Vayeira- Non-standard Units of Measure

"The water of the skin was finished, and she cast off the boy beneath one of the trees. She went and sat herself at a distance, some bowshots [away], for she said, 'Let me not see the death of the child.' And she sat at a distance, lifted her voice, and wept." ~Bereishit 21;15-16

Non-Standard Units of Measure:
We are all familiar with standard units that we use to measure on a regular basis- we measure length with inches, feet, miles, centimeters, meters, kilometers; we measure liquids with cups, pints, quarts, gallons; we measure weight with ounces, pounds, grams, kilograms. Sometimes, though, the standard units that we use either aren't available or aren't necessary for the purposes of what you're doing.

When children are first learning about measuring, a common activity is to choose a standard by which to measure different items, and then students can compare the items based on their measurements. For example, they may use stacking cubes (all of the same size) to measure items in their surroundings- a pencil, a chair, a water bottle, etc. They can record their findings and then compare which items are shorter and which items are longer (or taller). As long as the same standard is used throughout an activity, all the items measured can be compared to each other.

Anything that you choose can be used as a non-standard unit for measuring- a paper clip, a pencil, a shoe- as long as the repeated measurement is using an item (or items) that are the same exact length. So, you can't use a mixture of large and small paper clips to measure items, but you can choose one or the other. You can see how many water bottles it takes to fill up a pitcher, but you need to fill the water bottles full each time to establish a temporary standard for your measurements. 

If you want, or need, you can always convert your non-standard measurements into a standard unit afterwards by measuring your non-standard unit. If your paperclip is 3/4 of an inch long, you have enough information to convert your measurements into inches. If your water bottle holds 2/3 C of water, then you can calculate how many cups your pitcher holds.

Parsha Connection:
In this week's parsha, we learn of Hagar and Ishmael's wandering after they are sent away from Avraham and Sarah's home. We are told that when Hagar believes that Ishmael is dying, she sits "some bowshots" from him, so as not to have to watch him die. What does this mean practically, for our understanding of the distance between Hagar and Ishmael at this time?

Bereishit Rabbah 53;13 explains two aspects of this in order for us to understand the distance:
1) first it explains that since it is written "bowshots", plural, but with no specific quantity, it must mean that the minimum plural is implied. Since the smallest plural number is 2, therefore it's 2 bowshots away.
2) second it explains that a standard bowshot during this time was 2,000 cubits, or a little more than today's measure of 1/2 a mile.

Based on this explanation, we can use the parsha's non-standard measurement of a bowshot to calculate that, by current day measurements, Hagar was approximately a distance of a mile away (or just over a mile) from Ishmael during this time.

Everyday Connection:
Let's say you have a recipe for a sauce that calls for equal parts of each ingredient. You don't need to measure exactly with a 1 cup measure- if you have a cup without measurement markings, you can still use that cup to measure out your ingredients. All you need to do is make sure that you measure each ingredient to the same point on the cup, and you'll have equal parts of each ingredient.

What if you need to measure the length of an item, but you don't have a ruler nearby? You can use a pencil, a piece of paper, or even your shoe- count how many "shoes" long your item is, and then you can measure the length of your shoe later to convert your measurement to a standard unit.