Education Technology

Linear Equations for Which the Product of the Coordinates is Constant

Published on 08/01/2007

Activity Overview

This activity allows students to explore situations in which points with a constant product of x-coordinate and y-coordinate are graphed. With TI-Navigator?s display, students can determine that a curve is formed from such points. This curve is in quadrants 1 and 3 if the product is positive or in quadrants 2 and 4 if the product is negative. The Learning Check enables the teacher to get immediate feedback from the students, thus giving opportunities to correct any errors in understanding.

Before the Activity

Before the Activity create a Learning Check that has the questions: If a graph has points for which the product of the x-coordinate and the y-coordinate is -24, what kind of curve is it? Line Curve in one quadrant Curve in two quadrants If a curve has points for which the product of the x-coordinate and the y-coordinate is -24, its graph has either an x-intercept of 24 and a y-intercept of -1 or an x-intercept of -24 and a y-intercept of 1. True False If a curve has points for which the product of the x-coordinate and the y-coordinate is -24, its graph passes through which quadrant(s)? Quadrant 1 Quadrant 2 Quadrant 3 Quadrant 4 Start TI-Navigator and begin the class.

During the Activity

See the attachment

After the Activity

Send a Learning Check file to the class to check for their understanding. The first question is a multiple choice one. If a graph has points for which the product of the x-coordinate and the y-coordinate is -24, what kind of curve is it? Line Curve in one quadrant Curve in two quadrants The second question is a true-false type. If a curve has points for which the product of the x-coordinate and the y-coordinate is -24, its graph has either an x-intercept of 24 and a y-intercept of -1 or an x-intercept of -24 and a y-intercept of 1. True False The third question is a multiple choice one for which there is more than one correct answer. If a curve has points for which the product of the x-coordinate and the y-coordinate is -24, its graph passes through which quadrant(s)? Quadrant 1 Quadrant 2 Quadrant 3 Quadrant 4 Collect the answer files from the classroom. Display the slide show of student responses and discuss the results.