Graphing and the Coordinate Plane

Abstract

This lesson is designed to introduce students to graphing ordered pairs of numbers on the coordinate plane.

Objectives

Upon completion of this lesson, students will:

  • have been introduced to the Cartesian coordinate plane
  • understand the four quadrants of the Cartesian coordinate plane
  • be able to plot points on the plane
  • be able to read coordinates for a point from a graph
  • be able to give the ratio of rise over run for slope

Standards Addressed

Grade 3

  • Geometry

    • The student demonstrates understanding of position and direction.

Grade 4

  • Geometry

    • The student demonstrates understanding of position and direction.

Grade 5

  • Geometry

    • The student demonstrates understanding of position and direction.

Grade 6

  • Geometry

    • The student demonstrates understanding of position and direction.

Grade 7

  • Geometry

    • The student demonstrates understanding of position and direction.

Grade 8

  • Geometry

    • The student demonstrates understanding of position and direction.

Grade 9

  • Geometry

    • The student demonstrates understanding of position and direction when solving problems (including real-world situations).

Grade 10

  • Geometry

    • The student demonstrates understanding of position and direction when solving problems (including real-world situations).

Fifth Grade

  • Geometry

    • Graph points on the coordinate plane to solve real-world and mathematical problems.

Functions

  • Linear, Quadratic, and Exponential Models

    • Construct and compare linear, quadratic, and exponential models and solve problems

Grade 7

  • Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

    • COMPETENCY GOAL 5: The learner will demonstrate an understanding of linear relations and fundamental algebraic concepts.

3rd Grade

  • Data Analysis and Probability

    • The student will demonstrate through the mathematical processes an understanding of organizing, interpreting, analyzing and making predictions about data, the benefits of multiple representations of a data set, and the basic concepts of probability.

6th Grade

  • Algebra

    • The student will demonstrate through the mathematical processes an understanding of writing, interpreting, and using mathematical expressions, equations, and inequalities.

4th Grade

  • Data Analysis and Probability

    • Standard 4-6: The student will demonstrate through the mathematical processes an understanding of the impact of data-collection methods, the appropriate graph for categorical or numerical data, and the analysis of possible outcomes for a simple event.

  • Geometry

    • Standard 4-4: The student will demonstrate through the mathematical processes an understanding of the relationship between two- and three-dimensional shapes, the use of transformations to determine congruency, and the representation of location and moveme
    • Standard 4-4: The student will demonstrate through the mathematical processes an understanding of the relationship between two- and three-dimensional shapes, the use of transformations to determine congruency, and the representation of location and movement within the first quadrant of a coordinate system.

8th Grade

  • Algebra

    • The student will demonstrate through the mathematical processes an understanding of equations, inequalities, and linear functions.

  • Geometry

    • The student will demonstrate through the mathematical processes an understanding of the Pythagorean theorem; the use of ordered pairs, equations, intercepts, and intersections to locate points and lines in a coordinate plane; and the effect of a dilation
    • The student will demonstrate through the mathematical processes an understanding of the Pythagorean theorem; the use of ordered pairs, equations, intercepts, and intersections to locate points and lines in a coordinate plane; and the effect of a dilation in a coordinate plane.

Elementary Algebra

  • Elementary Algebra

    • Standard EA-3: The student will demonstrate through the mathematical processes an understanding of relationships and functions.
    • Standard EA-5: The student will demonstrate through the mathematical processes an understanding of the graphs and characteristics of linear equations and inequalities.
    • Standard EA-6: The student will demonstrate through the mathematical processes an understanding of quadratic relationships and functions.

Intermediate Algebra

  • Algebra

    • The student will demonstrate through the mathematical processes an understanding of quadratic equations and the complex number system.

3rd Grade

  • Probability and Statistics

    • 3.21b The student, given grid paper, will construct a line plot, a picture graph, or a bar graph to represent the results. Each graph will include an appropriate title and key.

7th Grade

  • Probability and Statistics

    • 7.17 The student, given a problem situation, will collect, analyze, display, and interpret data, using a variety of graphical methods, including frequency distributions; line plots; histograms; stem-and-leaf plots; box-and-whisker plots; and scattergrams.

4th Grade

  • Geometry

    • 4.15.b The student will describe the path of shortest distance between two points on a flat surface.
    • 4.16 The student will identify and draw representations of lines that illustrate intersection, parallelism, and perpendicularity.
    • 4.18 The student will identify the ordered pair for a point and locate the point for an ordered pair in the first quadrant of a coordinate plane.

  • Geomety

    • 4.15.b
    • 4.16
    • 4.18

  • Probability and Statistics

    • 4.20
    • 4.20 The student will collect, organize, and display data in line and bar graphs with scale increments of one or greater than one and use the display to interpret the results, draw conclusions, and make predictions.

Secondary

  • Algebra II

    • AII.20 The student will identify, create, and solve practical problems involving inverse variation and a combination of direct and inverse variations.
    • AII.20

Textbooks Aligned

6th

  • Module 7 - Wonders of the World

    • Section 5: Temperature, Integers, and Coordinate Graphs
      • Reason for Alignment: This lesson is quite similar to the Cartesian Coordinate System lesson and can be used interchangably. It contains discussions and teacher directions included to guide students through the concepts. The level is appropriate for this stage of a student skill. The discussion in the lesson should be useful for working with students in understanding the four quadrants and examples.

7th

  • Module 1 - Search and Rescue

    • Section 2: Integers and Coordinates
      • Reason for Alignment: The Graphing and the Coordinate Plane lesson is a good beginning look at coordinate graphing. It covers the basics, which should be review, and vocabulary. Students should appreciate the review from Book 1. All four quadrants are used and explained.

Student Prerequisites

  • Arithmetic: Students must be able to:
    • perform integer and fractional arithmetic.
  • Technological: Students must be able to:
    • perform basic mouse manipulations such as point, click and drag.
    • use a browser for experimenting with the activities.
  • Algebraic: Students must be able to:
    • work with very simple linear algebraic expressions.

Teacher Preparation

Key Terms

coordinates

A unique ordered pair of numbers that identifies a point on the coordinate plane. The first number in the ordered pair identifies the position with regard to the x-axis while the second number identifies the position on the y-axis

Lesson Outline

  1. Focus and Review

    Remind students what has been learned in previous lessons that will be pertinent to this lesson and/or have them begin to think about the words and ideas of this lesson.

  2. Objectives

    Let the students know what it is they will be doing and learning today. Say something like this:

    • Today, class, we are going to learn about graphing lines on the coordinate plane.
    • We are going to use the computers to do this but please do not turn your computers on until I ask you to. I want to show you a little about this activity first.

  3. Teacher Input

    • Lead a discussion on the number line and the coordinate plane.

  4. Guided Practice

    • Practice the students' point plotting skills by having them play the Coordinates! Game The game allows users to figure out and to practice using the coordinate plane for giving the "address" or exact location of particular points.

  5. Independent Practice

  6. Closure

    • You may wish to bring the class back together for a discussion of the findings. Once the students have been allowed to share what they found, summarize the results of the lesson.

Alternate Outline

This lesson can be rearranged in several ways:

  • Omit one or the other of the computer activities to reduce the amount of time spent.
  • Add a discussion about fractional movement on the coordinate plane
  • For students who aren't ready to handle negative numbers yet, replace the Coordinates activity with the positive numbers only alternate versions:
  • Introduce students to the next lesson by using Simple Plot to plot the tables of points that the students generated.

Suggested Follow-Up

After these discussions and activities, students will be have learned to plot points on the coordinate plane and to read the coordinates off of a graph. The next lesson Graphs and Functions will introduce students to the graphical representation of functions.