Lately a lot of teachers have asked me if I have a circuit for a particular topic. Sometimes I do, and I point them in that direction. Sometimes I don’t, but if I have the content knowledge and time I will write one for them. [Here are two recent custom circuits: Function Operations & New Operations.] Other times, the topic might be better understood through a matching activity. This is particularly true when our students need more practice toggling between multiple representations such as set builder notation and interval notation.
The first matching activity I ever wrote is Fun with Functions. This activity has 32 cards: 8 graphs, 8 equations, 8 tables, and 8 families (i.e quadratic, linear, etc.). Without the use of technology, students work cooperatively to match each equation with the appropriate graph, table and family. Students record their matches on a separate sheet of paper, which makes it easy for the teacher to grade! You can not believe the conversation that takes place with a well-crafted matching activity. Like the circuits, the cards need to be similar enough so that student can not make one-dimensional matches (this is the only one with a 5, e.g.).
Another thing to be aware of is to make all the variables the same. I had a student teacher many years ago who wrote a cute matching pumpkins activity but most of the variables were different so when the kids were finished in ten minutes, it was clear that they had a good knowledge of kindergarten letter recognition, but didn’t need to know anything about solving inequalities. I learned a lesson too. Now student teachers must give me their plans at least two days in advance. Kelsey Atkinson, a former student teacher who now teaches a few hours south of me wrote a great matching activity for students to make sense of linear functions’ multiple representations. I typed it up and you can download Linear Functions for free.
Just last month I wrote a matching activity for Solving/Graphing Inequality Word Problems (also FREE) which includes absolute value and compound inequalities. This activity really emphasizes making the “best” match out of the available options.
Now, how about that Parabola? Yes, our students need practice recognizing the different forms of a quadratic function: standard form, factored form, vertex form. This Quadratic Functions matching activity gives students great practice toggling between these different forms, and identifying the salient characteristics (vertex, opening up, y-intercept, zeros, etc.). Notice how they are NOT using their calculators!
Speaking of quadratics, this Solving Quadratics matching activity is great for reviewing the different methods for solving a quadratic: factoring, graphing, completing the square, and quadratic formula. I wrote it for my algebra one students but I have used it with precalculus students in the first few days of school as a “what you should know from prior math classes.” I answered only one question per group for my precalculus students — and gave each group a white index card (I think you can see one under the pink calculator in the picture). We called it the “white surrender card” and they saved it until the end, which forced them to do a lot of talking amongst themselves. (It is mind-boggling what they forget over the summer… but that is the subject of another blog post!)
I got the activity “Super Systems” at a regional NCTM conference down in Biloxi over a decade ago (pre-Katrina… maybe 2002?). I have completely lost touch with the teacher who wrote it. I have made some changes to it over the years and I finally got a chance to type it up with full directions and post it. It is always a great cap to the systems of equations unit. Download it for free here.
I use matching activities with my AP Calculus students too, but all of the ones I use I got from other teachers. UPDATE: I wrote a differential equations card sort and solve. Not so much a matching activity, but more of an exercise in classification.
Finally, I got a great idea for a Factoring matching activity a few weeks ago while I was walking my dogs… I wrote it, then typed it, then had several colleagues check it. [The entire process, like writing a tight circuit, takes a few days.] I can not wait to watch my students puzzle through it in late January! Will let you know how it goes! UPDATE: It went great… then I thought about an activity they could do BEFORE they learn to factor… Here is a new matching activity on Equivalent Polynomial Expressions that I wrote in the summer of 2017 and just got to watch my students work this week!
To access all of my matching activities, click here.