"But Hashem became angry with me because of you, and He did not listen to me; Hashem said to me, 'It is much for you! Do not continue to speak to Me further about this matter. Ascend to the top of the cliff and raise your eyes westward, northward, southward, and eastward, and see with your eyes, for you shall not cross this Jordan. And command Joshua, and strengthen him and give him resolve, for he shall cross before this people and he shall cause them to inherit the land that you will see.' And we stayed in the valley, opposite Beth-peor." ~Devarim 3:26-28
In this section of this week's parsha, we have Moshe retelling the Children of Israel about how he begged Hashem to let him join them when they entered the land of Israel, and Hashem's response to his request. He confirms that he is not allowed to enter the land, but he is told to go up to the top of the cliff and look around in all directions- West, North, South, East- to see the land that will be given.
Last year, in Parshat Behaalotcha, I wrote about the difficulties that children have in making sense of right and left and how the use of right and left is specifically confusing when trying to assign it to different people or objects- my left, your right, to the left of the desk, etc. An overlay to that understanding is the concept of cardinal directions, which is used here (and in many other descriptive sections of the Torah).
Cardinal directions are north, south, east, and west. While these are classically a geographically linked concept, they tie into students understanding of direction, and therefore expand beyond just the basic map-reading skills and fall into spatial understanding and reasoning, which promotes their understanding of geometry and spatial awareness.
The biggest aspect for students to explore is based on the idea that the descriptions of left and right change based on a person's orientation. For example, when a stand here, the window is on my left, but when I turn, now the door is on my left. However, with cardinal directions, they maintain their location and description no matter how you move around. If the window is on the north side of the room, and the door on the east side, they will remain on the north side and the east side, respectively, no matter which way I turn around.
Students can also rely on the fact that once they remember the relationship of the directions to each other, then as long as they can definitively identify the location of one direction, they can figure out the remaining directions. In other words, if I know that my window is north, and I need to figure out the direction of my door, if, when I face my window the door is 90 degrees on the right, then I know that my door is to the east.
As students advance, they can extend their knowledge throughout a building. So, if I give my students a mock blueprint of a school, and I tell them that the chalkboard in the 2nd grade classroom is on the northeast side of the building, they should be able to use that information to determine the cardinal location of any other item on the floor, or even in the entire building, that I ask them to locate. Going another step beyond, rather than just lining up blueprints or maps in front of them, can they use identifying markers to physically move through the building, or school campus, or beyond and identify the cardinal directions of specific requested items?
While knowing left from right is a critical skill for life, knowing cardinal directions is an even greater skill, since the cardinal directions allow for greater extrapolation of the relationship of the space that you're moving in.
Extension Thought:
Visually, students can make a connection between the directions on the compass and a coordinate plane. Imagine:
- The N-S line = y-axis
- The W-E line = x-axis
- Center point of the compass = the origin or (0, 0)
- NE = the 45 degree split of the (+, +) Quadrant I
- NW = the 45 degree split of the (-, +) Quadrant II
- SW = the 45 degree split of the (-, -) Quadrant III
- SE = the 45 degree split of the (+, -) Quadrant IV
Conceptually speaking, these may not have a strong connection to each other, but connecting information in different ways can make a big difference in the way that students make sense of, understand, and internalize disparate information to create meaningful and useful practical applications of the information for themselves. This is why we teach, use, and create mnemonic devices for ourselves when trying to remember information.
"I implored Hashem at that time, saying, 'My Lord, Hashem, You had begun to show Your servant Your greatness and Your strong hand, for what power is there in the heavens or on the earth that can perform according to Your deeds and according to Your mighty acts? Please let me cross and see the good land that is on the other side of the Jordan, this good mountain and the Lebanon.' But Hashem became angry with me because of you, and He did not listen to me; Hashem said to me, 'It is much for you! Do not continue to speak to Me further about this matter...'" ~Devarim 3;23-26
"When you beget children and grandchildren and you will have been long in the land, you will grow corrupt and make a carved image of the likeness of any thing, and you will do evil in the eyes of Hashem, your G-d, to anger Him." ~Devarim 4;25
Rashi on Devarim 4;25:
"And you will have been long"- He hinted to them that they would be exiled from [the land] at the end of eight hundred and fifty-two years, like the numerical value of the word v'noshantem (and you will have been long in the land). But [G-d] advanced the date and exiled them at the end of eight hundred and fifty years. He advanced the exile two years ahead of the number represented by v'noshantem so that "you will surely perish" should not be fulfilled in them. This is the meaning of that which is said, "Hashem hurried regarding the evil and brought it upon us for Hashem, our G-d, is charitable; that is, He acted charitably with us for He hurried to bring [the exile] two years ahead of time.
Gematria & Simple Addition:
For young students who are trying to improve their simple addition skills, practice is critical. While a student might be able to handle the process of addition, every opportunity for practice that a student has will contribute to his fluency and speed in mental calculation. Gematria is the Jewish concept that every letter of the Hebrew alphabet has a numerical value assigned to it. Using these values, it is possible to add the value of each letter in a word, phrase, sentence, etc. to find a deeper meaning between the meaning of the word or phrase and the numerical value assigned to it through Gematria. This Gematria chart gives the values assigned to each hebrew letter. There are places throughout Judaism where you can find Gematria based interpretations for things- throughout the Torah, related to holidays, etc. Younger students can calculate the Gematria of their name or of individual words and phrases. I've had older students search for Gematria patterns in words related to specific holidays.
Parsha Connection:
In this week's parsha, alone, we have at least two instances of significant Gematria that is explained. The very first word of the parsha- "va'etchanan"- is discussed in Midrash Rabbah. In the beginning storyline of th e parsha, Moshe is praying to Hashem to please allow him to enter the land of Israel along with the Jewish people, and Hashem subsequently angers towards Moshe insisting that Moshe stop this line of prayer. The explanation is given that the Gematria value of the the word va'etchanan (the word meaning Moshe prayed) is 515. Let's check this:
vav- 6
aleph- 1
taph- 400
chet- 8
nun- 50
nun- 50
6 + 1 = 7 + 400 = 407 + 8 = 415 + 50 = 465 + 50 = 515
Midrash Rabbah explains that Moshe offered 515 prayers (the Gematria value of va'etchanan) to Hashem to plead to be allowed to lead the Jewish people into Israel. If Hashem had not cut him off, but had allowed him to pray for the 516th time, it is explained, then Hashem would have had to allow Moshe to enter Israel with the Jewish people.
The second instance of Gematria significance in the parsha come in 4;25, where we are told of the Jewish people being settled and living for many generations in Israel, and then they will anger Hashem. Rashi here uses the Gematria value of the word "v'noshantem", which means "you will have been long in the land". Rashi explains that the Gematria value of the word is 852- let's check this:
vav- 6
nun- 50
vav- 6
shin- 300
nun- 50
taph- 400
mem- 40
6 + 50 = 56 + 6 = 62 + 300 = 362 + 50 = 412 + 400 = 812 + 40 = 852
According to Rashi, this means that the Jewish people should have been settled in the land for 852 years before they were exiled. However, when looking at the timeline of Jewish History, the Jews were actually only settled for 850 years before they were exiled. Why this discrepancy? Rashi explains that if they had been settled for the full 852 years, then they would have strayed so far that their behavior would have caused Hashem to not only exile them, but they would have also been destroyed. In an act of mercy, Hashem caused the Jewish people to be exiled 2 years early so that when they were exiled, they did not perish as well.
Everyday Connection:
Gematria offers one way of integrating interesting, deeper insights into Judaic studies concepts while practicing simple addition and even offering opportunities for students to look for patterns within a given topic. While I find these added spiritual connections interesting and insightful, each person has their own subjects, ideas, or activities that they connect with. In what ways can you find basic math skills, patterning skills, etc in your everyday activities to help offer skills review and practice to the math students in your life? One person might naturally calculate all around them- calculating time until an alarm should go off, combining any types of numbers that may appear in their surroundings -street signs, page numbers, etc; someone else might need to search out problem solving scenarios within their daily activities to find meaningful calculation practice- if I can read a page every 3 minutes, how long will it take me to finish this book? how many pages do I have left to read? if I want to finish the book and walk my dog for 10 minutes before dinner time, do I have enough time to do both if I start right now?
