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Carl Brandt Long

@carlblong.bsky.social
317 followers 153 following 251 posts

Math teacher, theatre-maker, husband, father. Pro-democracy. I mostly post #MathEd stuff. Sometimes I make videos on Youtube. www.youtube.com/@carllong1991

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Carl Brandt Long @carlblong.bsky.social · 01/10/2026
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:
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Reposted by Carl Brandt Long
Adrienne Hestenes @ahestenes.bsky.social · 30/09/2026
In #MathsToday my seniors read Francis Su’s speech to Harvey Mudd frosh and then wrote a page reaction. They generally enjoyed the reading and honored me with their personal stories and thoughts about math and caring for others. Here is the article they read.
share.google
Science, in Service of Love
My exhortation to the first-year class at Harvey Mudd College
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Carl Brandt Long @carlblong.bsky.social · 29/09/2026
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
Three triangles with sides 6 and 8.  Included angles are 90, 60, and 120.Two triangles with sides 6 and 8.  Included angles are 40 and 140.
Then one generic triangle with sides/vertices labeled a, b, c, A, B, C. c=?
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Carl Brandt Long @carlblong.bsky.social · 28/09/2026
In #MathsToday, introduced composite functions to #Alg2. Started with Collatz Conjecture, then these 3 prompts. Ss worked in groups for each, leading to full-class sharing/discussions. Keeping it grounded at first, with units in mind. e.g. "Are you adding to the mileage, or to the money?" #MTBoS
	The surface area of a sphere, as function of the length of the radius, r, can be represented by S(r)=4πr^2.  Match each of the following expressions with its description:
1.05∙S(r) 	The radius of the sphere is increased by 5%
S(r+5) 	The surface area of the sphere is increased by 5%
S(1.05r) 	The surface area of the sphere is increased by 5 square units
S(r)+5 	The radius of the sphere is increased by 5 units.
	F(m) is the fare, in dollars, for a taxi ride of m miles.  Write an expression for each of the following:
	The amount paid if the taxi driver charges you for 5 more miles than the actual distance of the trip
	The amount each rider pays if the fare is divided equally among 3 passengers
	The amount paid if the driver charges you for twice the number of miles you actually travelled
	The total amount paid if you tip the driver $2
	The total amount paid if you tip the driver 20%
	Ulrich’s bakery normally charges C(N) Euros (€) for N pretzels.  The expressions below represent various coupons for buying N pretzels.  For each expression, provide text for the coupon.
	C(N-2)
	1/2 C(N)
	C(N)-2
	C(1/2 N)
	0.90∙C(N)
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Reposted by Carl Brandt Long
Andrew Stacey @mathforge.org · 24/09/2026
www.bbc.co.uk/news/article... I can't even ... so I won't! Instead, let's make this an alternative headline competition. I'll start: Farmer rounds down sheep, instead of rounding them up. #MathsToday #UKMathsChat #mathsky
bbc.co.uk
Jeremy Clarkson's sheep 'theft' turns out to be miscount on farm
Jeremy Clarkson reported the theft of sheep from his Diddly Squat Farm to police earlier this month.
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Carl Brandt Long @carlblong.bsky.social · 22/09/2026
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?
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Carl Brandt Long @carlblong.bsky.social · 16/09/2026
In #MathsToday #Alg2 Ss learned domain, range, inc/dec features of graphs. HW before class was classroom.amplify.com/activity/6aa... In class, formalized the ideas and notation. Then Ss did this to learn domain/range: classroom.amplify.com/activity/5f5... Finished w/ stations to practice/deepen.
classroom.amplify.com
Looking at Graphs v1.26
by Carl Long
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Carl Brandt Long @carlblong.bsky.social · 12/09/2026
#ITeachMath #MathEd I can attest that this works to build stronger community and deeper understanding. Its also more fun to teach this way.
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Carl Brandt Long @carlblong.bsky.social · 11/09/2026
#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.
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Carl Brandt Long @carlblong.bsky.social · 10/09/2026
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
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Carl Brandt Long @carlblong.bsky.social · 24/08/2026
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
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Reposted by Carl Brandt Long
Nathan Day @nathanday.bsky.social · 08/07/2025
Calling all Maths teachers! What are some of your all-time great tasks for secondary Maths? Ones that could have their place in any curriculum, one that should be studied in PGCE courses, ones that started whole new genres of tasks... ... or just ones you really like. (see some of mine below)
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Carl Brandt Long @carlblong.bsky.social · 13/08/2026
Re-reading #DungeonCrawlerCarl this summer, and picked up this fun math problem for my students this year! (Exponential Functions, Sequences & Series) #ITeachMath #MTBos #MathEd #MathSky #BookSky
In Dungeon Crawler Carl (p. 277), Carl receives a box of 100 ninja stars:

Small, low-damage throwing stars.  These bad boys aren’t anything special upon first glance.  They’re the same black stars you wannabe ninjas purchased at the knife shop and the swap meet when you were kids…. And while these throwing shuriken don’t have the ability to turn you into a ninja, … they are enchanted with a Bloolust enhancement.  For every monster you damage with a shuriken from this set, the damage against that monster type rises by 8%.

I looked at Mordecai.  “When it says the damage increases by 8%, does it mean 8% from the original amount, or 8% compounded.  That’s a big deal after a while.”
…
“Good news.  It’s compounded,” he said after a minute.  “So each hit will be 8% higher than the previous amount.  The bad news is, the stars are very fragile.”
That sounded pretty awesome at first, but I suspected it wasn’t that great of an enchantment.  It’d take a long time to power them up. I’d have to do a ton of throwing to make them worthwhile.  I only had 100 of them.  I’d have to collect them back each time.  And if they broke a lot, then I might only get one chance to really use them.

Assuming that the first throwing star does a single point of damage against a Tuskling, how much damage will the 100th throwing star do?
A little while later (p. 295):
I’d shown [Brandon] the shuriken and allowed him to read the description.  “These things are more powerful than you realize,” he’d said, voice filling with awe.  “Do the math.  Compounding damage means if you poke something 200 times, it’s like literally millions of points of damage.”  

Is Brandon correct?
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Carl Brandt Long @carlblong.bsky.social · 08/08/2026
Mathin the wild #iteachmath #mtbos #mathed #mathphoto
Raspberries
6 oz: $2.99
9 oz: $4.99
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Carl Brandt Long @carlblong.bsky.social · 06/08/2026
Here's a @desmos.com Notebook I made for students to explore the relationship between circles and angles. Suggestions appreciated. #iteachmath #iteachmaths #mathsky #mathed #mtbos #geometry www.desmos.com/notebook/gyq...
desmos.com
Circle Angles and Arcs
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Carl Brandt Long @carlblong.bsky.social · 03/08/2026
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...
desmos.com
Guess 4
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Carl Brandt Long @carlblong.bsky.social · 31/07/2026
My perennial question: Are there newer/better resources that can help students see the ideas and purpose behind probability/statistics concepts, or do I stick with the ones older than my students? #mtbos #iteachmath #iteachstats #mathstoday #coremaths #alevelmaths #mathchat #mathsky
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Carl Brandt Long @carlblong.bsky.social · 30/07/2026
I had a lot of fun making this @desmos.com Notebook about misleading data visualizations. Suggestions appreciated. #mtbos #iteachmath #iteachstats #mathstoday #mathsky www.desmos.com/notebook/jhh...
desmos.com
Bad Graphs
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Carl Brandt Long @carlblong.bsky.social · 28/07/2026
This is the first @desmos.com Notebook I started working on, and I've been tweaking it for a while. It guides the reader through a derivation of the Law of Sines and provides some worked examples. Suggestions appreciated. #mtbos #iteachmath #mathstoday #mathsky www.desmos.com/notebook/mxy...
desmos.com
Law of Sines
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Carl Brandt Long @carlblong.bsky.social · 24/07/2026
Another @desmos.com Notebook, showing how the unit circle creates the sine function. Suggestions welcome. #iteachmath #mathstoday #mtobs #mathsky www.desmos.com/notebook/ieb...
desmos.com
Sin graph
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Carl Brandt Long @carlblong.bsky.social · 23/07/2026
Here's another @desmos.com Notebook I made. I'll be sharing the Notebook tool with my department, not all of whom are Desmos-savvy, so I was going for something simple to create. Is it effective? Suggestions appreciated. #iteachmath #mathstoday #mtbos #mathsky www.desmos.com/notebook/umo...
desmos.com
Derivative graph
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Carl Brandt Long @carlblong.bsky.social · 22/07/2026
I've been playing more with the @desmos.com Notebook. Here's one I made about conditional probability. Suggestions appreciated. I feel like something might be missing. #iteachmath #mathstoday #mtbos #mathsky #iteachstats www.desmos.com/notebook/epc...
desmos.com
Conditional Probability
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Carl Brandt Long @carlblong.bsky.social · 22/07/2026
#tmwyk
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Carl Brandt Long @carlblong.bsky.social · 12/07/2026
I made a @desmos.com notebook about an iterative function and its bifurcation diagram: www.desmos.com/notebook/e9x... Suggestions welcome. #iteachmath #mathstoday #mtbos #mathsky
desmos.com
Iterative Function
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Carl Brandt Long @carlblong.bsky.social · 10/07/2026
I made a silly thing on @desmos.com Notebook: www.desmos.com/notebook/14d... #iteachmath #mtbos
desmos.com
Game
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Carl Brandt Long @carlblong.bsky.social · 09/07/2026
I've been playing with the @desmos.com notebook tool over the past few days. Here's one with parametric trig equations. Suggestions welcome. www.desmos.com/notebook/xf0... #iteachmath #mathstoday #mtbos
desmos.com
Parametric trig graph
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Carl Brandt Long @carlblong.bsky.social · 07/07/2026
Lots of pedagogical food for thought. This is the sort of blog post that I will ruminate on for a while and come back to again and again. www.mathed.page/teaching/not... #iteachmath #mtbos
mathed.page
Nothing Works | www.MathEd.page
Henri Picciotto shares some of his thoughts about teaching mathematics
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Carl Brandt Long @carlblong.bsky.social · 25/06/2026
You've idolized your last Billy.
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Carl Brandt Long @carlblong.bsky.social · 25/06/2026
Better to create a third, more liberal, party to siphon off votes, thereby guaranteeing the further entrenchment of the current corrupt GOP, who DID use their party's resources to move the party hard to the right. Is that the plan?
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Justin Lanier @jlanier.bsky.social · 19/06/2026
Hi! In July I'm once again running a free online program for K-12 math teachers called "21st century mathematics". Its goal is to help teachers to connect math they teach with some math that has been discovered in the 21st century. Pass it along! Info+register: justinlanier.org/21st-century...
A 4x4 puzzle grid, indicating an example of an alternating sign matrix; an example of a configuration of 21 points that maximized the number of pairs that are a unit distance apart. These are the two mathematical themes of the 2026 program.
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Carl Brandt Long @carlblong.bsky.social · 05/06/2026
My kids (8 and 10) are debating whether Escher'd drawings are "buildable." #tmwyk
Escher prints
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Reposted by Carl Brandt Long
Carl Brandt Long @carlblong.bsky.social · 06/05/2026
In #Mathstoday, my 11th grade (Y12) precalculus class started series/summation. We did sequences in Jan/Feb, are are coming off of limits. I gave them these photos/problems to introduce sums & motivate and introduce sigma notation. (Photos by me and a friend) 1/3 docs.google.com/presentation...
docs.google.com
Cannonballs
Cannonballs
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Carl Brandt Long @carlblong.bsky.social · 26/04/2026
Film you've watched more than six times with a gif. Boss mode: no film produced by a major studio
media.tenor.com
a man is drinking a cup of coffee and making a funny face
Alt: Hudson Hawk, finally drinking a cappucino
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Reposted by Carl Brandt Long
Andrew @andrewmaths1.bsky.social · 25/04/2026
As @mr-man-maths.bsky.social has covered International A-level Maths syllabi offered by Edexcel, Cambridge and Oxford AQA, I'd like to cover the local A-level syllabi that are taken in various countries just to see the differences in content and expectations. This is part 1 of the series.
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Carl Brandt Long @carlblong.bsky.social · 07/03/2026
My 8yo, learning about multiplication: 1 is the mother of every number. #tymyk
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Carl Brandt Long @carlblong.bsky.social · 23/02/2026
Not knowing anything else about the situation, I'd guess that Duke was #2, and #5 Michigan beat the #1 team.
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Reposted by Carl Brandt Long
Gwen C. Katz @gwenckatz.bsky.social · 09/02/2026
Macbeth: SHIT
135100162018
Reposted by Carl Brandt Long
IMANI! ✍🏿 CREATING STUFF & THINGS ✒️ @kaoscryptid.asalwaysimani.com · 07/02/2026
Welcome to the Winter Olympics don't ask about how many people died or were injured in the making of this sport please and thank you.
Alesbuchanan

Summer Olympics: Who can run the fastest? :)

Who can swim the fastest? :) Who can do the best somersault? :)

Winter Olympics: WHO CAN MAKE IT TO THE

BOTTOM OF THIS ICE SLIDE OF DEATH AND SURVIVE?? WHO CAN GET AROUND THE RINK WITHOUT GETTING THEIR HANDS SLICED OFF BY EVERYONE ELSE'S FEET BLADES?? CAN THIS GUY DO A 1080 DEGREE FLIP WITHOUT DYING??

legionoftuna

Summer Triathlon: Don't run too fast, you have

to save your energy for a swim and a bike ride! :)

Winter Biathlon: I see you've been skiing for five miles now here's your gun

Source: lesbuchanan #olympics
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Carl Brandt Long @carlblong.bsky.social · 13/01/2026
In #mathstoday, I motivated z-scores by asking who was faster - Michael Phelps or Usain Bolt? In past years, I had done this after introducing z-scores, but starting with the question prompted great discussion: "You can't compare them. They're different sports." www.desmos.com/calculator/d... 1/5
desmos.com
Bolt vs. Phelps
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Carl Brandt Long @carlblong.bsky.social · 06/12/2025
www.currentaffairs.org/news/ai-is-d...
currentaffairs.org
AI is Destroying the University and Learning Itself
Students use AI to write papers, professors use AI to grade them, degrees become meaningless, and tech companies make fortunes. Welcome to the death of higher education.
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Carl Brandt Long @carlblong.bsky.social · 21/10/2025
media.tenor.com
Hudson Hawk Hat Trick GIF
ALT: Hudson Hawk Hat Trick GIF
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Reposted by Carl Brandt Long
Emily Pitts Donahoe @empittsdonahoe.bsky.social · 10/10/2025
Please do not use AI to grade. If demands on your time are such that you cannot provide students with timely and substantive feedback, that is a labor issue, and you should join your union. open.substack.com/pub/marcwatk...
open.substack.com
The Dangers of using AI to Grade
Nobody Learns, Nobody Gains
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Carl Brandt Long @carlblong.bsky.social · 16/09/2025
Field testing a new question for our upcoming trigonometry test. #iteachmath #todayinmaths #mtbos
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Carl Brandt Long @carlblong.bsky.social · 08/09/2025
Question for @amplifyeducation.bsky.social. Is there a way to see which assignments I have assigned to a given class?
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Carl Brandt Long @carlblong.bsky.social · 31/07/2025
Hey #MathEd folks, I'm looking for resources to supplement my #stats class - videos, articles, etc. that: -provide real-world examples of the concepts in action -discuss the development of concepts/tools -describe concepts and tools in intuitive or animated ways -etc. #iteachstats #iteachmath
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Larry Ferlazzo @larryferlazzo.bsky.social · 25/07/2025
How to Help Students See the Relevance of Math with @mathillustrated.bsky.social is new @edweek.org post www.edweek.org/teaching-lea...
Relevance is often found simply in what inspires curiosity
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Carl Brandt Long @carlblong.bsky.social · 28/05/2025
Five black and white films: The Cabinet of Dr. Caligari M Dr. Strangelove Holiday It Happened One Night
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Seth Abramson @sethabramson.bsky.social · 25/04/2025
Whenever rich men known to be liars—and exactly the sort of people who'd never give up any power granted to them—claim that they're telling the truth and are extremely willing to give up any power granted to them, there's something endemic in major media that seems predisposed to accept such claims.
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Carl Brandt Long @carlblong.bsky.social · 23/03/2025
##mathphoto #iteachmath
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Carl Brandt Long @carlblong.bsky.social · 06/03/2025
This changes everything! (Well, many things.)
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