Re'eh- Activity investigations related to yearly tithings

In this week's parsha, we have two mentions of the tithings that were to be given at different times over the course of the shmita cycle. Additionally, tithings are referred to again in 3 weeks, in Parshat Ki Tavo. These three instances are looked at collectively in commentaries regarding the shmita cycle. 

• "You may not eat in your cities: the tithe of your grain, and your wine, and your oil; and the firstborn of your cattle and your flocks; all your vow offerings that you vow and your free-will offerings; and what is raised of your hand. Rather you shall eat them before Hashem, your G-d, in the place that Hashem, your G-d, will choose- you, your son, your daughter, your slave, your maidservant, and the Levite who is in your cities- and you shall rejoice before Hashem, your G-d, in your every undertaking. Beware for yourself lest you forsake the Levite, all your days in your land." ~Devarim 12:17-19
• Rashi on 12:18- regarding eating the tithings with the Levite in your city:
• Eat your first tithing together with him (1/10 portion of the crop given to Levites in each of the first 6 yrs of shemita)
• If you have no first tithe, then give from tithe for poor (1/10 of portion given to poor in third and sixth years (additional reference see 14:28-29, 26:12)
• If you have no poor tithe, then share your peace offering
• "At the end of three years you shall take out every tithe of your crop in that year and set it down within your cities. Then the Levite shall come- for he has no portion or inheritance with you- and the convert, and the orphan, and the widow who are in your cities, and they shall eat and be satisfied, in order that Hashem, your G-d, will bless you in all your handiwork that you may undertake." ~Devarim 14:28-29
• "When you have finished tithing every tithe of your produce of the third year, the year of the tithe, and you will have given to the Levite, to the convert, to the orphan, and to the widow, and they will have eaten in your cities and will have been satisfied, then you shall say before Hashem, your G-d, "I have eliminated the holy things from the house, and I have also given it to the Levite, to the convert, to the orphan, and to the widow, according to the entire commandment that you commanded me; I have not transgressed any of Your commandments, and I have not forgotten..." ~Devarim 26:12-13 (from Parshat Ki Tavo)

What were the tithings and the cycles?

• 1st tithe- 1/10 to the Levites
• 2nd tithe- 1/10 to be brought to Jerusalem and eaten there
• poor tithe- 1/10 to be given to the poor

The cycle of tithings over the shmita cycle was as follows:

Year 1- 1st tithes and 2nd tithes given

Year 2- 1st tithes and 2nd tithes given

Year 3- 1st tithes and tithes for poor given

Year 4- 1st tithes and 2nd tithes given

Year 5- 1st tithes and 2nd tithes given

Year 6- 1st tithes and tithes for poor given

Year 7- shmita year- no tithings

Activity suggestions:

• Younger children could investigate what it means to give 1/10. If you have a set-up for them to take a collection of items and divide them into ten groups, they would be donating one of those groups. The idea of 1 out of 10 might be conceptually easier for some than 1/10. In other words, for every 10 that's count out, 1 is going to be donated. 
• As children get to a point where they understand the concept of division by 10, they can practice some simple sample calculations of how much might have been donated based on a given monetary value. 
• Older children could be presented with sample scenarios of realistic incomes- some monetary based and some agriculturally based- and have them calculate projected tithings (per tithe and total donations) that families may have made over a 7 year shmita cycle. 
• Note that older students should also be able to make the connection that each 1/10 tithing would be equivalent 10% of their produce or earnings.
• It's also possible that, for some students, it would need to be clarified that all tithings were 1/10 of the total earnings; the 2nd tithing would not be calculated as 1/10 of what's left after the 1st tithing is given. This may be obvious to many, but for students who are making sense of the process, this may be a question that is unclear to them without explicit clarification.
• Extension thought- Based on these calculations, how could they think about how much the Levites had to live off of in a given year? This type of investigation could include researching information such as census information for each tribe listed in recent parshiot- if all the Levites were living off of tithings from those families, how much did they really have to live off of, per Levite family?

Ki Tisa- One-to-One Correspondence

"Hashem spoke to Moshe, saying: 'When you will take a census of the Children of Israel according to their counts, every man shall give Hashem an atonement for his soul when counting them, and there will be no plague among them when counting them. This is what they shall give- everyone who passes among the counted- half of the shekel, by the holy shekel, the shekel is twenty geirah, half of the shekel as a portion to Hashem. Everyone who passes among the counted, from the age of twenty years and up, shall give the portion of Hashem. The wealthy shall not increase and the destitute shall not decrease from half of the shekel- to give the portion of Hashem, to atone for your souls. You shall take the silver of the atonements from the Children of Israel and give it for the work of the Tent of Meeting; and it shall be a remembrance before Hashem for the Children of Israel, to atone for your souls.'" ~Shemot 30:11-16

One-to-One Correspondence Activity:
[K-2 concept]
In this week's parsha, we learn of Hashem telling Moshe that at such time as he chooses to take a census- a counting of the number of people, either total Children of Israel or a portion of the population- he should not just count the people. Rather, he should have each person being counted give a half-shekel as a donation to the Holy Tabernacle. It explicitly states that a rich person should not give more, and a poor person should not give less; any person being counted must give exactly a half-shekel. 

Socially, an important message about the value of human life can be embedded into this lesson- each person is equally as important; a rich person's life isn't worth more, and a poor person's life isn't worth less.

Mathematically, if each half-shekel is representative of a person in the given community, it is important for each person to give exactly a half-shekel (no more, no less). Children can discuss what would happen if someone put in an extra half-shekel, or if other people gave less than a half-shekel. 

An activity of playing out taking a census in the classroom with a given token can help students understand the one-to-one correspondence of each person giving in one specific coin to represent their presence as part of the community. Together, they can look at the coins collected to see that the number of coins matches exactly to the number of people in the class. 

A follow-up activity would be to have some students with extra coins and some students with fewer coins (or no coins). Children could be allowed to give as many coins as they want. Then go back, as a class, to look at how many coins were collected and see if they can figure out how many people are in the class based on the coins collected. How does the number of coins compare to the actual number of students in the class? Students will be able to see the confusion caused by the discrepancy- the missing aspect of the one-to-one correspondence.

Base-10 Connection:
[3-5 concept]
Students can also talk about the idea that, in Judaism, we don't count out individual people. If we need to know how many people are in a group, we use another method of tallying the number of people in the group. Rather than counting people, for example, we could count people by their shirts (17 shirts in a room means 17 people who are wearing those shirts). If you do need to "point and count" people in a group, there is a custom to use the passage:

"הושיע את עמך וברך את נחלתך ורעם ונשאם עד עולם" 

"Save Your people, and bless Your inheritance; And tend them, and carry them forever" 

~Tehillim 28:9 

Mathematically, using this Hebrew phrase from Tehillim works out very nicely, since there are 10 words in the phrase. Each word represents one person, so every full phrase represents 10 people. Students can discuss different example situations of how many full passages and a number of extra words represents how many people in a group. For example, if I'm counting people in a crowd, and I go through the full passage 3 times and then begin the passage again, ending on the word "וברך", that would mean that there are 34 people in the crowd.

Toldot- Base-10 and Number Sense related activity ideas

"Yitzchak sowed in that land, and in that year he reaped a hundredfold; thus had Hashem Blessed him." ~Bereishit 26;12

Rashi on 26;12-
"A Hundredfold- For they assessed [the field] to determine how much it is fit to produce and it produced for every unit they estimated it could produce a hundred units. Our Rabbis said, This assessment was done for tithes."

In this section of the parsha, we learn of Yitzchak's time living in Gerar, under the rule of Avimelech. Bereishit Rabbah (64;6) asks: if we're not supposed to find a blessing in a measurable quantity, how could this crop be considered a blessing? You are not supposed to count on a crop before it is harvested (like the old adage- "Don't count your chickens before they hatch"). How does this make sense? The Mizrachi explains that the crop was traditionally estimated in order to make an advanced calculation for tithings to be easily set aside. The midrashim (Tosafot HaShalem citing Rivah) teach us that this crop that is referred to was sowed during a time of famine in the land. Yitzchak had estimated what his tithe should be in order to be able to set it aside for the poor as soon as possible, and he had estimated much less of a crop due to the famine in the land.  It is with this understanding that we see how this was such a blessing for Yitzchak. 

Activity Connections:
There are two primary mathematical concepts that connect to this crop:
1) the concept of calculating and setting aside tithings
2) the concept of one hundredfold 

Interestingly enough, both of these concepts connect to powers of 10. 
*Tithings are classically 1/10 of a crop (the root of the hebrew word- מעשרות/מעשר- is actually related to עשר, the number 10)
*one hundredfold means times 100, which is a power of 10 (10²;or X10 and then X10 again)

Activity ideas in increasing conceptual difficulty:
*What does a tithing or 1/10 of a group really look like? For the youngest students, they could begin by just taking a group of items and separating the items into 10 equal groups. Having a set-up of 10 cups, bowls, or plates to sort the pieces into will help students keep track of their sorting. This is doable even for preschool children. After they divided their items into 10 piles, they can count each pile to make sure that they all have the same number of items in them. From there, they can act out separating 1 of the piles to give away and keeping 9 of the piles for themselves. For beginners, you want to simplify the process for them by making sure that the number of items they start with is a multiple of 10 (so that it divides equally into 10 piles).

*As a step up from the previous activity, you can have students divide larger groups of items, and incorporate estimation or calculation of what amount the tithing will actually be when it's separated out. Students who have had exposure to the concept of fractions and decimals could also estimate and calculate the value of tithings for amounts that are not strictly multiples of 10.

*One hundredfold- what does x100 really look like? What if Yitzchak had anticipated having 5 bundles of grain? How much did he actually have that year? What if he had anticipated 10 bundles of grain? Younger students can physically count or draw out the difference of a group of 5 and a group of 500. Small or medium sized graph paper can be good for drawing out a model of these differences (with each box modeling 1 unit). If students have the dexterity, small manipulatives like paper clips can also be good. For younger students, these can be modeled with blocks or Legos, but you need to have a good supply in order to model the hundreds. (Tip: Creating stacks or grouping of 10 to count everything out will help make counting easier and will help children develop their number sense.)

*Older students can graph the difference between the anticipated crops and the actual crops. Is there a pattern to the difference? How would the difference be expressed as an algebraic expression?

*Another activity for older students would be a comparison of the tithings between the anticipated crops and the actual crops. What would a graph of these differences look like? How could the differences be expressed algebraically? How does the pattern of the difference in tithings (anticipated vs. actual) compare to the pattern of the difference in crops (anticipated vs. actual)? How do the algebraic expressions of each comparison compare to each other?

Re'eh- Overlapping Patterns

"At the end of seven years you shall institute a release. This is the matter of the release: Every creditor shall release his authority over what he has lent his fellow; he shall not press his fellow or his brother, for He has proclaimed a release for Hashem." ~Devarim 15;1-2

Rashi on Devarim 15;1:
Rashi here explains that one might think that each time a person makes a loan, they count seven years on that particular loan. Rather, we learn here that the seven years mentioned are referring to counting of the year according to the shmita cycle, and all loans are released every time we come to a shmita year, regardless of when they were made.

I'd like to use this information about a different aspect of shmita years to build on the shmita cycle information that we looked at in Parshat Behar. 

In the shmita/yovel chart in that post, you can see that every 7 years is a shmita year. At the time of the post, I made the chart based on my understanding of the text- with shmita every 7 years, and a final yovel year in the 50th year (after 7 groups of 7 years). With further research, I found a discrepancy in the understanding of how the cycle works. One explanation of the discrepancy can be seen here in an explanation on Parshat Behar.

In essence, the calculation discrepancy is as follows:
*Rabbi Yehuda understood that the yovel cycle was independent from the shmita cycle. In his view, there was a shmita cycle occurring every 7 years and a yovel cycle occurring every 50 years. The separate cycles overlapped in such a way that yovel fell in the 1st year of every 8th new shmita cycle.

*The sages understood that the yovel cycle was a final year within the larger shmita cycle. In their view, yovel was the 50th and final year of the previous shmita cycle, and the next shmita cycle would start the following year at year 1.

Here is a chart that compares the calculation implications in these differing understandings (bear with me- the chart gets lengthy in order to start to see the difference as we get into the second set of cycles):

Regular Counting year	Rabbi Yehuda	Sages
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7	Shmita	Shmita
Year 8
Year 9
Year 10
Year 11
Year 12
Year 13
Year 14	Shmita	Shmita
Year 15
Year 16
Year 17
Year 18
Year 19
Year 20
Year 21	Shmita	Shmita
Year 22
Year 23
Year 24
Year 25
Year 26
Year 27
Year 28	Shmita	Shmita
Year 29
Year 30
Year 31
Year 32
Year 33
Year 34
Year 35	Shmita	Shmita
Year 36
Year 37
Year 38
Year 39
Year 40
Year 41
Year 42	Shmita	Shmita
Year 43
Year 44
Year 45
Year 46
Year 47
Year 48
Year 49	Shmita	Shmita
Year 50	Yovel (yr 1 of new shmita cycle)	Yovel (yr 50 of old cycle)
Year 51		(yr 1 of new shmita/yovel cycle)
Year 52
Year 53
Year 54
Year 55
Year 56	Shmita
Year 57		Shmita
Year 58
Year 59
Year 60
Year 61
Year 62
Year 63	Shmita
Year 64		Shmita
Year 65
Year 66
Year 67
Year 68
Year 69
Year 70	Shmita
Year 71		Shmita

Just looking at the comparison chart, we can see that after the first full shmita/yovel cycle, the Sages' cycle falls behind Rabbi Yehuda's. For the next 7 shmita cycles, Rabbi Yehuda's shmita years fall one year earlier than the Rabbi Yehuda's. If we continue this pattern, after the next 7 shmita cycles, the Sages' shmita years will fall two years earlier. This discrepancy continues over time. Although the Sage's will fall farther and farther behind, every certain number of cycles, they will be in line again. Can you figure out how frequently that alignment will occur? To connect with counting in different bases, discussed in Parshat Behar, can you count the years in base-7 (as I started in the chart there) to help identify the alignment shift?

We can look at how this discrepancy in understanding changes the meaning of loan release that we learn of in our parsha this week. It says clearly that the loan release takes place after 7 years, which Rashi explains is in the shmita year. According to Rabbi Yehuda, the math works, and every 7 years is a shmita year, even when a yovel year follows a shmita year. According to the sages, though, when a yovel year falls out, there are actually 8 years between the shmita year before and the next shmita year. What happens if someone makes a loan during a yovel year? According to my understanding of the sages, a loan made during the yovel year would not be required to be released until the following shmita year, which would actually be 8 years. Following the sages, of the calculation were to keep to 7 years, then in the 2nd yovel cycle loans would actually be released the year before shmita, and in the 3rd yovel cycle loans would be released two years before shmita, and so on.

Although I did try to research this question, I was not able to find an answer. It seems that the Gaonim followed the Sages calculation of the yovel cycle, but at the time of exile from Israel, yovel was discontinued and the 50th yovel year was removed from the cycle. With this new calculation, the counting cycle looks like the column for Rabbi Yehuda's cycle, but with the yovel label taken out, since the new shmita cycle is bumped up a year.