Carl Brandt Long

Not knowing anything else about the situation, I'd guess that Duke was #2, and #5 Michigan beat the #1 team.

d/C

I'd give them throughout problem and see what they do with it. If they need help, I'd try to follow through on their lines of thinking. If they can't start, I'd suggest drawing a picture.

@ end of class, walk through & connect approaches.

It is. The motto is "This is the way."

Macbeth: SHIT

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

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

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.

Empty theaters for Melania movie

What's he talking about? NO ONE, not even ICE, is in the theater:

All of us, possibly of old age.

They want to push anyone out who hasn't bought 10-12 homes.

YouTube video by Carl Long Factoring Quadratics (Area model)

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!

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.

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!

I love that! Picking apart indices and coming up with alternatives is a great way to advance numeracy and creativity!

100m? 200m?

"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

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: 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

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

"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

Bolt vs. Phelps

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

Agree.

YouTube video by Carl Long Factoring Quadratics (Area model)

Your method is very similar to mine! I can't believe how long I went before doing it this way.
youtu.be/7PMyAG3mgZE

I had the same question recently. There's a recent activity dashboard on the home stream.

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.

www.currentaffairs.org/news/ai-is-d...

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.

Operations with rational expressions.