Hi all! I will try to get pictures into a folder soon. Otherwise I'll email each person a few of their kids' photos, especially the bridges.
On Friday we had "Engineering" day. After solving a few puzzles about bridges and crossing rivers, we built bridges using 1 lb spaghetti, 10 glue sticks, and a roadbed. Some bridges were beautiful and mathematical, some were along the lines of, "Put all the spaghetti on the roadbed and use all the glue." Unfortunately, the less elegant ones were stronger, but I hope everyone enjoyed the process.
Here is a video describing the forces a bridge faces, and demonstrating bridge destruction:
https://www.khanacademy.org/partner-content/mit-k12/mit-k12-physics/v/bridge-design-and-destruction-part-1
We also built a geodesic dome. Here is a link to the design we used: http://www.pbs.org/wgbh/buildingbig/educator/act_geodesic_ho.html
The site has lots of examples of geodesic domes.
The previous day was probability. We talked about Pascal's triangle and its link to combinatorics.
Here is a website with lots of activities:
http://www.korpisworld.com/Mathematics/diversions/exploring_pascal.htm
We also talked about experimental vs. theoretical probability using Skittles, which was very popular.
Thanks for sending your kids! I enjoyed having them, even though it was chaotic at times. I hope to have the opportunity to do math with them again!
Saturday, August 11, 2018
Wednesday, August 8, 2018
Math Camp Day 3!
So for day 3 of math camp we made bubbles and parabolic solar ovens.
The bubbles were a HUGE success. I got the projects from here:
https://www.stevespanglerscience.com/lab/experiments/backyard-bubbles/
We made bubbles within bubbles, towers of bubbles, huge bubbles, square bubbles, and played bubble bop (bouncing bubbles from one person to another).
Then we made parabolic solar ovens. The project was from here:https://www.education.com/science-fair/article/solar-hot-dog-cooker/
I'm not sure I'd actually use this to cook hot dogs. I wanted to cook marshmallows, which didn't work because marshmallows don't heat up in the sun (they reflect the light...) but I wasn't impressed. I am giving bonus points for anyone who actually succeeds at this.
It was interesting, the project was a lot more difficult than I thought it would be, and some of the things I thought were clear in the directions were definitely NOT clear. But live and learn!
Two interesting websites on paraboloids:
https://gizmodo.com/heres-why-you-shouldnt-leave-a-giant-parabolic-mirror-i-1827858823
Paraboloids and buildings which set things on fire.
Tomorrow should be calmer and less crafty. The only problem might be the skittles for doing combinatorics and probability...
The bubbles were a HUGE success. I got the projects from here:
https://www.stevespanglerscience.com/lab/experiments/backyard-bubbles/
We made bubbles within bubbles, towers of bubbles, huge bubbles, square bubbles, and played bubble bop (bouncing bubbles from one person to another).
Then we made parabolic solar ovens. The project was from here:https://www.education.com/science-fair/article/solar-hot-dog-cooker/
I'm not sure I'd actually use this to cook hot dogs. I wanted to cook marshmallows, which didn't work because marshmallows don't heat up in the sun (they reflect the light...) but I wasn't impressed. I am giving bonus points for anyone who actually succeeds at this.
It was interesting, the project was a lot more difficult than I thought it would be, and some of the things I thought were clear in the directions were definitely NOT clear. But live and learn!
Two interesting websites on paraboloids:
https://gizmodo.com/heres-why-you-shouldnt-leave-a-giant-parabolic-mirror-i-1827858823
Paraboloids and buildings which set things on fire.
Tomorrow should be calmer and less crafty. The only problem might be the skittles for doing combinatorics and probability...
Tuesday, August 7, 2018
Mathmom's Math Camp: Day 2
We had day 2 of math camp today: logic. We did not do truth tables (much to the dismay of one of the kids) but we played with cryptarithms, where each letter represents a number. For example. if W+O=OF, then you know that O=1, which means that W=9 and F=0.
We then played Giotto, where one team chooses a word and the other team guesses, being given hints about how many letters are in both words. The best part was when the students realized that getting a score of zero was better than getting a score of 1 or 2. The teams of older kids and younger kids competed fiercely and came out...about equal. Amazing.
We talked a little about invariants at the end of the time. The easiest puzzle asks whether if you have 5 cups up and one down, can you turn all the cups up if you turn them two at a time. What stays the same when you turn over the cups?
I got the puzzles from the book "Camp Logic".
Tomorrow: Parabolic ovens (which may or may not actually heat anything up...but the theory is good, and the parabolas are for real...) and bubbles.
Unfortunately, I totally neglected to take any pictures. I will try to do better tomorrow.
We then played Giotto, where one team chooses a word and the other team guesses, being given hints about how many letters are in both words. The best part was when the students realized that getting a score of zero was better than getting a score of 1 or 2. The teams of older kids and younger kids competed fiercely and came out...about equal. Amazing.
We talked a little about invariants at the end of the time. The easiest puzzle asks whether if you have 5 cups up and one down, can you turn all the cups up if you turn them two at a time. What stays the same when you turn over the cups?
I got the puzzles from the book "Camp Logic".
Tomorrow: Parabolic ovens (which may or may not actually heat anything up...but the theory is good, and the parabolas are for real...) and bubbles.
Unfortunately, I totally neglected to take any pictures. I will try to do better tomorrow.
Tuesday, March 10, 2015
Pi day resources
There are so many resources out there for celebrating Super Pi Day! 3/14/15. Here are some of my favorites. If you have some you like, post them in the comments!
Another magical quality of pi is that it isn't a whole or counting number, like the numbers you learn about in kindergarten. It isn't a fraction, like the things you learn about in 3rd grade. It isn't even an algebraic number like the solution to x^2=2. It is something called a transcendental number. The name makes it sound like transcendental numbers are hard to find, but it turns out that if you are looking at a number line, most of the space is taken up by transcendental numbers. Only a few of them have names, though, and one of the named ones is pi.
There are two people I associate most strongly with the history of pi. The first was Archimedes, who estimated pi by "trapping" a circle between two polygons. You know that the circumference of the circle is bigger than the perimeter of the inside polygon, but smaller than the perimeter of the outside polygon. The more sides you have, the better the estimate! Archimedes used a 96-side polygon for his calculations, which is really something in the days before calculators (even the days before using the Hindu-Arabic number system...) (Of course, another significance of his calculations was the idea of the limit...but we'll save that for Calculus Day.)
Archimedes is also famous for shouting "Eureka!" and running down the street in his birthday suit after making a discovery while taking a bath. He invented several war weapons for his kingdom of Syracuse. When the Romans did invade Syracuse, they had instructions to take Archimedes alive. The story goes, however, that a soldier came upon Archimedes making math drawings in the sand (no white boards) and messed up his pictures. When Archimedes complained, the soldier ran him through.
The other person I associate with pi is the Swiss mathematician Euler. Euler (say it, "oiler") popularized the use of the Greek letter "pi" to mean the circle constant. Euler popularized many other notations as well (e, i, f(x), trigonometric functions, etc.). He thousands of papers and over 900 books, despite the fact that he was blind in the later part of his life.
There are many useful websites for the history of pi, including
http://www.techhive.com/article/191389/a-brief-history-of-pi.html
http://www.piday.org/learn-about-pi/
Pi, pi, mathematical pi...https://www.youtube.com/watch?v=_BwKZEp2K_0
The Pi rap (Lose yourself in the digits): http://teachpi.org/music/rap/
Vi Hart's singing pi gram: https://www.youtube.com/watch?v=4C9PALaDh2U
Vi Hart and John Sims: https://www.youtube.com/watch?v=NsKH5h7j2_o
What is pi?
Briefly, pi is the circle constant. If you find a random circle somewhere around, take the circumference of the circle (the distance around) and divide it by the diameter of the circle (distance across), you always get the same number. The magic of pi is that it doesn't matter how big the circle is.Another magical quality of pi is that it isn't a whole or counting number, like the numbers you learn about in kindergarten. It isn't a fraction, like the things you learn about in 3rd grade. It isn't even an algebraic number like the solution to x^2=2. It is something called a transcendental number. The name makes it sound like transcendental numbers are hard to find, but it turns out that if you are looking at a number line, most of the space is taken up by transcendental numbers. Only a few of them have names, though, and one of the named ones is pi.
History
Back in the day ancient societies used pi for various tasks, even if they didn't know what it was. (I know about the ancient Egyptians and the ancient Greeks, but I assume most ancient cultures discovered the basics of pi) . They may have used a fraction, 22/7, which is accurate to 2 decimal places. Frankly, that's all most of us ever need.There are two people I associate most strongly with the history of pi. The first was Archimedes, who estimated pi by "trapping" a circle between two polygons. You know that the circumference of the circle is bigger than the perimeter of the inside polygon, but smaller than the perimeter of the outside polygon. The more sides you have, the better the estimate! Archimedes used a 96-side polygon for his calculations, which is really something in the days before calculators (even the days before using the Hindu-Arabic number system...) (Of course, another significance of his calculations was the idea of the limit...but we'll save that for Calculus Day.)
Archimedes is also famous for shouting "Eureka!" and running down the street in his birthday suit after making a discovery while taking a bath. He invented several war weapons for his kingdom of Syracuse. When the Romans did invade Syracuse, they had instructions to take Archimedes alive. The story goes, however, that a soldier came upon Archimedes making math drawings in the sand (no white boards) and messed up his pictures. When Archimedes complained, the soldier ran him through.
The other person I associate with pi is the Swiss mathematician Euler. Euler (say it, "oiler") popularized the use of the Greek letter "pi" to mean the circle constant. Euler popularized many other notations as well (e, i, f(x), trigonometric functions, etc.). He thousands of papers and over 900 books, despite the fact that he was blind in the later part of his life.
There are many useful websites for the history of pi, including
http://www.techhive.com/article/191389/a-brief-history-of-pi.html
http://www.piday.org/learn-about-pi/
Activities
Here are some things I like to do on pi day:- Buffon's needle: estimate pi using needles and parallel lines. (https://vimeo.com/38580856, http://www.numberphile.com/pi/pi_matches.html, http://www.mathsisfun.com/activity/buffons-needle.html) Note: some people use frozen corn dogs and tape on the floor.
- Estimate pi directly. measure the circumference of a round object, Then measure the diameter. Find the ratio. How close did you get? (http://illuminations.nctm.org/lesson.aspx?id=1849 there is a PDF worksheet for recording your answers.)
- make pi bracelets: You can use different numbers of beads with spacers (3 black beads, 1 white, 1 black, 1 white, 4 black, 1 white, and so on) or choose a color for each number (3=red, 1=blue, 4=tan, and so on) (http://cheerstoschool.blogspot.com/2012/03/pi-day-and-teachers-notebook.html)
- Learn to draw circles (surprisingly difficult!) (https://www.youtube.com/watch?v=QncgmzH6yQU)
- search for numbers within pi (http://www.facade.com/legacy/amiinpi/)
- memorize pi using fun mnemonics (http://en.wikipedia.org/wiki/Piphilology)
- recite pi
- and of course, eat pie (and other round foods).
Videos
Some of my favorites:- Danica McKellar (includes a song): https://www.youtube.com/watch?v=8-cazxAL_tU
- Vi Hart: Anti pi rant, (I am going to memorize all the digits of 1/3!) https://www.youtube.com/watch?v=5iUh_CSjaSw
- More Vi Hart: pi is still wrong: https://www.youtube.com/watch?v=jG7vhMMXagQ
- (There are many other Vi Hart videos you want to see. Trust me on this)
- Estimating pi with pies: https://www.youtube.com/watch?v=ZNiRzZ66YN0
- (There are lots of other Numberphile videos that are fun, but some of them are very serious mathematics. Try the one on math in the Simpsons https://www.youtube.com/watch?v=K305Vu7hFg0).
Music
What pi sounds like: https://www.youtube.com/watch?v=wK7tq7L0N8EPi, pi, mathematical pi...https://www.youtube.com/watch?v=_BwKZEp2K_0
The Pi rap (Lose yourself in the digits): http://teachpi.org/music/rap/
Vi Hart's singing pi gram: https://www.youtube.com/watch?v=4C9PALaDh2U
Vi Hart and John Sims: https://www.youtube.com/watch?v=NsKH5h7j2_o
Friday, October 31, 2014
Welcome to the Math Club!
Welcome to my Math Club blog. The purpose of this blog is to provide inspiration for homeschool and other math teachers who are fine with the curriculum for mathematics but would like to explore other areas of mathematics.
This blog is for you if you have students who "hate" mathematics. Frankly, I hate dividing and multiplying decimals by hand, solving repetitive algebra equations, and graphing a million and one functions. There is so much more to math than this! There is enough depth in mathematics that there is something for everyone to not hate.
This blog is for you if you have students who "love" mathematics. Sometimes you go through all the workbooks right after another, having great success, but there is nothing to do but the next workbook. In reality, mathematics has so many areas and subjects, the possibilities are endless.
The reason this is a blog and not an ebook is that there are so many other people who have had an influence on this work, I can't right now ask people to pay for it. But maybe someday, it will become a book. We will see.
This blog is for you if you have students who "hate" mathematics. Frankly, I hate dividing and multiplying decimals by hand, solving repetitive algebra equations, and graphing a million and one functions. There is so much more to math than this! There is enough depth in mathematics that there is something for everyone to not hate.
This blog is for you if you have students who "love" mathematics. Sometimes you go through all the workbooks right after another, having great success, but there is nothing to do but the next workbook. In reality, mathematics has so many areas and subjects, the possibilities are endless.
The reason this is a blog and not an ebook is that there are so many other people who have had an influence on this work, I can't right now ask people to pay for it. But maybe someday, it will become a book. We will see.
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