Ki Tisa- Proportions

"Hashem spoke to Moshe, saying: 'Now you, take for yourself prime spices: five hundred shekel-weights of pure myrrh; and aromatic cinnamon, half of it, two hundred and fifty; and cane of aromatic spice, two hundred and fifty; and kiddah, five hundred- in the sacred shekel-weight, and a hin of olive oil. Of it you shall make oil of sacred anointment, a blend of mixture, the work of a spice-blender; it shall be oil of sacred anointment...'" ~Shemot 30;22-25

"To the Children of Israel You shall speak, saying: 'This shall be for Me oil of sacred anointment for your generations. He shall not smear on the flesh of man and in its measure you shall not make anything like it; it is holy, it shall be holy for you...'" ~Shemot 30;31-32

"Hashem said to Moshe: 'Take yourself spices- stacte, onycha and galbanum- spices and pure frankincense: they shall be equal one to another. You shall make it into incense, the work of a spice-blender, thoroughly mixed, pure and holy...'" ~Shemot 30;34-35

"'...The incense that you shall make- in its measure you shall not make for yourselves; it shall be holy to you for Hashem...'" ~Shemot 30;37

In this week's parsha, we are given 2 recipes, one for anointing oil and one for incense - both for use in the Mishkan, and given explicit instruction about whether or not they can be replicated in any form. There is an interesting commentary by the Nachalat Yaakov explaining Shemot 30;32 and 30;37. The commentary explains that while the recipe for the anointing oil can be recreated in proportion to the recipe in the Torah (but not in the exact recipe itself), the recipe for incense may not be recreated itself or in any proportional recipe, greater or lesser.

Definitions:
Proportion- comparative relation between things or magnitudes as to size, quantity, number, etc. (dictionary.com)
What does this mean? Back in Parshat Vayishlach we took a look at ratios and compared how quantities of items in a group compare to each other. The idea of proportion is maintaining these existing ratios within the whole group. Here we'll look at what that means.

Baking is always a fun, hands-on way of incorporating math skills into an activity. In lower grades, just measuring out ingredients and following the directions is an important skill. As students get older, calculating proportionally larger or smaller recipes gets them working with multiplication, division, ratios, and fractions. When working with recipes, the traditional form of a recipe (3 eggs, 1 C flour,...) is good for multiplying and dividing to make it larger or smaller, but a more basic, generic recipe that is solely based on proportions (1 part water, 2 parts flour,...) actually fits much more easily into lessons on proportionality, since the nature of the recipe is based on comparison from the start.

Let's take a look, now, at the recipes in this week's parsha.
Anointing Oil:
*500 shekel-weights pure myrrh
*half of it, 250 shekel-weights aromatic cinnamon (commentary explains that it's actually 500 total, but weighed out in half-size portions)
*250 shekel-weights cane of aromatic spice
*500 shekel-weights kiddah
*1 hin of olive oil

Incense:
*stacte
*onycha
*galbanum
*additional spices (7 other spices, according to Rashi citing the Mishna)
*pure frankincense
they shall be equal one to another.
Rashi's interpretation here is that the spices specifically mentioned (stacte, onycha, galbanum, and pure frankincense) were all equal amounts (1 to 1 ratio for all 4). Rashi explains that the amount for each was 70 maneh in weight. Rashi does not explain the possible ratio for the other additional spices.

It's interesting to note, that the recipe for the anointing oil, which can be replicated in larger or smaller quantities, is given in specific weight amounts, and the incense, which may not be replicated in any proportion, is given in a proportional recipe, without any measurements. Perhaps the missing proportions are missing to keep us from actually attempting to replicate the recipe?

So what if we wanted to make some nice tiny vials of anointing oil to use as a perfume? How could we make a smaller recipe? Let's divide the whole recipe by 5 to get our smaller proportionally similar recipe:

*500 ÷ 5 = 100 shekel-weights pure myrrh
*half of it, 250 ÷ 5 = 50 shekel-weights aromatic cinnamon (commentary explains that it's actually 500 ÷ 5 = 100 total, but weighed out in half-size portions)
*250 ÷ 5 = 50 shekel-weights cane of aromatic spice
*500 ÷ 5 = 100 shekel-weights kiddah
*1 ÷ 5 = 1/5 hin of olive oil

Therefore, our new, smaller recipe would be:
*100 shekel-weights pure myrrh
*two batches of 50 shekel-weights aromatic cinnamon (100 total weight)
*50 shekel-weights cane of aromatic spice
*100 shekel-weights kiddah
*1/5 hin of olive oil

Want to make it larger, rather than smaller? Just multiply each ingredient by the same number instead of dividing.