Derivative Matching Cards

This is a very simple matching activity for Calculus. Students are give a set of cards with either a linear, quadratic or cubic function on them. Their job is to pair them up so that one is a function and the other is its derivative. There are a total of 12 functions with 12 derivatives. The first six are all linear or quadratic graphs and the second six are either quadratic or cubic graphs (if you wanted to give students an easier set you could only give them the first six). This is not meant to be a brain buster of an activity but it does help to solidify thinking in terms of the characteristics of the connections between a function and its derivative.
NEW: Desmos has turned this activity into one of their new CardSort activities. You can get that version here

• MCV4U - A2.2 - generate, through investigation using technology, a table of values showing the instantaneous rate of change of a polynomial function, f(x), for various values of x (e.g., construct a tangent to the function, measure its slope, and create a slider or animation to move the point of tangency), graph the ordered pairs, recognize that the graph represents a function called the derivative, f ’(x) or , and make connections between the graphs of f(x) and f ’(x) or y and dy/dx
• MCV4U - B1.1 - sketch the graph of a derivative function, given the graph of a function that is continuous over an interval, and recognize points of inflection of the given function (i.e., points at which the concavity changes)

• As mentioned above, there are 12 cards and their derivatives but you could break them up into sets of 6 cards and their derivatives where the first set was made of linear and quadratic functions and the second set is made of quadratic and cubic functions (or you could just put them all together). On each page there are six graphs. The first column are the functions and the second column are the matching derivatives.
• Print the sheets out on card stock (and laminate if possible). We tend to print each set out on different colours. This way if they get mixed up all you need to do is collect 24 cards of one colour and you will know you have a full set
• You may also want to print a copy of the teacher answer key which has all 24 graphs on one page so you can easily check student's answers.

• Put students in groups of two or three
• Distribute cards and tell them they have to pair the cards up in terms of a function its derivative. 
• Instruct them that every card is paired up and they will likely be correct if they have no cards left over
• Encourage them to use properties of functions and derivatives (zeros, max/mins etc) to speed up the process 

• Derivative Match Cards (Google Doc, PDF)
• Derivative Match Teacher Key (PDF)
• Desmos CardSort version
• For an online version (Flash based) try out this link from the MAA. Thanks to @EulersNephew for pointing this out

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks