"For only Og king of the Bashan was left of the remaining Rephaim. Behold! his bed was an iron bed, in Rabbah of the Children of Ammon; nine cubits its length and four cubits its width, by the cubit of a man." ~Devarim 3:11
In this week's parsha, we have Moshe retelling about the journey of the forty years through the desert. This is actually the second retelling, since last week in Parshat Masei we also had a retelling of the journey. Last week we read a more factual retelling (traveling from point A to point B to point C...), while this week we read a more emotionally connected retelling by Moshe to the Children of Israel. Within this week's parsha, we learn more details about when The Children of Israel were fighting various groups of people towards the end of their journey, as they approached the land of Israel. In the specific section quoted above, we learn that Og the king of Bashan was the only remaining giant from the Rephaim following their battles with the Rephaim.
Math Connection:
In this section, we are told the dimensions of Og's bed, and Rashi specifically explains that the measurements given were proportional to Og's size, rather than an average man. I first explained about non-standard units of measure back in Parshat Vayeira. Here, we have an interesting measurement- Og's bed is described by measure of cubits. A cubit is commonly defined as the distance from a man's elbow to the tip of his middle finger. Would this be considered a standard or non-standard measurement? While the definition is based upon using a standard measure using reference points on a person's arm, relatively speaking, each person's cubit will be measured differently. It is for this reason that it was meaningful for the parsha to specify "by the cubit of a man" and for Rashi to clarify that this specifically meant that it was a cubit measured by Og's arm. The argument could be made that general measurements based on cubits measured using measurements from an average man would result in fairly standardized sizes- maybe give or take a foot or so if you have final measurements of the same item measured with cubits from a shorter man compared to final measurements measured with cubits from a taller man.
Activity Suggestions:
- How long is a cubit by your arm?
- Take measurements for the entire class.
- How does the data compare for all the students in the class?
- What would the average cubit size for your class be?
- Does that include or exclude your teacher's cubit?
- Which measure of statistical average is most appropriate in this case- mean, median, or mode?
- How big would Og's bed be if it were built according to your cubit?
- Compare your measurements with measurements for your classmates.
- How do the measurements compare for all the students in the class?
- What would the average bed size for your class be?
- Does that include or exclude your teacher?
- What would the average bed size be for your class?
- Would everyone in the class fit on that bed?
- Which measurement would you choose to use if you needed to build a bed to any student in your class?
- Would your teacher fit?
- Using sizes for current-day standard bed sizes- twin, double, queen, king-
- How would your calculated bed(s) compare to a modern-day standard bed? Which bed is the closest in size to your calculated bed?
For Further Thought:
The following question is one that would make an interesting follow-up and "self-to-text" connection for students, but I was unable to find enough clear information regarding Og's height to confirm that this is an answerable question. I am including it here as a follow-up and would love to hear from anyone who might know of sources that offer information regarding Og's height.
- How big was Og? How can we estimate what size the bed might have been based on Og's cubit?
- How would Og's calculated bed compare to a modern-day standard bed? Which modern day bed is the closest in size to your calculated bed for Og?
"You stayed in Kadesh many days, [as many] as the days that you dwelt." ~Devarim 1;46
"We turned and journeyed to the wilderness by way of the Sea of Reeds, as Hashem spoke to me, and we went around Mount Seir for many days." ~Devarim 2;1
"The Emim dwelled there previously, a great and populous people, and tall as the giants." ~Devarim 2;10
"Sihon went out toward us- he and his entire people- for battle, to Jahaz. Hashem, our G-d, gave him before us, and we smote him and his sons and his entire people. We captured all his cities at that time, and we destroyed every city- the men, the women, and the small children; we did not leave a survivor." ~Devarim 2;32-34
"All these were fortified cities, with a high wall, doors and a bar, aside from open cities, very many." ~Devarim 3;5
"For only Og king of the Bashan was left of the remaining Rephaim. Behold! his bed was an iron bed, in Rabbah of the Children of Ammon; nine cubits its length and four cubits its width, by the cubit of a man." ~Devarim 3;11
Math Connection:
There are mathematically related words that we use on a regular basis, words that have a general meaning. If the people using the words don't have the same understanding of the meaning, then it can create great confusion. From a recent, personal example, my daughter was supposed to do something 5 or 6 times a day. I was checking-in with her nightly to find out how many times she had taken care of this responsibility, and she would consistently answer, "Several." Then, one night I asked her how many she thought several was, and she told me that it meant 2 or 3. What a difference!
Words such as "all" or "none" are clear even when we don't know how many are in a group, since we know that the situation refers to either the entire group or none of the group. Other words have commonly understood meanings (although even my ranges can be subjective):
a couple = 2
a few = 3-4
several= 5-6
many = 7+
Parsha Connection:
In this week's parsha, we have many examples of non-numerical vocabulary from which we should still be able to understand a certain quantity. Some of the words are concrete and give clear meaning, even without giving specified quantities, while other words leave us with the need for common understanding in order to have a full understanding of the meaning.
Examples of non-numerical concrete vocabulary:
*Devarim 2;32-34 Sihon went out with his entire people, his entire people were smote, and all his cities were captured and destroyed
Examples of non-numerical subjective vocabulary:
*Devarim 1;46 Children of Israel stayed in Kadesh many days.
*Devarim 2;1 Children of Israel traveled around Mount Seir for many days.
*Devarim 2;10 The Emim were a great and populous people, and tall as the giants.
*Devarim 2;32-34 The Children of Israel conquered Sihon and his people, including the men, the women, and the small children
*Devarim 3;5 The cities captured from Og "were fortified cities, with a high wall, doors and a bar, aside from open cities, very many."
Sometimes, even when measurements are given, clarification is needed. When we are told in Devarim 3;11 of the measurements of Og's iron bed (Og being a giant), we are given the measurements in Amot, which is a standard biblical measurement from the elbow to the tip of the middle finger of an average sized man. However here, Rashi specifies for us that Og's bed was actually measured in Amot based on Og's proportions, not that of an average man. This would make quite the difference in the size of his bed!
Everyday Connection:
Have you ever had a situation when you were given non-numerical quantitative information and you felt that you needed to research or discuss further to fully understand the information? Are you always clear when using such vocabulary yourself? How often do we think that we are being clear, when really we end up with a misunderstanding? I know that my daughter has helped me try to be more conscious of my own clarity when using such terms.
