Intro to Infinity

My second period class is Integrated Math 1. These students are 9th graders, many of whom have some type of exceptionality, so their prior knowledge is excitingly limited. Last week, we talked about infinity in the context of domain and range.

Teaching an integrated sequence makes it uniquely obvious to me what’s important for the students to know when they leave each class. Learning about domain and range will set them up for other situations of infinity later on, like limits and asymptotes. Some of the most interesting mathematics happens where infinity is involved, and I’m particularly excited to introduce this group of students to these abstract ideas. A distinct advantage to a small school like ours is that chances are it will be me teaching their second and third courses.

Almost to the extent of future infinite math, domain and range is abstract and not intuitive. To ease them into the topic, I had them in pairs, matching graphs to domains and ranges.

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Even though there were only 4 students in the class that day, the pairings were unlikely, because practically any pair of these kids is unlikely. This might have been part of why this activity worked so well. I would definitely use this again.

School Camping Trip

Last week was the high school camping trip, 2 nights of sleeping in a field with almost all of the students. I was in charge of food, so this happened:

Kyle: Rachel, did you use any math as you were cooking this spaghetti?
Me: Ummmm, I don’t think so.
Kyle: You probably did, math is everywhere.

Yes! That is exactly the right attitude! Awesome trip.

Polar Graphing

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:

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Spirals:

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Circles:

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Rose Curves:

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