This Shabbat, being Chol HaMoed Sukkot, we will be reading a portion from parshat Ki Tisa. However, since next week (on Monday in Israel and Tuesday outside of Israel) we read V'Zot HaBracha and Bereishit in the same week, I felt it would be appropriate to appropriate V'Zot HaBracha for this week.
"And of Naphtali he said: Naphtali, fulfilled of desire, and filled with the blessing of Hashem; take possession of the sea and south." ~Devarim 33:23
Rashi on 33:23:
Take possession- Rashi explains that The Sea of Kinnereth (or Sea of Galilee) were Naphtali's portion, and at the Southern section of the sea, he took an additional section that was the width of a length of fishing net rope so that they would be able to fish by spreading out their nets and snares.
Baba Kamma 81b further explains that while the land of Naphtali was actually to the north and west of the Sea, the tribe was also given a strip at the south of the Sea that was wide enough to allow for their finishing nets to be pulled.
Parsha/Math Investigation:
Based on the usage of non-standard units to indicate the southern section of the Sea that was portioned to Naphtali, how can we estimate a section that could have realistically been given to them?
Using current information on the Sea of Galilee (source: Wikipedia.org), we know that the Galilee is 13 km (or 8.1 mi) at it's widest section. It's narrower sections lead from the Upper Jordan River and lead down into the Lower Jordan River. In our case of Naphtali's land portion, we are looking at the southern section of the Sea, so we are looking at the section that leads down into the Lower Jordan River. Using even just basic visual estimation, the narrowest southern section is approximately 1/6 of the widest section of the Sea. That would mean that, even at its narrowest, it's still about 2 km wide, or a little over a mile wide. If their section of inheritance from the Sea was only wide enough for fishing ropes, then we have to understand that they didn't receive a full section from one shore to the opposite shore. Rather, it had to be a section with a border somewhere between the two shores. Without knowing too much about standard lengths of fishing nets, based on some quick research, my best guess would be that the nets themselves wouldn't be more than a couple hundred yards at absolute most, which would seem to necessitate only needing to grant access or propriety to about 1/10 of a mile or approximately 1/10 of the distance out from the western shoreline on the southern section of the Sea.
More extensive researching of specific maps of the Sea of Galilee and historical fishing nets and techniques could offer information for a closer estimate to the exact Sea area that was given to Naphtali.
Related Math Investigations:
- Younger students could use different items as base units for non-standard measurement around the classroom-
- How many paper-clips long is the table?
- How many blocks tall (using identical blocks) is the bookshelf?
- Older students could measure things around the room using non-standard units, but then also compare these measurements to standard measurements.
- For older students, an idea for the classroom that is similar to the concept above from the parsha might be:
- How many papers long is the table?
- How many inches/feet/meters long is the table?
- If I need to work on one side of the table and have space for my paper, how many inches/feet/meters of space do I need to allow myself on my end of the table?
- A step above for even older students might be to consider how much space would need to be allotted to individuals in order to have space to work at the table, and then consider, based on their estimates, how many students could effectively share the table and be able to get their work done without bumping into each other or invading each other's work space.
Parshat Haazinu is made up entirely of a single Chapter- Perek 32- towards the end of the book of Devarim. The majority of the parsha is a song written by Moshe. If you look at the parsha directly in the Torah scroll, the section of the song is written completely in two divided columns. Below is a picture that I took of this section from a tikun, or book that people use to practice the cantillation and pronunciation of the words. It is written exactly as it appears in the Torah scroll, but I took pictures of the practice side rather than the actual Torah side. (Please note that because these pictures contain G-d's name written out in them, please do not print them out or print them out and discard them.)
The reading is in the two larger print righthand columns on each page. The pictures only include the sections with the song, not the entire parsha.
If you've ever studied poetry in school, you'll be familiar with patterns of rhyme, beat, measure, line fragments, word placements, etc. that writers use to enhance the aesthetics of their poetry. Reading through the parsha as it is written in the Torah, do you find any patterns? Lyrical patterns- beat or measure to the pattern of the words? Visual patterns- patterns in the placement of the words or repetitions of words in the scroll? Is there a pattern in the number of words in the lines, or the way the words are broken up into columns or lines throughout the song?
Younger students can listen to the parsha being read and listen for beat or measure. Older students can investigate this on their own, or in partners. Students of all ages can look at patterns in numbers of words per line, or looking for any alliteration of letters that may appear. Younger students could handle smaller sections and maybe look at the whole as a class, while older students can look at the entire text as in partners.
Please note that I have not investigated these questions myself, yet, but rather this is a proposed investigation.
"Take this book of the Torah and place it at the side of the Ark of the Covenant of Hashem, your G-d, and it shall be there for you as a witness." ~Devarim 31:26
Rashi on 31:26
At the side of the Covenant of Hashem- The Sages of Israel argued about this in Tractate Bava Basra. There are those among them who say that there was a board protruding from the Ark on the outside and there [the Torah scroll] was placed. And there are those who say that it was placed beside the Tablets inside the Ark.
Discussion Point:
Clarity of descriptions and directions are a key aspect of communication. If I say something that I think is clear, it's only really as clear as the way the other person hears and understands it. Sometimes there are language or cultural barriers that create a need for extra-specific clarity or explanation, but, in general, even in an everyday setting with people who speak the same language and use the same cultural cues, it is still important to include details and descriptions that add to the clarity of the information that you are trying to communicate. In the statement above from this week's parsha, there is enough ambiguity that it's unclear exactly where the Torah should be stored in relation to the Tablets in the Ark.
Consider the following- I could tell you to:
- get the dish from the kitchen
- get the dish from the cabinet in the kitchen
- get the dish from the bottom left cabinet under the window in the kitchen
All three of those directions request the same item and sound fairly clear, but the third one will leave my messenger the most sure of their task and help them formulate their plan for following my directions.
Suggested Activity:
Students of any age who have reached a level of interactive play and communication with peers can practice formulating a direction and sharing it with the class or in partners. Partners should test their friend's direction to see how clear it really is when they try to follow through. How much do you need to amend your directions or help your friend in order for them to do what you asked? The fewer changes you need to make, and the less help you need to give, the clearer your original directions are. Younger students might want to do this with directions for a physical task- moving around the room to complete a task. Older students can give directions for a physical or written task- moving around the room, following a specific path through a section of the school, creating a drawing, a pattern, or a sequence.
Students can adapt this activity to whatever their developmental level. Moving from verbal directions to clear, specific written directions also increases the difficulty level for students.
