Any Learning Objectives:
1. Students will demonstrate competency and fluency in graphing linear equations on the TI-82/83+ graphing calculator.
2. Students will practice using the system solving functionality of the calculator.
3. Students will acquire screen shots of their systems of equations graphed on the calculator and save them to a file. Materials:
Means of projecting the screen shots from a TI-82/83+
Classroom set (or students' individual) TI-82/83+ calculators
TI-Connect software connected to a computer accessible to students
Students researched cost curve/revenue curve information (from previous lesson)
Attached calculator skills worksheet Procedures:
Have students take out their graphs and equations from the previous lesson. Give them 5 minutes in which to prepare for their presentation to the class with their partner.
Call the group back together and have each pair present their products with the conclusions they arrived at for that product. Focus in particular on the different cost curves and break even points. Lead the students in a brief discussion about which product(s) they think make the most sense to sell, considering the cost and revenue information that we have just analyzed.
Next, remind the students that they are going to need to present this data to the principal. Ask them if they think that a hand-drawn graph carries as much weight as a computer-generated graph? Why or why not? (Allow for discussion.) Regardless of whether or not it looks more professional, would it at least be true to say that it would be nice to be able to graph these curves quickly on a calculator, instead of spending all the time that you did last night? Today, we’re going to learn how to use the TI-83+ to do just that! These are graphing calculators, and today is the day that we’re going to learn how to use the graphing (and trace) functions in order to graph our information from last night and analyze it.
Have each student get out their calculator and turn it on. Walk through step-by-step how to clear the memory on the graphing (y=) function and how to get a standard scale so that they all are starting in the same place.
Now, put the fictitious cost curve from the last lesson (for the grilled-cheese sandwiches on the board): y = 20 + 0.57x Remind students that this is the equation from the previous lesson. Ask them what they found to be appropriate scales for their graphs on their own work (lead a brief review/discussion of scale of axes if there is confusion). Because we needed a special scale for those graphs, we will undoubtedly need to do the same for the calculator. Let’s set that up right now.
Lead students through how to set the scale for the graph window. Have them set the scale for the y-axis from 0 through 75 and “5” for the scale and the x- axis for 0 through 55 with “5” for the scale.
Next, lead students how to enter the equation into the appropriate screen of the calculator and graph the equation. Walk them through the trace function of the calculator and how to read the information from the trace. Have students work with their partners to ensure that they understand how to follow all of the instructions. Circulate and ensure that all students understand before moving on.
Next, remind students that we wanted to find the points of intersection between the cost curve and different revenue curves representing different prices. Place the revenue curve equations on the board from the last lesson’s example:
y=x ; y = 1.25x ; y = 1.5x ; y = 1.75x ; y = 2x
Next, have the students enter in the first equation into the second line of the graphing window and graph the equation. Show them that the equations are graphed on the same coordinate plane and demonstrate how the trace function can be used to find the point of intersection. Allow students to explore this functionality with the other four equations with their partners as I circulate through the room.
Next demonstrate how to find the actual value for the intersection by using the functionality in the “CALC” part of their calculator (option 5 under CALC). Walk through finding the intersection of just two of the curves, in order for the students to be able to clearly see what they are doing.
Once students are comfortable with this, have them capture screen shots of their own cost/revenue analyses. Then, once seated, pass out the attached worksheet for them to practice their skills. Attached Files: