Chanukah Activities- Chag Sameach

When I first stopped posting weekly, I had intended to post holiday ideas a few times a year, as the chagim came up. Although life has gotten in the way, since I'm planning some activities for my classrooms, I thought I'd quickly share what I have. Chag Chanukah Sameach!

Activity 1:
For younger grades, I always love playing dreidel with the students and having them track and graph the results of their spins as bar graphs. If the students play for long enough, their results should approximate even results for all 4 letters. You can combine data from students in the class to have them see how the comparisons change and the results (usually) even out across the letters as they combine the data from more people. 
**For younger grades to visualize the graph, you can have the students cut out their bar graphs from their own papers and tape them together on the wall or board to quickly see the growth of adding together the data without having them tediously count and add the bar graphs. 
**For older students, they can calculate statistics for the results of each letter and compare how the statistics change when they combine data from classmates together.

Activity 2:
In my Algebra 1 class, we recently began graphing, distinguishing between discrete and continuous graphs, identifying restricted graphs, identifying domains, ranges, and graph intercepts. With these topics in mind, I created the following worksheet with practical application problem solving for my classes.

Chanukah Algebra

Question 1:

Thinking about Discrete vs Continuous-

Graphs of candles vs oil used over Chanukah.

1)    What would be the difference in a graph of the number of candles used over time or by number of people and the amount of oil used over time or by number of people?

2)    Assuming that 1 oz of oil burns for the minimum zman, make an argument for why the graphs of candles and oil should actually be similar.

a.     Can you make a counter-argument for why the graphs should still be different?

Question 2:

For your doughnut sale, you’re charging $1.50 for jelly doughnuts and $1.25 for glazed doughnuts. Assuming you sold $375 worth of doughnuts, draw the graph of your possible sales. Use the following questions to help guide you in creating your graph.

1)    The equation that represents your sales would be: __________________________

2)    What are the two intercepts of your graph? 

3)    What do they each represent? 

Question 3:

For your Chanukah carnival, each student is allowed 3 turns at a booth for each ticket that they have.

1)    Write a function for the number of turns that a student gets based on the number of tickets they have.

2)    Draw a graph of this function.

3)    What is the domain, if each student is allowed no more than 10 tickets? (use the table below to organize your answers)

4)    What is the range, given this limit on the number of tickets? (use the table below to organize your answers)

__________
__________

Question 4:

You’re lighting an oil menorah this year, which takes 1 oz of oil for each light. Assuming you use this menorah for all 8 nights, and you use a regular candle for the shamash-

1)    How many ounces of oil will you need for the full chag?

2)    You want to buy oil for a number of people to be able to light menorah for the whole week. Write a function for how much oil (in oz) you will need based on the number of people you give oil to.

3)    You bought the oil in 4 qt bottles (160 oz) and were able to buy 18 bottles, which gives you 2,880 oz of oil. What is the most number of people you can give oil to for them to have for the whole week?

4)    What are the domain and range for this situation? 

5)    Draw a graph to represent the possible number of people who you could provide oil to and how much oil you will have given out.

V'Zot HaBracha- Estimating based on Non-Standard units

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.

Haazinu- Looking for patterns

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.