Exploring Open Middle Math

 

I have always loved books and loved to read.  As a kid, I loved spending time in our town library and as an adult, used book stores are some of my favorite places.  In my home office, I have multiple bookcases of math / math-ed books and even have a healthy dose of "to-be-read" books on my Kindle regarding math (but that's another post for another day....)

Over the summer, one of the books I picked up was Open Middle Math by Robert Kaplinsky.  I was already familiar with the idea of Open Middle and had used some of the problems from the website in my classroom in the past, but I was interested in learning more about how they could be used.  Here's a quote from early on in the book:

To be sure, using Open Middle problems does not eliminate student misconceptions entirely. However, since using them, I now see student misconceptions more clearly and can use them as talking points to strengthen mathematical understandings during the lesson instead of simply lamenting missed opportunities afterward.

I should say that prior to reading the book, I had watched the webinar and had looked at the DOK Matrix for Open Middle Problems, so I was very familiar with the idea, but I thought of Open Middle problems more as a warmup or a formative assessment piece rather than to explore misconceptions.  I was intrigued by this concept and decided I wanted to try more of these in my classroom....

Again, early in the book, Mr. Kaplinsky has this suggestion to introduce the process of Open Middle:

Using the digits 1 to 9 at most one time each, place a digit in each box to create a sum that is as close to 1,000 as possible. What’s great about this problem is that very few children or adults get it right the first time, yet very few give up either because it doesn’t feel unreasonable.

Okay - I can do that!  I made a quick template for Sum of 1000, printed off one per table, put them into dry erase sleeves with a small envelope of numbers and set it aside to use as one of my first days of school non-curricular tasks. 

But, as often happens, life got in the way and this task didn't get used until a few weeks later when I was doing another activity and needed something for the groups that finished first.  This task was a great one for that purpose as it was challenging, yet do-able, but it didn't quite meet the goal of introducing all students to the idea of an Open Middle Problem.  

Still, I really liked this idea.  I dug through the website, looking for all of the Geometry problems that I thought would apply to my classes and made 8.5x11 sized printouts for each of them.  

A few weeks later, we were looking at the midpoint of a line segment, so I decided to give my students this problem to see how they would tackle it.  This group started with the points that gave a negative slope, then drew in the horizontal and vertical lines to show those values could NOT be used for the positive slope points.  As was noted above, one misconception that I noticed while my students were working was the tendency to want to make all of the line segments have a slope of 1 or -1.

In the book, Mr. Kaplinsky really ties in a lot with the idea of the 5 practices, including the element of how to have students share their work with others.  To be honest, I haven't made it to that point yet and I need to re-read the book on a better way to do that, but right now, I'm just trying to figure out how to make them better fit into my classroom.

Our last chapter before Winter Break was an Intro to Triangles, so I think this Pythagorean Task might be one that I try next week before we continue into our next unit on Congruent Triangles.  As recommended by the book, I need to sit down and try it myself first so I can anticipate issues!

I really like the idea of using Open Middle tasks more, but honestly, I run into the problem of want.to.try.all.the.things. I hear of these wonderful and great ideas and I want to try them, but there's just not enough time in the day / school year to do all that I want to do! 

But I really do see the value in Open Middle, so here are other tasks I am looking at for next week....  Now to sit down, give it a shot and see which one I really want to do!
- Area of a Triangle (Coordinate Plane)

- Creating a Right Triangle (Coordinates)
- Creating a Right Triangle (Equations)
- Creating a Right Triangle (One Coordinate Given)
- Triangle Sum Theorem 

If you have experience using Open Middle Tasks in Geometry (or Statistics) or want to collaborate, please let me know!