Systems of Equations Navigator Activity

SYSTEMS OF EQUATIONS NAVIGATOR ACTIVITY

INTRODUCTION: This lesson is intended to help students transform equations in standard form to slope-intercept form and to solve the system using tables and graphs. It could also be used to help students write equations in slope-intercept form given a system of equations. Use as an introduction to the unit or as a review activity.

SET-UP: Open TI-Navigator™ on the computer; choose the class from the list and press Begin Class to start the session.

SETTINGS: In Activity Center make these settings.  Contribute: Equations  Configure: # of equations per student:  Check the following: Let students view graphs of equations Let student resubmit equations  Students start with: Empty equations

Press OK Window settings: X Min -15 X Max 15 X Scale 1 Y Min -15 Y Max 15 Y Scale 1

ACTIVITY :  Instruct students to select Activity Center  On the computer, click on the Graph-Equation tab and enter the first system of equations in slope-intercept form in the Y= box and click Add after each equation. The lines should appear on the graph of the Activity Center. Highlight the equations and go to View and select Mask Teacher Input to hide the equations. Note: the color of the lines can be changed so they are different.

SAMPLE PROBLEMS:

x – y = 0 y = x x – y = -5 y = x + 5 x + y = 4 y = -x + 4 x + y = 1 y = - x + 1 answer: (2,2) answer : (-2,3)

4x – y = 15 y = 4x - 15 5x + 5y = 0 y = -x x – y = -3 y = x + 3 x – 2y = 30 y = ½ x - 15 answer : (6,9) answer : (10,-10)

x + y = -1 y = - x - 1 -3x + y = -15 y = 3x - 15 2x + y = 4 y = -2x + 4 -5x + 5y = -5 y = x - 5 answer : (1,2) answer : (7,6)

 Once students see they have submitted the wrong equation, you can highlight it and then delete it. This keeps from getting too many lines on the graph.  This activity can be conducted by giving the students the standard form and having them transform to slope-intercept form to match the teacher graphs or just give the students the graphs have them try and come up with the equations on their own.  Press Start Activity to begin.  Students will enter the equations in slope-intercept form in Y1 and Y2.  Remind students that they can check their graphs before sending to the teacher. If they have entered the equations correctly, their graphs should be on top of the initial equations.  Demonstrate to the students how to solve the system graphically by moving the cursor to the point of intersection and discuss what the corresponding x and y values are for the point of intersection.  Demonstrate to the students how to solve the system numerically by clicking on the Equation tab in the Activity Center and select Y1 in the first column and Y2 in the second column. Scroll until the expressions have the same x and y values.  Pause the activity to discuss submissions that have errors and why they may have occurred.  Press Stop Activity when you are finished.

CALCULATOR:  Students should exit NavNet.  Have them enter the equations in Y1 and Y2 and use the table and graph functions to find the solution.  Teachers can use Screen Capture to check for student understanding.

QUICK POLL:  Have students log into NavNet.  On the computer, from the pull-down menu select Open Response and check Resubmit so that students may change their answers.

SAMPLE QUESTIONS: Q. Solve 3x – y = 1 x – y = -5 A. (3,8)

Q. Solve x + y = 4 2x – y = -7 A. (-1,5)

Q. Solve 4x + y = 1 2x – y = 5 A. (1, -3)

Q. Solve 6x –y = 15 5x – y = 11 A. (4,9)

Display each system on board one at a time and have students answer : Q. What is the slope and y-intercept for each equation in the system?

 Press Stop Poll when you are ready to solve the next system or are finished with the activity.