Connect students directly to the concept in a personal way. Capture students' attention by initiating a group problem-solving activity before delivery of instruction. Begin with a situation that is familiar to students and builds on what they already know. Construct a learning experience that allows diverse and personal student responses. Facilitate the work of cooperative teams of students.
Mini-drama, arithmetic reversals.
Objective: To reduce math anxiety by allowing the students to become aware of their everyday use of inverse functions. To simulate an everyday experience which illustrates the concept of inverse functions. To further illustrate inverse functions by shifting into the language of simple arithmetic.
Activity: Choose three students to participate in a minidrama. One will be the student, one will be the mother of the student, and the third will be the brother of the student. Have them line up in a row, with the mother on one end, the student in the middle, and the brother on the other end. Tell them that the student has no money at present, that the brother owes the student $5, but the student owes the mother $5. This situation is probably familiar to the students. Then have the brother give $5 to the student, making the student $5 richer. Making the student $5 richer is the FUNCTION. Point out to the class that the student now has $5 more than when the drama started. Now have the mother reach over and take the $5 away from the student. The student is back to where s/he started from. Making the student $5 poorer is the INVERSE FUNCTION. Point out that the student started with no money and now has no money again. Therefore, an INVERSE FUNCTION undoes the action of the FUNCTION. This point is the main concept of inverse functions and should be stressed throughout the lesson. Next, have the students sit down and tell the class to close their eyes. Have them choose a number between 1 and 10. Then have them add 54 to that number. Wait, and then have them subtract 54 from their new number. Now have them open their eyes. Tell them that although you cannot guess the exact number they picked, you CAN tell them that it is the same number they started with. They will not be very impressed, so have them close their eyes again, and tell them to start with the same number they had before, and add 120 to it. Wait, then have them subtract 80 from the new number. Tell them that this number is different from their old number. In other words, adding one number, and subtracting a different number are not inverse functions. One more time, have them close their eyes, and start with their old number once again, tell them to multiply it by 4. Wait, and then have them divide their new number by 2. This number will not be the same as the one they started with. Again, multiplication and division are inverse functions only when you multiply and divide by the same constant.
