"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.
