Bamidbar- Reading, Comparing, and Calculating with large numbers

Note that the section of quotes from this week's parsha is quite long in order to show the context for Levite and firstborn census numbers. As always, I organize all of the information for you beginning below the quotes. If your time is short, feel free to scroll past the citations.

"Hashem spoke to Moshe in the Wilderness of Sinai, saying, 'Count the sons of Levi according to their fathers' house, according to their families, every male from one month of age and up shall you count them.' Moshe counted them according to the word of Hashem, as he had been commanded.

These were the sons of Levi, by their names: Gershon, Kohath, and Merari. These were the names of the sons of Gershon according to their families: Livni and Shimei. The sons of Kohath according to their families: Amram and Izhar, Hevron and Uzziel. The sons of Merari according to their families: Mahli and Mushi. These are the families of the Levites, according to their fathers' house.

For Gershon- the Livnite family and the Shimeite family; these are the Gershonite families- their counted ones according to the number of every male, from one month of age and up: their counted ones [were] seven thousand, five hundred." ~Bamidbar 3:14-22

"And for Kohath- the Amramite family, the Izharite family, the Hevronite family, and the Uzzielite family; these were the Kohathite families- the number of every male from one month of age and up [was] eight thousand, six hundred; the guardians of the charge of the sanctity." ~Bamidbar 3:27-28

"For Merari- the Mahlite family and the Mushite family; these were the Merarite families- their counted ones according to the number of every male from one month of age and up [was] six thousand, two hundred." ~Bamidbar 3:33-34

"All the counted ones of the Levites, which Moshe and Aaron counted by the word of Hashem according to their families, every male from one month of age and up, were twenty-two thousand.

Hashem said to Moshe, 'Count every firstborn male of the Children of Israel from one month of age and up, and take a census of their names. You shall take the Levites for Me- I am Hashem- in place of every firstborn of the Children of Israel, and the animals of the Levites in place of every firstborn of the animals of the Children of Israel.' Moshe counted- as Hashem had commanded him- every firstborn of the Children of Israel. Every firstborn male according to the number of their names, from one month of age and up, according to their countings, was twenty-two thousand, two hundred and seventy-three.

Hashem spoke to Moshe, saying, 'Take the Levites in place of every firstborn of the Children of Israel, and the animals of the Levites in place of their animals, and the Levites shall be Mine, I am Hashem. And as for those redeemed of [the firstborn], the two hundred and seventy-three of the firstborn of the Children of Israel who are in excess over the Levites, you shall take five shekels each according to the head count, in the sacred shekel shall you take; the shekel is twenty geirah. You shall give the money to Aaron and his sons, of those redeemed in excess among them.'" ~Bamidbar 3:39-48

In this week's parsha, we learn of multiple censuses that were taken in the desert. Last year, I looked at the census information for the 12 Israelite tribes. This census was taken for men from the age of 20 years old and older. In my post last year, I analyzed that information from a basic statistical averages viewpoint- exploring the mean, median, and mode for the data set of the census. 

This year, I would like to look at the census information for the Levites. Since we're dealing with a lot of information here, let's first focus and pull out the numerical information that we're trying to look at. The census information for the Levites is first broken down into smaller census numbers from the individual Levite families, and then summed up at the end. Then, following that information, there is another census of the firstborn Israelites. We will look at all of these sets of information.

Let's begin by weeding through the information above to organize the pertinent information that we need:

Gershon- 7,500 males from 1 month of age and older

Kohath- 8,600 males from 1 month of age and older

Merari- 6,200 males from 1 month of age and older

Then, the total sum listed for all Levites is 22,000 males from 1 month of age and older

Stop for a minute and test out this calculation. 

• Does 7,500 + 8,600 + 6,200 = 22,000? In fact, it actually adds to 22,300. 

So what's going on here? Why does the Torah omit 300 Levites in it's calculation? Rashi on 3:39 deals with this exact question. He explains that the total number of Levites was needed in order to redeem the firstborn Israelites. For every 1 Levite, 1 firstborn Israelite would be redeemed. Rashi says that the 300 Levites who are not included in the total sum were actually firstborns, themselves, and therefore would not count towards being able to redeem other Israelite firstborns, since they would be redeeming themselves.

Let's look on further- We are told that the firstborn Israelite males from 1 month of age and older totaled 22,273. 

So, if we replace one-for-one each firstborn Israelite with a non-firstborn Levite, we have 22,273 firstborns & 22,000 Levites available for redeeming:

22,273 - 22,000 = 273

Now, it seems that we have 273 firstborns who do not have a Levite to redeem them. If we continue reading, though, we see that Hashem has told Moshe that there are, in fact, 273 firstborns "in excess" of the Levites, and these 273 should be redeemed by collecting 5 shekels per person for each of them and that money will go to the Kohanim. 

Some other thoughts & activities:

• It my be interesting to compare the census for the Levites with the census of the rest of the Israelites that's listed in the first part of the parsha. In making a comparison of the numbers, it would be important to keep in mind that the census for the 12 Israelite tribes was taken from 20 years and older, while the Levite census was taken from 1 month and older. Even more so, what interesting findings do you see when comparing the numbers of the two groups?
• An interesting discussion topic may be to think about whether there is a way to compare the information given for the general Israelite census to the firstborn Israelite census to figure out any further information regarding numbers of Israelites between certain ages? Is there enough information given to create comparisons of smaller age groups- either from each tribe or from the whole group?
• For younger students, it might be interesting to just think about place value and reading large numbers. Students could have a matching activity in which they have to identify the numbers of the censuses and match them to the appropriate tribes. Students could also talk about how to think about comparing which numbers are larger and which numbers are smaller- place values and how you can use place values to compare numbers to each other to figure out which is larger and which is smaller. Students who catch on quickly to this concept could think about ordering the numbers from smallest to largest or largest to smallest.
• Follow-up activity- values are given for how many shekels were collected for the 273 "excess" firstborns who did not have Levite redeemers (Bamidbar 3:50). Older students could check the calculations for the values to see if it matches the amount that they calculate should have been donated. We are also told (Bamidbar 3:47) that a shekel was worth 20 geirah. Students can calculate a conversion of the value to also figure out the value of the donation in geirahs.