I’m teaching a Math 4 class that is almost entirely collaborative tasks. Common Core has less guidance for an integrated fourth course, so I’m feeling free to teach whatever strikes my interest. Honestly, at times this is overwhelming – there’s a lot of math out there in the world! But I’m pleased with the way things are going. I’m using this as an opportunity to teach visually interesting, complex topics. This week they worked with polar coordinates. I had each group use a computer program to graph 20 functions, then sort them into 4 different groups based on their shapes.

This worked really well as an introduction to the different types of polar functions. They discovered not only their basic shapes, but the general equations that create them.

The next day I had them explain the different shapes and the equations that form them, and we determined what impact each component of the equation has on the shape. I love these things!

**Cardioids:**

**Spirals:**

**Circles:**

**Rose Curves: **

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