Graphing Rational Numbers on the Coordinate Grid

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SWBAT identify and graph points representing rational numbers on the coordinate plane.

Big Idea

Each point on a coordinate grid can be described with a pair of coordinate values (x, y) that describe the horizontal (x) and vertical (y) distance from the origin.

Think About It

8 minutes

In pairs, students label the coordinate graph in the Think About It problem.  I expect students to label the x-axis, y-axis, origin, quadrants, and the grid lines.

Instructional Note: After this lesson, students won't be expected to label every grid line. Because this lesson focuses on graphing rational numbers (rather than just integers as in the previous lesson), it is important that students are thinking about the scale on each axis.

After 3 minutes of work time, I ask a student to tell me one thing that (s)he labeled.  I label that part on my exemplar on the document camera.  I then ask that student to 'roll it' to another student, who identifies another piece that needs to be labeled.  This process continues until we have everything correctly labeled.

To end this section, I ask students to identify the difference between this grid and the one we worked with in the previous lesson.  Students identify that this grid has grid lines that represent decimals/fractions.  I frame the lesson by stating that we will be plotting points today using rational numbers. 

Intro to New Material

15 minutes

For the Intro to New Material, I guide students through labeling all parts of the graph, including the grid lines.  Students are familiar with how to determine the scale on a number line from our work in the Integers and Rational Numbers unit. I want students to think about decimal and fraction equivalents.  For this grid, I have students label the grid lines as both multiples of .2 and 1/5.  

The steps students follow to plot or identify points on the graph are included in the Visual Anchor.


Partner Practice and Discussion

17 minutes

Students work together on the Partner Practice problems.  As students work, I am circulating around the room.  I am looking for:

  • Are students correctly labeling the graph with all of the necessary components?
  • Are students correctly identifying the scale of the x and y axis?
  • Are students correctly labeling the coordinate pair on the grid?
  • Are students correctly identifying the coordinate pair on the grid?
  • Are students correctly identifying the quadrant in which a point is located?
  • Are students accurately describing how to identify and plot a coordinate pair on the grid?
  • If asked to draw a coordinate grid, are scholars correctly using the right scale?

I am asking pairs:

  • How did you know what the scale of the x and y axis was?
  • How did you know to draw the coordinate pair in that particular place?
  • How did you know that was the correct name of the coordinate pair?
  • How did you know that the point was located in that quadrant?
  • What would happen if you reverse the order of the ordered pair?
  • What would happen if you change the signs of the ordered pair?

Before moving on to the Independent Practice, I have all students complete the final check for understanding problem independently.  After 2 minutes of work time, I have students put their fingers on the point that they've graphed.  This gives me a quick way to see if students are in the correct quadrant.  I then have one student read his/her written response to the question.

Independent Practice

15 minutes

Students work on the Independent Practice problems.  As they are working, I am looking for and asking the same things as I did during partner practice.

Closing and Exit Ticket

12 minutes

After independent work time, I bring the class back together for discussion.  I have students turn and talk with their partner about how they determined the scale for the grid lines on the second page of the independent practice.  After 1 minute of talk time, I have 2-3 students share out their strategies with the entire class.

Students then work independently on the Exit Ticket to end the lesson.