Apply derivative rules to polynomials, trigonometric, exponential, and logarithmic functions
I can write and solve equations for derivatives
I can evaluate derivatives at a point
I can apply properties of derivatives of sums and differences
Quick Lesson Plan
Review FRQ (Word | PDF | Answer Key)
Students begin the class period by working on a free response question that incorporates content from Units 1 and 2. In Trashketball, teams solve a series of derivative problems and then attempt shots at paper baskets to earn points.
This FRQ is a great cumulative review of concepts covered in the course so far and gets students used to seeing functions in different representations in a problem stem. Give students 10 minutes to work (the problem is much shorter than a traditional FRQ) and then take 5 minutes to go over answers. Emphasize proper justification in part c) that uses the formal limit definition of continuity.
To set-up the game, you will need to print several copies of the activity page (corresponding to the number of groups you have) and cut up the questions and sort them into piles. Have students in groups of 3-4. Arrange the piles at a central location at the front of the room where you will be sitting such as your desk or a table. You will also need two waste baskets one closer and one further away, and some way to mark where students will stand (we use a yard stick).
Each team will send up one group member and grab a problem from your desk. The order that they take the problems does not matter, and groups do not have to solve them in the same order. The lettering on the questions allows groups to keep track of which ones they already solved. The student will bring the paper back to their group and they will solve it together. When they are done they return the paper to you and you tell them either “Yes” or “No” depending on if they got the problem correct or not. Do not give further clues on where they made a mistake if you gave them a ‘No’, simply send them back to their group to try again. If the student got a ‘Yes’, they get to line up, crumple up their piece of paper and try to make a basket. If they make it into the closer basket they get 3 points for their team. If they make it into the further basket, they get 5 points for their team. If they miss both baskets, they can still get 1 pt for getting the question correct. We have students keep track of points on the front whiteboard. The student then sits down and sends a different group member to grab the next problem. We insist that groups rotate who they send up to pick up the problem and attempt the shot.
At the end of the time period, whichever team has the most points wins.