"...your small children, your women, and your convert who is in the midst of your camp, from the hewer of your wood to the drawer of your water..." ~Devarim 29:10
"Hashem, your G-d, will bring you to the land which your forefathers took possession and you shall take possession of it; He will do good to you and make you more numerous than your forefathers." ~Devarim 30:5
"...that which I command you today, to love Hashem, your G-d, to walk in His ways, and to keep His commandments, His statutes, and His ordinances; and you will live and you will multiply, and Hashem, your G-d, will bless you in the land to which you come, to take possession of it." ~Devarim 30:16
"...I tell you today that you will surely be lost; you will not lengthen your days upon the land that you cross the Jordan to come there, to take possession of it." ~Devarim 30:18
Math Connection:
I first wrote about mathematical language back in my 1st posting on Parshat Shemot. When speaking about mathematically related words and descriptions, students (and sometimes adults) will mix up or interchange terms without realizing the implications of the words that they choose to use. Careful word choice is important in any use of language, and that applies to mathematical language, as well.
Some specific mathematically related descriptions to consider from this week's parsha:
- "small children"- what information does that tell you? why is that an important detail? how might you define small?
- First it says "make you more numerous", and later it says "you will multiply"- (note that my quotes are from my Artscroll edition; in the Sefaria.org translation, it actually translates both locations as "multiply") How does the second description further define the first description? Does it make it clearer? In what way will you become more numerous? How much greater will you be? In what way will the numbers increase?
- Later it says "lengthen your days"- what's the difference between multiplying and lengthening? Is one description more specific than the other? Or do they indicate different meanings?
This week we have the only double-parsha of this year's cycle of reading of the complete Torah. Due to this year being a leap year, we had an extra month in the calendar, so these two parshiot are the only 2 that need to be combined in order to get through reading the entire Torah within one Jewish calendar year.
In this week's double parsha, we read of Moshe bringing together all of the Jewish people, leaders of all levels and laypeople alike. He then reviews with them the promises that Hashem made to Abraham, Isaac, and Jacob; he reviews how Hashem saved the Jewish people from slavery in Egypt; and he reviews that if they follow the commandments, they will be blessed, and if they don't, they will be cursed. Then, Moshe discusses that he has lived his complete life, and he will pass on leadership to Yehoshua ben Nun to bring the Jewish people into the land of Israel.
The content of this double-parsha struck me as the beginning of the conclusion of the first 5 books of the Torah. As we approach the end of the cycle, I thought it would be interesting to look at some statistics related to all the parshiot.
Statistics:
If we look back over the math concepts that have been touched on this year, we looked at statistics back in Parshat Bamidbar. There, we talked about the purpose of statistics for comparing data in order to learn patterns and trends about the situation you are looking at. We also looked at using statistics to create graphs in Parshat Vayikra and Parshat Tzav, where we used the graphs to help us look for trends and comparisons of information.
Below I've complied data related to the 5 Books of Torah and each of the individual parshiot. (Note: These statistics were compiled using a combination of information found on Wikipedia.org and torahtots.com.)
If we look at the charts, we can see that there are:
12 parshiot in Bereishit
11 parshiot in Shemot
10 parshiot in Vayikra
10 parshiot in Bamidbar
11 parshiot in Devarim
For some basic statistics, while we see that the parshiot are approximately evenly divided between the 5 books, Vayikra and Bamidbar have the least number of parshiot (10 each), and Bereishit has the greatest number (12). The number of parshiot in each of the 5 books ranges from 10-12 (so there is a range of 2--> 12 - 10 = 2). If we wanted to find out how many parshiot, on average, each book has, we would find the mean- add the 5 numbers together and divide by 5.
If we take a look into the statistics related to the number of letters in each parsha, number of words in each parsha, and number of pesukim (verses) in each parsha, we will find that:
V'Zot Habrachah has the fewest letters with 1,969 letters.
Nasso has the most letters with 8,632 letters.
Overall, the parshiot have a range of 8,632 - 1969 = 6,663
V'Zot Habrachah has the fewest words with 512 words.
Nasso has the most words with 2,264 words.
Overall, the parshiot have a range of 1,752 words.
Vayeilech (one of this week's parshiot) has the fewest verses with 30 verses.
Nasso has the most verses, with 176 verses.
Overall, the parshiot of a range of 146 verses.
In a full statistical analysis of each of these, a student would use either a line plot or stem-and-leaf plot to see the full view of how the number of letters, words, or verses fall on a number line. They would look to see if the numbers cluster in any spots (is there a pattern to be able to identify a smaller number range where most parshiot fall when looking at number of letters? number of words? number of verses?).
Students could calculate mean, median, and mode for the number of letters, words, or verses in the parshiot.
Students could graph the numbers of letters, words, or verses for on a bar graph to see how the numbers increase and decrease over the progression of the parshiot throughout the year.
Students can also look at how the other double-parshiot are paired for regular years, and how that effects changes in the numbers if we combine numbers for double-parshiot.
There are many statistical questions that a student could ask related to this data to compare the statistics of individual books and parshiot. These are just a sampling of some ideas.
