Lesson: Introduction to the Cartesian Coordinate System
Essential Questions for Students (Objectives):
Can you plot points in a coordinate plane and identify the quadrants?
Can you explain how the Cartesian Coordinate system works and provide possible reasons for why it was developed?
Common Core Standard: 5.G.1, 6.NS.8
Book: "The Fly on the Ceiling"
Teacher-led instruction, student partner work
Vocabulary for a Word Wall:
x-axis, y-axis, quadrant, x-coordinate, y-coordinate, coordinate plane, order pairs, origin, Cartesian coordinate system
Prior Knowledge/ Possible Warm-up Activities:
1) Introduction - Read The Fly On The Ceiling - A Math Myth by Dr. Julie Glass to the students.
2) Part 1: Discussion of the Cartesian Coordinate System. Introduce the coordinate system by asking students to brainstorm landmarks in your own area (for example in Reno we could use the Nugget, the Grand Sierra, the mall, etc). Draw these landmarks in a general overview map. Lead students through a discussion (defining and describing vocabulary as you introduce each new word) knowing that every place can be given a location. Where should we put the origin? What would be a good spot (does the origin have to be in the middle)? Have the students discuss in partners how they would label the locations of a few landmarks (share out and discuss). Concerns to address, what if you are describing a large area (northwest neighborhood)? Students need to be aware that if you give descriptions of your area/item it doesn't matter if it is located in a positive location or negative.
3) Part 2 discussion and student practice: Why do we call the horizontal x and the vertical y and where do the letters come from? Why do we list the x before y in the parenthesis? How can we help ourselves remember the location of the x-axis and y-axis? A quick discussion that x and y also describe the input and output as well as the independent and dependent variable can be very advantageous at this point. Introduce quadrants and their roman numeral notation. Show a graph with points on it, and ask students to give the location for the points and list the quadrant. I would also recommend having a blank graph and asking for volunteers to come up and put a location on the graph. Make sure to point out (or have students discuss) that the 1st quadrant has positive x and y values, the 2nd quadrant has negative x and positive y values, the 3rd quadrant has negative x and y values, and the 4th quadrant has positive x and negative y values.
4) Extension - Introduce other coordinate systems - radar grids or polar graphs.
5) Activity (see attached activity sheet) - Give students two pieces of graph paper. Have them draw a Cartesian Coordinate system on both, numbering all the axes. On one of the pieces of graph paper, students will draw a map of their bedroom, including major furniture. On a separate piece of white paper, students will list the items in their bedroom and put their corresponding coordinates for each. Some large items will require a set of coordinates (example: bed - (1,5)(1,15)(-8,5)(-8,15). Ask that students use all 4 quadrants. When students are finished making their maps, they will need to fold up their graph paper with their bedroom on it and store it away. Then, they exchange their lists of coordinates with another person. On their other sheet of graph paper, they will need to draw the new person's bedroom using the provided list of coordinates. They are not to talk to the author until they are done, even if they notice problems in the list or drawing. When both students are done, they check their drawing with the author's original bedroom map. This is the time for students to correct errors in understanding through discussion.
6) Optional Homework (see attached direction sheet) - Students will write their own children's book about how THEY discovered the Cartesian coordinate system. They need to explain how the coordinate system works and what happened that required them to have to discover it (no, they can't use a messy room). The book needs to explain all the vocabulary words from the word wall and have 3 examples of how to graph points. The book must be illustrated and be a minimum of 6 pages. On the day it is due, make sure that you have rubrics copied for students to assess one another's books.
Assessment (Acceptable Evidence):
Student's bedroom maps (their own and their partner's), Cartesian coordinate book
Attached worksheets or documents:
Bedroom map activity (pdf)
Homework Assignment/Rubric (pdf)
Cautionary notes/ misconceptions:
When students are drawing their coordinate grids on graph paper at the beginning of the Draw Your Own Bedroom activity, it is common for them to not put tick marks directly on the blue lines of the graph paper, so I look for that as they are working. Also, it is impossible for them to finish their drawings completely all at the same time, so I have the students who are working more quickly add more detail, and I help the strugglers work on getting major pieces of furniture graphed and listed. They don't really have to be "finished" to exchange papers and start graphing someone else's map, just as long as they have some pieces done. I really encourage teachers to assign making the book as a homework project. I have even passed out the paper and had the blank books ready-made. The most important thing is to have them assess one another's books, so that they are interacting with the vocabulary an additional time.