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).

Stairway to Multiples

Different stairwells had different numbers. Brilliant kinesthetic way to learn.

IMG_1244 IMG_1243 IMG_1230 IMG_1229

Water under the Bridge

On the way home from monitoring the NYS math test at 372K, I crossed over the beautiful, retractable Carroll Street bridge that crosses the Gowanus Canal. I saw a whole section of the ground under water. It is the area where there are pulleys that could, in theory, pull the sections of the bridge to the side should a large barge pass through. This patch of ground to the side of the actual canal is usually NOT underwater.

Carroll Street Bridge over the Gowanus Canal

Carroll Street Bridge over the Gowanus Canal

It reminded me of the subway tracks that were under water I wrote about in December 2010 (see “Water under the G” below).

SWAT

I just finished six weeks of SWAT — Students Will Ace Testing — in preparation for the New York State mathematics test. Everyday in one of two schools, working one-on-one with targeted students. We focused on particular math topics that were discovered to be the most common topics on the tests for the past five years. I hope the students that I worked with did well.

SWAT

SWAT T Shirt

November 2018
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