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Sonobe Cube Ratios and Construction

Last week’s hexagonal prisms of linear ratio 1:2:3 brought us to a discussion of dimensions of a cube. We looked at the building blocks of a cube: square faces, edges, and vertices, each a face, edge and vertex. The cube itself or any solid is three dimensions (we can use any three of the words “base, length, width, height, depth, or breadth” as long as they are on different planes. All solids are three dimensional (like the cube).

Halloween Hexagonal Coffin Prism x1, x2, and x3 -- Linear, Area, and Volume Ratios

We had an exploration this week comparing solids with a linear ratio of 1:2:3, an area ratio of 1:4:9, and a volume ratio of 1:8:27. We were able to prove that the small prism held 10 pieces of candy while the medium prism held exactly 80 pieces and the large prism held exactly 270 pieces. 

Halloween Candy Nutrition Calories, Grams, Ratios and Budget

Instead of ruining the funnest night of the year with “don’t do candy” proclamations, I always like to educate the Mathletes on responsible candy consumption. The national average consumed by children on Halloween is approximately 3000 calories just in candy. Of course, it tapers off during the year but this is alarmingly high. The daily budget of a 6-7 year old low active male is 1,600 calories per day.

Equation Game Dollar Words Algebra

After mastering the ABC valuation method (A=1, B=2 … Z=26) and the ZYX valuation method (Z=1, Y=2 … A=26), I introduced my newest valuation method I call the EAR method. E=26, A=25, R=24 since they are the most commonly used letters in the English language.  

 

Dollar Words ZYXs Descending Value Method

THE DESCENDING METHOD OF VALUATION (a=26, b=25, c=24 ... z=1)

THIS IS MORE DIFFICULT SINCE WE ARE USED TO THE ABC SONG