Vayechi- Some Basic Arithmetic

"Joseph dwelt in Egypt- he and his father's household- and Joseph lived one hundred and ten years. Joseph saw three generations through Ephraim; even the sons of Machir son of Manasseh were raised on Joseph's knees." ~Bereisit 50;22-23

Subtraction/Passing of Time:
In math, when trying to calculate the distance between two numbers, there are a couple of ways that students begin to work with the concept. Some students will begin by counting up from the lower number to the higher number, while keeping track of how many "steps" or numbers they pass as they count. Some students will use the same method, but count their "steps" backwards, moving from the higher number to the lower number. Ultimately, we want students to recognize that in order to calculate the distance between two numbers, the fastest calculation method is to take the higher number and subtract from it the lower number. Although calculation and "regrouping" with time can become more complex, this process works in exactly the same way to calculate passage of time; we take the later date, time, etc and subtract from it the earlier date, time, etc. Through this calculation, we can see how much time has passed between two identified time periods.

Note that I said "take the higher number and subtract from it the lower number" instead of the more direct "subtract the lower number from the higher number". This is because a common confusion among children occurs when you say "subtract" and then put the subtrahend (second number) before the minuend (first number).

Some numbers that we know about Joseph:
--We know from back in Parshat Vayeishev (Bereishit 37;3) that Joseph was 17 yrs old when his brothers threw him into the pit and he was sold and brought down to Egypt.
--We know from back in Parshat Miketz (Bereishit 31;45-46) that he was 30 yrs when Pharoah gave Joseph Poti-phera's daughter as a wife and made him viceroy of Egypt.
--We are now told that Joseph lived to be 110 yrs and lived to see three generations (see below for specifics).

Let's try out some questions that would just require basic calculation.
*How long had Joseph been living down in Egypt when he died?
To answer this, we need to subtract his age at his death minus his age when he was sold and went down to Egypt:
110 - 17 = 93; So, Joseph lived in Egypt for 93 years

*How long had Joseph been married when he died?
To answer this, we need to subtract his age at his death minus his age when he was married:
110 - 30 = 80; So, Joseph was married for 80 years

To add some complexity:
If we want to create a more complex problem for a higher level learner, we could ask them to think about some approximate ages of Joseph's generations given the information presented.

What we know here:
--Joseph's married life spanned 80 yrs (see our subtraction above)
--Joseph saw 3 generations of children through Ephraim (children, grandchildren, great-grandchildren, and great-great-grandchildren)

If all generations were spaced evenly, we could divide 80 ÷ 3 to tell us the approximate years between each generation. 80 ÷ 3 = 26.7; This would mean that every 26-27 years, a new generation was born. Let's count this up according to Joseph's comparable ages:
Joseph get's married= Joseph is 30 yrs old
Ephraim is born/Joseph becomes a father= Let's assume Joseph is 31 yrs old
Ephraim becomes a father/ Joseph becomes a grandfather= 31 + 26 = Joseph is 57 yrs old
Ephraim becomes a grandfather/ Joseph becomes a great-grandfather= 57 + 27 = Joseph is 84 yrs old
Ephraim becomes a great-grandfather/Joseph becomes a great-great-grandfather= 84 + 26 = 110