We love a good card sort around here and what better reason to create one than to review the various function types and features students encounter in AP Precalculus? But what if one set of cards could serve just not as one activity, but five? All that printing and cutting will have been worth it! Enter our new MEGA card set: 24 x 4=96 cards that can be used for a plethora of review activities!
Here’s what’s on the cards:
24 graphs of polynomial, rational, exponential, or logarithmic functions
24 function equations to match the graphs
24 verbal descriptions describing the rate of change of the function and other key features
24 limit statements describing each function, including end behavior, holes, and vertical asymptotes
1 Card Set, 5 Review Activities
Here are at least five ways you can use these cards, but the world is your oyster. If you find new uses for these cards, let us know!
Classic Card Sort: an oldie, but a goldie! Give each group a set of cards and have them work as a team to match each graph with its equation, limit statements, and verbal description. The cards are intentionally similar, so get ready to hear some lively debates as students attend to precision. They can record their answers in a sheet like this one. You can differentiate this activity by removing certain categories. To make the activity easier, remove the equation cards. To make the activity more challenging, remove the graph cards. To check your work, here's our answer key.
Equivalent Equations: Use only the equation cards for this activity. Essentially, students should come up with an equivalent equation to represent the function. You can facilitate this in many different ways. One option is to have students work in pairs. For each equation, partner A writes an equivalent equation, partner B determines if the equation partner A wrote is in fact equivalent and proves why. They then switch roles for the next equation card. You can also post each equation around the room with a piece of paper or whiteboard near it. Students travel around the room trying to add an equivalent equation to as many of the equations they can. You can have them verify other equations on the paper to see if they are correct and put a mark next to ones they think might be incorrect. The functions were chosen intentionally to be able to produce multiple equivalent forms. If you find students focusing only on “surface” equivalencies (distributing terms, for example), up the ante by asking for specific criteria (e.g. “Can you write an equivalent equation using a different base?” or “Can you write an equivalent equation that doesn’t include a horizontal translation?”)
Draw a Function That…: Use only the limit statement cards for this activity. Have students sketch a function that matches the limit descriptions. Students should check each others’ work to make sure the graph meets all the conditions. This can be done in a single group of students or with a gallery walk where students look at the graphs produced by other groups (attach the limit statement card to the graph and give students sticky notes to leave feedback). Note: students will likely not produce the same graphs as given in the graph cards of the card set. An interesting extension question is “How many graphs are possible that satisfy these limit statements?”
Which Type Are You?: This is a great one whether you have 5 extra minutes or 20! Use only the limit statement and verbal description cards for this one. Students must identify the function type by the verbal description or by the limit statements. The options are quadratic, cubic, rational, exponential, or logarithmic. For the whole-class version, we recommend projecting the card on the screen so the whole class is viewing the same card. You can have students make cards with the 5 function types on them to hold up or write their answer on a mini-whiteboard and hold it up. You can also just have them say the function type out loud. This can also be facilitated as a quiz, quiz trade activity. Have each student start with one card, then write the function type on the back on a sticky note. To play Quiz, Quiz, Trade students will stand up and walk around the room, finding their first partner. Partner A will show the card to their partner (Partner B) and Partner B identifies the function type. Partner A checks their partner’s solution against the one on the sticky-note. If the answers agree, Partner A now identifies the function type for the limit statement or verbal description on Partner B’s card. If the answers do not agree, the partner should indicate that the answer is incorrect and let them try again. Once both partners have identified the function type that describes their partner’s card, they trade cards and then find a new partner, starting the routine again.
Match Mine: Use only the graph cards and the equation cards for this one. Remove half the cards in each set, making sure that each function type is still represented (we recommend keeping A, B, F, H, J, L, O, P, Q, S, T, and X and their corresponding equations 6, 23, 21, 14, 5, 8, 11, 1, 19, 24, 13, and 15 for moderate challenge). This activity should be done in pairs. Have Partner A place their equation cards in a 3x4 configuration in any order that they want so that the other partner does not see it. We have students face each other and put up folders between their desks (think battleship). Partner B's job is to ask questions that will allow them to match the configuration of their partner on their own desk, but with the matching graphs! Partner A can only respond with 'Yes', 'No' or a numerical value. Remind students that a match will not be identical cards but cards that represent the same function, just represented differently. When a student thinks they have matched their partner's configuration, check their work. If some are in the wrong position, tell them to keep working on it. To vary the activity, you can have Partner A set a pattern with the graph cards and Partner B tries to match their equation cards with Partner A’s configuration. This is slightly harder than the original.
We hope you see that these cards are extremely flexible and can be used in dozens of ways. So what are you waiting for? Time to head to the paper cutter!