ALEX Lesson Plan

     

Introduction to the Cartesian Coordinate Plane

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  This lesson provided by:  
Author:Jerry Weeks
System: Escambia County
School: W S Neal High School
  General Lesson Information  
Lesson Plan ID: 11546

Title:

Introduction to the Cartesian Coordinate Plane

Overview/Annotation:

This lesson consists of two Powerpoint presentations that use animation (motion) to demonstrate how to obtain a 1-1 mapping between a plane and ordered pairs of Real numbers. These can be teacher presented or if you have enough PCs students can do these as independent activities.

 Associated Standards and Objectives 
Content Standard(s):
Mathematics
MA2015 (2015)
Grade: 5
23 ) Use a pair of perpendicular number lines, called axes, to define a coordinate system with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). [5-G1]

Insight Unpacked Content
Column Definitions

Evidence of Student Attainment:
Students:
Given a point on a coordinate plane,
  • Explain how to identify its coordinates using appropriate vocabulary (x-axis, y-axis, x- coordinate, y-coordinate, distance from the origin).
Given an ordered pair of numbers,
  • Justify the placement of the corresponding point on a coordinate system.
Teacher Vocabulary:
  • Axes
  • X-axis
  • Y-axis
  • Coordinate system
  • Origin
  • Ordered pair
  • Coordinates
Knowledge:
Students know:
  • Coordinate system vocabulary: axes, x-axis, y-axis, origin, ordered pair, coordinates, x-coordinate, y-coordinate,
  • Techniques for constructing a coordinate grid and plotting points on that grid.
Skills:
Students are able to:
  • Construct a coordinate system,
  • Explain how to identify the coordinates of a point on a coordinate system,
  • Graph points corresponding to ordered pairs.
Understanding:
Students understand that:
  • Graphing points on a coordinate plane provides a representation of a mathematical context which aids in visualizing situations and solving problems.
AMSTI Resources:
Other Units
Growth Patterns:
Sess. 1.1-1.5, 2.3-2.8
ACT Aspire Documents:
Curriculum Guide:
Objectives:
M. 5.23.1: Define ordered pair of numbers.
M. 5.23.2: Define x-axis, y-axis, and zero on a coordinate.
M. 5.23.3: Specify locations on the coordinate system.
M. 5.23.4: Illustrate vertical and horizontal number lines.
M. 5.23.5: Label x- and y-axis and zero on a coordinate.
M. 5.23.6: Locat negative numbers on a horizontal number line.
M. 5.23.7: Locate positive numbers on a horizontal number line.
M. 5.23.8: Locate positive numbers on a vertical number line.
Examples: thermometer, map
Mathematics
MA2015 (2015)
Grade: 5
24 ) Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. [5-G2]

Insight Unpacked Content
Column Definitions

Evidence of Student Attainment:
Students:
Given real world and mathematical problems involving a relationship between two variables,
  • Create a first quadrant graph and explain its relationship to the context of the problem (e.g., Tickets cost $0.75 each. If 20 tickets are sold, the cost is $15, if 21 tickets are sold the cost is $15.75. Create a graph that shows the cost of any number of tickets.).

Given a graph of a real world or mathematical situation,
  • Interpret the coordinate values of the points in the context of the situation.
Teacher Vocabulary:
  • Coordinate plane
  • First quadrant
  • Coordinate values
Knowledge:
Students know:
  • Coordinate system vocabulary; axes, x-axis, y-axis, origin, ordered pair, coordinates, x-coordinate, y-coordinate.
Skills:
Students are able to:
  • Explain how to identify the coordinates of a point on a coordinate system,
  • Graph points corresponding to ordered pairs,
  • Represent real world and mathematical problems on a coordinate plane,
  • Interpret coordinate values of points in the context of real world/mathematical situations.
Understanding:
Students understand that:
  • A variety of representation (e.g., diagrams, number lines, charts, and graphs) can be used to illustrate mathematical situations and relationships,
  • These representations help in conceptualizing ideas and in solving problems,
  • Graphing points on a coordinate plane provides a representation of a mathematical context which aids in visualizing situations and solving problems.
AMSTI Resources:
Other Units
Growth Patterns:
Sess. 1.1-1.5, 2.3-2.8
ACT Aspire Documents:
Curriculum Guide:
Objectives:
M. 5.24.1: Define ordered pair of numbers, quadrant one, coordinate plane, and plot points.
M. 5.24.2: Label the horizontal axis (x).
M. 5.24.3: Label the vertical axis (y).
M. 5.24.4: Identify the x and y values in ordered pairs.
M. 5.24.5: Model writing ordered pairs.

Local/National Standards:

 

Primary Learning Objective(s):

Students will learn the names of the components of the Cartesian plane along with how to plot points and determine the coordinates of points.

Additional Learning Objective(s):

 
 Preparation Information 

Total Duration:

31 to 60 Minutes

Materials and Resources:

Make sure the Powerpoint presentations are copied unto the PCs being used. The teacher should view the presentations first to ensure the students are instructed on how to run the presentations, if they are being done independently by the students.

Technology Resources Needed:

If the teacher is to present these Powerpoint presentations to the class as a whole then he/she will need a PC with Powerpoint and a multimedia projector or a large screen TV and scan converter. If the students are to do these independently as a programmed instruction activity, then sufficient access to PCs with Powerpoint is required.

Background/Preparation:

Students need to understand the term perpendicular lines and know how to draw them.

  Procedures/Activities: 
1.)The Cartesian Plane presentation presents the steps to setting up the 1-1 mapping between a geometric plane and ordered pairs of Real numbers. It allows the students to repeat this until they are proficient. Then, the students can continue. The second part presents how to determine the coordinates of points plotted on the plane. It also talks about the six sets that comprise the Cartesian plane and the properties of the ordered pairs in each set.

2.)The Cartesian Plane Practice presentation illustrates how to graph points on the plane then gives students exercises to practice this skill.


Attachments:
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  Assessment  

Assessment Strategies

I hope this material will be appropriate at several grade levels, so I am not including a test as it would have to be developed for the specific grade.

Acceleration:

 

Intervention:

These presentations can be done by the teacher to the class as a group then individuals who need more help or the material presented at a slower pace can work through them independently.

Each area below is a direct link to general teaching strategies/classroom accommodations for students with identified learning and/or behavior problems such as: reading or math performance below grade level; test or classroom assignments/quizzes at a failing level; failure to complete assignments independently; difficulty with short-term memory, abstract concepts, staying on task, or following directions; poor peer interaction or temper tantrums, and other learning or behavior problems.

Presentation of Material Environment
Time Demands Materials
Attention Using Groups and Peers
Assisting the Reluctant Starter Dealing with Inappropriate Behavior
Be sure to check the student's IEP for specific accommodations.