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Fraction Genealogy

Over 40 students shared their fraction genealogy. It is extraordinary how diverse we are in this region of the country. The younger students had a hard time understanding that very few of us have any fraction of American in our genealogy. After we distinguished our place of birth from our place of origin, the children began to see how they are the products of their parents and they of their parents and so on.

Fraction Capture: Hexahedral and Dodecahedral Dice

We continued our exploration of fractions by having the students learn a dice game where they have to capture a square or other polygon by coloring in more than half of it.

If the square is split into halves then they need to color in both halves to capture that square.  

If the square is split into thirds then they need to color in only two thirds to capture that square. 

If the square is split into fourths then they need to color in only three fourths to capture that square. 

Fraction Equivalents

We continued our exploration of fractions this week with three objectives:

1) Physically match up fraction equivalents such as 1/5 = 2/10 = 3/15 = 4/20 = 5/25 = 6/30 (see page one of both  attached pdfs named Fraction Equivalents K-1 and 2-5).

2) Create fraction equivalents by multiplying both the numerator and denominator by the same number by playing the dice game (K-1 would only need to double the numbers whereas 2-5 would roll another die for the multiplier; this is on pages 6-10 of each Fraction equivalent pdf).

Exponential Decay and Fraction Folding Strategies

Last week with One Grain of Rice, we learned about the extraordinary power of doubling starting with one. This one grain of rice increased to over one billion after 30 doubles and to over 18 quintillion after 64 doubles. This is called exponential growth.

Doubling From 1 Grain of Rice to 18 Quintillion

The power of exponential growth is astounding. One of the most important sequences of numbers for mathematicians to know is the powers of two. These are numbers generated by raising 2 to consecutive powers (multiplying 2 by itself the number of times indicated by the “power”). Two to the zeroth power is 1 (even though we did not focus on powers, all numbers raised to the zeroth power are one). Two to the first power is 2; 2^2=4; 2^3=8; 2^4=16 or we could say that 2^5 or two to the fifth power is 2 x 2 x 2 x 2 x 2 = 32.