Because I had different warm-up routines I wanted to try, I’m this week ending my second go at Counting Circles, and won’t be using them again until next year. But they’ve had a great run! I think the students got a lot out of them, and I experimented with them in lots of different ways, a few of which I captured as pictures, so I wanted to share them below.
Posts tagged ‘counting circles’
At #TMC14, I made the following tweet,
while I was in a session about warm-ups as review. I was reminded of what Jessica posted about her warm-ups, and how she does something different each day of the week.
I was thinking of doing something similar, but I also wanted to include things like Counting Circles. But…I’m having trouble with the disparity. Something like Counting Circles is very different from Estimation180 which is very different from a Throwback Thursday review problem. How can we get used to the norms of a counting circle if we only do it once a week?
I could just commit to one of these things, but I feel they are all important, so I didn’t know what to do. But now I had the thought…what if I did these routines but, instead of once a week, I did them for, saying, a marking period, then switched to another?
This could work because many of the routines match up with certain units – Counting Circles would be very helpful for linear functions, while Visual Patterns would be useful for functions in general (or perhaps for when we do quadratics). Does this sound like a good idea?
So there’s a good chance I’ll be teaching Algebra II next year (will everyone leading a morning session in TMC14 change courses before it arrives?) and so I was thinking about my future routines. My students will be (mostly) students that I taught last year, plus the current freshmen who are advanced in Geometry. Last year and this year I was big on Estimation180 but, because I was so big on it, they’ve seen a lot of it. There’s still plenty they haven’t seen, but I wanted to expand. I remember reading someone who said they used Estimation180 one day, Visual Patterns another, Counting Circles another, and I think there was a fourth but I don’t remember what. I thought it sounded like a good idea.
I was hesitant about counting circles at first because, yeah, my students do need to boost their mathematical fluency, number sense, and mental math, and that is always helpful, but it’s a lot of time to spend on stuff that is technically not part of the curriculum. But then I started to think about all the things we could count that would specifically enhance the Algebra II curriculum, and I got excited.
Things We Can Count
- Monomials (2x, 4x, 6x, 8x…)
- Polynomials (a + 2x, 2a + 4x, 3a + 6x…)
- Fractions of etc)
- Sin/Cos/Tan values of those values above
- Imaginary numbers
- Complex numbers
- Geometric Sequences (1, 2, 4, 8….)
- Geometric Sequences with Negative Ratios (1, -2, 4, -8….)
- Monomials geometrically (x, x^2, x^3, x^4…)
- Irrational numbers (…)
What else could we count?