New unit of measurement

I just had a brilliant idea for a new unit of measurement: the “covid.” And how big is the covid? You guessed it, six feet long.

“Hey Bob, I just hit a jump shot from two covids away.”

“That is great Mary. Did I tell you my new livingroom is four covids in length?”

Ad nauseum.

1 covid = 6 feet

Metric conversion, 2020

By this time, most conversions between metric units (grams, etc) and regular, i.e., American standard, units (ounces, etc) are pretty well established.

So how is it that Trader Joe’s and Urban Meadow’s brands have different conversions?

This can of TJ beans and this can of Urban Meadow Beans have the same serving size (130 grams) yet different cup amounts! TJ converts 130 grams into 3/4 cup, while UM converts 130 grams into 1/2 cup. That is a difference of 50%!

So which is correct? It is not so simple. According to this online-calculator.org, 130 grams equals .55 cups of water, which is very close to the 1/2 cup mark, but only .38 cups of honey and over a cup of flour.

And what about canned beans?

According the the USDA , 1/2 cup of kidney beans is only 117 grams (not 130)

And according to the Bush’s, the venerable baked beans company, 1/2 cup is 130 grams.

What do you think? Have you seen confusion when it comes to bean serving size conversion?

Mathigon

One of the pleasant surprises at FETC 2020 was passing by a “STEM Theater” area of the convention floor and seeing a presentation on Telling Stories in Math (or something like that) about to begin. I sat down and listened to a fellow with a slight German accent describe how their are many stories that can be told to keep mathematics interesting. He had a slide deck to accompany the talk.

Little did I know that it was by the Philipp Legner, founder of Mathigon, one of my most favorite online math textbook/resource. And Mathigon is just a side project of his (he works at Google).

This slideshow requires JavaScript.

 

Best buddies!

Tangram or Pattern Blocks. I forget which.

Here are designs from the Math Learning Center App “Pattern Shapes.” What do YOU see in these images? There is a prize for the most original answer.

Another Math Movie

Here is another math movies, made using Stop Motion Studio Pro app.

Math Movies, stop motion-style

Students made these stop motion videos using Stop Motion Studio Pro app. I approve!

Go Math Didn’t Add Up

Many schools use Go Math for their math instruction.

it is published by Houghton Mifflin Harcourt publishers.

I turned to a random page in a Go Math student workbook.

Question 28 states that 36 people are going camping for Max’s family reunion. They need to sleep in cabin tents (which hold ten people) and vista tents (which hold eight people). The student must determine the exact number of tents that the campers will need. If a student needs more help, they can use their ipad or phone to scan the QR code, which directs the student to an online video of “Math on the Spot with Professor Burger,” who helps explain how to solve the problem.

Here is a still shot from the video.

According to Professor Burger, there are only 34 people camping at the reunion. Two people are missing!

Bad math bro!

All I can think about is that two children must have wandered off into the woods, and instead of the adults sending a search party right away, they all want to get a good night’s sleep in their cabin and vista tents.

9ines

A Student (okay, my son Sammy, who is a 7th grade student), gave me this math puzzle:

“Use 6ix (sic) nines to equal 100, you can use +, -, x, ÷, ( ). [No exponents]. 9, 9, 9, 9, 9, 9. Good Luck, Sammy”

Welp, I was stumped and had to have him give me an answer.

This was his solution:

(9 x 9 + 9) + (9 ÷ 9 + 9)

which equals

90 + 10 = 100


I brought the problem to some colleagues of mine, and here are their answers:

Dennis wrote:

(999 – 99) ÷ 9

which equals

900 ÷ 9 = 100


Greg wrote:

(9 ÷ 9 + 9) x (9 ÷ 9 + 9)

which equals

10 x 10 = 100


I don’t remember who gave me this one:

99 + (9 ÷ 9) x (9 ÷ 9)

which equals

99 + 1  x  1

which equals

99 + 1 = 100


I finally came up with my own solution:

(99 ÷ 99) + 99

which equals

1 + 99 = 100

 

I happen to like my solution, since it uses the same numbers each time (99). However, Dennis’s is lovely, since it goes from three digits (999) to two digits (99) to one digit (9).

Which do you think is the most beautiful solution? The one that uses the most operations, or the one that uses the fewest?

3D Gears Math

SO here is the information for making 3D gears that all fit together. I used Sketchup for the design. All the gear convexities and concavities are 3-inch half-circles.

Screen Shot 2015-08-06 at 8.40.28 AM6-Spoke Gear

12-sided circle

6-inch radius (12-inch diameter)

Rotated 7.5 degrees

 

12-Spoke GearScreen Shot 2015-08-06 at 8.42.34 AM

24-sided circle

12-inch radius (24-inch diameter)

Rotated 15 degrees

 

biggear

24-Spoke Gear

48-sided circle

24-inch radius (48-inch diameter)

Rotated 3.75 degrees

 

Screen Shot 2015-08-06 at 8.54.54 AM Rectangular 14-Spoke Gear

12- by 24-inch rectangle

6-inch radius circles at ends

3D Gears

After having discussions with my math peeps, I decided to make gears. From scratch, in Sketchup. Many failures ensued. Thankfully, a Youtube video showed me the light (granted, I had to watch the video about 20 times).

Anyway, the gear ratio works (don’t ask me what that means), and different sizes of gears spin with each other. I even got fancy with irregular shapes (see the long gear) as well as gears with cut-outs (to save filament) and a gear with holes (to create abstract designs a la Spirograph).

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