- License:
- Creative Commons Attribution Non-Commercial
- Language:
- English
- Media Formats:
- Interactive, Text/HTML

# Coordinate Plane Plotter

# Coordinate Plane

## Overview

Students play a game in which they try to find dinosaur bones in an archaeological dig simulator. The players guess where the bones are on the coordinate plane using hints and reasoning.

# Key Concepts

- The coordinate plane consists of a horizontal number line and a vertical number line that intersect at right angles. The point of intersection is the origin, or (0,0). The horizontal number line is often called the
*x*-axis. The vertical number line is often called the*y*-axis. - A point’s location on the coordinate plane can be described using words or numbers. Ordered pairs name locations on the coordinate plane. To find the location of the ordered pair (
*m*,*n*), first locate*m*on the*x*-axis and draw a vertical line through this point. Then locate*n*on the*y*-axis and draw a horizontal line through this point. The intersection of these lines is the location of (*m*,*n*). - The coordinate plane is divided into four quadrants:
- Quadrant I: (+,+)
- Quadrant II: (−,+)
- Quadrant III: (−,−)
- Quadrant IV: (+,−)

# Goals and Learning Objectives

- Name locations on the coordinate plane.

# Understand the Coordinate Plane

# Lesson Guide

Review the names of the four quadrants on the coordinate plane, and discuss a few examples of points in different quadrants.

Choose two volunteers to demonstrate how to play the game. Tell students that they must work together to decide where they are going to dig next, and whether the team will use a hint. Students will place the point on the plane and enter the coordinates to direct the dig bot to the correct location.

## Opening

# Understand the Coordinate Plane

Watch students in your class play the Coordinate Plane Game.

There are four quadrants on the coordinate plane.

- Is (−2,−3) located in quadrant III?
- Name a point in quadrant IV.

INTERACTIVE: Coordinate Plane Game

# Math Mission

# Lesson Guide

Discuss the Math Mission. Students will name locations on the coordinate plane.

## Opening

Name locations on the coordinate plane.

# Play the Coordinate Plane Game

# Lesson Guide

- Have students play the game in pairs.
- After students have been playing for a while, tell them that they can only use numbers for communicating with each other to select digging points—no words.

SWD: Make sure all students with disabilities are communcating their reasoning in choosing coordinates to dig at (to minimize frustration if they are struggling). Ask students what might happen to the plotted information if there are errors in descriptions. This will help to reinforce for students the importance of precision in mathematics.

# Interventions

**Student has difficulty getting started.**

- Describe the game in your own words to your partner.
- What is the goal of the game?
- What does the hint do?

**Student has a solution.**

- Describe how you used words to give the location of the bone.
- Describe how you used only numbers to give the location of the bone.
- Did you try any hints that did not work? What happened?

# Mathematical Practices

**Mathematical Practice 1: Make sense of problems and persevere in solving them.**

Students may have difficulty at first using reasoning to find where the bones are. Watch for students who persevere and revise their strategies during the game.

**Mathematical Practice 7: Look for and make use of structure.**

After playing for a while, players may make use of structures to create a convention for finding the location of the bones.

## Work Time

# Play the Coordinate Plane Game

Play the Coordinate Plane Game with a partner.

INTERACTIVE: Coordinate Plane Game

Think about a way to give directions using only numbers.

# Prepare a Presentation

# Preparing for Ways of Thinking

As student play the game look for:

- Students who are just randomly selecting places
- Students who mix up the
*x*and*y*values - Students who are using hints
- Students who have a systematic strategy to find bones

# Challenge Problem

# Answers

- Answers will vary.

## Work Time

# Prepare a Presentation

- Explain the strategy you used to play the game.
- Explain how you identified points on the coordinate plane.

# Challenge Problem

- Share your strategies and play the Coordinate Plane Game again.

INTERACTIVE: Coordinate Plane Game

# Make Connections

# Lesson Guide

Discuss the game by asking the following questions:

- How did you find the location of the bones at the beginning of the game?
- How did you describe the location that you wanted to dig in after I told you that you could use only numbers?
- What do you think of [Name]’s method? Did anyone use a different method?
- Did you and your partner develop any ways to use only numbers so that you both understood what the number meant when communicating?

Some partners may have had trouble communicating when they could only use numbers. Have students describe what happened. For example, if a partner said "*x* = 3," they may not have known whether to go 3 up or 3 down or 3 to the left or 3 to the right.

Some students may have developed some conventions so they could have the same understanding when a number was said. For example, they might have agreed that the first number given told them whether to go up or down: up if it was a positive number and down if it was a negative number.

Make sure that all the conventions that students used get shared. Then ask:

- What if you had a different partner who used a different convention? What do you think would happen?

Tell students that because of this problem, there is a convention for naming locations on the coordinate plane. When they went 4 units to the left and 3 units up, they came to a point that is named (−4,3). (−4,3) is an ordered pair. –4 tells you to move 4 units to the left from (0,0) along the *x*-axis, and 3 tells you to move 3 units up from (0,0) along the *y*-axis.

Ask questions to make sure students understand:

- How does the first number in an ordered pair tell you where to place the digbot? (Answer:
*It tells you to move from the origin (0,0) to the right if it is positive or to the left if it is negative.*) - How does the second number in an ordered pair tell you where to place the digbot? (Answer:
*It tells you to move from the origin (0,0) up if it is positive or down if it is negative.*) - Point to a quadrant and ask students to name a point that is in that part of the graph.

Be sure to emphasize that all of the conventions they invented work but that people want to have standard conventions that work no matter who you are talking to.

ELL: Be sure that ELLs feel encouraged to share. Some ELLs will prefer to stay quiet, but it is important for them to speak aloud in a group and to hear their own voice as they address a large audience in a second language.

SWD: Check to make sure that all students have this information in their Notebook. Provide some students with certain things to listen for during this portion of instruction. Some students may need copies of the notes from this portion of the lesson.

## Performance Task

# Ways of Thinking: Make Connections

Take notes about how to plot points on the coordinate plane and about strategies for playing the Coordinate Plane Game.

As your classmates present, ask questions such as:

- How did you describe the location of the bones using only numbers?
- What strategy did you use to find the bones?
- How is your strategy different from the other strategies mentioned so far?

# Name That Point

# Interventions

**Ask questions such as the following as students are working:**

- What is the difference between the first coordinate and the second coordinate?
- What do the signs of the coordinates tell you?
- Where is the origin on the coordinate plane?
- How do you know the name of that quadrant?
- Can you find a point that lies in each quadrant?

ELL: Monitor that ELLs understand the meaning of each of these questions. If there are concerns, explain them one by one to allow them to fully participate in the activity.

# Answers

- Answers will vary.

## Work Time

# Name That Point

Remember that ordered pairs name locations on the coordinate plane. The first coordinate tells how many units to go left or right of the origin (0,0) along the *x*-axis. The second coordinate tells how many units to go up or down from the origin along the *y*-axis. For example, the ordered pair (−2,3) means go 2 units left and 3 units up from the origin.

- On the Coordinate Plane Plotter, choose four coordinate points so that each point lies in a different quadrant.
- First represent each point in the form (
*x*,*y*). - Then plot your four points on the coordinate plane.
- Identify in which quadrant each point lies.
- Confirm with a partner that the quadrants you identified are correct.

- First represent each point in the form (

INTERACTIVE: Coordinate Plane Plotter

- What does the first number of the coordinate pair name?
- Which is the negative direction on the coordinate plane on the x -axis?
- Which is the negative direction on the coordinate plane on the y -axis?
- Remember that (–2, –3) is in quadrant 3.

# Describe a Coordinate Plane

# A Possible Summary

You can use words like up, down, right, and left to describe locations on the coordinate plane. You can also use ordered pairs like (−6,4) to give a location on the coordinate plane.

# Additional Discussion Points

- The coordinate plane consists of a horizontal number line and a vertical number line that intersect at right angles. The point of intersection is the origin, or (0,0).
- The horizontal number line is often called the
*x*-axis. The vertical number line is often called the*y*-axis. - A point’s location on the coordinate plane can be described using words or numbers.
- Ordered pairs name locations on the coordinate plane. To find the location of the ordered pair (
*m*,*n*), first locate*m*on the*x*-axis and draw a vertical line through this point. Then locate*n*on the*y*-axis and draw a horizontal line through this point. The intersection of these lines is the location of (*m*,*n*). - The coordinate plane is divided into four quadrants:
- Quadrant I: (+,+)
- Quadrant II: (−,+)
- Quadrant III: (−,−)
- Quadrant IV: (+,−)

## Formative Assessment

# Summary of the Math: Describe a Coordinate Plane

Write a summary of what you leaned about coordinate planes and how to name locations on the coordinate plane.

Check your summary.

- Do you describe what the coordinate plane is?
- Do you explain what the different quadrants are on a coordinate plane?
- Do you explain how to find a location on the coordinate plane using only numbers?

# Reflect On Your Work

# Lesson Guide

Have each student write a brief reflection before the end of class. Review the reflections to find out what students know about locating points on the coordinate plane.

## Work Time

# Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

**One thing I know about locating points on the coordinate plane is …**