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. 

Miketz- How high can you count?

"Joseph amassed grain like the sand of the sea, very much, until he ceased counting, for there is no number." ~Bereishit 41:49

For this week, I want to focus on the statement above, where Joseph was overseeing the collection of grains in Egypt during the 7 abundant years in preparation for the upcoming 7 years of famine. Using the commentaries of Rashi and Sforno we learn that Joseph was amassing as much grain as possible, until the grain counter stopped counting (Rashi) and the reason that he stopped counting was that he had run out of names of numbers to use for his counting (Sforno).

This statement struck me as one that would make for an interesting discussion with students on place-value and increasing numbers. For information on place value and thinking about how it works, functionally, see my post from Parshat Bereishit.

Concepts related to the progression of counting:

• Children first start by learning the base pattern in counting from 1-10. Once they have a solid ability to count 1-10, we begin working with them on recognizing the pattern of how we loop through 1-9 in each set of tens (teens, twenties, thirties,...) to make another set of 10. Interestingly, the tens places increase in the same numerical order as the ones.
• After tens, usually somewhere in the grades K-2, students solidify their counting from 1-100. Next, they practice understanding the next loop- counting from 100-200 will follow the same pattern as 1-100, but with "one hundred" before each number. Once they reach 199, they increase the hundreds place to 200. Again, interestingly enough, the numbers continue to loop in the same pattern with the hundreds place increasing in the same numerical order as the ones and tens did.
• As students move up in their understanding of place value through the hundreds, then we work with them on extending their understanding exponentially by reviewing with them the idea that this loop continues on and on, and as we reach our maximum capacity for each place value, we just add on the next place value and continue the pattern loop that we've created.
• Once students have mastered the concepts of the unlimited potential for counting by increasing numbers, we then extend the concept in 2 directions: 
• 1) negative numbers and comparing how "increasing" negative numbers and place values relates to increasing positive numbers and place values
• 2) decimal numbers and comparing how "increasing" decimal numbers and place values relates to increasing positive/negative numbers and place values. 
• Note that while positive and negative numbers are fairly comparable, conceptually, when we think about magnitude, or size, of the numbers, an added conceptual difficulty that decimals offer is the idea that the "larger" the number, the "smaller" the piece. The numbers we talk about as decimals, really means the number of pieces that 1 unit or whole is broken into- so more pieces, means cutting the same piece into smaller pieces.

The most basic construct that children are building on as they increase their understanding of counting through each level is that you can always make a bigger number by just adding one more; cycling through the understood loop of numbers and adding new place values as needed will always result in a new, bigger number.

Based on this construct, how can we understand the statement above in the parsha? An interesting Social Studies connection might be for the students to see if they can find information on how many of our place values the Egyptians actually used. Clearly, based on our understanding of counting, even if we didn't know how to read the number of counted grain, we would at least be able to write out the number representing how much grain was collected, and we could have kept on counting. 

Some questions to consider for a conversation on the topic:
Obviously, the Egyptians had a limit- did they stop counting because they thought they couldn't have any more grain? No, they stopped counting because they reached a point where they could no longer track their collection. What implications might extend from such a situation?

Bereishit- Place Value and Regrouping

Addition and Place Values:
When younger children begin learning to add (and subtract) multi-digit numbers, the algorithms alone for these calculations can be confusing. As a starting point, children first need to understand the meaning behind what each digit in a number represents. As they expand their understanding, it is helpful for children to recognize the pattern of every three place values from the decimal point moving towards the left. Larger decimal place values come later, but, again, understanding the pattern of place value will help students pick up the larger picture of what's happening with the numbers.

Basic place values to the millions:

The biggest hurdle for students to overcome is that each place value can't have more than 9 of it's kind, and every time you reach a group of 10, you have reached the next place value and need to "regroup" your numbers.

*10 ones = 1 ten and 0 ones [10]
*10 tens = 1 hundred and 0 tens and 0 ones [100]
*10 hundreds = 1 thousand and 0 hundreds and 0 tens and 0 ones [1,000]
*10 thousands = 1 ten-thousand and 0 thousands and 0 hundreds and 0 tens and 0 ones [10,000]
*10 ten-thousands = 1 hundred-thousand and 0 ten-thousands and 0 thousands and 0 hundreds and 0 tens and 0 ones [100,000]
*10 hundred-thousands = 1 million and 0 hundred-thousands and 0 ten-thousands and 0 thousands and 0 hundreds and 0 tens and 0 ones [1,000,000]

It helps for children to visualize this concept using manipulatives such as base-10 blocks, which have models for ones, tens, hundreds, and thousands. Paper clips are a good make-shift manipulative, since students can clip and unclip into and out of groups of 10, 100, etc. as they make sense of the numbers.

One key that is critical for students to remember is that they need to line up the place values- you can only add ones with ones, tens with tens, hundreds with hundreds, etc. (and then regroup as needed).

Parsha Connection:
Chapter 5 of this week's parsha gives details of the direct lineage from Adam to Noah. We are given information on names and ages for this direct line of descendants. We are given enough information about each person to provide 9 sample addition problems, where we can check the numbers that we are given in the parsha.

As a first step, let's organize the individual pieces of information that we are given. As we organize information for each person, we can check the math.

1st generation:
"This is the account of the descendants of Adam- on the day of G-d's creating of Man, He made him in the likeness of G-d. He created them male and female. He blessed them and called their name Man on the day they were created- when Adam had lived one hundred and thirty years, he begot in his likeness and his image, and he named him Seth. And the days of Adam after begetting Seth were eight hundred years, and he begot sons and daughters. All the days that Adam lived were nine hundred and thirty years; and he died." ~Bereishit 5;1-5

Adam was 130 years old when Seth was born.
Adam lived 800 years after Seth was born.
Adam died at 930 years old

  130
+800 
  930    so this works

2nd generation:
"Seth lived one hundred and five years and begot Enosh. And Seth lived eight hundred and seven years after begetting Enosh, and he begot sons and daughters. All the days of Seth were nine hundred and twelve years; and he died." ~Bereishit 5;6-8

Seth was 105 years old when Enosh was born.
Seth lived 807 years after Enosh was born.
Seth died at 912 years old

  105
+807
  912    so this works

The above example offers regrouping in the ones (to tens) digits.

3rd generation:
"Enosh lived ninety years, and begot Kenan. And Enosh lived eight hundred and fifteen years after begetting Kenan, and he begot sons and daughters. All the days of Enosh were nine hundred and five years; and he died." ~Bereishit 5;9-11

Enosh was 90 years old when Kenan was born.
Enosh lived 815 years after Kenan was born.
Enosh died at 905 years old

   90
+815
  905    so this works

The above example offers a sample with different sized numbers (one tens and one hundreds), which offers a good check on understanding lining up the place values. Also, we have regrouping in the tens (to hundreds) digits here.

4th generation:
"Kenan lived seventy years, and begot Mahalalel. And Kenan lived eight hundred and forty years after begetting Mahalalel, and he begot sons and daughters. All the days of Kenan were nine hundred and ten years; and he died." ~Bereishit 5;11-14

Kenan was 70 years old when Mahalalel was born.
Kenan lived 840 years after Mahalalel was born.
Kenan died at 910 years old

   70
+840
  910    so this works

Again, here we have different sized numbers and regrouping in the tens (to hundreds) digits.

5th generation:
"Mahalalel lived sixty-five years, and begot Jared. And Mahalalel lived eight hundred and thirty years after begetting Jared, and he begot sons and daughters. All the days of Mahalalal were eight hundred and ninety-five years; and he died."  ~Bereishit 5;15-17

Mahalalel was 65 years old when Jared was born.
Mahalalel lived 830 years after Jared was born.
Mahalalel died at 895 years old

   65
+830
  895    so this works

Again, here we have different sized numbers.

6th generation:

"Jared lived one hundred and sixty-two years, and begot Enoch. And Jared lived eight hundred years after begetting Enoch and he begot sons and daughters. All the days of Jared came to nine hundred and sixty-two years; and he died." ~Bereishit 5;18-20

Jared was 162 years old when Enoch was born.
Jared lived 800 years after Enoch was born.
Jared died at 962 years old

  162
+800
  962    so this works

7th generation:
"Enoch lived sixty-five years, and begot Methuselah. Enoch walked with G-d for three hundred years after begetting Mehuselah; and he begot sons and daughters. All the days of Enoch were three hundred and sixty-five years. And Enoch walked with G-d; then he was no more, for G-d had taken him." ~Bereishit 5;21-24

Enoch was 65 years old when Methuselah was born.
Enoch lived 300 years after Methuselah was born.
Enoch died at 365 years old

   65
+300
  365    so this works

8th generation:

"Methuselah lived one hundred and eighty-seven years and begot Lamech. And Methuselah lived seven hundred and eighty-two years after begetting Lamech, and he begot sons and daughters. All the days of Methuselah were nine hundred and sixty-nine years; and he died." ~Bereishit 5;25-27

Methuselah was 187 years old when Lamech was born.
Methuselah lived 782 years after Lamech was born.
Methuselah died at 969 years old

  187
+782
  969    so this works

Again, here we have regrouping in the tens (to hundreds) digits.

9th generation:
"Lamech lived one hundred and eighty-two years, and he begot a son. And he called his name Noah, saying, 'This one will bring us ease from our work and from the toil of our hands, from the ground which Hashem had cursed.' Lamech lived five hundred and ninety-five years after begetting Noah, and he begot sons and daughters. All the days of Lamech were seven hundred and seventy-seven years; and he died." ~Bereishit 5;28-31

Lamech was 182 years old when Noah was born.
Lamech lived 595 years after Noah was born.
Lamech died at 777 years old

  182
+595
  777    so this works

Again, here we have regrouping in the tens (to hundreds) digits.

10th generation:
"When Noah was five hundred years old, Noah begot Shem, Ham, and Japheth." ~Bereishit 5;32

Noah was 500 years old when Shem, Ham, and Japheth were born.

Follow-up Activities:
If you take this base information and use it to try to place the births and deaths in a timeline, students can calculate how old each person was at the births of successive descendants, as well as how old each of the descendants was at the time of death of their ancestors. These calculations will offer students more, similar calculation practice.

For an added exercise, having students identify which numbers to use for these different comparative calculations offers practice with problem solving and identifying important information.