Balak- Mathematical Insights Using Percentages and Other Basic Math

"These are the counted ones that Moses, Aaron, and the princes of Israel counted- twelve men, one man for his father's house, were they- these were all the counted ones of the Children of Israel, according to their fathers' house, from twenty years of age and up, everyone who goes out to the army in Israel: All their counted ones were six hundred and three thousand, five hundred and fifty. The Levites according to their fathers' tribe were not counted among them." ~Bamidbar 1;44-47 (Parshat Bamidbar)

In this week's parsha, following the plague as punishment for Israel becoming attached to Baal-peor:
"Hashem said to Moses, 'Take all the leaders of the people, and hang [the idol worshipers] before Hashem  opposite the sun- and the flaring wrath of Hashem will withdraw from Israel.' Moses said to the judges of Israel, 'Let each man kill his men who were attached to Baal-peor.'" ~Bamidbar 25;4-5
"Those who died in the plague were twenty-four thousand." ~Bamidbar 25;9

Rashi on Bamidbar 25;5 says:

Let each man kill his men: Each and every one of the judges of Israel would kill two and the judges of Israel were seven myriads (seventy thousand), and eight thousand as stated in Sanhedrin.

At first, Rashi's commentary confused me. At the end of the parsha, we are explicitly told that 24,000 died as the result of the plague. Rashi here is stating that 78,000 judges each killed 2 people. The numbers alone don't make sense- how did 78,000 judges kill only 24,000 people (comparing numbers- good lower elementary skill)? If we do the basic multiplication (middle elementary skill), to calculate Rashi's understanding that each judge killed 2 sinners, then 

78,000 Judges x 2 sinners killed = 156,000 men killed.

How does this make sense? I did a little more research, and it seems that Gemara Sanhedrin 82a talks about the Israelite man and the Midianite woman being Zimri son of Salu (from the tribe of Shimon) and Cozbi daughter of Zur (Midianite princess). In the gemara, it says that Zimri brought with him 24,000 Israelites from his tribe, which is what led him to sin (that's some peer pressure!). While it's not stated explicitly, my understanding from this explanation would then be that the 24,000 that we are told of in Bamidbar 25;9 are just the 24,000 Israelites from the tribe of Shimon, and that the additional sinners who were killed by the judges actually did number 156,000.

Now that we have some numbers to go on, let's work with some calculations:

*Let's start by figuring out how many people actually died all together as a result of this situation: (Good practice of long addition algorithm for younger students- remember to line up place values)

24,000 + 156,000 = 180,000 total Israelites who died 

*If we go based on these two accountings, how many Jews were left in the general population (non-Levite) after the plague? (Good practice of long subtraction algorithm for younger students- remember to line up place values)

603,550 - 180,000 = 423,550 total non-Levite Israelites who were left

*What percentage of the general population of Jews were killed in the plague? (Good calculation practice for Middle School)

Following our methods from Parshat Vayigash:
180,000/603,550 = 0.29823544031, or approximately 30%
This means that approximately 70% of the general population was left after the plague was finished. Let's check and see if those numbers are consistent:
423,550/603550 = 0.70176455968, or approximately 70%

An interesting follow-up activity:
If we are assuming that the 24,000 mentioned in Bamidbar 25;9 were all from Shimon, how would our percentage calculations look if we just took the census information for Shimon from back in Bamidbar and compared what percentage of Shimon died as a result of the plague. When making these calculations, we could also consider that Zimri was from Shimon and was killed, but not accounted for in the 24,000. Also, the Judges from Shimon each killed 2 people, so the Israelites from Shimon who were killed by the Shimonite judges would also need to be added into the Shimonite death toll for an accurate calculation.