Cut ups Activity

Duration: 40 minutes
Subject: most subjects (the example provided is a review of Precalculus functions that I do at the beginning of the Calculus course)
Material: The cut ups should be cut, and ideally laminated.

Cut ups (pdf here) are a hands on way of reviewing material. Students get 9 (or sometimes 16) cards with descriptions on each side. They need to place these cards in a 3x3 (or 4x4) shape, and each pair of touching sides must match.

Here is an example of three cards that match correctly. The graph facing "Inverse of..." is indeed the correct graph. The graph facing "Three real zeros" does indeed have three real zeros.

Notes:
Some students tend to jump on the first matching they find without considering that other cards might also match that particular position.

There are different ways of differentiating the exercise to make it less difficult. For example, the cards can be printed on different colored papers. The three cards from the top row could be of a different color, so that students only work with these first. Or the 4 corners can be of a different color. And so on.

Bingo activity

Duration: 50 minutes
Subject: any subject (the example attached is about Exponential Growth and Decay)

This activity (pdf here) is another way of bringing diversity to drill/textbook exercises. There are many ways of playing bingo in the classroom, but here is how I do it.

(1) Hand out an empty grid to every student.

(2) Project all the answers on the board.

(3) Have students fill up their grid randomly with the answers.

(4) Then project questions one by one. When students solve the questions, they will look at their grid and cross out the box where the answer is. The winner is the first student to get a line, a column, or a diagonal complete. You may want to have a little price for the winner.



Notes:
The setup takes a little long, but it allows students to all have a different grid when the game is played.

As students place the answers in the grid, it is crucial that they are focused and methodical. If not, some students will have an empty box and won't know which answer they missed.

Even though there are 24 squares, you don't need to prepare more than about 12 questions as there will "always" be a student who gets a bingo before that. For each question, I suggest to have the correct answer and a wrong answer. It is an important to add wrong answers that are credible for each question.

Back To Back Activity

Duration: 40 minutes
Subject: any subject (the example provided is Integrals of Polynomials including x^(-1) and Trigonometric functions)
Material: mini-whiteboards, with pens and erasers.

This activity (pdf here) can be used to change from textbook exercises. Students are paired up. They will have to turn their chairs so that they sit back to back (hence the name of the activity). As the teacher projects exercises on a screen, students solve them individually and write their answers on their whiteboard. After a given time, all students need to raise their whiteboards to show their answers.

Each pair will earn a point if and only if BOTH students in a pair have the correct answer. If one of them doesn't have the correct answer, or if neither has the correct answer, the team won't earn any point.

Sudoku activity

Time: 60 minutes
Subject: Any math section (the example provided is about Areas under a graph using geometry)

This activity (pdf here) uses a sudoku as an incentive for students to work on drill exercises. Some of the sudoku grid's numbers are substituted with letters. As students solve exercises, they can place the correct number instead of the letter. When they are done with the exercises, they can focus on solving the sudoku.

For instance, this particular activity is entirely based on the study of the following graph:

And the first two questions are: 

Once you find the value of the integrals, you can place those digits (always a whole number between 1 and 9) in the grid.

Mental Math Activity

Duration: 10 minutes
Subject: anything (the example provided is for Integration or polynomials)

This very short in-class activity (pdf here) is designed to be presented to students at the very beginning of the unit on integration. I simply called it "Mental Math" as students won't be allowed to use any material. You can design "Mental Math" games for almost any section of any class. It needs not be Calculus, or even Math. But it applies mostly when questions are short and easy to solve. It is my experience that the students get so focused on keeping the letters memorized that the class turns completely quiet. Here is how it works:

There are 5 basic polynomial integration questions that the teacher will project on a screen. Each of them is a multiple choice. However, teachers shouldn't show the multiple choice answers immediately, as that would enable students to simply differentiate instead of integrating.

Once students have figured out the answer, the teacher will show the multiple choices. As usual, each answer is associated with a letter, but note how the multiple choice letters aren't necessarily A B C D E but may be P L S T R or anything else. Students have to memorize the letter of the answer for each question.

After they have answered the 5 questions, students will have collected 5 letters along the way. To complete the activity, there is a final general question and the answer is an anagram of the 5 letters. It is best when the final question is also related to the material that is being studied.

Integrals key project

This project (pdf here) is designed to be presented to students at the end of the unit on integrals. It is a long-term project which will enable students to demonstrate what they have learned and apply it. Beyond Calculus, this project will also improve students' sense and understanding of geometry, and their skills with graphing softwares. All together, it requires about 3 lessons (75 minutes each) and additional work at home.

The idea is to design a key that fits given requirements. Then graph each part of the key on a computer software. And finally create the key itself to scale. All requirements about the key are based on an imaginary key lock that the key should fit in. In particular, in terms of Calculus, students will need to decide on the shape of their key and use integrals to find volumes of revolution. After the work is done, students will have to write a reflection about the process of creating the key and show what they have learned.

                                                  (download pdf here)

Study of an "unknown curve"

"A chewing gum is stuck to the wheel of a bicycle. As the bicycle rides, the chewing gum traces a curve in the air..."

This activity (pdf here) combines hands-on work, research of information on the internet, and applications of the rectangular method of approximation of integrals (Riemann Sums). It is a good and fun activity to apply Riemann sums in a meaningful way, and it will greatly interest students who are curious about math.

The "unknown curve" referred to is actually the cycloid. It is assumed that students don't know this curve at the beginning of the lesson, or at least not very well.

Using are assigned the task of drawing a curve on a large sheet of paper that is stuck to the wall, by attaching a felt pen (or whiteboard pen etc.) to the edge of a classroom (circular) trashcan, and roll the trashcan in order to create a curve. (This is actually the geometric definition of the cycloid: the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line).

Several tasks are then explained. Students need to estimate the area under the arch using Riemann sums, as well as the volume of revolution that is formed by rotating the curve about the "x-axis". They will also investigate online to find the name of the curve, historical background and other properties of the curve.

Given that the area under the curve is three times the area of the generating circle, students will also be able to check the accuracy of their Riemann sum for the area. But finding the area under the curve analytically is beyond the curriculum in AP Calculus AB.

                                              (download the pdf here)