Friday, March 20, 2009

Differentiation Card Game

Differentiation Card Game

In secondary school calculus, one must be proficient in differentiating algebraic expressions. One way for students to practise the power rule and get them to learn from one another is to use a card game. I have tried this last year with my sec 4 students.

Basically, the differentiation card game consists of a stack of cards and a group of players. I recommend about 50 cards and about 4 players so that each player can have 10 or more cards. It would also be good to form the group of mixed ability so that each group has at least someone who has understood the concept of power rule.

Each card consists of an algebraic expression. For instance, I have (painstakingly) printed cards with polynomial expressions such as 1, x, x^2 and so on. besides these, we can have more complicated cards such as x^2-x+1, 1/x, sqrt(x) and so on. The objective of the game is for players to take turns to throw out one card at a time, in the order of derivative. For example, Suppose player A throws x^2-x. The next player B, will have to throw 2x-1. If player B does not have this card, he/she misses his/her turn and this will continue until someone has this card. The deck can be designed such that each set of derivatives is unique except possibly having more than one "0". The player who disposes all of his/her cards correctly wins. Once "0" is reached or once no one has a card to throw, the last player who threw his/her card will have control over the game. He/she can throw what ever card he/she prefers. Hence there is obvious strategy in the game.

At the end of the game, it would be good for the teacher to do some consolidation. What do you notice about the derivative as we progress? Students will notice that polynomial expressions will eventually have derivative 0, while rational functions such as 1/x will continue indefinitely. Such thinking and reflection will help students understand power rule better. Without a firm understanding of this basic rule, students would have problems with the other rules, such as product rule and quotient rule.

Moreover, one can extend this game by including exponential and logarithmic expressions.

Of course, we will need a few e^x in the deck!