How to Write a Circuit

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You’ve seen how much fun math can be for your students in the circuit format.  I mean, as math teachers we already know how much fun math is on its own is and part of that comes from pushing through the struggle and finally getting the answer.  The circuit format creates that “I’m having fun but I’m also struggling” experience for your students.  The circuit format enables your students to engage with mathematics and talk about mathematics.  The circuit format turns your students into teachers.  So you want to write a mathematical circuit for your students.  There are a couple of things you must consider…

Is the topic / skill one that is well-suited to the circuit format?

Let’s say your students need to practice with multiple representations such as a table, graph, equation and story.  Then a circuit is not a good format for this.  A cooperative pairs matching activity would be better.  Perhaps students need to practice solving equations, or taking the derivative using the chain rule, then yes!  The circuit format is perfect for this.  Circuits are good for when students need to practice procedural fluency.  I recently wrote a circuit for AP Statistics.  Many topics in statistics are NOT well-suited for the circuit format, but, probability is.  So I wrote a circuit.  I can’t wait to watch my students work it.

Have you done all the problems?

In other words, you plan to write a circuit with 20+/- problems that you create.  But have you done 300+ of these problems written by other people?  If the answer is no, you’re not ready to write.  You might not even be ready to teach.  Go back and practice more.

Have you watched students struggle to learn this topic / skill?

If the answer is yes, particularly if it is over many years, then you are ready to write.  If the answer is no, then you might write a circuit that will keep your students busy, but you might not include problems that will give them those ah-ha moments or snag them in a common error or misconception.  Your circuit might (if you haven’t taught the topic / skill for a while) not have enough “easy” problems to get them going, or enough “hard” problems to challenge those who think they know everything.  It’s also ideal if you understand where this topic came from (prior courses) and where it is heading (future courses).  If you don’t know this, you can ask other teachers in your department or district.  I really enjoyed watching my own children come through the math K – 7.  Now I know that they learned first quadrant graphing in fourth grade and how to find horizontal and vertical distances on the full coordinate plane in 6th grade.  Yes they did.

Is your choice of topic / skill one where students could work backwards from their answers?

Factoring is a perfect example of this.  If you want your students to practice factoring polynomials, don’t have them search for the complete factorization or all they have to do is multiply all the answers (an easier skill) and then work backwards to match.  Have them search for ONE of their factors — I have written so many factoring circuits so don’t bother.  Just use mine.  But there are lots of topics / skills that fall into this category.  Make sure to think deeply about what you want your students to practice and make sure you are designing the circuit to force their hand on that topic / skill.

Does your choice of topic / skill have many similar answers?

All of the answers on circuit must be unique so that there is only one way to travel the path otherwise the circuit might close too soon (unless that is your intention which is why Mark Kiraly writes möbius circuits).  If you are asking students to evaluate limits (calculus), a lot of these answers end up as 0 or 1 or DNE.  You’ll have to dream up a way to work around this.  Or, if you are writing probability problems, a lot of the answers could be matched by just seeing the denominator.  In this case, I would write all of my answers to be decimals.  So, you have to be clever in the way that you write problems and present the answers.  If you have never worked a circuit and have gotten this far in this blog post, now is the time.

Think about the progression of problems.

I like to write in sets that are multiple of 4.  16, 20, 24, … you get the idea.  The reason I do this is I like to have my students “level up” about every four problems.  This keeps them on their toes.  In addition, before you begin writing, think about what your target problems are.  What should a student scoring proficient on a state test or passing an AP exam be able to do?  These target problems should not come at the end of the circuit where students can just work backwards from their answers.  Harder problems where your advanced students should get challenged should come at the end of the circuit because (shocker) some students will never finish the circuit.  They work on it in class and then they will go to another class and then to another class and then they will go home and play video games or take care of their little siblings or head off to work or make TikToks or whatever.  They don’t finish their assignments for whatever reason.  So you need to make sure your circuit has the target problems about 2/3 of the way into it.  That way everyone gets to the target problems.

Put Pencil to Paper.

When I get an idea for a circuit, or when someone makes a request, I write a crude outline of the types of problems I want to make sure to include.  There is no faster way to kill they joy of math for your students then to have them do “find the slope” problems by giving them 20 pairs of points.  BORING!  Have them find the slope from two points, yes… but not 20 times.  Maybe 3-4 times and not in a row.  Have them also find slope from a graph, a table, a story, a verbal description… What is the slope of a horizontal line? or What is the slope of a line with an x-intercept of 3 and a y-intercept of 2?  Again, don’t bother writing this circuit.  I already did.  Use mine.  LOL.  But seriously.  In terms of writing, start with an outline.  Know what you want to include.  Know what your target problems are.  Try to make the answers as similar as possible with no duplicate answers.  Lay out the circuit so that the problems build in difficulty.

Type it up!

When I type up my circuits I just open up a big table with the same number of cells as problems and scatter the problems around.  I type it in the same order the students will work it.  Then I hopefully remember to type the last answer back in the first cell.  But, if I don’t, my fellow circuit afficanados will let me know that I forgot — because here is the most important part…

Send it off to be checked!

The ultimate PLC (Professional Learning Community) is the one you create yourself.  Hopefully you have colleagues near and far that you can send your work to.  This is what people who write knitting patterns do.  This is what test kitchens are for.  Someone wrote the pattern, the recipe.  But can anyone follow it?  Does it work?  Your trusted colleagues will let you know what mistakes they find, how your wording should be fixed, etc.  Make edits before you give it to your students.

And that’s it!

But it’s not.  It takes a lot of prior planning and expertise to write something that is fit for public consumption.  Many people have asked me how to write a circuit.  So now you know.  A good first idea for a circuit is to take something you have already written (a test review for example) and get it into the circuit format.  I hope I have inspired you to try your hand at writing and if you are proud of you results, share them with me!