In this week's parsha, there were a number of smaller activity ideas that caught my attention. Different activities apply to different learning levels, and some are more easily modified up or down for varying age learners. Below I've listed each passage pertaining to the activities, with the specific activity ideas summarized directly below the applicable passage.
"Hashem spoke to Moshe, in the Wilderness of Sinai, in the second year from their exodus from the land of Egypt, in the first month, saying: 'The Children of Israel shall make the pesach-offering in its appointed time. On the fourteenth day of this month in the afternoon shall you make it, in its appointed time; according to all its decrees and according to all its laws shall you make it.' Moshe spoke to the Children of Israel to make the pesach-offering. They made the pesach-offering in the first [month], on the fourteenth day of the month, in the afternoon, in the Wilderness of Sinai; according to everything that Hashem had commanded Moshe, so the Children of Israel did." ~Bamidbar 9:1-5
"In the second month, on the fourteenth day, in the afternoon, shall they make it; with matzot and bitter herbs shall they eat it." ~Bamidbar 9:11
- Calendar activity- In the above passage we are given dates for when the Israelites first offered the pesach offering in the desert, and then when they offer the secondary pesach offering for anyone who was impure at the time of the first offering. Using a calendar, students can map out the dates given in this passage, and they can also compare them to the dates listed on modern-day Jewish calendars to make the connection between the dates listed in the passage and the dates on which we now celebrate Pesach and Pesach Sheni.
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"Hashem spoke to Moshe, saying, 'Make for yourself two silver trumpets- make them beaten out, and they shall be yours for the summoning of the assembly and to cause the camps to journey. When they sound a long blast with them, the entire assembly shall assemble to you, to the entrance of the Tent of Meeting. If they sound a long blast with one, the princes shall assemble to you, the heads of Israel's thousands. When you sound short blasts, the camps resting to the east shall journey. When you sound short blasts a second time, the camps resting to the south shall journey; short blasts shall they sound for their journeys. When you gather together the congregation, you shall sound a long blast, but not short blasts. The sons of Aaron, the Kohanim shall sound the trumpets, and it shall be for you an eternal decree for your generations.'" ~Bamidbar 10:1-8
- Codes- The above passage gives directions for Moshe to make two silver trumpets and use different combinations of blasts to indicate different messages to the groups of Israelites. Students could first map out the different blasts and what they indicate- long blasts? short blasts? combinations of long and short? number of each type of blast? Younger students could role play having the teacher sound a trumpet or call out a sound in a certain way and following different directions (move to the front of the room, sit down in a circle, sit down at the project tables,...) based on the sounds made. Older students could use this as a launching point into a discussion of other coding that is used- morse code, for example- and create a code of their own to then share with the group.
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"Moshe said, 'Six hundred thousand foot soldiers are the people in whose midst I am, yet You say I shall give them meat, and they shall eat for a month of days!...'" ~Bamidbar 11:21
- Rounding numbers & Comparing numbers- Rashi on this passage wrote about how when Moshe is complaining about having to provide meat for the Israelites after they complained about the manna, he lists the foot soldiers at an even 600,000 men, yet when we read about the census in Bamidbar 1:46, there were 603,550 soldiers counted. What happened?
- Rashi offers 2 explanations:
- Moshe was not focused on the detail of the specific numbers. Thinking about it, this makes sense- when you are upset or excited about something, you are focused on the big picture or larger situation, not the very specific details.
- Students can talk about how we round numbers mathematically. Find the greatest place value that we want to round to, and then look at the next smaller place value. If the number in that place is 5 or greater, then we round our desired place value up by one number; if the number in that place is 4 or less, then we round down by keeping our desired place value at its current number. In Moshe's excitement, did he round accurately according to the rules of mathematics?
- Moshe was only referring to the men who left Egypt, who were the ones who complained, since only those who left Egypt had something to compare their experience to and say that this was worse.
- Students can refer back to Shemot 12:37 to compare the numbers. Students can calculate that, based on this comparison, there were therefore 3,550 men who were born and raised in the desert.
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"Moshe left and spoke the words of Hashem to the people; and he gathered seventy men from among the elders of the people and had them stand around the tent. Hashem descended in a cloud and spoke to him, and He set aside some of the spirit that was upon him and gave it to the seventy men, the elders; when the spirit rested upon them, they prophesied, but did not continue to do so. Two men remained behind in the camp, the name of one was Eldad and the name of the second was Medad, and the spirit rested upon them; they were of those who had been written, but they had not gone out of the Tent, and they prophesied in the camp." ~Bamidbar 11:24-26
- Probability- In the passage above, Hashem instructed Moshe to gather 70 elders to help in the spiritual guidance of the Israelites. Rashi explains that there were supposed to be 6 elders from each tribe (12 x 6 = 72) who were to gather and draw lots. The lots would indicate 70 spiritual leaders and 2 who were not able to attain prophetic status. Eldad and Medad, however, assumed that they would not achieve prophetic status, so they did not join the group. When the lots were drawn, 2 of the present elders drew blank lots, and the lots for Eldad and Medad were left undrawn. A few questions to begin thinking about this statistically:
- What was the probability of each elder drawing a prophetic lot? What was their probability of drawing a blank lot?
- Was their probability changed in any way by Eldad and Medad abstaining from drawing lots?
- What percentage/fraction of the elders achieved prophetic status? What percentage/fraction of the elders did not achieve prophetic status?
"The Children of Israel journeyed from Rameses to Succoth, about six hundred thousand on foot, the men, aside from the children." ~Shemot 12:37
Rashi here explains that the distance from Rameses to Succoth was 120 mils, and that Hashem made their travel there as if in an instant.
To gain a better understanding of this explanation in today's measurements, 1 mil = 2,000 amot, and 1 amah is estimated between 18-24 inches. Based on this estimate, 1 mil would be anywhere from 3,000-4,000 ft.
Rashi also explains that the estimated number that is given here is men from twenty years and older, possibly draft age, which would be men 20-60 years old.
As I was reading this, I wondered how much distance a group of this size would cover when they're traveling as a whole group (ie, how much land would the whole group cover at once?). If Hashem hadn't brought them immediately through a miracle, would the first person have reached Succoth before the last people left Rameses?
To begin to figure this out, we have 2 calculations to consider:
1) What would be today's equivalent of the distance they needed to travel?
2) What would the full population estimate be for the group?
Distance Traveled:
Based on Rashi's information above, they traveled 120 mils, where each mil is anywhere from 3,000-4,000 ft. For an easier calculation, you can choose either the lower estimate or the upper estimate. I'm going to work through both calculations and offer a range.
To calculate, we will multiply the distance in feet for 1 mil times the number of mils that was their travel distance (120).
For the lower estimate, that means 3,000 (ft) x 120 (mils) = 360,000 ft
For the upper estimate, that means 4,000 (ft) x 120 (mils) = 480,000 ft
So, the distance from Rameses to Succoth was anywhere from 360,000 - 480,000 ft.
Another level of unit conversion to consider:
If we know that 5,280 ft = 1 mile, we can convert this range into miles. Do we multiply or divide here? This question will stump many students. Let's think, we are trying to convert a number of feet into miles. We know that every group of 5,280 ft together make 1 mile. We are taking big chunks of feet and changing them each out for 1 mile. To make this conversion, we are finding out how many chunks of 5,280 ft can be fit into, say, 360,000 ft. This means division.
So, 360,000 ft ÷ 5,280 ft = approximately 68.18 miles
and 480,000 ft ÷ 5,280 ft = approximately 90.91 miles
So, the distance from Rameses to Succoth was anywhere from 68.18 - 90.91 miles.
Population Estimate:
If we use the estimate that there were approximately 600,000 men between the ages of 20-60, it's probably a fair estimate to say that this is 1/3 of the male population (men younger than 20 and men older than 60 making up the other 2/3 of the male population). We can also say that the male population is only half of the total population, assuming that the population was roughly 1/2 male and 1/2 female.
To calculate how many men there were, we can multiply 600,000 x 3 = 1,800,000 men.
To calculate the total population, we can double this number: 1,800,000 x 2 = 3,600,000 total estimated population.
So, we can safely estimate that there were more than 3.5 million people who left Egypt and traveled from Rameses to Succoth.
Final Calculations:
Although the numbers are larger to calculate with, I'd like to use the distance measured in feet to finalize our calculations. One important aspect of understanding the information and numbers that you're working with is recognizing which numbers make the most sense to use for a calculation. If we want to estimate how much space a person needs, it's easier to estimate this number using a measurement of feet rather than miles.
If we estimate, conservatively, that each person needs 2 feet of space, then with a distance of 360,000 ft, you could have a line of 360,000 ÷ 2 = 180,000 people, at most.
With the same conservative estimate, then with a distance of 480,000 ft, you could have a line of 480,000 ÷ 2 = 240,000 people, at most.
So, with little space in front or back of them, you could have a line of between 180,000 - 240,000 people reaching all the way from Rameses to Succoth.
But we have an estimate of 3,600,000 people!?
3,600,000 (population) ÷ 180,000 (people in each line) = 20 lines of people
or
3,600,000 (population) ÷ 240,000 (people in each line) = 15 lines of people
So, without consideration for all the animals and possessions that the Israelites left with, if they lined up almost front to back with each other, there would have been 15-20 lines of people spanning the entire distance from Rameses to Succoth.
An Extra Look:
In Judaism, we often speak of a person's "daled amot" or 4 amot of personal space. With this measurement in mind, we could use the distance from Rameses to Succoth and calculate how much space each person would have needed if we allowed each person 4 amot.
Let's go back to the first equivalency above: 1 mil = 2,000 amot
We know that there were 120 mil, so that would be
120 x 2,000 = 240,000 amot as the distance between Rameses and Succoth.
If we want to allow 4 amot each to 3,600,000 people, we need to calculate
3,600,000 x 4 = 14,400,000 amot needed.
Ok, so now we need to figure out how many times the distance from Rameses to Succoth would be needed in order to accommodate all the space needed by the population.
14,400,000 amot (population) ÷ 240,000 amot (distance) = 60 lines of people.
Another way to look at the same calculation is to follow the same calculation process that we did above for feet.
The distance was 240,000 amot ÷ 4 amot for each person = 60,000 people would fill a line reaching from Rameses to Succoth.
Our population of 3,600,000 ÷ 60,000 people in each line = 60 lines of people.
We just confirmed the same answer through 2 different calculation approaches!
So, again, if each person had 4 amot of space to travel (not accounting for animals or possessions), they would have had 60 lines of people lined all the way from Rameses to Succoth.
"And Moshe said, 'So said Hashem, 'At midnight I shall go out in the midst of Egypt. Every firstborn in the land of Egypt shall die, from the firstborn of Pharaoh who sits on his throne to the firstborn of the slave-woman who is behind the millstone and all the firstborn of the animal." ~Shemot 11;4-5
"It was at midnight, and Hashem smote every firstborn in the land of Egypt, from the firstborn of Pharaoh sitting on his throne to the firsborn of the captive who was in the dungeon, and every firstborn animal." ~Shemot 12;29
In his commentary on 11;4 above, Rashi explains that "[Midnight] means when the night is divided". This is understood to mean when the night is divided exactly in half, into two equal portions. In other words, the exact time in the middle of the night when the nighttime that has passed and the nighttime that remains is exactly the same.
Midpoint:
In math, the midpoint is the exact point at which half is before the point and half is after the point. There are different areas of math where midpoint is needed.
*In Geometry, we can measure the midpoint of lines or sides of shapes (exactly halfway along a line or side).
*In Statistics, given a set of data, there is often a need to calculate the midpoint between two numbers.
Calculating to find a midpoint is the same as trying to find the mean or arithmetic average of two numbers. We can find the midpoint by adding the two numbers together and dividing the sum by 2.
*So, if you want to locate the midpoint of a 10 ft wall, think about the measuring tape along the side of the wall: the measuring tape starts at 0 (the beginning of the wall) and ends at 10 ft (where the wall ends). You would add 0 + 10 = 10, then divide 10 ÷ 2 = 5. So, the 5 ft mark would be the midpoint of the wall.
*If you want to find the midpoint between any two numbers, say 10 and 70, you would add 10 + 70 = 80, then divide 80 ÷ 2 = 40. So, the midpoint between 10 and 70 is 40.
Connection to the parsha:
In this week's parsha, we learn that Hashem promises that he will kill the non-Jewish firstborns (humans and animals) at the exact midpoint of the night- the exact midpoint between sunset and sunrise. This is actually a calculation that we still use nowadays when calculating times according to Jewish law. Let's go through a sample calculation for finding "midnight", according to the Torah understanding of the term (ie. the midpoint of the night).
Let's take some data for sunset 1/2/2014 and sunrise 1/3/2014 in Boston, MA. The midpoint between these two times, should be exact midnight.
--sunset 1/2/2014 is 4:23 pm
--sunrise 1/3/2014 is 7:14 am
*First, we need to calculate how many hours there are between sunset and sunrise (ie how many hours of darkness). This time difference is 14 hrs and 51 min.
*Next, we divide this time in half. 14 hrs and 51 min divided in half is 7 hrs and 25.5 min.
*Finally, we can either add the 7 hrs and 25.5 min to 4:23 am or subtract it from 7:14 pm (get it? because it's exactly halfway between the two times, you can get to it either way). Since it's usually more intuitive to add rather than subtract, especially when working with time, let's add 7 hrs and 25.5 min onto 4:23. This give us 11:48:30 pm (that's hrs:min:sec)
For fun, let's make a connection directly to the parsha; let's calculate midnight in Egypt in the month of April, to get an idea for what time the parsha is referring to.
This year Pesach begins on April 10, so let's take data for sunset on 4/10/2014 and sunrise 4/11/2014 in Cairo, Egypt.
--sunset 4/10/2014 is 6:19 pm
--sunrise 4/11/2014 is 5:33 am
* First, we calculate how many hours between sunset and sunrise. This time difference is 11 hrs and 14 min.
*Next, we divide this time in half. 11 hrs and 14 min divided in half is 5.5 hrs and 7 min, in other words, 5 hrs and 37 min.
*Finally, we add 5 hrs and 37 min to 6:19 pm. This gives us 11:56 pm.
Whatever date and time you choose- any season, any region- it should always approximate midnight as we know it (12 am). Test it out and see what you find!
