Yitro- Sequencing over time

Rather than dealing with a specific section of the parsha, this week I will look at the parsha as a whole. Parshat Yitro (Shemot 18-20)

Sequencing, or putting items in proper order, is a skill that children begin working on at a preschool level and work their way up to more complex sequencing. Younger students can begin by taking pictures or statements of given related tasks and putting them into the proper order. Older students can be asked to identify the tasks for a given project or series of events in the order in which they happen. They can also be asked to break down a task into individual, minute steps, which may ordinarily be overlooked or assumed.

A basic, younger level example is having pictures of (pictured not necessarily in proper order)

1. a child waking up in the morning
2. a child being dropped of at school
3. a child learning or eating in school with other students
4. a child coming back home from school
5. a child getting into pajamas 

Students can be asked to cut out these 5 pictures and paste them onto a chart numbered 1-5 in order. 

Another, similar level example would be pictures of 

1. a child taking out ingredients to make a sandwich
2. a child setting up the food to make a sandwich
3. a child assembling the sandwich
4. a child eating the sandwich

There are many examples of such picture sequencing projects. As students become more proficient, they can handle a series of pictures that involve more pictures or pictures that require more careful scrutiny in order to identify the proper order. A more complex example for elementary students might be 3 pictures of a child eating, but cues on the table, a clock in the background, or sun and lighting positioning through a window could indicate how to identify breakfast, lunch, and dinner. 

Older students (grades 5-8 and older) can be given a task and asked to break it down into steps themselves. How can you give someone step by step instructions for making a sandwich? For getting ready to go to school? For your daily schedule? Remembering that the minute details are all important is key to the complete picture of the task. Often the clues to proper sequence are found in the minute details.

In this week's parsha, we are given a series of events that happened over a period of time. According to the order in which they are presented in the parsha:

• Yitro brings Tzipporah, Gershom, and Eliezer into the desert to rejoin Moshe
• Yitro brings olah and peace offerings and eats with Aaron and the elders of Israel
• Moshe judges the Israelites in disputes and matters that require judgement & Yitro advises him to appoint elders as judges over segments of the population
• In the 3rd month after the exodus from Egypt, the Israelites arrived in the wilderness & Moshe speaks with Hashem
• Hashem directs Moshe to give the people 3 days to prepare for receiving the Torah
• Moshe directs the Israelites to prepare for receiving the Torah
• Hashem speaks to Moshe
• Moshe relays 10 commandments to the people

Understood at face value, it would appear that if we wanted to put these events on a timeline, the events with Yitro, Moshe and family would be placed within the first 3 months after the exodus from Egypt. They appear to have happened after the exodus, but before the Israelites arrive in the wilderness to prepare for receiving the Torah. 

Rashi, in response to Shemot 18:13, explains that it's not possible that Moshe sat in judgement for the Israelites before they received the Torah- how could he judge for them before they received laws and statutes by which to live? This sequence doesn't make sense, logically. (The details are key!) This means that, minimally, the order of events of the parsha should actually be:

• Yitro brings Tzipporah, Gershom, and Eliezer into the desert to rejoin Moshe
• Yitro brings olah and peace offerings and eats with Aaron and the elders of Israel
• In the 3rd month after the exodus from Egypt, the Israelites arrived in the wilderness & Moshe speaks with Hashem
• Hashem directs Moshe to give the people 3 days to prepare for receiving the Torah
• Moshe directs the Israelites to prepare for receiving the Torah
• Hashem speaks to Moshe
• Moshe relays 10 commandments to the people
• Moshe judges the Israelites in disputes and matters that require judgement & Yitro advises him to appoint elders as judges over segments of the population (note that this event had originally been 3rd in the list)

Note: For a timeline consideration, Rashi indicates that this judgement actually began the day after Yom Kippur in their 2nd year in the desert. 

Rashi also makes reference to the gemara in Avodah Zarah 24a and Zevachim 116a where there is a dispute as to whether the entire section with the events involving Yitro actually took place after the Israelites received the Torah. If that were the case, than rather than the interpretation above, the actual sequencing of events would have been:

• In the 3rd month after the exodus from Egypt, the Israelites arrived in the wilderness & Moshe speaks with Hashem
• Hashem directs Moshe to give the people 3 days to prepare for receiving the Torah
• Moshe directs the Israelites to prepare for receiving the Torah
• Hashem speaks to Moshe
• Moshe relays 10 commandments to the people
• Yitro brings Tzipporah, Gershom, and Eliezer into the desert to rejoin Moshe
• Yitro brings olah and peace offerings and eats with Aaron and the elders of Israel
• Moshe judges the Israelites in disputes and matters that require judgement & Yitro advises him to appoint elders as judges over segments of the population (note that these 3 events had originally been the first 3 events in the list)

In actuality, these events would not even just be moved to the end of the parsha to be put in proper sequence. What follows in the next parshas are itemizations of laws that were given from Hashem to Moshe- the laws that were given before Moshe was able to sit in judgement for the people. So these events would, according to sequence, be moved much farther back, possibly to the end of the book of Shemot, or even to a different book, if we were to look at proper timeline sequencing alone.

Yitro- Basic division with large numbers

"And you shall see from among the entire people, men of means, G-d-fearing people, men of truth, people who despise money, and you shall appoint them leaders of thousands, leaders of hundreds, leaders of fifties, and leaders of tens." ~Shemot 18;21
"Moshe heeded the voice of his father-in-law, and did everything that he had said. Moshe chose men of accomplishment from among all Israel and appointed them heads of the people, leaders of thousands, leaders of hundreds, leaders of fifties, and leaders of tens." ~Shemot 18;24

Rashi on 18;21--
Leaders of Thousands- They were six hundred of these leaders for six-hundred-thousand adult male Israelites.
Leaders of Hundreds- Of these there were six thousand
Leaders of Fifty- twelve thousand
And Leaders of Tens- sixty thousand

From Parshat Bo (Shemot 12;37) we know "The Children of Israel journeyed from Ramses to Succoth, about six hundred thousand on foot, the men, aside from the children"

In this week's parsha, we learn about Moshe trying to arbitrate on issues for the Jewish people. We hear of how he sits from morning until evening just hearing cases for people. When Yitro sees all the time that Moshe dedicates to arbitration, Yitro makes a suggestion to appoint levels of leaders to help relieve some of Moshe's burden; a suggestion which Moshe heeds.

In Rashi's commentary on the suggested levels of leaders, he does some basic division for us to let us know how many leaders there were at each level. This division calculation is important for us to understand that the leaders were not separated from the whole group of Jewish people, but rather, when calculating how many leaders are needed, the leaders themselves are included in the number of Jewish people.

Definitions: Division: The process of separating a group or item into a number of smaller, equal-sized groups or pieces. With smaller numbers, it's easy to model the actual division with manipulatives (pieces that can be laid out and moved around to model a mathematical situation) or draw a diagram to aid in calculation until students become proficient with basic math facts.

Dividend: The whole group that is being divided

Divisor: The number of groups into which you are separating the dividend

Quotient: The answer to a division calculation

When we write basic division problems, we write dividend ÷ divisor. When we write division as a fraction, the dividend goes on top (numerator) and the divisor goes on the bottom (denominator). Many students find the algorithm set-up for long-division confusing, because when we set-up the division box, the dividend goes inside the box and the divisor goes on the outside. 

When we need to start dividing very large numbers- in the tens, hundreds, thousands, etc.- the numbers become too big to model, and students begin to rely more on algorithmic notations (those big long division bars that we all remember) to keep track of their calculations. The other option is to draw representative diagrams to help students feel more comfortable with their number sense and help them connect meaning to the division of large numbers. For example, students can draw cubes to represent numbers of thousands, squares to represent hundreds, lines to represent tens, and dots to represent ones. In this way, they can visualize the breakdown of the numbers into equal groups. For students who have difficulty switching to the algorithm, working through calculations side-by-side visually and with the algorithm can help them to connect the concept.

Division trick: When dividing with large numbers that end in zeros (are multiples of tens, hundreds, thousands, etc.), you can remove any number of zeros from the end of both dividend and divisor as long as you can remove the same number of zeros from both. You can then do your division and your quotient will be the same as it would be for the larger number. For example, 100 ÷ 20: we can take one zero away from each number, divide 10 ÷ 2 = 5, so, 100 ÷ 20 = 5. 

Connection to Parsha:
So, if we know how to divide, we can check on Rashi's calculations and make sure that all the numbers match up.

For 600,000 adult males, we have:
--Leaders of thousands- 600,000 ÷ 1,000 = 600 (same as 600 ÷ 1, if we remove the 3 zeros at the end of both numbers)
--Leaders of hundreds- 600,000 ÷ 100 = 6,000 (same as 6,000 ÷ 1)
--Leaders of fifties- 600,000 ÷ 50 = 12,000 (same as 60,000 ÷ 5)
--Leaders of tens- 600,000 ÷ 10 = 60,000 (same as 60,000 ÷ 1)

So, here we have a total of 78,600 leaders total for the whole group.

If the numbers of leaders had not been included in the number of the whole group, the numbers would have been much different. How different? Let's assume that the leaders from each previous tier are not included in the next lower breakdown.

600,000 - 600 (leaders of thousands) = 599,400 ÷ 100 = 5,994

600,000 - 6,594 (leaders of thousands + leaders of hundreds) = 593,406 ÷ 50 = 11,868.12 (let's assume 11,868)

600,000 - 18,462 (leaders of thousands + leaders of hundreds + leaders of fifties)= 581,538 ÷ 10 = 58,153.8 (let's assume 58,153)

So, all the number of leaders here would have been 76,615 (leaders of thousands + leaders of hundreds + leaders of fifties + leaders of tens) for the whole group.

All together, then, by having the leaders included in the total count of Jewish people, there were a minimum of about 2,000 additional leaders who were assigned to help Moshe with arbitration of matters.