Go around the room and ask each student to repeat one of the points. If the first coordinate is negative, it will appear in the opposite quadrant.ĭrill, drill, and drill these facts into students.A negative value is measured clockwise from the polar axis.A positive value is measured counterclockwise from the polar axis.Explain that they will now be able to predict in which quadrant a point in polar notation appears. Use both the Step of 10 degrees and Step of 15 degrees to give students lots of practice. When students are comfortable with this step, have them label the angles on the grids found on this link. The problematic angles will be dealt with when students use a graphing calculator. Have students find the measure of for these angles in terms of π. A straight line (the diameter of a circle without a circumference) is 180°, so a 15° angle is expressed as 15π/180 or π/12. When you have a straight line, the diameter of the circle is π. The circumference of a straight line is 0. Use this reasoning for a circle that surrounds a straight line. To discuss, you are referring to the angle formed by the line that goes through the pole (origin) and the polar axis (positive x-axis). Do not move on from this concept until students have mastered it. Substitute x, y, and r into the Pythagorean equation to get x² + y² = r²įrom this equation, students can find the value of r. From the point, sketch in the line segments that form a right angle with the line going through the origin and the point you selected.įrom the angle formed at the origin, call the adjacent line segment x, the opposite line segment y, and the hypotenuse r. Select a point in the first quadrant of the Cartesian grid that has readily determined x and y values. Use it to help students determine the length of r. Pre-calculus students should be very comfortable with the Pythagorean Theorem. Therefore, it is suggested to use simple examples for understanding the basics. The last tier of the scaffold is using a graphing calculator. Unless students understand each step of the process, will really be foreign to your students. Students are no longer graphing (x, y) coordinates, but (r, ) coordinates, where r = the distance from the pole that was formerly called the origin is the angle measured from the polar axis that was previously referred to as the positive x-axis. Now we expect them to use a polar coordinate system that has an infinite number of coordinates for the same point. Up to this point, students have worked with the Cartesian coordinate system where any point on the graph has only one set of coordinates. Tier 1įirst students must know what polar coordinates are and how to graph them. Here is a list of the different tiers to that scaffold. The approach to introducing polar coordinates must be made using that same philosophy.įor students to understand how to graph polar coordinates and equations, these lessons must use a scaffolding method where students understand each piece leading to graphing the equations. You've heard the saying "talk to me like I am three" when trying to explain or understand something complex.
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