Bechukotai- Finding a rule...or not?

"I will provide peace in the land, and you will lie down with none to frighten you; I will cause wild beasts to withdraw from the land, and a sword will not cross your land. You will pursue your enemies; and they will fall before you by the sword. Five from among you will pursue a hundred, and a hundred from among you will pursue ten thousand; and your enemies will fall before you by the sword." ~Vayikra 26;6-8

Rashi on 26;8 says:
Five [from among you will pursue] a hundred, and a hundred from among you [will pursue] ten thousand. Is this the correct calculation? Should it not have rather said, "and a hundred from among you will pursue two thousand?" But, you cannot compare, a few who perform the commandments of the Torah to many who perform the commandments of the Torah.

This week, rather than teaching a new concept, I want to focus on using some preexisting knowledge to think about mathematical brainstorming. Sometimes, more than teaching new information, it's just as important to allow students the opportunity to think and learn how they best organize information and think about how numbers work together- using their number sense to work through real applications of what they know. 

In this week's parsha, we learn that when the Jews are to enter the land of Israel, they will be protected and supported by Hashem. When pursuing their enemies, we are told that 5 people could overcome 100 enemies, and 100 people could overcome 10,000 enemies.

Rashi's commentary picks up on a big mathematical question with these numbers:
Back in Parshat Ki Tisa we looked at maintaining proportions, or keeping fractions of a group the same even if we make a larger group or smaller group. In this week's parsha, Rashi points out that the numbers in the Torah here are not proportional. If...

5 people can overcome 100 enemies, and 
5 x 20 = 100, then 
100 people should be able to overcome 2,000 enemies (100 x 20 = 2,000).

Rashi explains that the numbers do not work like this in our case, because the strength of many righteous people is increased more than just proportionally. So if we look at the strength of 100 people, maybe it should be an exponential relationship? This is when the number being used is multiplied by itself. We see that 100 x 100 = 10,000.

So did we find the rule for how we can figure out the strength of a group of any size? Unfortunately, no, because it needs to work in both cases. Since 5 x 5 = 25 (not 100), then this rule only works for the second set of numbers, not the first.

How can we try to find a rule here? This is where brainstorming and playing around with numbers comes in. We lay out what we know:

5 people can overcome 100 enemies (this is x20).
100 people can overcome 10,000 enemies (this is x100)

Is there are rule to be found where for 5 people we would multiply x20, and for 100 people we would multiply x100? It's possible that breaking down the numbers into factors (e.g. 4x5- for 20; 20x5 for 100) will help us see a more intricate relationship that isn't visible with the larger numbers.

I've been playing around with the numbers this week to see what relationships I can find between the two comparative situations. I'm still playing with it. Sometimes there isn't enough information to definitively form a rule, and sometimes there just isn't a straightforward relationship. Can you find a relationship or rule that would fit both of these situations?