Shmini- Sharing portions

"Moshe spoke to Aaron and to Elazar and Ithamar, his remaining sons, 'Take the meal-offering that is left from the fire-offerings of Hashem, and eat it unleavened near the Mizbe'ach; for it is that which is holy of the highest degree. You shall eat it in a holy place, for it is your portion and the portion of your sons from the fire-offerings of Hashem, for so have I been commanded. And the breast of the waving and the thigh of the raising you are to eat in a pure place, you and your sons and your daughters with you; for they have been given as your portion and the portion of your sons from the sacrifices of the peace-offerings of the Children of Israel. They are to bring the thigh of the raising and the breast of the waving upon the fire-offering fats to wave as a wave service before Hashem; and it shall be for you and your sons with you for an eternal decree, as Hashem has commanded.'" ~Vayikra 10:12-15

In the above section of this week's parsha, Moshe explains to Aaron about how the meal-offering (mincha-מנחה), the wave offering (tenupha-תנופה), and the raise offering (terumah-תרומה) are divided amongst Aaron and his children. Rashi discusses the apportioning on 10:13 and 10:14, where there is differentiation between the mincha, which is the holiest, and the tenupha and terumah, which must be eaten in a pure place.

If we look at the comparison of these different sacrifices, we see that the mincha is to be apportioned between Aaron and his sons, with no mention of daughters at all. Regarding Tenupha and terumah, however, Moshe mentions both the sons and daughters eating along with Aaron, but he mentions portions for only Aaron and his sons. Rashi explains these differences in wording to mean that the mincha should only be portioned for and eaten by Aaron and his sons- his daughters may not partake. For tenupha and terumah, the portions are again only to be divided between Aaron and his sons, but for these, when they are eating their portions, they may share their portions with their daughters and wives. 

Practically speaking, what does this mean? For ease of calculating, let's think about the portions of sacrifices based on made up weights that would be divided between Aaron and his sons. Before we begin, we also need to know about the composition of Aaron's immediate family, to the best of our knowledge. 

*Aaron was married to Elisheva
*Their 2 oldest sons, Nadav & Avihu, were killed at the beginning of this chapter for bringing a fire onto the altar without checking with Moshe.
*Aaron and Elisheva's son Elazar was married
*Elazar and his wife had a son Pinchas
*Aaron and Elisheva's 4th son was Ithamar

So, in sum, there were 4 Kohanim (priests)- Aaron, Elazar, Ithamar, and Pinchas. Then, there were 2 women in the immediate family- Elisheva and Elazar's wife.

Now let's look at a sample situation to understand the calculations. Let's assume that there's 8 lbs. of each sacrifice to be apportioned. 

Mincha- This will be divided evenly between the 4 Kohanim, and each Kohen will have 2 lbs. (8 lbs. ÷ 4 Kohanim = 2 lbs. per Kohen). Each Kohen will also eat the full 2 lbs. on their own.

Tenupha & Terumah- This will also be divided evenly between the 4 Kohamin, and each Kohen will, again, have 2 lbs. (same calculation as above). However, they will not each have 2 lbs. of each sacrifice to eat.
*Aaron will share his 2 lbs. with Elisheva. So, if divided evenly, Aaron & Elisheva will each have 1 lb. of tenupha and 1 lb. of terumah.
*Elazar will share his 2 lbs. with his wife. So, as with Aaron, Elazar and his wife will each have 1 lb. of each of the 2 sacrifices.
*Pinchas and Ithamar having no family at this point, would each eat their entire portions of 2 lbs. of each sacrifice.

If we think about this situation related to fractions, we would say that each sacrifice was divided the same, and each Kohen received 1/4 of the sacrifice. When it came to eating the sacrifices, though, while each Kohen ate 1/4 of the mincha, this was not the case for the tenupha & terumah. Let's think about those fractions:
*Aaron had 1/4 of each, which he shared with Elisheva- What is half of 1/4? If we take our 1/4 pieces and break them each into half, we would have 8 pieces out of our original 4, so Aaron's 1/4 was the same as 2/8, and he and Elisheva each had 1/8 of each the tenupha & terumah.
*Comparably, Elazar and his wife also each had 1/8 of each of these 2 sacrifices.
*As with the portion weights sampled above, Pinchas and Ithamar each ate their entire 1/4 of each of these sacrifices.

To help students internalize these calculations (by weights and/or by fractions), we could have them personalize these calculations by applying them to their own family compositions. How much of each of the 3 sacrifices would the people in their own families receive? After they calculate for their own families, they can compare calculations with their peers, to extend their thinking again to a third sample size.