"Every first issue of the womb of any flesh that they offer to Hashem, whether of man or of animal, shall be yours; but you shall surely redeem the firstborn of man, and the firstborn of an impure animal shall you redeem. And those that are to be redeemed- from one month shall you redeem according to the valuation, five silver shekalim by the sacred shekel; it is twenty geirah." ~Bamidbar 18:15-16
Towards the end of this week's parsha, we read of what items are set aside to be given to Aaron and the Kohanim. Within this section, we learn that firstborn male infants and firstborn animals are part of what is to be given to the Kohanim. However, we also learn that firstborn children and impure firstborn animals are to be redeemed at the age of one month. The value for redeeming them is 5 silver shekalim, and we are told that one silver shekel is equivalent to 20 geirah.
Activity Suggestions related to Monetary Equivalence:
Learning equivalencies of monetary values can be confusing for young children. Opportunities for hands-on acting out with manipulatives, repetition, and practice help them become proficient in working with monetary conversions.
- Students can convert between geirahs and shekalim.
Given that 1 shekel = 20 geirah:
- Representing the conversion-
- Younger students could calculate how many geirahs would be in 5 shekalim, by using manipulatives for representation. They could have cups to represent 1 shekel, and small chips or counters representing a geirah. Students could work together to create shekel value cups, each filled with 20 geirah. Once they have the cups set up, they can then go back and count out 5 shekalim. 5 cups would represent 5 shekalim.
- Students who are ready could draw representative circles or boxes for shekalim and show 20 tally marks within each one to represent the geirahs in each. In this case, 5 circles or boxes would represent the 5 shekalim.
- Making the calculations-
- Youngest students can work together (or as a class) to count out how many geirahs there are all together in the 5 shekalim.
- Slightly older children could use their knowledge of "skip counting" or addition of simple large numbers to add the twenties together and make the calculation.
- Older students can use their knowledge of multiplication to problem solve and calculate how many geirahs would be in 5 shekalim.
- Follow-up calculations:
- Can students (young and old) figure out how many shekalim would be needed to redeem multiple firstborns? If 7 families redeem their firstborns, how many shekalim would be given to the Kohanim all together? How many geirahs would be given to the Kohanim all together?
- If you chart the redemption values in shekalim and geirahs for different numbers of firstborns, can you identify any patterns?
- For upper elementary or middle schoolers- can they convert the patterns that they find into functions? How would these functions look when graphed?
- Older students can also research conversion values to current day currencies. Based on the researched conversion rates, what is the value today of a geirah? of a shekel? How much would families need to pay to redeem firstborns in different countries today? Can they write a function to calculate redemption values for multiple firstborns using current currencies?
"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?
