#MTBoS 1 – John is a Parallelogram

It’s no wonder I’m known by my students as the ADHD teacher. So, I never finished blogging for the very good MIT course Learning Creative Learning. And I will now attempt to repurpose this blog for the #MTBoS Project and do my very best to keep at it and not become distracted by watching John Green YouTube videos or something…

As a brief introduction, I teach in The Netherlands, both within a Dutch context and within the International Baccalaureate. I really love teaching within the IB (Middle Years Program), which is wildly different from a standard American curriculum (which I was raised with and cut my teacher teeth on). Within the IB the students are expected to write math essays, do investigations, work on projects, etc. It is not a test-driven culture, which coming from NY is a huge relief. It also allows you do to more exciting things.

My “Rich Task”

A project I’m always really excited about I’ll call “John is a Parallelogram.” At this point in the term, students have learned:

  • How to find the distance between two points
  • How to find the midpoint of two points
  • Calculating gradient
  • Gradient of parallel and perpendicular lines

I then set them in groups of 3-4 to work on a “Formative Assessment” (thus not for a grade). They make their way through various application problems, armed with only the following guidelines:


Here is a sample of one such problem (the easiest):

J (6, 8)       O (14, 6)         H (-1, -3)          N(-9, -1)

What kind of quadrilateral is John? What kind of quadrilaterals isn’t he? PROVE IT!


There is a catch, though. Students have only 12 minutes to work on the project in their group. When the buzzer sounds, the entire group switches to a new table and must pick up where the last group left off. This means that students must clearly communicate their work, be neat, organized and logical in their steps. Some groups do this very well, even including little notes to the next group like “Your next step is to talk about diagonals” or “Find gradient to prove sides are parallel.” Other groups leave extremely cryptic work, meaning that the next team has to start from scratch.

Here are some of the finished products.





Students then were asked to do brief reflections on their experiences via a Google Docs survey. One student said:

The good things were that you could take off where other people where stuck and so in the end you can get an answer and it’s easier to get. Also the fact that we were timed made sure that we had to work quickly and efficiently but still put good answers otherwise you’re letting the others down and just make it harder for everyone. The bad thing was that if indeed someone did bad calculations you had to first correct whatever was wrong and therefore you lost time. But otherwise it was mostly helpful to change station every time and work in a group. I tried to help with whatever I could think of so that we left something helpful for the following group.

Another said:

We knew everything that we needed to know for this exercise, so I didn’t learn anything new, I just got to practice it in a funner way that normal. This is a good way to do so because you get to discuss with your peers and you also learn to be open minded to other ideas that you might think are stupid in the first place.

Last one, I promise:

I thought this approach was very useful as I had to use my brain and see which formulae I had to use. I always had to think and recognize the problem given.

I think this is so often the problem with math textbooks. It’s always like, learn a skill, and now practice 40 problems just like it. So there’s actually no deep thought occurring because the students already recognize that they have to find the distance between the two points, for example. But then when we ask them to synthesize the material in an unfamiliar circumstance, they can’t do it and we wonder why.

I’ll be doing this project again in about a month. I think this year I’ll follow it up with a much smaller problem that each student needs to work on on their own to make sure that every team member understood what they were doing (something simpler like showing a triangle is isosceles). Any other feedback as to how I can make it better?

Edit to clarify: This task is done with MYP 4 Extended Math, which is the equivalent year group as 9th Grade in USA and 3e klas in The Netherlands. The curriculum covers all branches of math, but this particular unit is on Coordinate Geometry.


About katenerdypoo

Middle Years and Upper Grades math teacher in the Netherlands teaching both within the Dutch national curriculum and the IB MYP and DP.
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5 Responses to #MTBoS 1 – John is a Parallelogram

  1. absolutepi says:

    Hi Kate – I love the format of this lesson! I also like that you followed up the project with a Google survey, what great insight your students provided you. Thank you for your post!

    • katelps says:

      google forms are fantastic; kids can answer them on their phones right after the lesson (but some phones have trouble submitting answers, so you might have to trouble shoot a bit).

  2. LeeAnn Allen says:

    Hi Kate,
    I loved the idea of rotating through where other students left off. What a engaging way to get students to think critically about work presented. How did you find students’ willingness to work in groups? Sometimes my students like it, sometimes they hate it. This activity seems like a great one though- definitely will be stealing it for other topics!!

    • katelps says:

      Hi LeeAnn,

      I think that most students really appreciate working in the groups because although it’s an “extended level” class, it’s a very mixed bag ability-wise. I don’t let them pick their groups for this, since they need to work on communicating with people other than the people they always confer with.

      But there it does happen that someone brings absolutely nothing to the table, whether because they’re too weak mathematically or because they’re totally asocial. When I do the Google Forms followup, I ask them to discuss their own contribution to the group and how the group functioned overall. In the Middle Years Program, this is part of their Approaches to Learning skills – collaboration – so they have to reflect on it. It’s hard – some kids really don’t go for the group work, but I sell it as they’re working on their math communication, without which knowledge is useless.

      Glad you enjoyed! 🙂

  3. Cleargrace says:

    I like this approach, and the other you mentioned, about individual work. The student comments, where they “debrief” appear to be what really adds value- and with that second comment you posted, I can see the formative assessment side. That student is ready to move on!

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