Lesson 3

Plot More Points

Warm-up: Notice and Wonder: Points with Zero (10 minutes)

Narrative

The purpose of this warm-up is for students to think about points on the axes. In previous lessons they have plotted points with non-zero coordinates. Thinking about the points with zero prepares them for plotting points on the horizontal and vertical axes which they will do in this lesson.

Launch

• Groups of 2
• Display the image.
• “What do you notice? What do you wonder?”
• 1 minute: quiet think time

Activity

• 1 minute: partner discussion
• Share and record responses.

Student Facing

What do you notice? What do you wonder?

Student Response

For access, consult one of our IM Certified Partners.

Activity Synthesis

• “How can we describe the location of the point?” (It is at the bottom left of the grid.)
• “The coordinates of this point are $$(0, 0)$$. What would be the coordinates of the point if we moved it up 2 units?” (0, 2)

Activity 1: What’s the Point? (20 minutes)

Narrative

The purpose of this activity is for students to plot several points with the same vertical or horizontal coordinate and observe that they lie on a horizontal or vertical line respectively (MP7). Students also plot points on the axes for the first time. Before plotting the points on a grid with gridlines, students first estimate the location of the points. This encourages them to think about the coordinates as distances (from the vertical axis for the first coordinate and from the horizontal axis for the second coordinate).

MLR8 Discussion Supports. Display sentence frames to support partner discussion: “First, I _____ because . . .” and “I noticed _____ so I . . . .”
Action and Expression: Internalize Executive Functions. Invite students to verbalize their strategy for estimating and plotting points before they begin. Students can speak quietly to themselves, or share with a partner.
Supports accessibility for: Organization, Conceptual Processing, Language

Launch

• Groups of 2
• “You and your partner will each complete a different set of 4 problems independently. After you’re done, discuss your work with your partner.”

Activity

• 5–7 minutes: independent work time
• 5 minutes: partner discussion
• Monitor for students who:
• use the halfway point on each axis as a benchmark for the coordinate grid without gridlines
• start at zero and count spaces along each axis for the marked coordinate grid with gridlines
• recognize the points should be aligned because they share a common horizontal or vertical coordinate

Student Facing

Partner A

1. Estimate the location of each point.

Point Coordinates
$$A$$ $$(5,1)$$
$$B$$ $$(5,2)$$
$$C$$ $$(5,3)$$
$$D$$ $$(5,4)$$
2. Plot and label the points on the coordinate grid.

3. What do the points have in common?
4. Plot the point with coordinates $$(5,0)$$ on the coordinate grid.

Partner B

1. Estimate the location of each point.

Point Coordinates
$$A$$ $$(4,3)$$
$$B$$ $$(5,3)$$
$$C$$ $$(6,3)$$
$$D$$ $$(7,3)$$
2. Plot and label the points on the coordinate grid.

3. What do the points have in common?
4. Plot the point with coordinates $$(0, 3)$$ on the coordinate grid.

Student Response

For access, consult one of our IM Certified Partners.

If students do not reasonably estimate a location for a point on the blank grid, point to the location half way between 0 and 5 on the horizontal axis and ask, “What number might go here?”

Activity Synthesis

• Ask previously identified students to share their thinking.
• “What can we say about a set of points when they share the same first coordinate?” (They will be on the same vertical line.)
• Display image from student solution showing points with first coordinate 5.
• “How did you know where to put the point with coordinates $$(5,0)$$?” (I put it on the horizontal axis. I went over 5 but did not go up at all.)
• “What happens when a set of points share the same second coordinate?” (They will be on the same horizontal line.)
• Display image from student solution showing points with second coordinate 3.
• “What does the zero in (0,3) tell us?” (It means the point will be on line zero of the horizontal axis, which is the vertical axis.)
• $$(0, 0)$$ is an important point because it's where we start when we plot a point on the coordinate grid. Find $$(0, 0)$$ on the grid you have been working with.”

Activity 2: Plotting Points Without a Grid (15 minutes)

Narrative

In the previous activity, students noticed that points with the same vertical coordinate lie on a horizontal line and points with the same horizontal coordinate lie on a vertical line. The purpose of this activity is to reinforce this idea by asking students to plot points on a blank coordinate grid given a single point. Using this point, they can plot other points with the same horizontal or vertical coordinate. Some students may keep one coordinate the same and double or halve the other as is shown in the student solution. Other students may label points on the axes. The given point, for example, allows students to identify $$(4,0)$$ and $$(0,2)$$. An advantage to working with points on the axes is that these are essentially number lines with which students have been working for several years. The synthesis highlights the special nature of the points $$(1,0)$$ and $$(0,1)$$. All of the points where the gridlines meet can be measured off exactly after $$(1,0)$$ and $$(0,1)$$ are plotted.

•  Groups of 2

Activity

• 3–5 minutes: independent work time
• 5 minutes: partner discussion

Student Facing

1. A point is labeled in the coordinate plane. Plot and label some other points. Explain or show your reasoning.

2. Can you plot $$(1,0)$$ and $$(0,1)$$ accurately? Explain or show your reasoning.

Student Response

For access, consult one of our IM Certified Partners.

If students need support getting started with the task, ask, “What do you know about the point $$(4,2)$$ that is plotted?”

Activity Synthesis

• Invite students to share the points that they plotted and their reasoning.
• Plot the points as they discuss their reasoning.
• “How did you plot $$(1,0)$$?” (I know where $$(2,0)$$ is on the vertical axis because it has the same horizontal coordinate as $$(2,4)$$. Then I just halved the distance to the vertical axis and that's $$(1,0)$$.)
• “Once you know where $$(1,0)$$ is, what other points can you locate on the vertical axis?” ((2,0), (3,0), (4,0),... I can just keep marking off that distance like I do when I am on a number line.)

Lesson Synthesis

Lesson Synthesis

“Today we plotted points that lie on the same horizontal or vertical line, including the horizontal and vertical axes.”

Display the first image from student A solution in first activity.

“Do these points have the same horizontal coordinate or vertical coordinate? How do you know?” (They all sit over the same place on the horizontal axis. That tells you the horizontal coordinate and it’s the same for all of the points.)

“Do any of the points have vertical coordinate 0? How do you know?” (No, if the vertical coordinate were 0, the points would be on the horizontal axis.)

“In the next section, we will be exploring rectangles and other quadrilaterals and sometimes we’ll put them on the coordinate grid.”

Cool-down: Missing Coordinate (5 minutes)

Cool-Down

For access, consult one of our IM Certified Partners.

Student Section Summary

Student Facing

In this section, we plotted and described points on the coordinate grid.

The point $$P$$ is 4 units from the vertical axis and 2 units from the horizontal axis. Its coordinates are $$(4, 2)$$. The point $$Q$$ is 0 units from the vertical axis since it is on the vertical axis. It is 7 units from the horizontal axis. Its coordinates are $$(0, 7)$$.

The first coordinate of a point tells us its horizontal position and the second coordinate gives its vertical position.