I’m a bit more into individual practice, these days. A few years ago, I think I was more “all groupwork, all the time”, but I’m appreciating the fact that a decent culture of groupwork at our school helps support our kiddos when they’re working individually while also allowing them to spend time on what they need.
We’re still working through how reference angles are related to tangent ratios (without really calling them that – most kiddos are sticking with opposite and adjacent sides). Also trying to balance procedural work (especially with ratios) and conceptual thinking. Someone made a decision with this curriculum to round some of the tangent ratios to numbers that made it easier to solve for unknown numbers. While this may take away from the actual ratios (which are a calculator button push away, anyway), it did give a lot of kiddos access who weren’t familiar with solving ratios. Lots of struggle today and I’m hoping kiddos got something out of it.What do you notice? What do you wonder?
We’re onto right triangle trigonometry. This year is flying by (and we’re a few days in at this point).
One of the many tricky things about right triangle trigonometry is that ratios are big. For classes where some kiddos don’t really know how to divide (let alone when it’s written as a fraction) while some (one) roll their eyes because the conceptual trigonometry we’re using has an approximation rather than the actual tangent ratio, the need to differentiate is real.
We took a bit of time today to talk about how to solve ratios. How many kiddos did we actually reach? Unclear, but the first step is important.
It’s fascinating for me to see the 4 papers I used (one per period) to show how to solve an with a variable in the denominator. By the end of the day, I’d realized that writing fewer steps cleanly is more important. I’ve also decided on “one finger if you understand, two fingers if you’d like to hear it again” is a nice way to hear what the class is thinking without being too judgemental (I’m so used to thumbs up/thumbs down, but that feels weighted).
We also did a reading guide where the kiddos used calculators to find the tangent ratio. It’s actually something that I remember relatively vividly from student teaching. I’m feeling a deep appreciation for this unit the third time I teach it.
Photo: 4 iterations of solving the same ratio
What do you notice? What do you wonder?