Nitzavim- Thinking about Mathematical Language

"...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?

Ki Tavo- Leveled activities for division

"Moshe commanded the people on that day saying, 'These shall stand to bless the people on Mount Gerizim, when you have crossed the Jordan: Shimon and Levi and Judah and Issachar and Joseph and Benjamin. And these shall stand for the curse on Mount Ebal: Reuven, Gad and Asher, and Zevulun, Dan and Naphtali...'"~Devarim 27:11-13

Some activity suggestions:

• Younger students can talk about dividing the 12 tribes evenly between the two mountains. How many should be on each mountain? Connect the separation to division of 12 by 2-- will have 6 on each mountain. 
• Pattern finding: If you cross-reference with charts of children from each mother (Rachel, Leah, Bilha, and Zilpah) and the birth order of the 12 sons, can you find any connection between the siblings who were grouped together on each mountain?
• For Older students- if we take the most recent census information- from Bamidbar 26:1-51, we have a listing of the numbers of men in each tribe. Taking these numbers, was the division of people equal between the two mountains? Did one mountain have more people and one have fewer people? Could there have been a different way to divide the tribes that would have made the division more equatable between the two mountains?

Ki Teitzei- Activity suggestions related to weights & measures and fractions

A couple of suggested activities related to this week's parsha:
In last year's post, I wrote about the algebraic connection to the mitzvah (commandment) of being honest in weights and measures. Here are some suggested pre-algebra activities-

• using a balance scale, students can have different sized blocks which they need to place on the scale to figure out which is greater (heavier) and which is lesser (lighter). From there, they can investigate how many of the lesser weights it takes to balance the greater weight.
• a more difficult variation- using multiple unlabeled blocks/weights, students can work to:
•  order them from lightest to heaviest
• determine if multiples of the same block are equal to (balance) any of the other blocks
• determine if any combinations of blocks are equal to (balance) any of the other single blocks
• determine if any combinations of blocks are equal to (balance) any combinations of other blocks
• using labeled weights, students can confirm different combinations of smaller weights that should equal (or balance) with a single larger weight- for example, they should find that 2+3 is equal to (balances) a 5.
• students can then "mix and match" to find different combinations of weights that are equivalent to each other- for example, they should find that a 2+5 is equal to (balances) a 3+4.

There are many commandments (mitzvot) enumerated in this week's parsha. It has been counted that, in fact, 74 out of the 613 commandments have a basis in this parsha. Students can consider-

• What fraction of mitzvot are based in the parsha?
• Can this fraction be reduced?
• a related concept- what is the prime factorization of these two numbers? Did you know that you can quickly reduce large fractions by finding the prime factorization of both the numerator and denominator and crossing out "pairs" of common numbers that appear in both.
• a simple example- to reduce 10/15, we could say that 10 = 2x5 and 15 = 3x5; since there is a 5 in the prime factorization of both the numerator and the denominator, we can cross out both 5's, and we are left with 2/3. In this way, we have reduced 10/15 to 2/3 using prime factorization.
• another related concept- investigating common factors and identifying prime numbers (numbers that have only 2 factors- 1 and the number itself)
• What fraction of mitzvot are not based in the parsha? In other words, what's the fraction of other mitzvot that are not listed?
• Can this fraction be reduced?
• What percentage of mitzvot are listed in this parsha? What percentage of mitzvot are not listed in this parsha?
• What is the ratio of mitzvot in this parsha to the mitzvot not in this parsha?