Desmosification: Building Custom Parabolas

After an emoji was named 2015 Oxford Dictionary word of the year, I am holding out hope for next years’ candidate:

des-mo-si-fy
/dez-MOH-suh-fahy/
verb
1.   to transform the condition, nature, or character of a classroom activity using Desmos.

Starting with a Dan Meyer post, the art of infusing dynamic software into student activities changes the ways that students encounter abstract, functional relationships in mathematics. Desmos’ activity builder gives teachers an extremely user friendly platform to create tasks that move students through semi-structured lines of inquiry. 

I decided to start with a task that I already liked.

Before:

I like to spend a few days at the beginning of a unit on vertex-graphing form of a quadratic function to focus on the roles of “a”, “p” & “q”. We do not run any calculations during this time; we do not input or output anything. We simply play with the parameters and decide their effects on the parabola’s attributes. 

I encourage discussion about how we can predict what the parabola will do without any technology. We have “sketch-offs” where they have 10 seconds to draw an extremely rough sketch of the parabola and then discuss in partners their thoughts and possible revisions. (Currently begging Desmos people to make a “sketch” screen option in Activity Builder) 

[Update October, 2018: Dreams do come true! “Sketch” has been a feature for a while now. The activity has been updated to include this functionality]

This particular activity is not timed. It gives 10 separate sets of requirements, and asks students to build an equation that satisfies them all. I structured it around the ideas of what MUST be true about “a”, “p” & “q”, what MIGHT be true, and what CANNOT be true. Again, I love this activity. I essentially give it to them on day three, and it requires a full hour of profitable talk. The original handout is posted here for download and possible revision. 

Transformation:

In the initial activity, students would sketch parabolas before making their final decisions. I noticed that they were mainly accurate for their purposes, but some were lost because they were forced to make both decisions: how to change the parameter (i.e. make “p” larger positive) and the effect on the parabola (i.e. shift to the right). The result was some were not pairing the parameter change and geometric results correctly.

I created two screens for each challenge. The first gave the challenge criteria and a vertex-graphing form mother function. Here, the student played around with the sliders until the criteria were met. The next screen is a question screen where they type what MUST be true for the criteria to be met. (I omitted the MIGHT and CANNOT for sake of brevity, but plan on having these conversations in the moment). Each question screen also includes a screenshot of a possible solution. Odds are they have landed on a different parabola, and providing an example is designed to encourage comparison and contrast (again, around themes of MUST and MIGHT). I also omitted the last challenge and added a simpler one as Challenge #1. 

Click to test my new Desmos activity. 

After:

All my favourite attributes of the activity remain intact, but the dynamics of the exploration are much improved. Students now have a visual aid to show why a particular parameter MUST be true, or provide a counter example as to why it only MIGHT be true.

Some clear benefits:

• it provided me the opportunity to reflect on why I loved this activity in the first place.
• it increased my fluency with this professional tool. 
• it created a resource I can easily share.
• it gives the students immediate feedback regarding how their decisions affect the mathematics of the situation.
• it adds to the accuracy of the geometric representations.