@futurebird
Physically rotated phone screen so that base of triangle was at x=0 & was 80% certain I was looking at an isosceles if base angles were actually, exactly identical.

Re pendulum & isosceles, maybe being too literal but pendulum angle:
1. Could also represent an equilateral triangle.
2. Decreases to zero over time & is no longer an isosceles.

I just realized that my default cognitive spatial map is x, y & z coordinates. So pendulum model example would not be intuitive heuristic.

@futurebird
Skimming through is showing me that clearly I'm in the minority of your sample, but nonetheless:

The three letter structure is what I grew up with, (but also/and so) was the easiest way to teach one of my kids. Line segments were intuitive to her, meaning the three letter system gave her all the angles on a figure without 'extra' labels. "Just follow the lines".

As a tangent to the thread, kudos once again to the effort you expend on your students.

@jetlagjen

@phpete @jetlagjen

The three letters eg ∠ABC where B is the vertex are also what I learned and I hated the numbers when I first saw them. But, from experience I find they just work better. My little grumble about "but numbers are for measuring" and also "that's not how I learned it" are something I've gotten past.

I go with what helps the most students get it. Hence I don't use greek letters with ninth graders. Learning the new symbols at the same time was too much for some.

@futurebird
I interpreted “pendulum could swing all the way around it would make a circle.” On z-axis, not y-axis

@phpete @jetlagjen

Also different populations of students have different needs. So, maybe I would switch if I thought it would work better with a new group.

I make a big deal about introducing the Greek letters in the spring when we start trig. This gives them time to learn how to write them.

So they do learn them by the end of the year? New symbols are a big deal and deserve space. Don't just spring them on people. I do find the numbers a little "janky" from a pure maths lens.

@futurebird
Solid thinking across the board, it sounds like you're the kind of teacher we'd all like to have.

I'm curious, has your class size ever affected your decision to introduce 'one more thing', (read: Greek letters in this example)

A 15:1 classroom is a different environment than a 30:1.

@jetlagjen

@Bumblefish @3TomatoesShort @EverydayMoggie

OK pizza good to know.

Anyway. Connecting the center of a circle to two points like that is a great way to create an angle. When you copy an angle you are just cutting two pizza slices that are the same.

If the pizzas are the same size, and the distance between the points on the circle is the same. The angle at the top (center) is the same.

@semitones @jetlagjen

Using color to identify angles means you can't use it to show which ones are the same. Which is a great use for color if you don't have color blind students. (I don't at the moment but it's always in the back of my mind. )

@futurebird @3TomatoesShort @EverydayMoggie But why use a compass to do that? Why not a ruler through the middle?

@Bumblefish @3TomatoesShort @EverydayMoggie

Rulers are less precise than a compass. You could use a ruler if you wanted. But it will only be as precise as the markings you have made on the ruler.

@futurebird @3TomatoesShort @EverydayMoggie But why use a compass to do that? Why not a ruler through the middle?

@futurebird @jetlagjen ps this is the system of arcs I was talking about, to identify which angles are the same size. It works pretty well until you have a more complicated shape with many angles. Is there a name for this system?

@futurebird @3TomatoesShort @EverydayMoggie Not measuring anything, just using it to get a straight line. Could use any straight edge.

@Bumblefish @3TomatoesShort @EverydayMoggie

But how would you get the angle at the center exactly the same with just ruler?

@futurebird @3TomatoesShort @EverydayMoggie Wherever the cross happens is the peak of the triangle.

@Bumblefish @3TomatoesShort @EverydayMoggie

The peak is the angle at the center, right? I don't see a "cross"

@futurebird @3TomatoesShort @EverydayMoggie That’s because you haven’t drawn one and for the life of me I don’t know why. You need the cross to cut the pizza.

@Bumblefish @3TomatoesShort @EverydayMoggie

OK great. I still don't see how to cut two slices that are the same size from the identical circles without measuring with the ruler or using the compass again.

@futurebird @3TomatoesShort @EverydayMoggie The opposite one will always be the same size.

@Bumblefish @3TomatoesShort @EverydayMoggie

Absolutely.

But if you want to copy an angle to a new location that won't help.