Last week, we learned that our good friends Dan Meyer and Christopher Danielson collaborated with Desmos to create Function Carnival, an online math tool to address the misconceptions students may have about graphs.

As Dan and Christopher explain on Desmos’ blog:

It’s often challenging for students to distinguish between (1) values, (2) the rate of change of those values, and (3) the rate of change of the rate of change.

Students also tend to have the idea that graphs are pictures—that the graph always describes the position of an object in space.

Their solution was to create this online tool, where students can watch a little animation, draw a graph of what they see, observe the animation again next to their graph to determine if they were right, and then revise and re-draw the graph so that it fits the image. They not only know if they had a right or wrong answer, they see it! Dan actually calls this process “echoing“. So simple and brilliant!

The student can graph the motion on three rides:

The Cannon Man‘s graph is piecewise quadratic and linear.

The Bumper Car‘s graph is piecewise linear, which has thrown a bunch of students.

The Ferris Wheel‘s graph is sinusoidal.

Furthermore, the students can make arguments on incorrect graphs, which help them have a stronger understanding of the concept by putting it into words.

Function Carnival also include filters for common misconceptions. With this tool, teachers can quickly see which students evoke those misconceptions about function graphs. A good way to start the conversation! Give it a try!

## Buzzmath likes graphing too!

More advanced students can draw graphs too in the Buzzmath activity Graphing Linear Equations.

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