Toldot- Base-10 and Number Sense related activity ideas

"Yitzchak sowed in that land, and in that year he reaped a hundredfold; thus had Hashem Blessed him." ~Bereishit 26;12

Rashi on 26;12-
"A Hundredfold- For they assessed [the field] to determine how much it is fit to produce and it produced for every unit they estimated it could produce a hundred units. Our Rabbis said, This assessment was done for tithes."

In this section of the parsha, we learn of Yitzchak's time living in Gerar, under the rule of Avimelech. Bereishit Rabbah (64;6) asks: if we're not supposed to find a blessing in a measurable quantity, how could this crop be considered a blessing? You are not supposed to count on a crop before it is harvested (like the old adage- "Don't count your chickens before they hatch"). How does this make sense? The Mizrachi explains that the crop was traditionally estimated in order to make an advanced calculation for tithings to be easily set aside. The midrashim (Tosafot HaShalem citing Rivah) teach us that this crop that is referred to was sowed during a time of famine in the land. Yitzchak had estimated what his tithe should be in order to be able to set it aside for the poor as soon as possible, and he had estimated much less of a crop due to the famine in the land.  It is with this understanding that we see how this was such a blessing for Yitzchak. 

Activity Connections:
There are two primary mathematical concepts that connect to this crop:
1) the concept of calculating and setting aside tithings
2) the concept of one hundredfold 

Interestingly enough, both of these concepts connect to powers of 10. 
*Tithings are classically 1/10 of a crop (the root of the hebrew word- מעשרות/מעשר- is actually related to עשר, the number 10)
*one hundredfold means times 100, which is a power of 10 (10²;or X10 and then X10 again)

Activity ideas in increasing conceptual difficulty:
*What does a tithing or 1/10 of a group really look like? For the youngest students, they could begin by just taking a group of items and separating the items into 10 equal groups. Having a set-up of 10 cups, bowls, or plates to sort the pieces into will help students keep track of their sorting. This is doable even for preschool children. After they divided their items into 10 piles, they can count each pile to make sure that they all have the same number of items in them. From there, they can act out separating 1 of the piles to give away and keeping 9 of the piles for themselves. For beginners, you want to simplify the process for them by making sure that the number of items they start with is a multiple of 10 (so that it divides equally into 10 piles).

*As a step up from the previous activity, you can have students divide larger groups of items, and incorporate estimation or calculation of what amount the tithing will actually be when it's separated out. Students who have had exposure to the concept of fractions and decimals could also estimate and calculate the value of tithings for amounts that are not strictly multiples of 10.

*One hundredfold- what does x100 really look like? What if Yitzchak had anticipated having 5 bundles of grain? How much did he actually have that year? What if he had anticipated 10 bundles of grain? Younger students can physically count or draw out the difference of a group of 5 and a group of 500. Small or medium sized graph paper can be good for drawing out a model of these differences (with each box modeling 1 unit). If students have the dexterity, small manipulatives like paper clips can also be good. For younger students, these can be modeled with blocks or Legos, but you need to have a good supply in order to model the hundreds. (Tip: Creating stacks or grouping of 10 to count everything out will help make counting easier and will help children develop their number sense.)

*Older students can graph the difference between the anticipated crops and the actual crops. Is there a pattern to the difference? How would the difference be expressed as an algebraic expression?

*Another activity for older students would be a comparison of the tithings between the anticipated crops and the actual crops. What would a graph of these differences look like? How could the differences be expressed algebraically? How does the pattern of the difference in tithings (anticipated vs. actual) compare to the pattern of the difference in crops (anticipated vs. actual)? How do the algebraic expressions of each comparison compare to each other?