Sunday, 31 May 2015

Exploring Graphs through Function Carnival

"So today in Maths class we are going to shoot a man out of a cannon."

The room filled with silence. On the big screen I hit play, a red and yellow cannon explodes and a little man in a green jumpsuit is shot directly up. He reaches his apex, and begins to fall. As a safety conscious cannon man he utilizes a parachute to mange the descent. Every eyeball is fixed on this silly little animation. No context is given and within 10 seconds the animation is complete.

"Who wants to see that again?"

Simultaneously all students hands go up

Instead of me just showing it again I make it available for students to access and control. I direct students to use their laptops to (preferably with Chrome, although other browser are generally okay)
Once most of the students are loading the site, I provide them with my classroom key (4 characters: eqzm). 

I had already registered at and organised the classroom activity to create a key before the students arrived. It literally took 2 minutes from log in, to select this activity.

As students are logging in, I show them how the graphing of the cannon man's trajectory works. They can plot points, moving the slider along the "time" axis to view a shadow of the changing cannon man's height. They then graph lines that join the points. Once students are satisfied with their graph, they press play, and watch the comparison of their graph versus actual movement of cannon man.

The students are shown an example graph with apparent errors and are asked to explain what is incorrect about the displayed graph. The students explain their opinion on the graph. 

The students then work through similar graph and discussion for other carnival rides including distance traveled by a Bumper Car, the Height of a Ferris Wheel carriage, then they can move to investigate speed (rather than height) of the Cannon man and of Roller Coasters.
Meanwhile as the teacher, I am able to monitor student progress. I have a dashboard, showing where students are up to, as well as thumbnail of their graph and length of their description. This allows me to see if students are skipping to graphing activities without completing the discussion section, or vise-versa. Additionally I can quickly see if students are plotting points without graphing the line. 

It may not be immediately obvious which students are struggling, so in each activity there are filters for students with common graphing issues, such as "multiple values", "holes" or generally "needs help".

Before I walk over to talk to a student I can click on them to see what they have entered. Some students are not confident enough to ask for help, and prefer to enter silly comments (some shown below). These students benefit from a few simple questions asked one on one to help them identify what is incorrect on the graph.

Sometimes less apparent are the slight misunderstandings of students, such as why the line can not move backwards? Why are there changes in velocity? How can the same event lead to different graphs (position vs time & speed vs time)?

These ideas are key to the summary of the class. As students completed (at differing times) the students were directed to consider what they had learnt during the class. The brightest often suggest they they already knew everything from the lesson, so we reflected on which graphs they needed to revisit (all had to at least reconsider speed vs time). Could they graph a situation without using the time slider?

To conclude the lesson, I invited students to write send me an email to summarise what they had learnt in the lesson, and for homework they were to find something from their lives to graph. 

The description of what they learnt was fine, discussing nature of graphs and rates of change. This supported what I had hoped (and directed students towards) but what impressed me was the activities they chose to graph. They come back with incredibly creative ideas, such as their trip home from school (with buses, cars, walking and lots of "waiting") others graphed their evening sports practice (movement of soccer balls, speed during running exercise and score in a scratch match) and one even graphed their hunger level over a 24 hour cycle. The inclusion of this skill into everyday life is really an area I want to foster with these students.

But the class wasn't perfect. During the class, I tried to skim read every students' input, and discuss key comments with students however some students comments were missed during the limited class time. Desmos helped me with this by leaving the students' input in the classroom for review later. I reviewed the students comments later in the day and noticed some potential misconceptions. Discussion of comments were then included at the start of the next lesson, and then lead into the linear functions for the next lesson.

All around this was a successful and enjoyable lesson, both for the students and as a teacher. Thank you to for providing the brilliant activity for the maths classroom.

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