Introduction to Cartesian Coordinates and Plane

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The students define the pertinent components of a Cartesian coordinate system. The students will also understand how to read and develop the coordinate grid system. A brief refresher on the Cartesian plane includes how points are written in (x, y) format and oriented to the axes, and which directions are positive and negative. Then students learn about what it means for a relation to be a function and how to determine domain and range of a set of data points. Print twice and hold together with connectors on the Axes. Printer Settings: Printer Brand: MakerBot Printer: MakerBot Replicator 2 Rafts: No Supports: No Resolution: Standard Infill: 10% How I Designed This The 3D printed parts were designed in Tinkercad. Overview and Background Students need to understand the term perpendicular lines and know how to draw them. Objectives Students will learn the names of the components of the Cartesian plane along with how to plot points and determine the coordinates of points. Students will also learn the term perpendicular lines and know how to identify them. 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). Additional Vocabulary Right angles are formed when two rays share a common end and measure ninety-degree angle. Perpendicular Lines is described as lines that meet to form right angles. Explore / Explain Quadrant While pointing at the first quadrant, the teacher asks: Why do you think this is the first quadrant? Why isn’t the first quadrant in the top left hand corner? Why do you think it progresses counter clockwise rather than clockwise? If the students cannot answer, the teacher will explain that the quadrants are labeled I, II, III, and IV. Lesson Plan and Activity Take students through labeling the axes with "x" and "y," as well as indicating that arrows at the ends of each axis show it goes on forever. Talk about the Cartesian plane quadrants, while having students point to "I, II, III and IV." Point out which directions are positive (right on the x-axis and up on the y-axis) and which directions are negative (left on the x-axis and down on the y-axis). Point out the origin, the point (0,0). Duration of Lesson 30-60 minutes Preparation Understand the number line (i.e. positive numbers ascend to the right of zero and negative numbers descend to the left of zero). Students should know vocabulary associated with the Cartesian coordinate system. 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. The Cartesian Plane Practice presentation illustrates how to graph points on the plane then gives students exercises to practice this skill. Rubric and Assessment Describe the Cartesian plane and correctly label its parts. Explain the source of the name "Cartesian." Describe the naming convention for coordinates in the form (x, y). Plot a set of data points.