Beha'alotcha- Mixed Bag of activity suggestions

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. 

*****

"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.

*****

"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: 
1. 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?
2. 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.

*****

"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?

Bamidbar- Reading, Comparing, and Calculating with large numbers

Note that the section of quotes from this week's parsha is quite long in order to show the context for Levite and firstborn census numbers. As always, I organize all of the information for you beginning below the quotes. If your time is short, feel free to scroll past the citations.

"Hashem spoke to Moshe in the Wilderness of Sinai, saying, 'Count the sons of Levi according to their fathers' house, according to their families, every male from one month of age and up shall you count them.' Moshe counted them according to the word of Hashem, as he had been commanded.

These were the sons of Levi, by their names: Gershon, Kohath, and Merari. These were the names of the sons of Gershon according to their families: Livni and Shimei. The sons of Kohath according to their families: Amram and Izhar, Hevron and Uzziel. The sons of Merari according to their families: Mahli and Mushi. These are the families of the Levites, according to their fathers' house.

For Gershon- the Livnite family and the Shimeite family; these are the Gershonite families- their counted ones according to the number of every male, from one month of age and up: their counted ones [were] seven thousand, five hundred." ~Bamidbar 3:14-22

"And for Kohath- the Amramite family, the Izharite family, the Hevronite family, and the Uzzielite family; these were the Kohathite families- the number of every male from one month of age and up [was] eight thousand, six hundred; the guardians of the charge of the sanctity." ~Bamidbar 3:27-28

"For Merari- the Mahlite family and the Mushite family; these were the Merarite families- their counted ones according to the number of every male from one month of age and up [was] six thousand, two hundred." ~Bamidbar 3:33-34

"All the counted ones of the Levites, which Moshe and Aaron counted by the word of Hashem according to their families, every male from one month of age and up, were twenty-two thousand.

Hashem said to Moshe, 'Count every firstborn male of the Children of Israel from one month of age and up, and take a census of their names. You shall take the Levites for Me- I am Hashem- in place of every firstborn of the Children of Israel, and the animals of the Levites in place of every firstborn of the animals of the Children of Israel.' Moshe counted- as Hashem had commanded him- every firstborn of the Children of Israel. Every firstborn male according to the number of their names, from one month of age and up, according to their countings, was twenty-two thousand, two hundred and seventy-three.

Hashem spoke to Moshe, saying, 'Take the Levites in place of every firstborn of the Children of Israel, and the animals of the Levites in place of their animals, and the Levites shall be Mine, I am Hashem. And as for those redeemed of [the firstborn], the two hundred and seventy-three of the firstborn of the Children of Israel who are in excess over the Levites, you shall take five shekels each according to the head count, in the sacred shekel shall you take; the shekel is twenty geirah. You shall give the money to Aaron and his sons, of those redeemed in excess among them.'" ~Bamidbar 3:39-48

In this week's parsha, we learn of multiple censuses that were taken in the desert. Last year, I looked at the census information for the 12 Israelite tribes. This census was taken for men from the age of 20 years old and older. In my post last year, I analyzed that information from a basic statistical averages viewpoint- exploring the mean, median, and mode for the data set of the census. 

This year, I would like to look at the census information for the Levites. Since we're dealing with a lot of information here, let's first focus and pull out the numerical information that we're trying to look at. The census information for the Levites is first broken down into smaller census numbers from the individual Levite families, and then summed up at the end. Then, following that information, there is another census of the firstborn Israelites. We will look at all of these sets of information.

Let's begin by weeding through the information above to organize the pertinent information that we need:

Gershon- 7,500 males from 1 month of age and older

Kohath- 8,600 males from 1 month of age and older

Merari- 6,200 males from 1 month of age and older

Then, the total sum listed for all Levites is 22,000 males from 1 month of age and older

Stop for a minute and test out this calculation. 

• Does 7,500 + 8,600 + 6,200 = 22,000? In fact, it actually adds to 22,300. 

So what's going on here? Why does the Torah omit 300 Levites in it's calculation? Rashi on 3:39 deals with this exact question. He explains that the total number of Levites was needed in order to redeem the firstborn Israelites. For every 1 Levite, 1 firstborn Israelite would be redeemed. Rashi says that the 300 Levites who are not included in the total sum were actually firstborns, themselves, and therefore would not count towards being able to redeem other Israelite firstborns, since they would be redeeming themselves.

Let's look on further- We are told that the firstborn Israelite males from 1 month of age and older totaled 22,273. 

So, if we replace one-for-one each firstborn Israelite with a non-firstborn Levite, we have 22,273 firstborns & 22,000 Levites available for redeeming:

22,273 - 22,000 = 273

Now, it seems that we have 273 firstborns who do not have a Levite to redeem them. If we continue reading, though, we see that Hashem has told Moshe that there are, in fact, 273 firstborns "in excess" of the Levites, and these 273 should be redeemed by collecting 5 shekels per person for each of them and that money will go to the Kohanim. 

Some other thoughts & activities:

• It my be interesting to compare the census for the Levites with the census of the rest of the Israelites that's listed in the first part of the parsha. In making a comparison of the numbers, it would be important to keep in mind that the census for the 12 Israelite tribes was taken from 20 years and older, while the Levite census was taken from 1 month and older. Even more so, what interesting findings do you see when comparing the numbers of the two groups?
• An interesting discussion topic may be to think about whether there is a way to compare the information given for the general Israelite census to the firstborn Israelite census to figure out any further information regarding numbers of Israelites between certain ages? Is there enough information given to create comparisons of smaller age groups- either from each tribe or from the whole group?
• For younger students, it might be interesting to just think about place value and reading large numbers. Students could have a matching activity in which they have to identify the numbers of the censuses and match them to the appropriate tribes. Students could also talk about how to think about comparing which numbers are larger and which numbers are smaller- place values and how you can use place values to compare numbers to each other to figure out which is larger and which is smaller. Students who catch on quickly to this concept could think about ordering the numbers from smallest to largest or largest to smallest.
• Follow-up activity- values are given for how many shekels were collected for the 273 "excess" firstborns who did not have Levite redeemers (Bamidbar 3:50). Older students could check the calculations for the values to see if it matches the amount that they calculate should have been donated. We are also told (Bamidbar 3:47) that a shekel was worth 20 geirah. Students can calculate a conversion of the value to also figure out the value of the donation in geirahs. 

Bamidbar- Basic Statistics: Mean, Median, and Mode

"Their counted ones, for the tribe of Reuven: forty-six thousand, five hundred." ~Bamidbar 1;20
"Their counted ones, for the tribe of Shimon: fifty-nine thousand, three hundred." ~Bamidbar 1;23
"Their counted ones, for the tribe of Gad: forty-five thousands, six hundred and fifty." ~Bamidbar 1;25
"Their counted ones, for the tribe of Judah: seventy-four thousand, six hundred." ~Bamidbar 1;27
"Their counted ones, for the tribe of Issachar: fifty-four thousand, four hundred." ~Bamidbar 1;29
"Their counted ones, for the tribe of Zevulun: fifty-seven thousand, four hundred." ~Bamidbar 1;31
"Their counted ones, for the tribe of Ephraim: forty thousand, five hundred." ~Bamidbar 1;33
"Their counted ones, for the tribe of Menasheh: thirty-two thousand, two hundred." ~Bamidbar 1;35
"Their counted ones, for the tribe of Binyamin: thirty-five thousand, four hundred." ~Bamidbar 1;37
"Their counted ones, for the tribe of Dan: sixty-two thousand, seven hundred." ~Bamidbar 1;39
"Their counted ones, for the tribe of Asher: forty-one thousand, five hundred." ~Bamidbar 1;41
"Their counted ones, for the tribe of Naftali: fifty-three thousand, four hundred." ~Bamidbar 1;43

"...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." ~Bamidbar 1;45-46

This week's parsha begins with Hashem telling Moshe to take a census of all the men in Israel from the age of 20 and older. Hashem appoints one person from each tribe as a prince to help Moshe take the census.

What is Statistics?
In simple terms, statistics is the mathematical study of data (numbers in a certain situation) in order to provide information about the situation. For example, if I have test scores from a class of students, I could use statistics to find out information about how the whole class performed on the test. Or, if I want to know information about the general height of students in the class, I can use statistics to analyze the heights of the students in the class. The data for these examples would be the list of all the test scores, or the list of each students' height.

What could we do with these sets of data? There are 3 different calculations that are known as the statistical averages: 
1) mean 
2) median
3) mode

Each of these averages can be more or less meaningful in given situations. 
*Mean is calculated by adding all of the numbers in your data set together and dividing by the number of numbers that were added together. So, if I have 5 numbers in my data set, I would add them together and divide that sum by 5. That quotient would be the mean of my data set. (This is the classic "average", or arithmetic average, that we learn about in Elementary school)

*Median is identified by finding the exact middle number of the data set. The first step is to put all the numbers in numerical order. Next, identify the middle number- for younger children, it's easier to methodically cross off numbers alternating between the top number that's left and the bottom number that's left until they're just left with the middle number (or two numbers). If there is an odd amount in the data set, then the middle number is the median; if there is an even amount, then the number that is exactly halfway between the two middle data points is the median. 

*Mode is identified by finding the number that appears the most times in the data set. If every number appears evenly in the data set, then there is no mode. There can also be more than one mode in a data set.

One other important term that is usually introduced with these 3 averages is range. Range is the distance spanned by the numbers in a data set. Range is calculated by taking the highest number in the set minus the smallest number in the set. The resulting difference is the range.

Parsha Connection:
We can take the census numbers from the 12 tribes and calculate the range and averages of the number of men aged 20 and older. Let's start by rewriting our data.

Reuven-          46,500
Shimon-          59,300
Gad-               45,650
Judah-             74,600
Issachar-          54,400
Zevulun-          57,400
Ephraim-          40,500
Menasheh-       32,200
Binyamin-        35,400
Dan-                 62,700
Asher-              41,500
Naftali-             53,400

Now, let's put those numbers in numerical order:

Menasheh-       32,200
Binyamin-        35,400
Ephraim-          40,500
Asher-              41,500
Gad-                45,650
Reuven-           46,500
Naftali-            53,400
Issachar-          54,400
Zevulun-          57,400
Shimon-          59,300
Dan-                62,700
Judah-             74,600

Before doing any calculations, we can look at the newly organized data and see that Menasheh had the smallest number of 20+ men, and Judah had the most. Now let's do those statistical calculations.

Range:
Most of the census numbers range between 32,000-60,000, while Judah had much more. The actual range of census numbers is
74,600 - 32,200 = 42,400

Mode:
We see that each tribe had a unique number of men, so there is no mode to this data.

Median:
Since there are 12 tribes here, the median will be exactly between the 6th and 7th tribes; between Reuven & Naftali. So how do we find the midpoint between 46,500 and 53,400? We can add them together and divide by 2.
46,500 + 53,400 = 99,900
99,900  ÷ 2 = 49,950
So, the median number of men in each tribe was 49,950.

Mean:
We start by adding all 12 numbers together. When added together, the sum is 603,550 (notice that this is the exact number that the parsha gives us for the total census for the 12 tribes together). Next we divide 603,550  ÷  12 = 50,295.8
So, the mean number of men in each tribe was 50,295.8 (or approximately 50,296 men)

Everyday Connection:
What are some hot topics in your house that you can use for data collection? How much time do your children spend, on average, working on homework each night? Are they getting enough sleep; what's the average number of hours of sleep that they get each night?