Devarim- Standard or Non-Standard Measurements?

"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?