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?