Carl Brandt Long
@carlblong.bsky.social
Math teacher, theatre-maker, husband, father
First pass: Starting to see things as triangles and hexagonal, but wanted to take it further.
2. Cut into common units of area.
24/50 = 13/25
2. Cut into common units of area.
24/50 = 13/25
February 8, 2026 at 2:40 AM
First pass: Starting to see things as triangles and hexagonal, but wanted to take it further.
2. Cut into common units of area.
24/50 = 13/25
2. Cut into common units of area.
24/50 = 13/25
Reposted by Carl Brandt Long
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.
February 7, 2026 at 4:24 PM
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.
What's he talking about? NO ONE, not even ICE, is in the theater:
January 29, 2026 at 5:37 PM
What's he talking about? NO ONE, not even ICE, is in the theater:
All of us, possibly of old age.
January 28, 2026 at 7:59 PM
All of us, possibly of old age.
They want to push anyone out who hasn't bought 10-12 homes.
January 20, 2026 at 6:43 PM
They want to push anyone out who hasn't bought 10-12 homes.
Yes to this!!!!
My only point of disagreement is when factoring both columns, a negative can make things tricky. Fortunately, you only need to factor the gcf once!
youtu.be/7PMyAG3mgZE
Thanks for doing such great outreach, Howie!
My only point of disagreement is when factoring both columns, a negative can make things tricky. Fortunately, you only need to factor the gcf once!
youtu.be/7PMyAG3mgZE
Thanks for doing such great outreach, Howie!
Factoring Quadratics (Area model)
YouTube video by Carl Long
youtu.be
January 15, 2026 at 6:36 PM
Yes to this!!!!
My only point of disagreement is when factoring both columns, a negative can make things tricky. Fortunately, you only need to factor the gcf once!
youtu.be/7PMyAG3mgZE
Thanks for doing such great outreach, Howie!
My only point of disagreement is when factoring both columns, a negative can make things tricky. Fortunately, you only need to factor the gcf once!
youtu.be/7PMyAG3mgZE
Thanks for doing such great outreach, Howie!
Whenever possible, have them do the thinking first, then name what they've done.
Despite knowing and adhering to this, I find I don't always actually do it. The lessons are so much more fun and meaningful when I do.
Despite knowing and adhering to this, I find I don't always actually do it. The lessons are so much more fun and meaningful when I do.
January 14, 2026 at 6:21 PM
Whenever possible, have them do the thinking first, then name what they've done.
Despite knowing and adhering to this, I find I don't always actually do it. The lessons are so much more fun and meaningful when I do.
Despite knowing and adhering to this, I find I don't always actually do it. The lessons are so much more fun and meaningful when I do.
I used their world record times (the minima of the datasets).
Their heat times are also included in the datsets. So Usain Bolt is not just considerably faster than other Olympians, he's also faster than himself!
Their heat times are also included in the datsets. So Usain Bolt is not just considerably faster than other Olympians, he's also faster than himself!
January 14, 2026 at 6:19 PM
I used their world record times (the minima of the datasets).
Their heat times are also included in the datsets. So Usain Bolt is not just considerably faster than other Olympians, he's also faster than himself!
Their heat times are also included in the datsets. So Usain Bolt is not just considerably faster than other Olympians, he's also faster than himself!
I love that! Picking apart indices and coming up with alternatives is a great way to advance numeracy and creativity!
January 14, 2026 at 6:17 PM
I love that! Picking apart indices and coming up with alternatives is a great way to advance numeracy and creativity!
"Standard scores" might be the more proper terminology.
January 14, 2026 at 6:15 PM
"Standard scores" might be the more proper terminology.
PS. I've taught this topic for ~17 years (many using the Bolt/Phelps example later in the lesson). This is _by far_ the best it's ever gone.
PPS. z-scores were a topic that felt pointless and artificial when I first learned them in high school.
6/5
PPS. z-scores were a topic that felt pointless and artificial when I first learned them in high school.
6/5
January 13, 2026 at 6:45 PM
PS. I've taught this topic for ~17 years (many using the Bolt/Phelps example later in the lesson). This is _by far_ the best it's ever gone.
PPS. z-scores were a topic that felt pointless and artificial when I first learned them in high school.
6/5
PPS. z-scores were a topic that felt pointless and artificial when I first learned them in high school.
6/5
Within 10 minutes, we'd gone from a seemingly impossible question to inventing a formula. They understand the purpose and the reason behind the calculations.
Ss had invented z-scores.
5/5
Ss had invented z-scores.
5/5
January 13, 2026 at 6:45 PM
Within 10 minutes, we'd gone from a seemingly impossible question to inventing a formula. They understand the purpose and the reason behind the calculations.
Ss had invented z-scores.
5/5
Ss had invented z-scores.
5/5
Ss: Subtraction. Lower. We make it negative.
Me: "So Phelps is 5 sec faster than avg. Bolt is less than 1."
Ss: "Yeah, but swimming has a bigger standard deviation."
Me: "How do you account for that?"
Ss: "Divide by the standard deviations."
We do.
Me: "And these are called z-scores."
4/5
Me: "So Phelps is 5 sec faster than avg. Bolt is less than 1."
Ss: "Yeah, but swimming has a bigger standard deviation."
Me: "How do you account for that?"
Ss: "Divide by the standard deviations."
We do.
Me: "And these are called z-scores."
4/5
January 13, 2026 at 6:45 PM
Ss: Subtraction. Lower. We make it negative.
Me: "So Phelps is 5 sec faster than avg. Bolt is less than 1."
Ss: "Yeah, but swimming has a bigger standard deviation."
Me: "How do you account for that?"
Ss: "Divide by the standard deviations."
We do.
Me: "And these are called z-scores."
4/5
Me: "So Phelps is 5 sec faster than avg. Bolt is less than 1."
Ss: "Yeah, but swimming has a bigger standard deviation."
Me: "How do you account for that?"
Ss: "Divide by the standard deviations."
We do.
Me: "And these are called z-scores."
4/5
I gave them the means and standard deviations of the times of all the competitors in the 100m running and 200m butterfly events from the 2008 Olympics.
Students, still: "Bolt is .71 sec away from the mean."
"Phelps is 4.94 away."
Me: "How did you get that? Higher or lower?"
3/5
Students, still: "Bolt is .71 sec away from the mean."
"Phelps is 4.94 away."
Me: "How did you get that? Higher or lower?"
3/5
January 13, 2026 at 6:45 PM
I gave them the means and standard deviations of the times of all the competitors in the 100m running and 200m butterfly events from the 2008 Olympics.
Students, still: "Bolt is .71 sec away from the mean."
"Phelps is 4.94 away."
Me: "How did you get that? Higher or lower?"
3/5
Students, still: "Bolt is .71 sec away from the mean."
"Phelps is 4.94 away."
Me: "How did you get that? Higher or lower?"
3/5
"On land, Bolt. In water, Phelps."
"I bet if you gave him time to train..."
"Count their gold medals."
Then: "Well, you could compare them to the other people in their events."
"Which one is more standard deviations from the mean?"
Now we had a quantifiable question. All student generated!
2/5
"I bet if you gave him time to train..."
"Count their gold medals."
Then: "Well, you could compare them to the other people in their events."
"Which one is more standard deviations from the mean?"
Now we had a quantifiable question. All student generated!
2/5
January 13, 2026 at 6:45 PM
"On land, Bolt. In water, Phelps."
"I bet if you gave him time to train..."
"Count their gold medals."
Then: "Well, you could compare them to the other people in their events."
"Which one is more standard deviations from the mean?"
Now we had a quantifiable question. All student generated!
2/5
"I bet if you gave him time to train..."
"Count their gold medals."
Then: "Well, you could compare them to the other people in their events."
"Which one is more standard deviations from the mean?"
Now we had a quantifiable question. All student generated!
2/5
Your method is very similar to mine! I can't believe how long I went before doing it this way.
youtu.be/7PMyAG3mgZE
youtu.be/7PMyAG3mgZE
Factoring Quadratics (Area model)
YouTube video by Carl Long
youtu.be
January 12, 2026 at 6:17 PM
Your method is very similar to mine! I can't believe how long I went before doing it this way.
youtu.be/7PMyAG3mgZE
youtu.be/7PMyAG3mgZE
I had the same question recently. There's a recent activity dashboard on the home stream.
January 12, 2026 at 5:57 PM
I had the same question recently. There's a recent activity dashboard on the home stream.
I don't do this with students because getting through Ptolemy's theorem that this requires takes too much time and doesn't add anything, but I love the elegance:
December 6, 2025 at 6:28 AM
I don't do this with students because getting through Ptolemy's theorem that this requires takes too much time and doesn't add anything, but I love the elegance:
@nkorpett.bsky.social is phenomenal.
November 25, 2025 at 2:17 AM
@nkorpett.bsky.social is phenomenal.
Operations with rational expressions.
November 8, 2025 at 8:27 PM
Operations with rational expressions.