Shelach- Activities with One-to-One Correspondence and Measurements

For younger students:

"Hashem spoke to Moshe, saying, 'Send forth for yourself men, and let them spy out the Land of Canaan that I give to the Children of Israel; one man each from his fathers' tribe shall you send, every one a leader among them.'" ~Bamidbar 13:1-2

"...Your children will roam in the wilderness for forty years and bear your guilt, until your carcasses shall cease to be, in the wilderness. Like the number of the days that you spied out the land, forty days, a day for a year, a day for a year, shall you bear your iniquities- forty years- and you shall know what parting from me [is]." ~Bamidbar 14:33-34

 I've addressed the idea of one-to-one correspondence a couple of times in the past (see Parshat Haazinu and Parshat Ki Tisa). In this week's parsha, we have 2 instances that deal directly with this idea. 

At the beginning of the parsha, Hashem instructs Moshe to have one leader from each tribe assigned to go out and visit the land of Canaan to see what the Children of Israel were to expect upon entering the land. 

• If there is one man from each tribe, how many men were sent? Since we know that there are 12 tribes, if each tribe sends one man, there will also be 12 men. 
• Acting it out- Students can be separated into 4 or 5 groups ("tribes"). Within each group, a "leader" can be chosen. Students can count how many groups/tribes there are. Based on this, ask students how many leaders there will be. Have the leaders come to a separate area in the room and have the class count the leaders. Were there predictions correct? Are the students all making the one-to-one connection?

In the middle of the parsha, Hashem becomes upset with the spies' report of Canaan, which led to fear-mongering amongst the Children of Israel. As punishment, Hashem decides that the Children of Israel will wander in the desert one year for each day that the spies were out in Canaan.

• If we know that the spies were in Canaan for 40 days, how many years would the Children of Israel wander the desert? If the spies were there for 40 days, then 1 year for each day would mean that they would wander the desert for 40 years.
• Extrapolation discussion- [Sample questions] If you received one present for every birthday that you've had, how many presents would you have now? (5yo would have 5, 6yo would have 6, etc.); If there are 10 classes in school, and each class makes a poster to put in the hallway, how many posters will be in the hallway? (10 classes = 10 posters)

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Multi-level: 

"Hashem spoke to Moshe, saying, 'Speak to the Children of Israel and say to them: When you will come to the land of your dwelling places that I give you, and you perform a fire-offering service to Hashem- an olah-offering or a [peace-offering] sacrifice by articulating a vow or a free-will offering, or on your festivals, to produce a pleasing fragrance to Hashem, from the cattle or from the flock- the one who brings his offering to Hashem shall bring a meal-offering of a tenth [of an ephah] fine flour, mixed with a quarter-hin of oil; and a quarter-hin of wine for a libation shall you prepare for the olah-offering or the [peace-offering] sacrifice for each sheep. If it is a ram- you shall prepare a meal-offering, two-tenths [of an ephah] fine flour mixed with a third-hin of oil; and a third-hin of wine for a libation shall you bring as a satisfying aroma to Hashem. When you prepare a young bull as an olah-offering or a [peace-offering] sacrifice, because of an articulated vow, or a peace-offering to Hashem, one shall bring with the young bull a meal-offering: three tenths [of an ephah] fine flour mixed with a half-hin of oil. You shall bring a half-hin of wine for a libation, a fire-offering, a pleasing fragrance to Hashem...'" ~Bamidbar 15:1-10

At the end of this week's parsha there is a list of information regarding different sacrifices. In this section, depending on the animal offered as part of the sacrifice, the specifications of the meal-offering ingredients differ. There are a number of activities that can be arranged around this information.

• The first step is to organize the information- I recommend charting the information based on the animal that each different meal-offering is assigned to. For younger students, you can have the information pre-charted for them, including pictures of ingredients for pre-readers.
• Comparing information: 
• Which sacrifice has the most flour? Which has the most oil? Which has the most wine? 
• Order them from least to greatest (or greatest to least) amounts of flour. Order by amounts of oil. Order by amounts of wine. 
• Are there any patterns that you see? Between the different sacrifices? When they are ordered by amounts?
• Conversions- Using current day equivalencies for ephah and hin, how much of each ingredient would be used for each sacrifice? 
• Note: For conversion reference, I posted a chart with conversions including ephah for Parshat Beshalach and Wikipedia has a page with Biblical measurements, including hin under liquid measures; as I wrote in Parshat Shelach last year, a se'ah is usually calculated between 2.25 and 4 gallons in current measurements.
• Interesting conceptual thought:
•  For younger students- When you convert from Biblical units to modern day units, does the amount that you have change? Another way of thinking about it- if you measure a table using inches and then using feet, does the size of the table change, or just the measurement you're using to think about the item?
• For older students- When you convert the measurements, will they still compare in the same ways when you order them? What about patterns? If there is a relationship between the measurements, will the relationships remain the same when you have converted into modern day measurements?

Shelach- More Unit Conversions

"[The spies] arrived at the Valley of Eshcol and cut from there a vine with one cluster of grapes, and they carried it on a pole, by two, and of the pomegranates and of the figs." ~Bamidbar 13;23 

Rashi on 13;23 says:
And they carried it on a pole, by two: From the implication of that which has been said, "And they carried it on a pole," am I not aware that it is carried by two people? Why does the Torah say "by two"? It means that it was carried by two poles, not by two people. How was this done? Eight of the spies took a cluster; one took a fig; and one a pomegranate. Joshua and Caleb did not take anything, for with [the spies'] entire being, i.e., they had no goal in bringing the fruit other than that they intended to spread slander against the Land of Israel, by saying, "Just as its fruit is unusual in its size, so are its people unusual." And if you wish to know how much the burden of one of them was, i.e., how much one of them was able to carry, you can go and derive this from the stones which they set up in Gilgal. They lifted for themselves, each individual, one stone from the Jordan onto his shoulder, and set it up at Gilgal. Our Rabbis weighed [these stones]. The weight of each one was forty se'ah. And we learned that the load that a person can raise onto his own shoulder is nothing but a third of the load of the entire load that can be raised when they assist him to raise.

Before I begin, I want to make note that I first got this idea from 2 of my students who used this topic as the basis for their Math 'n Torah Fair project.

Back in Parshat Chayei Sarah we converted between two Biblical units to be able to compare weights that were measured with different Biblical measurements. What if we want to figure out, here, the weight of each fruit? Or what about how much weight each person was carrying? Again, we'll need to look to unit conversion to find out answer. In order to figure out these weights, we'll need to know the equivalent weight of a se'ah.

A se'ah is usually used for measuring volume. However, the reference which Rashi is using here is from Gemara Sotah (34a), where they chose to use the weight measure of se'ah. Most modern day estimates for the weight of a se'ah are between 2.25 gallons and 4 gallons. For our purposes, let's use the 2.25 gallon reference, as this will tell us the smallest possible estimate for the weight of the fruit. 1 gallon of water is just over 8 lbs, so the weight of the fruit, if we use the weight of water, would be 2.25 x 8 = 18 lbs. 

Let's think about:
1) What was the weight of each fruit?
2) How much weight was each person carrying?

To begin, let's organize the information that we have from Rashi.
*The fig was carried by one person
*The pomegranate was carried by one person
*The cluster of grapes was carried by 8 people

According to Rashi, each of the spies could carry a weight of 40 se'ah. This would mean that the spies carrying the fig and pomegranate were each carrying 40 se'ah x 18 lbs each, which is 720 lbs.

Now, for the grapes, Rashi says that the load that a person carries on his own is only 1/3 of the load that a person can carry with assistance. By this reasoning, 40 se'ah was only 1/3 of what each spy could carry; in other words, each spy carrying the grapes would be able to carry 40 x 3= 120 se'ah. This is the same as 120 x 18 = 2,160 lbs.

By this reasoning, the 8 spies carrying the grapes together should have been able to carry a total of:
120 x 8 = 960 se'ah or 
2,160 x 8 = 17,280 lbs

So, by our calculations the weights were:
pomegranate = 40 se'ah = minimum of 720 lbs
fig = 40 se'ah = minimum of 720 lbs
cluster of grapes = 960 se'ah = minimum of 17,280 lbs

The parsha does say that the fruit was big...

To give a little perspective, 
*Arnold Schwarzenegger is recorded as deadlifting 710 lbs. This would mean that each of the spies was approximately as strong as Arnold Schwarzenegger.
*A large elephant is approximately 15,000 lbs, which means that, based on the estimates here, 8 Arnold Schwarzeneggers could possibly carry 1 reasonably patient large elephant.

Everyday Connection:
Let's test the premise- The idea that each spy carrying with a group was able to carry 3x the amount that they could carry individually is an interesting one. I wonder how this would test out in everyday life. How much weight can you lift on your own? How much weight can you lift with one other person? Two other people? Is there are pattern that emerges in the ratio of [# of people] to [weight lifted]?