Graphing Integers on the Coordinate Grid

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Objective

SWBAT identify and graph points with integer coordinates 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

5 minutes

Students work on both problems in the TAB  section in pairs.  The purpose of these problems is to activate prior knowledge - at my school students mastered graphing ordered pairs in the first quadrant in 5th grade (5.G.A.1, 5.G.A.2).  

The key point I want to be sure students master before we move on is

Ordered pairs are listed as (x, y) and that we move along the horizontal axis x-units from the origin before moving y-units on the vertical axis from (x, 0) when plotting a point.

After 3-4 minutes of partner work time, I call on an enthusiastic raised hand to share out his/her thinking about how to plot point A.  As the student is sharing, I am scanning the room to note how many students are erasing (which tells me they plotted (3,2) instead of (2,3).

For the second problem on this page, I ask for the entire class to reply.  I have students raise their hands if they think Matthew is correct, scan the room, and then ask students to raise hands if they think Matthew is incorrect.  This is another way I can check to see how comfortable students are with graphing ordered pairs.

Intro to New Material

15 minutes

This is the first lesson in the coordinate grid unit, which I teach right after my integers unit. Students have just finished a unit in which they get to practice graphing rational numbers on number lines, both vertical and horizontal.  The coordinate grid is just two perpendicular number lines.  With this frame, this lesson is engaging for kids and one in which they're successful pretty quickly.  

Students mastered graphing points in the first quadrant in 5th grade (5.G.A.1, 5.G.A.2).  The new material for this lesson is the idea that there are actually 4 quadrants, and that ordered pairs can have both positive and negative coordinates.  

This lesson only contains integers, and not rational numbers.  I want students comfortable with plotting points in all four quadrants before introducing rational numbers in the coordinate grid.  

In this lesson, students are also asked to generalize how they can determine the quadrant of a point, when given the x and y coordinate (i.e. they will conclude that you can determine the quadrant of a coordinate point based on the signs of the x and y coordinate). 

For the INM section, I move the class through the problems.  Students plot the first three points on their own (if the Think About It problem suggests that students need more guidance, I'd model graphing the first point explicitly).  For the 4th point, (-5,0), I have students put their finger on where they think the point should go.  I ask, "what do you notice about this point?"  Students notice that we don't move up or down to plot this point; it is on the x-axis.  I then ask them what we can say about the final point, (0,3).  I want students to come up with the idea that we can describe this point as being on the y-axis.

 

 

 

 

Partner Practice and Discussion

15 minutes

Students work together in pairs on the Partner Practice problems.  As they are working together, I circulate around the classroom. 

I am looking for: 

  • Are students correctly labeling the graph with all of the necessary components?
  • Are scholars correctly labeling the coordinate pair on the grid?
  • Are scholars correctly identifying the coordinate pair on the grid?
  • Are scholars correctly identifying the quadrant in which a point is located?
  • Are scholars accurately describing how to identify and plot a coordinate pair on the grid?

 

I'm asking students:

  • 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?
  • What would happen if you reverse the order of the ordered pair?
  • What would happen if you change the signs of the ordered pair?
  • In which quadrant is the point located? How do you know?

 

After 10 minutes of partner work time, the class comes back together for the final Check for Understanding.  Students complete this problem on their own, and then I cold call on a student to share his/her work on the document camera.  The feedback from the class will be around how much the student chose to write, and we'll generate ways to make the response stronger.  

Independent Practice

15 minutes

After our class discussion, students work on the Independent Practice section for about 15 minutes.  

I'm circulating around the room, looking for and asking students the same things as I did during the partner practice.  

Question 23 asks students to think about distance on the coordinate grid, which will show up in another lesson in this unit.

For question 26, I'll ask students what they can tell me about all points in quadrant four (they all have a positive x coordinate and a negative y coordinate)

Closing and Exit Ticket

6 minutes

Before students begin work on the Exit Ticket, I have us all turn to Problem_24.  The point in this problem is in quadrant three.  I have students turn and talk to their partner for 45 seconds about a generalization they can make about all points in quadrant three.  I am looking for them to decide that all points in quadrant three have a negative x coordinate and a negative y coordinate.  

To share out, I ask for students to share something really insightful that their partner said.  This helps to hold them accountable for being active listeners when working together.

Students end class by working on their exit tickets.