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. 

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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: 
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.

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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?

Acharei Mot/Kedoshim- Probability

"[Aaron] shall take the two he-goats and stand them before Hashem, at the entrance of the Tent of Meeting. Aaron shall place lots upon the two he-goats: one lot 'to Hashem' and one lot 'to Azazel.' Aaron shall bring near the he-goat designated by lot to Hashem, and he shall make it a sin-offering. And the he-goat designated by lot to Azazel shall be stood alive before Hashem, to atone upon it, to send it to Azazel to the wilderness." ~Vayikra 16:7-10

Rashi on 16:8 explains what is meant by placing lots on the goats. He explains that one goat was placed to Aaron's right and the other to Aaron's left. He had a lottery box with the two lots (presumably these were labels or markers of some sort)- one lot indicated to Hashem, and one lot indicated to Azazel. Aaron placed both his hands into the box and picked out one lot in each hand. The lot in his right hand labeled the goat on his right, and the lot in his left hand labeled the goat on his left. 

Based on this explanation, we understand that until the lots were chosen by Aaron, either goat could be the one going to Hashem and either goat could be the one going to Azazel. This leads us to the concept of probability.

I wrote about probability once before, in my post last year on Parshat Beshalach. There, I explained probability as follows:

Definition- the chance that something will happen (merriam-webster.com)
Probability is expressed as a fraction between 0 and 1, where 0 means that there is no chance for the event to happen and 1 means that the event will definitely happen. For clarification, chance and probability are the same, however, chance is the number expressed as a percentage and probability is the number expressed as a fraction.

In my previous post, I explained how to calculate compound probabilities. Here, I would like to look at explaining simple probability for younger students. 

We can think about this as simply as possible through some basic examples:

Case #1:
If you have 2 marbles in a bag- one blue and one red- and you want to pick out one marble, you can not say that you will certainly pick the blue or certainly pick the red. You have an equal chance of picking out one or the other. 

How do we show this mathematically?
We can express the probability as a fraction where the denominator tells us how many total options we have, and the numerator tells us how many opportunities we have for picking the item that we want. 

In this case, we have:
*2 marbles (our denominator) and 
*if we prefer the red marble, we have 1 of those in the bag (our numerator)

Therefore, the probability of picking the red is 1/2. 
This could be expressed as 50% chance of picking the red. 

If we wanted to pick the blue marble, there are still the same 2 marbles in the bag and only 1 of the blue in the bag, so the probability of picking the blue is also 1/2. 

Parsha Connection Interjection:
With this understanding, we see that each goat has a 50% chance of being sent to Hashem or to Azazel. They have equal chance of being sent to for either purpose.

More on Simple Probability:
As long as there are the same number of each type of item, then the probability of picking any of the items will be the same as the probability of picking any of the other items. 

Case #2:
If you have 12 marbles in a bag, with 6 red and 6 blue, then the probability of picking 1 marble of either color would be 6/12, or still 1/2 (when the fraction is reduced). 

Case #3:
What if you had 12 marbles in 4 different colors? 
If you had 3 marbles of each color- blue, red, yellow, and green- then the probability of picking one in any of those 4 colors would be 3/12, or 1/4 when reduced. 

Case #4:
What happens if we don't have the same number of each color? 
Let's say we had 10 marbles:
*5 green
*2 red
*2 blue
*1 yellow. 
What would be the probability of picking each color when picking 1 marble?

Green- 5/10 (reduces to 1/2)
Red- 2/10 (reduces to 1/5)
Blue- 2/10 (reduces to 1/5)
Yellow- 1/10

So, we have the best chance of picking a green, a smaller, but equal chance of picking red or blue, and it is the least likely that we'll pick yellow. 

Activities to Test Probability: (Theoretical vs. Experimental Probability)
There are many similar ways of testing probability:
*flipping a coin (chance of heads or tails)
*rolling a die (chance of rolling numbers 1-6, or 6 colors, or 6 other labels)
*picking items unseen from a group (it's important that the objects aren't distinguishable by size, or touch)

Theoretical Probability is what the probability is for picking an item based on calculation.
Experimental Probability is what the probability looks like as you actually test picking item.

Students can chart their probability findings by setting up a bar graph on large graph paper (eg 1in x 1in squares) or large chart graph paper on an easel. If they are tracking the probability of heads vs tails on a coin, they would have a column for each result, and flip the coin multiple times. Each time they flip, they color in 1 square on the chart above the corresponding picture (heads or tails). Different students can test this individually and then compare their results. If you collate all the graphs from the class onto a single graph, students should start to see that the more trials they have, the closer experimental probability comes to looking like theoretical probability.

Thinking about the difference between theoretical and experimental probability- Just because you flip a coin 100 times doesn't mean that you will have exactly 50 heads results and 50 tails results. Some people might have 50-50, while another might have 48-52, and a third person could have 40-60. But if after 4 flips you have 3 heads and 1 tails, you could still end up with 50 heads and 50 tails after 100 flips. 

Beshalach- Probability

"The enemy said, 'I will pursue, I will overtake, I will divide spoils; my soul shall be filled with them. I will draw my sword, my hand will impoverish them.'" ~Shemot 15;9

"...אמר אויב ארדף אשיג אחלק שלל"

Transliteration: "Amar oyeiv erdof asig echaleik shallal..."


In this section of the parsha, Moshe and the Jewish people are singing a song of praise to Hashem after he's taken them safely out of Egypt. The specific phrase above is unique in that it is the only instance in the entire Torah of a 5-word alliteration (in the Hebrew text). The first 5 words of the pasuk all begin with the letter aleph (א). While we believe that every word, and even every letter, in the Torah was carefully chosen and is included with purpose, this alliteration still raises the question: What is the probability of having 5 words in a row beginning with the same letter?

Probability:
Definition- the chance that something will happen (merriam-webster.com)
Probability is expressed as a fraction between 0 and 1, where 0 means that there is no chance for the event to happen and 1 means that the event will definitely happen. For clarification, chance and probability are the same, however, chance is the number expressed as a percentage and probability is the number expressed as a fraction.

Let's look at a simple example:
Let's imagine a bag with 10 marbles, where 3 are red, 3 are yellow, and 4 are blue. If we want to know the probability of picking 1 red marble, we see that there are 3 red marbles out of the total 10, so the probability is 3/10. (Remember when we converted fractions to percentages back in Parshat Vayigash? We can use that here to calculate the chance of any probability)

Now, let's make it a little harder and think about how to calculate the probability of picking out a red marble from that bag twice in a row. Assuming that we pick a marble, put it back in the bag, and pick again...
The probability of picking the red marble the first time is 3/10 and the probability of picking it out the second time is also 3/10. To find the compound probability you multiply these two together so
3/10 x 3/10 = 9/100

If we didn't put back the red marble after picking the first time, then the calculation would be slightly different. The probability of picking the red marble the first time would still be 3/10, but, assuming that first marble is red like we want, and we're holding it out of the bag, the there are only 9 marbles left in the bag, and only 2 of them are still red. This means that the probability of picking a second red marble in this case is 2/9. Now, to calculate the compound probability, we still multiply the first probability times the second, so...
3/10 x 2/9 = 6/90, which can be reduced to 1/15

Connection to the parsha:
Let's think about how to apply this to our question. First of all, there are 22 letters in the Hebrew alphabet. Now, in our situation, we're talking about probability of something happening 5 times in a row, so we're looking at compound probability. Does our situation match with the marble being replaced or not replaced? Since letters can be used and reused without limit in language, our case matches with the marble being replaced.

So, we have 1 aleph out of 22 letters in the alphabet, and it appears at the start of the word 5 times in a row. So, the probability is:
1/22 x 1/22 x 1/22 x 1/22 x 1/22 which equals 1/5153632. Rounded off, we can say that the probability of this alliteration happening is 1 in 5 million.