Carl Brandt Long

In #MathsToday, I introduced radians by having Ss think of splitting semicircular transom windows. Then measuring radius of circle w/ Twizzler, marking radians along. How many radians fit in circle? How many degrees/rad? Think of splitting half circle. That's the bridge between deg and rad.

In #MathsToday, Precalc Ss (11th grade) revisited Geometry through Law of Cosines. Reframed Tri Congruence Thms so that it's not about comparing corr. sides/angles, but that, i.e., given 3 lengths, there is exactly one triangle possible. Today was abt. connecting the algebra, geom, & trig:

We do Law of Cosines before Law of Sines. SSA triangles create quadratic eqns, which Ss have studied extensively. They KNOW roots are symmetrical across the line x=vertex. How do these elements connect to the Geom of making triangles? When 0 ,1, 2? Why no more? www.geogebra.org/geometry/q4b...

In #MathsToday, Precalc Ss (11th grade) revisited Geometry through Law of Cosines. Reframed Tri Congruence Thms so that it's not about comparing corr. sides/angles, but that, i.e., given 3 lengths, there is exactly one triangle possible. Today was abt. connecting the algebra, geom, & trig:

In #MathsToday, 11th grade pre-calc Ss invented the Law of Cosines (and realized its usefulness). Started w/ right triangle, changed it up. Derivation took a while, but w/ a _little_ guidance, every group found the formula! Tonight, practice. Next class, ambiguous case! #MTBoS #ITeachMath

For #MathsToday, ProbStats Ss had to read Strawberry Jam ch. from The Numbers Game, about how counting in real life is HARD! We went to the library to count red books. Discussed afterwards: -what is "red"? -what makes a book "red"? -how do you sample? -how do you use sample to extrapolate to pop?

Continuing the theme, we watched part of @chadtopaz.bsky.social's @breakingmath.bsky.social interview about balancing granularity & ability to make statistical conclusions & how you necessarily need to put disparate people into the same box sometimes. youtu.be/nyrBAnQFYWg?... #ITeachMath

#MathsToday (2 days late) 1st day of Prob.Stats class. Kids made up a string of 10 fake die rolls. Then rolled die 10 times, wrote down that string. Each S wrote both strings on the board. Class guessed the real string A game: 1 pt for each correct guess, 1 pt for each person fooled by your list.

On day 1, it's a discussion abt how humans are bad at randomness - creating & recognizing. (Though most beat my score) Ss noticed that most of the real die rolls had doubles in a row, and did not include all 6 digits.

Yesterday was our first day of school. In #Alg2 #Algebra2, I put the kids into groups of 3 and asked, if we all shook hands with everyone in the room, how many handshakes would that be? I LOVE this problem, esp. on Day 1. 🧵 #ITeachMath #MathEd

In terms of curriculum design, our dept treats Algebra 2 and Precalculus as sort of a 2-yr course. (In practicality, it's not. Sections shuffle, some Ss move in and out, teachers do not teach both years.) But the ideas thread through the 2 courses. And the handshake problem is one Ss remember.

Yesterday was our first day of school. In #Alg2 #Algebra2, I put the kids into groups of 3 and asked, if we all shook hands with everyone in the room, how many handshakes would that be? I LOVE this problem, esp. on Day 1. 🧵 #ITeachMath #MathEd

Some groups recognized the pattern for increasing population size: 1,3,6,10,... and continued to class size. Some realized (informally) the 1st person shook n-1 hands, the 2nd n-2, etc. down to 1. Others recognized each person shook n-1 hands, and that we'd double-counted each handshake. #MTBoS

Yesterday was our first day of school. In #Alg2 #Algebra2, I put the kids into groups of 3 and asked, if we all shook hands with everyone in the room, how many handshakes would that be? I LOVE this problem, esp. on Day 1. 🧵 #ITeachMath #MathEd

Before the school year starts, I teach rising 7th and 8th graders (not my forte!) for a week. It's part review, part enrichment. Fractions, decimals, negatives, along with general problem-solving and strategy. #ITeachMath #MathEd

In #MathsToday, "Which Deal is Better" sparked discussion about how percentages stack, and whether you can just choose a starting value arbitrarily (Yes!) docs.google.com/presentation... (Sorry - don't remember the source) 3/4

Before the school year starts, I teach rising 7th and 8th graders (not my forte!) for a week. It's part review, part enrichment. Fractions, decimals, negatives, along with general problem-solving and strategy. #ITeachMath #MathEd

Last Day of 7-8 graders! Lots of fun problems in #MathsToday! Cannonballs is one of my favorites. I use it to generate Qs w/ younger students, and to introduce Sigma notation with older. Good @howiehunt.bsky.social-style "how did you count" discussions, too! docs.google.com/presentation... 1/4

Before the school year starts, I teach rising 7th and 8th graders (not my forte!) for a week. It's part review, part enrichment. Fractions, decimals, negatives, along with general problem-solving and strategy. #ITeachMath #MathEd

In #MathsToday, we looked at - the riddle of Fire and Ice. I played till 1:25 and let the Ss loose. Good trial-and-error, figuring out strategy. www.youtube.com/watch?v=jMA7... - the shipwrecked sailor problem (without the monkey) - parsing information, fraction ops. #ITeachMath #MathStratChat

Before the school year starts, I teach rising 7th and 8th graders (not my forte!) for a week. It's part review, part enrichment. Fractions, decimals, negatives, along with general problem-solving and strategy. #ITeachMath #MathEd

Here are the more interesting two problems from #MathsToday. The first allowed for multiple methods, but the key to solving the problem was finding a 'unit' they could scale. The second showed how a systematic approach can be helpful, especially if you couple it with pattern recognition.

I've played this 'game' with my Probability&Statistics students. I was inspired to make it a @desmos.com Notebook. Suggestions apprecaited. #iteachmath #iteachstats #mtbos #mathstoday #mathsky #mathEd www.desmos.com/notebook/qiy...