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?
New unit on exponents, about to be differentiated like whoa.
We started off with a group task (with varying levels of success) about a pyramid scheme. Lots of modeling. Sometimes I wish I’d done more, though frankly the class where I opted to not do modeling got the furthest.
Photo: We made posters. I told them I cared more about their process than their aesthetics. (One kiddo pays the first kiddo on a list $3, then makes 8 of their friends the next kiddo $3. Those 8 kiddos choose 8 friends to pay the next kiddo $3 and so on)
What do you notice? What do you wonder?
We do some more work measuring angles, but this time with protractors. It feels like quite a few kiddos have some traction and understanding here. We do some more individual work with measuring lines and angles, which feels worthwhile.
Fun fact: the Spanish word for “protractor” is “transportador”. Wild.What do you notice? What do you wonder?
Is it clickbait if the content and photos don’t actually match the title?
Back from Professional Development to start talking about angles (so that we can talk about similarity, eventually). We measure with angles and give directions using turns and degrees.
Teaching similarity is still a bit of a mystery to me, but we get some good thinking done about sides and angles and how they change.What do you notice? What do you wonder?
We’re fortunate enough to have a strong mathematics Curriculum and Instruction department in our district. Once a year, we take a day to do some district learning and site-based learning.
Gotta shout out my school here (even though I don’t think they read this – am I subtweeting?) because we were short several subs and lots of (amazing) teachers filled in so that our departments could go and work together. Thank you thank you thank you.
We spent the first part of the day doing math and then thinking about how we could assign competence (recognize smartness) in each other. So many ways to talk about this and think about this. We also got a chance to talk about some best practices in our work at our school, which was cool.
Photo: Poster form teams assigning competence to each other:What do you notice? What do you wonder?
Our similarity unit doesn’t really have a project. We had a picture project where we dilated candy bar wrappers when we taught the course 2 years ago, but it was more a project than mathematics (and they aren’t mutually exclusive, though we didn’t strike that balance here), so we shortened it to one day. Fascinating to watch students take art and grapple with how to make it bigger. Not pictured: Sailor Moon or an elephant.What do you notice? What do you wonder?