Based on a previous lesson, students will be given the following Do Now problems based on rational numbers. We discussed the difference between rational numbers and integers, so these problems are a quick assessment of students understanding.
1) Write three rational numbers between -1 and -2.
2) Write three integers between 2 and -2.
3) Order from greatest to least: -0.24, 0, -1, -1/4, 50%
For problem 1, students should realize that they may have different answers.
For problem 2, students should have the same answers of 1, 0, and -1.
For problem 3, students may have different strategies for comparing the numbers. Some students may decide to change the numbers to decimals, while others may change them to fractions.
To heighten students' interest in the lesson, I will share the rumored story of how Rene Descartes developed the coordinate plane.
Rene Descartes was a French mathematician. When he was a child, he was often sick. On the days he was sick, he would stay home from school. One day, Rene was lying in bed, not feeling well, and noticed a fly buzzing around. When the fly landed on the ceiling he noticed that the ceiling tiles created a grid. He realized that using this grid, he could describe the location of the fly both horizontally and vertically. This was the beginning of the development of the coordinate plane.
This lesson will introduce students to the coordinate plane. I will introduce the coordinate plane in three stages.
The first stage will just focus on what it looks like and basic terminology. I will show students a picture of a coordinate plane with a large C on it. (See Coordinate plane picture with C)
What does the C stand for?
Most students will know of the coordinate plane.
"C" stands for 3 things: 1. Coordinate plane, 2. Cartesian plane (named after Rene Descartes), and counter clockwise.
The coordinate plane is divided into 4 sections. What do we call those sections? What is the prefix that means two? three? four?
(See Coordinate plane picture with quadrants)The coordinate plane has four quadrants. We number them moving in a counter clockwise direction.
The second stage will focus on modeling for students how to create a coordinate plane. Students will be given graph paper. We will label and number the x and y axes together. Students often make mistakes when numbering so it is important to model it for them.
For the third stage, students will plot coordinates.
In order to plot a point, you need an ordered pair (x,y). What does the x value tell you? What does the y value tell you?
Students often confuse the x and y coordinates and which direction each indicate. It may help to use the analogy of an elevator. If you're standing in front of the elevators on the main floor, first you have to figure out if you're taking the elevator on the left or right, then you have to decide whether you're moving up or down.
Students will plot the following points on their coordinate plane. At the same time, I will call students up to the board to plot each point.
Since students have the most difficulty when the x or y coordinate is 0, we will review this concept. I will call on a few students to share their ideas for the following questions.
If you were giving someone directions to locate (0,8), what would you say?
In their directions, students should mention that you shouldn't move left or right from the origin, only up 8 units.
If you were giving someone directions to locate (-5,0), what would you say?
In their directions, students should mention that you should only move left from the origin 5 units, not up or down.