Thursday, August 20, 2015

Shoftim- Activity Suggestions related to Understanding Fractions

"This shall be the due of the Kohanim from the people, from those who perform a slaughter, whether of an ox or of a lamb/kid: he shall give the Kohen the foreleg, and the jaw, and the stomach. The first of your grain, wine, and oil, and the first of the shearing of your flock you shall give to him." ~Devarim 18:3-4
Rashi on 18:4 "The first of your grain":
"This is terumah. [Scripture] did not specify an amount regarding it, but our Rabbis established an amount regarding it: One who has a nice eye, i.e., one who is generous, give one part out of forty. One who has a bad eye, i.e., one who is miserly, gives one part out of sixty. One who is in the middle, i.e., who tends toward neither extreme, gives one part out of fifty. And they drew support from Scripture not to give less than one out of sixty, for it says, "[This is the terumah which you shall separate:] a sixth of an ephah from a chomer of wheat." A sixth of an ephah is half of a se'ah. When you give a half se'ah per kor, see now, there is one part out of sixty, for the kor is thirty se'ahs.

Activity Suggestions:
One of the most difficult conceptual aspects of fractions is that, when comparing sizes of fractional pieces, the larger the denominator (bottom number), the smaller the piece size. Once students understand fractions, they realize that this incongruence is because the denominator explains how many equal size pieces you have cut the whole into, and the more pieces you make, the smaller each piece will be. 

  • With this in mind, younger students could test this by having fractional templates to cut or count and compare. Starting with the same size whole, which fractional pieces are larger and which are smaller? 1/2, 1/3, 1/4, etc. 
  • Students who can make sense of this concept can extend the idea to larger number without comparing visually- compare 1/27 and 1/30, for example. And then extend to connect back to our Parsha. There, we are comparing donations of 1/40, 1/50, and 1/60. Understanding this idea, why does it make sense that 1/40 is considered generous, 1/60 is considered miserly, and 1/50 is considered average?
  • Older students can look more carefully at the end section of Rashi's commentary and investigate the fractional equivalences for ephah, chomer, se'ah, and kor. Rashi's explanation indicates a comparable equivalency that relates directly to the fractions that he lists in the first part of his explanation. How do these equivalences support his explanation of the appropriate amounts to be given in donation from the first crops?

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