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Cake Method: Converting Any Decimal Number to Any Base Number Using Repeated Short Division

When I was your children’s age and I discovered the short division method, I became entranced with dividing any number by 2 and then dividing that quotient by 2 and so on. I began dividing each number right on top of the other and it resembled a multi-tiered cake. 

Short Division by 2, 3, 5, 11, 17, and 36 with and without Remainders

Ever since I was in 2nd grade and became fascinated by division, my teachers were relentless in their preoccupation with long-division. I could not believe that this was the fastest way to do division without a calculator so I endeavored to develop my own strategy I call “short division.” Why is it better?

Hexadecimal Number System Converted to Decimal

We spent several weeks studying the Mayan vegidecimal (Base 20) number system with 20 symbols, then the binary (Base 2) system used by computers with only 1s and 0s, and last week, used the binary system to look at exponential decay using 1/2, 1/4, 1/8 and so on. 

Super Blood Blue Moon

The Mathletes were in for a rare treat on Wednesday, January 31, 2018 that hasn't been witnessed since 1866, 152 years. We spent the first part of class discussing this astronomical phenomenon. 

Folding Paper in Half - Exponential Decay - Fraction Denominators Resemble Binary Numbers

I had the Mathletes folding a paper plate in half. They were only able to do this four times: 1/2, 1/4, 1/8, 1/16. The children noticed that each time the paper got a half smaller, the denominator of the fraction doubled like the binary numbers.