"Joseph amassed grain like the sand of the sea, very much, until he ceased counting, for there is no number." ~Bereishit 41:49
For this week, I want to focus on the statement above, where Joseph was overseeing the collection of grains in Egypt during the 7 abundant years in preparation for the upcoming 7 years of famine. Using the commentaries of Rashi and Sforno we learn that Joseph was amassing as much grain as possible, until the grain counter stopped counting (Rashi) and the reason that he stopped counting was that he had run out of names of numbers to use for his counting (Sforno).
This statement struck me as one that would make for an interesting discussion with students on place-value and increasing numbers. For information on place value and thinking about how it works, functionally, see my post from Parshat Bereishit.
Concepts related to the progression of counting:
- Children first start by learning the base pattern in counting from 1-10. Once they have a solid ability to count 1-10, we begin working with them on recognizing the pattern of how we loop through 1-9 in each set of tens (teens, twenties, thirties,...) to make another set of 10. Interestingly, the tens places increase in the same numerical order as the ones.
- After tens, usually somewhere in the grades K-2, students solidify their counting from 1-100. Next, they practice understanding the next loop- counting from 100-200 will follow the same pattern as 1-100, but with "one hundred" before each number. Once they reach 199, they increase the hundreds place to 200. Again, interestingly enough, the numbers continue to loop in the same pattern with the hundreds place increasing in the same numerical order as the ones and tens did.
- As students move up in their understanding of place value through the hundreds, then we work with them on extending their understanding exponentially by reviewing with them the idea that this loop continues on and on, and as we reach our maximum capacity for each place value, we just add on the next place value and continue the pattern loop that we've created.
- Once students have mastered the concepts of the unlimited potential for counting by increasing numbers, we then extend the concept in 2 directions:
- 1) negative numbers and comparing how "increasing" negative numbers and place values relates to increasing positive numbers and place values
- 2) decimal numbers and comparing how "increasing" decimal numbers and place values relates to increasing positive/negative numbers and place values.
- Note that while positive and negative numbers are fairly comparable, conceptually, when we think about magnitude, or size, of the numbers, an added conceptual difficulty that decimals offer is the idea that the "larger" the number, the "smaller" the piece. The numbers we talk about as decimals, really means the number of pieces that 1 unit or whole is broken into- so more pieces, means cutting the same piece into smaller pieces.
The most basic construct that children are building on as they increase their understanding of counting through each level is that you can always make a bigger number by just adding one more; cycling through the understood loop of numbers and adding new place values as needed will always result in a new, bigger number.
Based on this construct, how can we understand the statement above in the parsha? An interesting Social Studies connection might be for the students to see if they can find information on how many of our place values the Egyptians actually used. Clearly, based on our understanding of counting, even if we didn't know how to read the number of counted grain, we would at least be able to write out the number representing how much grain was collected, and we could have kept on counting.
Some questions to consider for a conversation on the topic:
Obviously, the Egyptians had a limit- did they stop counting because they thought they couldn't have any more grain? No, they stopped counting because they reached a point where they could no longer track their collection. What implications might extend from such a situation?
"When you shall come to the Land and you shall plant any food tree, you shall treat its fruit as orlah; for three years it shall be orlah to you, they shall not be eaten. In the fourth year, all its fruit shall be sanctified lauding to Hashem. And in the fifth year you may eat its fruit- in order to increase its crop for you- I am Hashem, your G-d." ~Vayikra 19;23-25
Rashi explains on 19;23: "...three years it shall be orlah to you..."
From when does he begin to count the three years for it? From the time of its planting, i.e., from the time that it was planted.
Counting:
The first number sets that we learn, beginning from a very young age, are the set of counting numbers- 1, 2, 3,...- and the set of whole numbers- 0, 1, 2, 3... We learn that when we have none of something, we label that as 0, and when we count items, we assign each item a number in counting order, and we can label the whole group with the number of items using the highest counting number used to count the group. So, if I have a group of pens, the first one is 1, the second one is 2, and so on. If I count up to 13 in labeling them all, then I would say that I have 13 pens.
When counting the passage of time, we enter into a more complex concept, which can be difficult to understand. Just like with other units of measurement (pounds, inches, etc.), "0" indicates that no time has passed, but we don't have "1" until we reach one completed unit of time. So, if we're counting days, the beginning of the counting of time would be 0 days. However, we cannot count 1 day until a full 24 hours has passed, we cannot count 2 days until a full 48 hours has passed, and so on.
So how do we refer to the time in between? There are two ways of dealing with this. The first way, similar to other units of measure, is to break the intermediate time into either fractions (5/24 of a day, 1/2 of a day, etc.) or a smaller unit of measure (hours, minutes, etc.). With this method, 8 hours after the first full day would be 1 and 8/24 days or 1 and 1/3 days. The second way is to refer to the entire time in between two full cycles as "the 1st day", "the 2nd day", etc. So, from the moment we start counting the days, 0-24 hrs is labeled as the 1st day, but we only have 1 complete day after a full 24 hours. After 24 hours, we are then in the 2nd day, but we only have 2 complete days after a full 48 hours. After 48 hours, we are then in the 3rd day, but we only have 3 complete days after a full 72 hours. And so on...
Parsha Connection:
When we look at the directions we are given related to orlah, we are told that fruit from trees may not be eaten for three years, in the fourth year the fruit is given to Hashem, and in the fifth year it may be eaten. So how do we know when to start counting? Rashi explains that we start counting from the time that the seeds are planted. Now Rashi has given us our 0 point. One year later, we can count 1 yr; after a full cycle of another year, we can count 2 yrs; and finally after one more full cycle of a year, we can count 3 yrs. During this time, any fruit that is harvested may not be benefited from in any way. After we have counted 3 full, complete years, we are then "in the fourth year". Using our understanding of counting time to understand the verse, it seems that once we have counted 3 complete years, we will then be "in the fourth year". At this point, fruit may be harvested, and throughout this 4th year, the fruit is all sanctified to Hashem. Once we count the 4th complete year, then we enter into the 5th year, at which time we can eat the fruit ourselves.
Everyday Connection:
Have you ever noticed how children (and even some adults) get flustered when they try to figure out how old they are in between birthdays? Or how to refer to the age of a newborn baby in its first year of life? The next time you find yourself trying to calculate the age of something, try thinking about it as explained above, and see if that helps make more sense of it.
So, for example, that newborn baby is in his/her 1st year of life from the moment that they're born all the way until their 1st birthday. The day after their birthday, they begin their 2nd year of life, which continues all the way until their 2nd birthday (signifying 2 completed years of life).
