Nasso- Activity ideas related to organization & calculation

"Hashem said to Moshe, 'One prince each day, one prince each day, shall they bring their offering for the inauguration of the Altar.' 

The  one who brought his offering on the first day was Nachshon son of Amminadav, of the tribe of Yehudah. And his offering was: one silver bowl, its weight a hundred and thirty [shekel], and one basin of silver, [its weight] seventy shekel in the sacred shekel, both of them filled with fine flour mixed with oil for a meal-offering; one ladle of gold, [its weight] ten [shekel] filled with incense; one young bull, one ram, one sheep in its first year for an olah-offering; one he-goat for a sin-offering; and for the sacrifice of the peace-offering, two cattle, five rams, five he-goats, five sheep in their first year- this is the offering of Nachshon son of Amminadav.

On the second day, Nethanel son of Zuar, prince of Issachar, offered...

On the third day, the prince of the children of Zevulun, Eliav son of Helon...

On the fourth day, the prince of the children of Reuven, Elizur son of Shedeur...

On the fifth day, the prince of the children of Shimon, Shelumiel son of Zurishaddai...

On the sixth day, the prince of the children of Gad, Eliasaph son of Deuel...

On the seventh day, the prince of the children of Ephraim, Elishama son of Ammihud...

On the eighth day, the prince of the children of Menasheh, Gamliel son of Pedahzur...

On the ninth day, the prince of the children of Benjamin, Avidan son of Gideoni...

On the tenth day, the prince of the children of Dan, Achiezer son of Ammishaddai...

On the eleventh day, the prince of the children of Asher, Pagiel son of Ochran...

On the twelfth day, the prince of the children of Naphtali, Ahira son of Enan...

This was the inauguration of the Altar on the day it was anointed, from the princes of Israel: twelve silver bowls, twelve silver basins, twelve gold ladles; each bowl was one hundred and thirty silver [shekels] and each basin was seventy; all the silver of the vessels was two thousand, four hundred in the sacred shekel. Twelve gold ladles filled with incense, each ladle was ten of the sacred shekel; all the gold of the ladles was one hundred and twenty [shekels]. All the livestock for the olah-offering: twelve bulls, twelve rams, twelve sheep in their first year, and their meal-offerings; and twelve he-goats for a sin-offering. All the livestock for the sacrifice of the peace-offering: twenty-four bulls, sixty rams, sixty he-goats, sixty sheep in their first year- this was the inauguration of the Altar after it was anointed." ~Bamidbar 7:11-88

At the end of this week's parsha we  learn about the gifts that were brought by the princes from each tribe for the inauguration of the Altar. Each prince took their turn bringing the gift from their tribe- each prince on their prescribed day over the course of 12 days. Although each tribe brought the exact same gift, the Torah repeats the gifts each time with the name of each prince from each tribe. At the end of the section, the Torah collates the information for us and tells the total amounts of each item that was brought altogether by the total 12 princes.

Activity thoughts:

• In Parshat Vayakhel-Pikudei this year, I wrote about organizing information in different ways to access the information for different purposes. In this week's parsha, we have an example of the same information being presented in two different formats. First, we are given the list of each individual prince with what they brought individually. Afterwards, we are given a collated list of the totals for each type of gift that was brought. Using multiplication (x12) students can check the calculation for the total amounts of each gift item brought. There are also total values of silver and gold listed, for which students can confirm the calculations.
• Younger students could start by looking at the individual gifts from single tribes. Which gifts were heavier? Which gifts were lighter? How heavy was the bowl? the basin? the ladle? Students could have individual students collect a model set of items to complete a mock set of the individual gift offering- maybe they could have a list to go through and make sure they collect all the necessary items. The students could then come together and put all their gifts together, sorted by type, to see the total amounts that were collected all together from all the gifts of the 12 tribes.
• Test your attention to detail- The Torah repeats the list of gifts 12 times- once for each prince. While the gifts brought by each prince were exactly the same, there are some differences in the text the way that some of the tribes donations are listed. Can you read through the 12 sections and see which sections are exactly the same and which ones are different? [Hint- Rashi comments on the differences to explain why they are different.]
• Rashi's meaning behind the values- At the start of the individual lists of gifts brought by each prince, Rashi breaks down the list of gifts to connect a deeper meaning behind the values that are associated with the different gifts. These explanations offer a more meaningful purpose to the specific gifts, while also reviewing numerical between other significant aspects of Judaism.

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. 

Behar/Bechukotai- Graphs, Patterns, and Calculation Activities

"Hashem spoke to Moshe, saying: Speak to the Children of Israel and say to them: When a man will express a vow to Hashem regarding the valuation of souls, the valuation of a male shall be: for someone twenty years of age to sixty years of age, the valuation shall be fifty silver shekels, of the sacred shekel. If she is female, the valuation shall be thirty shekels. And if from five years of age to twenty years of age, the valuation of a male shall be twenty shekels and of a female ten shekels. And if from one month of age to five years of age, the valuation of a male shall be five silver shekels; and for a female, the valuation shall be three silver shekels. And if from sixty years of age and up, if for a male, the valuation shall be fifteen shekels; and for a female, ten shekels. But if he is destitute for the valuation, then he should have him stand before the Kohen, and the Kohen should set his valuation; according to what the hand of the person who makes the vow can attain should the Kohen set his evaluation." ~Vayikra 27:1-8

In this section of this week's parsha, we learn about the standard valuation for donations that are vowed to the Beit HaMikdash on behalf of family members. We have the standard valuations, and we are also told that if someone makes a vow but doesn't have the funds to meet the standard valuations, the Kohen can make a determination of an appropriate valuation for that person. This week I would like to look at some activities for students of varying levels based on the standard valuations that are listed.

To begin, let's organize the information (older students could be asked to chart this information for themselves by identifying and organizing the information in the passage):

Note that this could also be organized into two charts- one for males and one for females. This breakdown might be clearer for some students when trying to separate information on males and females in follow-up activities.

Related Activity Suggestions:

• Graph It!- A good way to compare data of this nature is by graphing it. This information lends itself well to a double bar graph, with a category for each age grouping, and two bars within each category (one for males and one for females). The left side of the bar graph (y-axis) would indicate the number of shekels donated. As always, grade levels recommended are an approximation, and individualization for students is necessary to meet their actual ability levels. K-2 students could fill in a pre-made class-sized graphing chart as a class activity, with older students also copying the information onto personal graphs. Grades 3-5 students could create individual graphs on pre-printed graph templates with spacing indicated for different levels of labeling, and then graphing the information. Students in grades 6+ could create their own double-bar graph from start to finish.

• Is there a pattern?- Looking at the table above and/or the double-bar graph created in the first activity, students can look for comparisons between males and females at each age group. They can also look for comparisons between the different age groups for males and then between the different age groups for females. 
• What trends do they see over a person's lifetime? Is this consistent for both men and women? Why do they think the valuations may have been set in the way that they were?
• After making note of comparisons, older students could look for specific numerical comparisons between males and females in each age group and then across the data for males and females at different age groups. Are any of the ratios between groups consistent in any way? Rashi's note on 27:7 is also relevant to these comparisons, as he specifically points out some differences in the ways that the valuations change between the different age groups.

• Problem Solving- Processing the information through sample family valuations- Using the valuations given, students could be provided with sample problems with different family groupings to calculate the valuation for each family. Students could also create their own sample families to calculate or switch with friends to calculate. What about students' own families? What would each student's personal family valuation be if they were donating to the Beit HaMikdash? Can older students come up with an algebraic formula for calculating the valuation for any given family scenario?

Emor- Calculation Activities with Fractions & Unit Conversions

"From your settled places you shall bring bread of elevation, two loaves made of two tenth-ephahs, they shall be fine flour,  they shall be baked leavened; first fruits to Hashem." ~Vayikra 23:17

"You shall take fine flour and bake it into twelve loaves; each loaf shall be two tenth-ephahs. You shall place them in two stacks, six the stack, upon the pure Table, before Hashem." ~Vayikra 24:5-6 

In this week's parsha, we find two instances of descriptions of loaves of bread. In our first quote (23:17), there are two loaves of bread that were offered for the meal offering. In our second quote (24:5-6), there are twelve loaves of bread that were put in the Mishkan and replaced each week on Shabbat. 

If you read these passages, you'll notice that in both cases, the size of each loaf of bread was standard- each loaf was to be made using two tenth-ephahs of fine flour.

Some activity thoughts based on this information:
*Note that I have posted information related to relevant, applicable calculations in my previous posts on Parshat Beshalach (equivalency table for biblical measurements equivalent to an ephah, including a se'ah) and Parshat Shelach (unit conversion calculations from se'ah to modern measurements).

**For younger students, they could be given representative 1/10 ephah pieces (representative weights) to think about the quantities necessary for each question below. A more developmentally concrete class activity could also be done using a pre-measured modern day equivalency of 1/10 ephah and then having students measure out the amounts necessary for individual loaves and each scenario listed below. While the first activity offers students the opportunity to think about how to count multiple fractions of weighted measures, the second activity offers students the opportunity to visualize and think about how much flour would have actually gone into each recipe.

**For older students, they could work through the paper and pencil calculations. Students could then take their calculations and, using baking flour, compare how their measurements compare to some of their own challah recipes from home or collected as a class from a quick recipe search ahead of time. They can think about how many loaves of challah the parsha recipes would make based on the way their own families make challah. Are their challahs bigger or smaller than the estimated size of the loaves in the parsha?

Questions:
*If you were batch baking the bread for the meal offering, how much flour would be needed to make the two loaves?
*If you were batch baking the bread for the Mishkan, how much flour would be needed to make the two loaves?
*How much flour was needed for the combined loaves of each stack, the way they were divided for storing in the Mishkan each week?
*If you were baking today, how much flour would be needed for each loaf of bread?
*If you were baking today, how much flour would be needed to batch bake the bread for the meal offering?
*If you were baking today, how much flour would be needed to batch bake the bread for the Mishkan?
*If you were baking today, how much flour would be needed for the combined loaves of each stack as they were divided in the Mishkan?