Vayigash- Family Tree and Information Organization related activity ideas

"So Jacob arose from Beer-Sheva; the sons of Israel transported Jacob their father, and their young children and their wives, in the wagons which Pharoah had sent to transport him. They took their livestock and their possessions which they had amassed in the land of Canaan and they came to Egypt- Jacob and all his offspring with him. His sons and the sons of his sons with him, his daughters and the daughters of his sons and all his offspring he brought with him to Egypt" ~Bereishit 46:5-7

What follows in Bereishit 46:8-27 is an enumeration of all the family members who traveled to Egypt with Jacob when Joseph sent for them to move to Egypt. We learn that, in total, there were 70 people who moved down to Egypt.

While it's not directly related to calculation, the ability to organize of information is a key skill for success in mathematics. For successful problem solving, students need to be able to identify important information, classify how the different pieces of important information relate to each other, identify the question or problem that they are tasked with answering or solving, identify the steps necessary to find the solution to their question/problem, follow through with their planned steps for finding the answer, and finally critically look at their answer to determine if it makes sense and is a sensible solution to the problem that are trying to solve. 

Activity Connections:
Activity ideas in increasing conceptual difficulty:

While the Torah offers us a certain amount of organization in the way in which information is given to us, it is often helpful to map out information to gain a broader picture or greater understanding of the information. Mapping out a family tree of Jacob's descendants based on the information provided to us in the parsha is an organizational task that students of many varying levels can benefit from. Note that the grade ranges that I've listed are guideline approximations. There will always be students for whom activities come more easily and other students for whom activities are more difficult. I recommend shifting up or down within activity suggestions to properly accommodate each student's level.

• At the lower levels (grades K-2), teachers can provide students with a cut and paste chart of a family tree and the names that need to be placed on the tree and the family tree map with all the appropriate slots organized where they should be. For younger students, 70 names will be particularly overwhelming. To make it more manageable, students can work in partners or groups and just work with a single branch- one group can cut and paste Reuven and his children onto the tree, another can work on Levi and his children, a 3rd can work on Shimon and his children, etc. When all the groups have put their trees together, the class can come together to see how all the brothers' families fit together on the tree as children of Jacob. 
• For slightly older students (grades 2-6), teachers can provide a blank family tree with the proper organization and slots provided. The students could find the information from the passages and write in the names. Again, to alleviate some of the pressure from the large number of names, students could be assigned a section of the tree and come together with all their pieces of the tree to see how they fit together. 
• For students attempting to fill in the full chart by themselves (grades 4+), a helpful accommodation could be to have some of the names pre-filled in order to help the students begin to envision the organization on the tree and to give them some guide-points to work with. In it's entirety, such a project would need to be broken up into smaller time chunks so that students can work on sections at a time without feeling overwhelmed or frustrated.
• As students get older (grades 6+), they can fill in more and more of the chart independently. Ultimately, the goal would be for the students to be able to read the passages, create an organizational system on a blank piece of paper, and place the names of the 70 family members in their organized family tree without assistance. This task takes a good deal of vision and organizational skill, and while some students are capable of this task by middle school, others may take well into high school to be able to master these organization skills.

Some organizational points to keep in mind when planning out the family tree- how do you want to organize the sons on the tree? are you going to follow the organization in the passages? are you going to organize the sons according to birth order? are you going to group the sons according to their birth mothers?

Some follow-up analysis of the family tree:

* Based on the passages, do you have 70 people on the family tree?

Note the following which will affect the actual counting of the people:

• Er and Onan are listed as sons of Judah, but it states that they died in Canaan (therefore, they aren't counted in the 70 people).
• Yocheved is missing from the list of children of Levi, since her mother was pregnant with her when they traveled to Egypt. Since she was born on their arrival in Egypt, she is counted in the 70 people even though she is missing from the list.

Miketz- How high can you count?

"Joseph amassed grain like the sand of the sea, very much, until he ceased counting, for there is no number." ~Bereishit 41:49

For this week, I want to focus on the statement above, where Joseph was overseeing the collection of grains in Egypt during the 7 abundant years in preparation for the upcoming 7 years of famine. Using the commentaries of Rashi and Sforno we learn that Joseph was amassing as much grain as possible, until the grain counter stopped counting (Rashi) and the reason that he stopped counting was that he had run out of names of numbers to use for his counting (Sforno).

This statement struck me as one that would make for an interesting discussion with students on place-value and increasing numbers. For information on place value and thinking about how it works, functionally, see my post from Parshat Bereishit.

Concepts related to the progression of counting:

• Children first start by learning the base pattern in counting from 1-10. Once they have a solid ability to count 1-10, we begin working with them on recognizing the pattern of how we loop through 1-9 in each set of tens (teens, twenties, thirties,...) to make another set of 10. Interestingly, the tens places increase in the same numerical order as the ones.
• After tens, usually somewhere in the grades K-2, students solidify their counting from 1-100. Next, they practice understanding the next loop- counting from 100-200 will follow the same pattern as 1-100, but with "one hundred" before each number. Once they reach 199, they increase the hundreds place to 200. Again, interestingly enough, the numbers continue to loop in the same pattern with the hundreds place increasing in the same numerical order as the ones and tens did.
• As students move up in their understanding of place value through the hundreds, then we work with them on extending their understanding exponentially by reviewing with them the idea that this loop continues on and on, and as we reach our maximum capacity for each place value, we just add on the next place value and continue the pattern loop that we've created.
• Once students have mastered the concepts of the unlimited potential for counting by increasing numbers, we then extend the concept in 2 directions: 
• 1) negative numbers and comparing how "increasing" negative numbers and place values relates to increasing positive numbers and place values
• 2) decimal numbers and comparing how "increasing" decimal numbers and place values relates to increasing positive/negative numbers and place values. 
• Note that while positive and negative numbers are fairly comparable, conceptually, when we think about magnitude, or size, of the numbers, an added conceptual difficulty that decimals offer is the idea that the "larger" the number, the "smaller" the piece. The numbers we talk about as decimals, really means the number of pieces that 1 unit or whole is broken into- so more pieces, means cutting the same piece into smaller pieces.

The most basic construct that children are building on as they increase their understanding of counting through each level is that you can always make a bigger number by just adding one more; cycling through the understood loop of numbers and adding new place values as needed will always result in a new, bigger number.

Based on this construct, how can we understand the statement above in the parsha? An interesting Social Studies connection might be for the students to see if they can find information on how many of our place values the Egyptians actually used. Clearly, based on our understanding of counting, even if we didn't know how to read the number of counted grain, we would at least be able to write out the number representing how much grain was collected, and we could have kept on counting. 

Some questions to consider for a conversation on the topic:
Obviously, the Egyptians had a limit- did they stop counting because they thought they couldn't have any more grain? No, they stopped counting because they reached a point where they could no longer track their collection. What implications might extend from such a situation?

Vayeishev- Timeline and basic arithmetic related activity ideas

"Then Jacob rent his garments and placed sackcloth on his loins; he mourned for his son many days." ~Bereishit 37;34

This week we learn of when Joseph's brothers sold him and implied to Jacob, their father, that he was attacked and killed by a wild animal. Upon seeing Joseph's bloody tunic and surmising his death, we are told that Jacob mourned for "many days". Rashi  here explains that "many days" actually means that he mourned for Joseph the entire time that Joseph was missing to him- which actually calculated to be 22 years.

Activity Connections:
Activity ideas in increasing conceptual difficulty:

• The most basic calculation connection would be to begin with the statement 1) in Bereishit 37;2 (at the start of this week's parsha) that Joseph was 17 years old at the time of the story of his sale and 2) in Bereishit 41;46 (in next week's parsha- Miketz) that Joseph was 30 years old at the time that he first was called to come before Pharoah. Younger students can just calculate the passage of time between Joseph's sale and his appearance before Pharoah. Before learning subtraction, this could be drawn on a time line for students where they can physically count the years. Children who are a little older can count up from 17 to 30 or subtract 30-17.
• The next step would be to look at the calculation that is offered by Rashi regarding the 22 years that pass before Jacob sees Joseph again. Children can take the calculation from the activity above and pull out (from Parshat Miketz) the additional years that passed- 7 plentiful years followed by 2 years of famine before Jacob travels to Egypt. Students would then add the 3 numbers together to confirm that the time that passed was truly 22 years.
• A larger activity, which could be leveled in many ways depending on the age and abilities of students, would be to pull out the information from larger segments of Sefer Bereishit and place the information onto a more comprehensive timeline. Students could either create timelines for individual sections, or a more comprehensive timeline that incorporates multiple people's storylines for students to see the crossover of time between the different stories that we are given throughout Sefer Bereishit. Along with Rashi's interpretations and explanations throughout the sefer, students can use their own calculations for comparison of information and calculating where everything that we learn would actually fall on a grand-scale timeline.

We can use the information given in this week's parsha and next week's parsha to analyze the passage of time that Rashi refers to on Bereishit 37;24. Creating a timeline helps students formulate an understanding of the chronology of events, which provides them a framework for the both the logical progression of events and the greater picture of how multiple events fit together with each other. In addition to the sequential understanding that is gained, students also practice basic addition and subtraction by calculating the time lapses between different events. Students also work on identifying which information needs to be added or subtracted in order to find missing information, which is a critical problem solving skill. Finally, when the completed timeline has been pieced together, students can look to compare and contrast information to gain a deeper insight that they may not have picked up on in their original, single-story understanding of the events.

Vayishlach- Leveled activity ideas related to organizing and analyzing information

"...then [Yaakov] took, from that which had come into his hand, a tribute to Esav his brother: She-goats, two hundred, and he-goats, twenty; ewes, two hundred, and rams, twenty; nursing camels and their young, thirty; cows, forty, and bulls, ten; she-donkeys, twenty, and he-donkeys, ten." ~Bereishit 32;14-16

In this week's parsha, we learn about Yaakov's gift to Esav to try to appease him and keep him happy.

Activity Connections:
When analyzing information, there are multiple levels of understanding that are needed. We can break down these levels for students in order for them to develop an understanding of each level of processing information.

Activity ideas in increasing conceptual difficulty:
*Last year, for Parshat Vayishlach, I used a chart to organize the information about Yaakov's gift to Esav. Figuring out a way to organize the information that you are given in the first step to analyzing the information. Younger students will need help to work together to put the information into a pre-written chart, while slightly older students can work on organizing and charting the information independently.

Here is the gift information organized into a chart:

Type of Animal	# of Females (& children)	# of Males	Total #
Goats	200	20	220
Ewes/Rams	200	20	220
Camels	30	0	30
Cows/Bulls	40	10	50
Donkeys	20	10	30
Total # of Animals	490	60	550

Children can also use this information to learn about representing the information in different types of charts- how would this look displayed in a pictograph? bar graph? double-bar graph (comparing Males & Females of each)?

Additionally, students can look at the chart or graphs and talk about quantitative comparisons between different groups.

*After children are comfortable organizing the information, they can use the information to talk about how pieces of the whole compare to each other as part of the whole or sub-parts of the whole. Ratios of males to females by animal or within the whole group; what fraction of each animal is male or female? what fraction of the whole? what fraction of the whole is each animal? What are the basic fractions? Can the fractions or ratios be reduced to simpler numbers? What is the significance of these reduced fractions/ratios? See last year's post for more on this.

*The next level of calculation would be converting the fractions into percentages of the whole. See here for my post explaining the concept of percentages. Students can calculate the percentages of the total gift that are made up for varying subcategories- how do the percentages breakdown comparing males to females? comparing different animals?

*An additional level of complexity to this organization of information could be to have students draw circle graphs with accurately calculated segments. See my post here to read about calculating the angle measures of the segments of a circle graph.