Haazinu- One to One Correspondence

"When the Supreme One gave nations their portion, when He separated the children of man, He set the borders of peoples according to the number of the Children of Israel." ~Devarim 32;8

Rashi on 32;8 makes reference to 70 languages which correspond to the 70 nations enumerated in Bereishit chapter 10, which developed from the descendants of Noah.

One to One Correspondence:
Have you ever heard a young child count pictures in a book and watched as they accurately count up to 13, only to see that there are actually only 5 pictures on the page? Have you watched a small child try to count items in front of them, trying to figure out which ones were already counted?

One to One Correspondence is one of the first concepts that young children need to understand in order to understand what numbers actually mean. One to one correspondence is the idea that each counting number correlates to one item that is being counted. The way to assign a number to an entire group is to have each item represented by a single number; we can then say that the size of the group is that of the largest counting number used to count the items. If I have 12 marbles, for example, I would be able to know this by counting each individual marble once, and identifying that when I've counted the last marble, the number that I used to count it was number 12. Since I ran out of marbles at number 12, that means that I have 12 marbles in my group.

Once children know the proper order of the counting numbers, the biggest confusion for them when learning to count is how to keep track of what they have already counted. The best strategy for teaching tracking while you're counting is to move the counted items to the side, out of the way, so that they can easily identify which items have already been counted and which items still need to be counted. So how can you help children practice counting when they are given pictures or drawings of items? The best thing to do in that situation is to line up or organize the drawings on the paper in such a way that children can methodically move through each section of the picture in a way that they can keep track of what has already been counted. Organized rows and columns work very well in this type of situation. The fancy books with dynamic types of designs tend to be more confusing and leave children less successful in their counting.

Parsha Connection:
When Rashi references the 70 languages which correspond to the 70 nations that came from the descendants of Noah, this is a perfect example of one to one correspondence. In this case, we have 70 descendants- each of those 70 descendants developed into their own nation, resulting in 70 nations (one descendant for each nation)- and each of the 70 nations had its own language, resulting in 70 languages (one nation for each language).

Another, year-long exercise in one to one correspondence is matching each parsha (or double-parsha) with each shabbat. There is a specific order to the parshiot readings, and there are certain parshiot that are specifically read at certain times. For example, Devarim is always read the week before Tisha B'Av, and Va'etchanan is always read the week  the week after Tisha B'Av; V'Zot Ha'Bracha is always read on Simchat Torah. Using these placeholders in the calendar, we can go through the year of parshiot and match them up to the shabbatot in which they will be read. This process of matching one to one is an exercise in one to one correspondence.

Everyday Connection:
The mere fact that we are each able to count items successfully on a daily basis for day-to-day activities shows that we have each internalized and successfully rely on our understanding of one-to-one correspondence. Interestingly, as we grow and our brains develop, we can start to automatically, accurately identify the quantities of small groups of items. Visually organizing items makes it easier for our brains to automatically, accurately identify the quantities of larger groups of items.

For a different example, musicians who play the harp need to identify the notes of the strings. As identification, the C note strings are all red, and the F note strings are all blue. Using these placeholders, musicians are able to identify which strings are which notes and what their finger placements need to be- 2 examples of one to one correspondence- matching strings to notes and matching fingers to strings.

What examples are in your daily life?