Monthly Archives: June 2014

Student Created 3-Act Math

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When will the world population reach 8 billion?

I integrated a bunch of 3-Act math tasks into my Algebra classes this year, and I love the spirit in which these can be presented.  3-Acts give math teachers the language of drama and storytelling, language often reserved for writing or drama class, revealing information bit by bit to students, and keeping them hungry for more through a regular dramatic format.  In my experience, this has been motivating for students, and this motivation has led to leverage for convincing students to care about mathematical rigor.  Thank you to everyone who creates and shares the work to make this possible, including 3-Acts, for the benefit of myself and my students.  MTBoS rocks, and it’s a verdant time to be a math teacher.

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How do slow and fast speeds compare in “Piano Tiles”?

For one of our final projects this year in my Algebra classes, I asked students to design their own 3-Act tasks.  Even though they had seen a number of these, and were familiar with this format, there was mixed reaction to this assignment from students (…and mixed results).  Some created really great work, but some still resent the idea that they are expected to be creative in math class.  Lots of students have a pretty narrow definition of math, and it’s really hard for many of them to shift in attitude – in spite of  my persistence this year in presenting tasks that required critical and creative thinking.  Lots of them have long since defined themselves as a certain kind of math student and have become accustomed to being taught procedures, and repeating them back on demand.  Just for context, while my school doesn’t totally track classes, in general the highest achievers are not in my sections, and I work with many concrete thinkers.

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What are Leroy’s chances of survival?

3-Acts are hard.  They are demanding on students, and they require rigor and precision, synthesis and critical thinking.  And this is a tough job for the teacher as well.  We need to craft the lesson in such a way that students actually feel a need for the math skills we want them to practice, and then make the right tools available and accessible at the right moment. I think that overall, I did have some success in shifting student attitudes in general towards math this year, and I think we created some good work together.  I think that just like me, students would get better at creative thinking in math with practice.  It would be good to try this assignment mid year, and then again at the end of the year.  During our share, they definitely enjoyed viewing and solving each others’ 3-Acts (some in spite of themselves).  And there is value in the final math class experience of the school year being so positive. Their 3-Act subjects ranged from estimation to frisbee to World of Warcraft.  Check out a few of their projects HERE or at the top of the page, and let me know what you think.

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How many mattresses?

BTW, I asked the following question on my end of year student survey: “What project/lesson/assessment have you learned the most from this year? Why?”  48/62 student responses included positive references to the 3-Act problems.  Here are a few excerpts:

  • “3 part problems- more realistic then normal word problems- feels like the math I know will be useful…”
  • “The 3 act problems. We did a lot of them and each time I could learn more of it. Culminating with creating one myself really helped to practice it even more.”
  • “3 act work because we never know what it’s going to be when you walk in class,”
  • “…you found something I was Passionate about and taught me how to make it in to a fun learning Experience.”

An aside: I’m heading out for an adventure, and will be teaching at an International School in Cyprus next year!  Even though I am excited about my new position, I am super sad about leaving my AWESOME school in Portland Maine: Casco Bay High School.  My colleagues were inspirational, demanding.  My math colleagues, and the junior team (BTW, check out the amazing 2014 Junior Documentary Work HERE) are world class educators, every one of them.  Derek Pierce, the school principal is a truly exceptional leader; supportive, inspiring, and kind.  I have been incredibly lucky to work for and with him.  Derek and my colleagues at CBHS encouraged me to take risks, and to push myself as an educator and a person, and helped me to encourage students to take risks.  Without their support, this kind of work would not be possible.  Thank you to everyone at CBHS! CBHS Staff Further Reading: I’m pretty sure that the 3-Act rubric I found HERE came from a Math Forum problem solving session.  I wonder how their students did?

Who Are You Calling Math Face? (How DO you turn that frown upside down?)

Awesome idea + powerful and GREAT tool + Sweet math wall = this year’s math faces.


Thank you Fawn, thank you Desmos, and thanks students for your cool ideas.

My students created their own “math faces” through graphing with linear equations, quadratics, conics, and a few trig functions.  They used (an online graphing calculator) to explore different facial expressions, and were asked to articulate the equations behind each feature of their graphs.  They practiced transforming linear and parabolic equations, and learned about restricting domain and range.  Students’ manipulations made subtle differences in their facial features as they figured out how to move eyes up, down or around a line of symmetry, or how to change amplitude or period of a sine function to make a thicker mustache.  I’ve done this project a couple of times now, and I am surprised each time how motivating creating a face can be for some students.

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Desmos has created this beautiful classroom interface, which allows the teacher to see all of the student work at once, or filter students by things like who’s used an inequality or which students have restricted the domain or range.  This gives me an instant formative assessment where at a glance, I can easily target my advice or questions for students.    But even more importantly, students can see each others’ work, and share ideas in real time.  We spent about one hour as a full class on this, and then students were asked to complete a math face of their own over the next week.   I did this project early this past Spring with both Algebra 1 and Algebra 2 students.

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I could see some students struggling with the transformations, but caring enough to work through the struggle.

Screen Shot 2014-03-26 at 9.39.59 AMI am very grateful to have discovered this task.  In my experience as an art teacher, differentiation is often natural and practically effortless.  A student can attempt to draw a portrait whether it is their first try or if they have been practicing for years.  There are different conversations I can have with students depending on his or her experience, but every one of them can approach the task  – and right from the start is set up for success.  Math teachers don’t often have this built in differentiation.  So often, our lessons are targeted to a highly specific set of procedures, for which students must be in exactly the right place in the Algebra sequence.  The low entry, high ceiling aspect of drawing with graphs makes it something we can return to with students again and again.