LLMによるシミュレーションも

PS> ?? prompt4
reasoning4
>> command4
simulation4
confirm: Y
result4

こんな感じに進められる。

LLM側では、
PS> #prompt4
PS> #
としてまずreasoning4とcommand4を推論させ、そのまま引き続きsimulation4まで推論させるだけ。

#ClassroomMath #prompt4

If you have pattern blocks...

...a tiny problem: make a red triangle.

...and a small problem: What is the area of the tan pattern block? (In the US: in square inches. Not sure whether that unit works with pattern blocks elsewhere.)

I've done this many times, with grades 4-10, and with teachers.

#prompt4. I know this is simple, but I love using completing the square. It’s a struggle for 8th graders for sure. (I’m talking about my high flyers here. ) Once students get it, I have them solve ax^2+bx+c=0. Couple hints along the way and the learners that see it own it and love to share. I also tell my students a story my daughter told me years ago. She was sitting in a college chemistry class and collectively they were stuck on a problem. All of the sudden this high school kid pops up and proclaims, “just complete the square!” That kid was a hero. I tell my kids they too may be a hero someday if they own completing the square.

So for #prompt4 I was stumped for a long time, and then I thought about the "Barfing Monsters" activity I use to introduce graphs of derivatives, which I got from @samjshah and I absolutely love. But then I realized I never wrote that blog post about it. There's a description of the basic structure from Pam Wilson https://pamjwilson.wordpress.com/2016/08/18/barfing-monsters/. I'm teaching Calc again this year so I'll write that blog post just to remember what the hell I'm doing and then share it. I don't think it matches the prompt very well, so I'm not going to use the math puzzle tag. The fact that I can't answer the prompt is bothering me a lot. #ClassroomMath

#ClassroomMath #Prompt4 #MTBoS #ThinkingClassroom

Here is an oldie, but a goodie: Having students calculate the perimeter and area of the Koch Snowflake over several iterations, derive a formula for the nth iteration, then determine if the perimeter and area are finite or infinite. In Algebra 2 this year I used it as a way to spiral back to sequences and exponentials while introducing infinite series and a look ahead to the idea of limits.

I always enjoy this lesson because it bends the students minds and gets them excited. It also comes during a point in the school year when everyone is tired/stressed, and this is a nice problem to get the class energized again. And of course, fractals are always fun!

#MathPuzzle #ClassroomMath #prompt4

Not a specific puzzle being shared, but...
I like having challenges available for my students should they finish their task before others. Sometimes I give challenges related to the content of what we are doing, and other times they are more generic. I keep on hand booklets of logic puzzles from Puzzle Baron and Inkies from Crazy Dad (otherwise known as Ken Ken puzzles). For both, you can choose a variety of difficulty levels on their websites.
https://logic.puzzlebaron.com/
https://krazydad.com/inkies/

#MathPuzzle #prompt4 #ClassroomMath

I had so many problems that came to mind that I wanted to share... But I chose this problem because I wanted to share something that brought ME joy when I figured it out... but also something that I use in my class because of it.

It all started with "The Block Problem" which then led me to think about higher dimensional cubes which then led me to a chart... A chart that ended up holding lots of cool mysteries!

I always get to the point in my Adv. Precalculus classes where I get kids to answer the first question I pose in the blogpost below. So that's how I use this problem in class. But the second and third problems, I just really love. One year we solve them in class (the year I discovered them). But mainly I felt so proud of myself that I *could* solve them!

https://samjshah.com/2023/07/17/hypercubes-and-more-two-problems-you-may-enjoy-working-on/

#classroommath #prompt4 I found this problem last summer on Play with Your Math. It was definitely one that kept kids and adults engaged! Enjoy!!

#ClassroomMath #prompt4

I have used this as a motivator at the start of calculus just to see where kids' abilities are and to see how easily they catch their usual misconception.

It's also nice for me to see their thinking strategies and variety of ways they solve it. I then revisit it at the end of the year when we do volumes of revolution.

#classroommath #prompt4 I asked this in my intermediate algebra. I get a lot of nice responses! The top pattern is interesting if you make it exponential or really explore the geometry.

How many triangles are shown in the diagram?
#Prompt4 #ClassroomMath #MathPuzzle
(image attribution in comment)

#classroommath #prompt4

This blog post from Mr. Draper has some great Don Steward-style segment addition problems that I used on the whiteboards last year with my students. It really encouraged some great logical thinking and problem solving

#geometry #mtbos #iteachmath

https://mrdrapermaths.wordpress.com/2018/10/21/reasoning-with-lengths/

#ClassroomMath #prompt4

Today, my math peeps, we’re going to be sharing and maybe doing math! Is there a problem that you love having your kids work on? A favorite problem that evokes conversation and ah hah moments? Or is there a math problem or puzzle you’ve seen or done that made you go “oh, wow!”?

In your post:
1. Write down your math problem! If you use it in your class, share the grade/class you use it with, and why you like the problem for your kids. If it’s just a recreational math problem or puzzle, feel free to just drop it in the post. You can decide whether you want to give a hint or not! (NOTE: you can use the “CW” button when writing a post to hide the post’s content until someone clicks on it… so you can type the problem in one post, and then in a reply to that post, you can use “CW” to hide the hint until someone decides they want to see it.)
2. Tag your post with #MathPuzzle and #prompt4 and #ClassroomMath

Don’t forget to bookmark any problem/puzzle you might want to use in the future!

To practice using the site, we have just one challenge for you: practice using the fancy math ability of mathstodon to write an equation in a post. The fancy math equations only show up when you read posts on the desktop (not in apps, yet…), but it’s pretty awesome.

From the desktop page, click on the “f(x)” button and click “inline equation.” Some slashes and parentheses will appear. In between those, type:

g(x)=\frac{\sqrt{3x-5}}{3}+\frac{x^{52}-x}{3\pi \sin^{2}(x)}-5x^{6}+a_{n}

See what happens! Believe it or not, you’ve typed pretty LaTex math.

#ClassroomMath #prompt4

Today, my math peeps, we’re going to be sharing and maybe doing math! Is there a problem that you love having your kids work on? A favorite problem that evokes conversation and ah hah moments? Or is there a math problem or puzzle you’ve seen or done that made you go “oh, wow!”?

In your post:
1. Write down your math problem! If you use it in your class, share the grade/class you use it with, and why you like the problem for your kids. If it’s just a recreational math problem or puzzle, feel free to just drop it in the post. You can decide whether you want to give a hint or not! (NOTE: you can use the “CW” button when writing a post to hide the post’s content until someone clicks on it… so you can type the problem in one post, and then in a reply to that post, you can use “CW” to hide the hint until someone decides they want to see it.)

2. Tag your post with #MathPuzzle and #prompt4 and #ClassroomMath

Don’t forget to bookmark any problem/puzzle you might want to use in the future!

To practice using the site, we have just one challenge for you: practice using the fancy math ability of mathstodon to write an equation in a post. The fancy math equations only show up when you read posts on the desktop (not in apps, yet…), but it’s pretty awesome.

From the desktop page, click on the “f(x)” button and click “inline equation.” Some slashes and parentheses will appear. In between those, type:

g(x)=\frac{\sqrt{3x-5}}{3}+\frac{x^{52}-x}{3\pi \sin^{2}(x)}-5x^{6}+a_{n}

See what happens! Believe it or not, you’ve typed pretty LaTex math.