Lesson 2

Points on the Coordinate Grid

Warm-up: Notice and Wonder: A Point (10 minutes)

Narrative

The purpose of this warm-up is for students to describe a point which will be useful when students locate points on a coordinate grid in a later activity. While students may notice and wonder many things about this image, the relationship between the point and the numbers on the vertical and horizontal axes is the main focus of the discussion. 

Launch

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

Activity

  • “Discuss your thinking with your partner.”
  • 1 minute: partner discussion
  • Share and record responses. 

Student Facing

What do you notice? What do you wonder?

Coordinate grid. horizontal and vertical axis, 0 to 10, by 1's. 1 point plotted at 5 comma 6.

Student Response

For access, consult one of our IM Certified Partners.

Activity Synthesis

  • "How can we describe the location of the point?” (It is kind of in the middle of the grid, but toward the top. It is where two lines intersect. It is where line 5 and line 6 cross each other.)

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

Narrative

The purpose of this activity is for students to describe coordinates for points. After playing a round of What’s the Point, students have an opportunity to write a description of the location of a point in the coordinate plane. The structure of this part of the activity mirrors what students did in the previous lesson when they were describing a rectangle. Some students may use the coordinates on the grid while others may use words to describe the location of the point.

Students make choices about how to revise their thinking based on what makes the description stronger and clearer to them. This activity not only supports students developing language to describe the location of a point but also develops a deeper understanding of the coordinate grid (MP6). Invite students to use language from the display from an earlier lesson if they find it helpful.

This activity uses MLR1 Stronger and Clearer Each Time. Advances: Reading, Writing.

Required Materials

Materials to Copy

  • What's the Point

Required Preparation

  • Create a set of cards from the blackline master for each group of 2.

Launch

  • Groups of 2.

Activity

  • 10 minutes: partner work time
  • Monitor for students who:
    • revise their thinking
    • refer to the numbers on the coordinate grid to communicate the location of the point

MLR1 Stronger and Clearer Each Time

  • “Share your description of the location of the point on the grid with your partner. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”
  • 3–5 minutes: structured partner discussion
  • Repeat with 1–2 different partners.
  • If needed, display question starters and prompts for feedback, such as:
    • “Can you use the numbers on the coordinate grid in your explanation?”
  • “Revise your initial draft based on the feedback you got from your partner.”
  • 2–3 minutes: independent work time

Student Facing

  1. Play 2 rounds of What’s the Point so each partner gets a chance to draw.

    • Sit back to back with your partner.
    • Partner A: Choose a card. Then, describe the location of the point to your partner.
    • Partner B: Draw the point on the blank coordinate grid.
    • Compare the card with your partner’s diagram.
    • Discuss: What’s the same? What’s different?
    Coordinate grid. horizontal and vertical axis, 0 to 10, by 1's. 
    Coordinate grid. horizontal and vertical axis, 0 to 10, by 1's. 
  2. Use words to explain the location of the point on the grid.

    Coordinate grid. horizontal and vertical axis, 0 to 10, by 1's. Point plotted at 3 comma 4

Student Response

For access, consult one of our IM Certified Partners.

Advancing Student Thinking

If students do not reference the axes or the directionality of the gridlines, show them point \((3, 4)\) and point \((4, 3)\) on a grid and ask, “What is the same and different about these two points?”

Activity Synthesis

  • Select previously identified students to share how they revised their explanation for the location of the point in the last problem.
  • Display the image of the coordinate grid with a point from the student workbook.
  • “The point can be described using the coordinates \((3, 4)\). Where do you think these coordinates come from?” (They describe the location of the point. The point is on gridline 3 and gridline 4. The point is where these gridlines intersect.)

Activity 2: Plot and Label Points (15 minutes)

Narrative

The purpose of this activity is for students to write ordered pairs of numbers to represent points in the coordinate plane and to plot points with given coordinates. Students may interpret the horizontal and vertical coordinates backward. With time and practice they will learn the convention that the first coordinate represents the horizontal location of the point and the second coordinate represents its vertical location.

Representation: Internalize Comprehension. Synthesis: Invite students to identify which details were most important to list coordinates. Display the sentence frame, “The next time name coordinates and plot points, I will look for/pay attention to . . . .”
Supports accessibility for: Memory, Attention, Conceptual Processing

Launch

  • Groups of 2
  • Display images of points \(P\) and \(Q\) from student workbook.
  • Poll the class:
    “What are the coordinates of point \(P\) and \(Q\)?”
  • “The coordinates for these points have the same numbers. We have a convention that we always list the number that corresponds with the horizontal axis first and the number that corresponds with the vertical axis second. The coordinates for point P are \((3, 4)\). How do these coordinates represent point \(P\)?” (The 3 is on the horizontal axis and the 4 is on the vertical axis.)
  • “What are the coordinates for point \(Q\)?” \((4, 3)\)
  • “In this activity, you are going to name coordinates of points and plot points with given coordinates.”

Activity

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

Student Facing

Coordinate grid. horizontal and vertical axis, 0 to 10, by 1's. point plotted. Labeled P.
Coordinate grid. horizontal and vertical axis, 0 to 10, by 1's. point plotted. Labeled Q.
  1. List the coordinates for each point.
    Coordinate grid. horizontal and vertical axis, 0 to 10, by 1's. point A, over 4, up 6. point B, over 1, up 4. point C, over 7, up 2.

    coordinates
    \(A\) ( ___ , ___)
    \(B\) ( ___ , ___)
    \(C\) ( ___ , ___)

  2. Plot points \(D\), \(E\), \(F\) on the same grid.

    coordinates
    \(D\) \((6, 4)\)
    \(E\) \((2, 5)\)
    \(F\) \((8, 3)\)

Student Response

For access, consult one of our IM Certified Partners.

Activity Synthesis

  • “What is challenging about naming the coordinates for a point?” (I need to remember which coordinate goes first and which one goes second. I have to be careful to make sure I get the right horizontal and vertical location of the point.)
  • “What is challenging about plotting points on the coordinate grid?” (I have to remember which coordinate goes with which axis. It is hard to remember the coordinates while you are also trying to find them on the grid. I could find each coordinate but finding the point with both of those coordinates is hard.)

Lesson Synthesis

Lesson Synthesis

Display a blank coordinate grid from the first activity.

“What new information did we learn about the structure of coordinate grids?” (We can use the numbers on the axes to plot and label points on the grid.)

Display the coordinates for all to see: \((4, 7)\) and \((7, 4)\).

“What do we know about the points with these coordinates?” (They each have a 7 and a 4 but the 7 and 4 are in different places. So \((4, 7)\) has a horizontal coordinate of 4 and a vertical coordinate of 7 and \((7, 4)\) has a horizontal coordinate of 7 and a vertical coordinate of 4.)

“How do we plot each of these coordinate pairs?” (The first coordinate says how far to go across horizontally and the second coordinate says how far to go up vertically.)

Plot the points \((4, 7)\) and \((7, 4)\) on the blank grid according to the directions students give.

Cool-down: Coordinates (5 minutes)

Cool-Down

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