Tuesday, 20 October 2015

MPM2D - Day 28: DAB Quadratic Transformations Part I

(DAB = Desmos Activity Builder)

About a week and a half ago, I created by first Desmos activity using Activity Builder. You can read more about it here. Today, I actually got to run the activity with my students!

They were investigating horizontal and vertical translations of y = x². It was weird yet informative to spend a fair amount of time sitting looking at my computer screen as they moved through the activity. Here are some of my observations.

  • Having only really worked in depth with linear equations, some students wrote about the slope of the parabola. They didn't have the vocabulary they needed to accurately describe what was happening.
  • The immediate feedback I received was fantastic. For example, all students got the question on screen 8 correct. I now know that I don't need to spend extra time on that concept.
  • The answers on screen 10 were very interesting! Having looked at vertical translations, I asked students to predict what the graph of y = (x + 4)² would look like. Here is a sample of the responses - there is a lot to dig into here:
  • Despite my best efforts, they still don't understand horizontal translations. Some students saw that it is counter-intuitive, and can use that, but even they don't seem to understand why. Screens 12 & 13 made this clear to me.
  • The value of h in (x - h)² also was a source of confusion. No surprise there.
  • However, almost all students got this question correct. Then many got the next one wrong when they were told the transformations and had to write the equation. They are definitely on shaky ground here!
  • My last two screens talked about 'input' and 'output' which also caused confusion. These students have not been introduced to the idea of a function, so I am not surprised that they had no idea what I was talking about. When I explained what I meant, they did a decent job answering the questions. However, not that many students got this far.

I stopped them with 10 minutes to go so that we could do a little consolidation before the end of class using this handout (which also has content for tomorrow's class). 

I am not sure how long I will need to spend working on horizontal translations tomorrow, but that is where we will start. Here is the link to part I of the activity in case you want to check it out. Here is homework set 21.


  1. Thank you for your Quadratic Transformation Desmos activities, they were awesome! It's also inspired me to try and create my own Desmos activities...hopefully sometime soon :)

  2. Your work is absolutely tremendous. It is not just pizzazy (sp) but also very well organized. I am starting with your work and thern will try my own. Forty years of teaching and this is the best i have seen yet. When do you sleep????

    1. Thank you for the kind words, Marsha. I'm glad that what I share is useful to you. And trust me, I sleep! No one would want to be around me if I didn't!