in order, would recreate a given image.  

In the digital version of the activity, students use an applet or graphing technology to recreate an image. The applet allows students to plot points by entering ordered pairs and then connect them using line segments.

Launch

If possible, provide access to graphing technology. Demonstrate how to use the technology available in the classroom to plot coordinate pairs. If using the applet or using Desmos in a web browser, consider using these instructions:

  • On a blank graph, add a new table by clicking on the “+” icon in the upper left and select “table” from the drop-down menu.
  • Enter pairs of xx- and yy-values in the table. Corresponding points should appear on the graph.
  • Click on the wheel icon on the upper right corner of the left sidebar. The circle next to the yy-label in the table will turn into a solid circle.
  • Click on the circle next to yy, and turn on the “Lines” option in the drop-down menu. Consecutive points on the graph will now be connected by line segments.

Give students 10–12 minutes of quiet work time, and follow with a whole-class discussion.

Action and Expression: Internalize Executive Functions. To support organization, provide students with a checklist that chunks the various steps of the project into a set of manageable tasks. Consider providing students with a starting point and ordered pairs for select key details, such as tips of the ears.
Supports accessibility for: Language, Organization

Student Task

Use graphing technology to recreate this image. If graphing technology is not available, list the ordered pairs that make up this image. Then compare your list with a partner.

<p>A cat drawn on a coordinate grid.</p>
<p>A cat drawn on a coordinate grid. Horizontal axis goes from negative 6 to 6, by 1s. The vertical axis goes from negative 6 to 6, by 1s. The outline of the cat is marked by the points negative 3 comma 4, negative 2 point 5 comma 1, negative 3 comma 0, negative 3 comma negative 3, negative 1 comma negative 5, 3 comma negative 5, 5 comma negative 3, 5 comma 0, 4 point 5 comma 1, 5 comma 4, 2 comma 2, 0 comma 2. An eye is marked by the points negative 0 point 5 comma 0, negative 1 comma negative point 5, negative point 5 comma negative 1, and 0 comma negative 0 point 5. Another eye is marked by the point 2 point 5 comma 0, 3 comma negative 0 point 5, 2 point 5 comma negative 1, 2 comma negative 0 point 5. The outline of the nose and mouth is marked by 0 point 5 comma negative 2, 1 point 5 comma negative 2, 1 comma negative 2 point 5, 1 comma negative 3, 0 comma negative 3, negative 1 comma 2 point 5, 2 comma negative 3 point 5, 3 comma negative 2 point 5.</p>  

 

If you have time, consider adding more details to your image such as whiskers, the inside of the ears, a bow, or a body.

Sample Response

For the outline of the head:

xx yy
0 2
2 2
5 4
4.5 1
5 0
5 -3
3 -5
-1 -5
-3 -3
-3 0
-2.5 1
-3 4
0 2

For the left eye:

xx yy
-1 -0.5
-0.5 0
0 -0.5
-0.5 -1
-1 -0.5

For the right eye:

xx yy
2 -0.5
2.5 0
3 -0.5
2.5 -1
2 -0.5

For the nose and mouth:

xx yy
-1 -2.5
0 -3.5
1 -3
1 -2.5
0.5 -2
1.5 -2
1 -2.5
1 -3
2 -3.5
3 -2.5

Synthesis

The purpose of this discussion is for students to share the challenges they experienced while graphing the image or determining the coordinates of points and how they overcame them. If not brought up by students, highlight the fact that the image’s line of symmetry was not on the axis, and ask them to share how this affected the coordinates.

Extension

If you are using graphing technology, add these statements to the list of things being graphed:

x>6x > 6
y>5y > 5
x<−4x < -4
y<−6y < -6

Describe the result. Why do you think that happened?

Extension Response

Sample response: There is a frame around the cat’s face and everything outside it is shaded. This happened because these are the places where it is true that x>6x > 6 or y>5y > 5 or x<−4x < -4 or y<−6y < -6.

Standards
Addressing
  • 6.G.3·Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
  • 6.G.A.3·Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
  • 6.NS.8·Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
  • 6.NS.C.8·Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

30 min