unit factor method
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ShareUse volume of מן to illustrate the unit factor method for high school science students.
וַיֹּ֣אמֶר מֹשֶׁ֗ה זֶ֤ה הַדָּבָר֙ אֲשֶׁ֣ר צִוָּ֣ה יְהֹוָ֔ה מְלֹ֤א הָעֹ֙מֶר֙ מִמֶּ֔נּוּ לְמִשְׁמֶ֖רֶת לְדֹרֹתֵיכֶ֑ם לְמַ֣עַן ׀ יִרְא֣וּ אֶת־הַלֶּ֗חֶם אֲשֶׁ֨ר הֶאֱכַ֤לְתִּי אֶתְכֶם֙ בַּמִּדְבָּ֔ר בְּהוֹצִיאִ֥י אֶתְכֶ֖ם מֵאֶ֥רֶץ מִצְרָֽיִם׃
Moses said, “This is what יהוה has commanded: Let one omer of it be kept throughout the ages, in order that they may see the bread that I fed you in the wilderness when I brought you out from the land of Egypt.”
Step 1) What measure of מן were we commanded to collect each day?
וְהָעֹ֕מֶר עֲשִׂרִ֥ית הָאֵיפָ֖ה הֽוּא׃ {פ}
The omer is a tenth of an ephah.
Step 2) Write a conversion factor between an עמר and an איפה
עשרית האיפה. הָאֵיפָה שָׁלֹשׁ סְאִין וְהַסְּאָה ו' קַבִּין וְהַקַּב ד' לֻגִּין וְהַלֹּג ו' בֵּיצִים, נִמְצָא עֲשִׂירִית הָאֵיפָה מ"ג בֵּיצִים וְחֹמֶשׁ בֵּיצָה, וְהוּא שִׁעוּר לַחַלָּה וְלַמְּנָחוֹת:
עשירית האפה [THE OMER] IS THE TENTH PART OF AN EPHAH — The Ephah is three Seahs, and the Seah is six Kabs, and the Kab is four Logs and the Log has the capacity of six eggs: it follows, therefore, that the tenth of an Ephah has the capacity of forty-three and a fifth eggs — and this is the minimum quantity of dough for the Challa (the minimum quantity to which applies the injunction to separate a portion of the dough; cf. Numbers 15:20), and the measure for the meal offering (cf. Rashi on Eruvin 83b).
Step 3) Still in volume! Write a conversion factor for איפה to סאה
כִּדְתַנְיָא: ״וְרָחַץ בַּמַּיִם אֶת כָּל בְּשָׂרוֹ״ — שֶׁלֹּא יְהֵא דָּבָר חוֹצֵץ בֵּין בְּשָׂרוֹ לַמַּיִם. ״בַּמַּיִם״ — בְּמֵי מִקְוֶה. ״אֶת כׇּל בְּשָׂרוֹ״ — מַיִם שֶׁכׇּל גּוּפוֹ עוֹלֶה בָּהֶן, וְכַמָּה הֵן? אַמָּה עַל אַמָּה בְּרוּם שָׁלֹשׁ אַמּוֹת, וְשִׁיעֲרוּ חֲכָמִים שִׁיעוּר מֵי מִקְוֶה אַרְבָּעִים סְאָה.
Rav Ḥisda said: The quarter-log measurement of the Torah is two fingerbreadths by two fingerbreadths in volume, by the height of two fingerbreadths and one half fingerbreadth and one-fifth of a fingerbreadth. This statement is as it was taught in a baraita concerning a ritual bath, about which the verse states: “And he shall bathe all his flesh in the water” (Leviticus 15:16), from which the Sages expounded: This phrase teaches that there should be nothing interposing between one’s flesh and the water. The expression “in the water” indicates that the verse is referring to a specific body of water, i.e., in the water of a ritual bath. The phrase “all his flesh” teaches that one must immerse in water that his whole body can enter at once. And how much is that? A cubit, by a cubit, by a height of three cubits. And the Sages measured the measure of the water necessary for a ritual bath at forty se’a.
Step 4) Let's go from volume to length3!!! Write a conversion factor:
מֵיתִיבִי: כׇּל אַמּוֹת שֶׁאָמְרוּ חֲכָמִים בְּאַמָּה בַּת שִׁשָּׁה, וּבִלְבַד שֶׁלֹּא יְהוּ מְכֻוּוֹנוֹת.
The Gemara raises an objection from a baraita: All cubits that were mentioned by the Sages are cubits of six handbreadths, provided that they are not precisely a cubit. Granted, according to Rava, the baraita means: So that these, the cubits of diverse kinds of seeds, should be measured with expansive handbreadths, and those, the cubits of sukka, should be measured with depressed handbreadths. However, according to Abaye, it is difficult.
Step 5) From cubic amot to cubic tefachim! Write a conversion factor, but make sure you account for cubing!
Step 6) There are a few opinions about the size of a tefach. Rabbi Moshe Feinstein says that a tefach is 9.0 cm. Write a conversion factor to take cubic tefachim to cubic centimeters.
Step 7a) convert from cm3 to ml, and then
Step 7b) from ml to liters.
Step 7a) convert from cm3 to ml, and then
Step 7b) from ml to liters.
