# Interesting Ways for Students to Be Right & Wrong #MTBoSBlaugust Post 11

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I have looked literally ALL summer for notes I took from Eli Luberoff’s NCSM Session on March 30. I have thought about it numerous times and because I took notes on loose leaf as opposed to in a notebook, the loose leaf ended up in a stack of unrelated papers for some reason. I usually try to start a notebook for my summer learning and into the next school year. I had not started one yet – I mean, we would be back in school right after spring break, right?

I wanted to find those notes though – because all that he said really resonated with me. As we did the task that day and he shared – I truly realized the benefit of how they plan the Desmos tasks. I knew this was a structure I wanted to follow to benefit my students. The task was Turtle Races (title is actually Eli NCSM20, Code: F2TX97 – if its still open).

Benefit #1

After watching the Turtle Race clip, we were asked to tell a story. By lowering the entry point, it will let more students ENTER the door. Start with tell a story – this allows underrepresented students to join-in.

Next we were asked to create our own Turtle Race by sketching graphs for up to four turtles, using a different color for each turtle on the graph.

Then we could click play and the clip modeled our graphs on the race track.

Benefit #2

Have students to create their own by changing the shapes/slopes, shifting shapes with transformation, etc. So often math is about getting information created by someone else – but we all know when the actual work is student created in classtime, it becomes more meaningful students become the thinkers and creators, not just consumers of mathematics. Yes!!!

We spent some time dragging points and creating shapes, then observed and described the shape shifters and how they affected our shapes. All of the students had their own shapes, but the transformations were the same.

He shared a cool math picture and then a Paiget quote – but I did not get either saved/written down. But went on to say Mathematics is diverse. Mathematicians are diverse. Math is still alive.

Our final task began with students dragging points to create a parabola that would pass through the red gate. Our first challenge was to create an equation that make a parabola that would pass through a different set of gates. Then press TRY IT. What I have loved about watching students in Desmos through the years – they are okay with getting a wrong answer – when they know they can try again. And most of the time, they do not give up. Or when they get stuck, they have a conversation with someone… perseverance and communication.

Benefit #3

These types of problems, like Parabola Slalom have built in differentiation.

Students get to “try it” without penalty. You can change the challenges to have them use 1) more points, 2) try equations, 3) try with more gates. Looking at several student examples:

• y = -x2+3
• y = -5x2+3
• y = -.25x2+3
• y = -.2x2+3
• y = -0.02x2+1
• y = -(x+4)(x-4) – 10.5
• y=-(x2-16)-10.5
• y = -.4(x-1)2+5

What do we notice? What do we wonder?

The final tasks was asking people to build their own challenges. Again, the built in differentiation continues. John Merrow- typically, students work on different tasks, but at what cost? This types of task allows students to join at their comfort level – “the same task, but at different depths.” I love this idea.

Again, Eli sharing that day was a big a-ha for me. Things I’ve done on occasion, not necessarily together with intention – that can truly benefit all learners.