Pinchas- Comparing and Collating Large Information Sets

This week, I'd like to focus on two sections from the parsha that offer opportunities for larger investigative approaches to help students make sense of the information given. I find, myself, that when I read through the sections of parsha that are more of a list format, I tend to lose focus rather than making meaning out of the information. So, if there are a list of census numbers, I'll make a mental note that the parsha talks about a census, but I don't usually fully process the numbers.

This week, we have at least two sections like this. The first is in Bamidbar 26:1-51, where we have current census from each tribe and then the tally of the entire group. The second is in Bamidbar 29:12-38, where we have a list of the sacrifices that are to be offered on each day of the holiday of Sukkot. Each of these is part of an even larger section that could also be looked at- census from Levi is also in the parsha, as are the lists of sacrifices for every holiday. I'm choosing these two larger sub-sections to focus on presenting my thoughts, but many of these ideas can be adapted or extended to other sections of the parsha, as well. Adaptations to meet differing developmental abilities are also possible.

The Census:
We can compare the current census for our parsha, found in Bamidbar 26:1-51, with the original census at the beginning of Bamidbar, found in Bamidbar 1:1-46.
Some ideas for comparisons:

• What are the similarities and differences between the text sections for each tribe? Do you notice any major differences in the texts? (Hint for one major difference- look carefully at the section for Yoseph's children in each of the two passages.)
• What are the similarities and differences between the individual census numbers for each tribe?
• Did the numbers for each increase or decrease?
• How do the census numbers for each tribe compare to each other? How did the original numbers compare to each other? If you order the tribes by according to size, does the order change from the first to the second census? If you create a graph for each group of census numbers, how do the graphs compare? 
• How do the total sum numbers compare between the two different census counts? Did the total sum increase or decrease?
• Some statistical thoughts for grades 5 or 6 and above: (Note that while the calculations may be straightforward or rote, the full understanding of the significance of these evaluations of the data may be hard for younger students to make sense of and truly understand and explain.)
• What was the average population per tribe after the first census? after the second census?
• In the first census, was each tribe above or below the average? What about in the second census?
• How far above or below the average was each tribe's population in each census? How do these statistics compare for each tribe between the two sets of census numbers?
• What fraction of the population was each tribe in the first census? in the second census? How do these compare?
• What percentage of the population was each tribe in the first census? in the second census? How do these compare?
• How would different types of graphs of the two sets of census data look and compare to each other? (Separate bar graphs, a double bar graph, line plots, box-and-whisker plot, pie charts.) Which graph would you personally choose to best represent the data, and why?
• Extra thought- when evaluating the data, does the 24,000 who were killed in the plague on the tribe of Shimon effect statistical changes from the first census to the second?
• Adapted but similar evaluations can be made between the original and new census for the tribe of Levi, as well.

Korbanot/Sacrifices:
As I mentioned above, there is a large section in this parsha that is dedicated to the description of the sacrifices that were to be brought on each holiday. I will focus, here, specifically on the sacrifices for Sukkot, but these questions can be extended and adapted to compare information related to other holidays or even to compare between different holidays.

Sacrifices for Sukkot:
The description for these sacrifices is found in Bamidbar 29:12-38.
Some ideas for comparisons:

• What are the similarities and differences in the text for the sacrifices for each individual day of the holiday?
• What are the specific lists of sacrifices that were to be brought on each day?
• How do the sacrifices for each different day compare to each other? How are they similar? How are they different? Are there any patterns that you notice? 

Some ideas for calculations with fractions and measurements:

• Think about making a collated list of the items needed for each sacrifice or each group of sacrifices-
• How much of each "ingredient" did they need for each sacrifice?
• How much of each "ingredient" did they need for all of the sacrifices on each individual day?
• How do the totals for each individual day compare to each other?
• How much of each "ingredient" did they need for the entire holiday?
• Do you see any significant numbers in your tally lists? Rashi on 29:35 refers to a significant connection to the tallies.

Vayakhel/Pikudei- Organizational thoughts for Creating an Activity

Note that I have a collection of various quotes this week from the double-parsha. The samples that I've chosen are just a couple examples of different types of information that are given and would be needed for the activity suggestions that I make below.

Samples of details from Parshat Vayakhel:

"He made fifty golden hooks and attached the panels one to the other with the hooks- so the Tabernacle-spread became one." ~Shemot 36:13 

"He made fifty copper hooks to attach the Tent-spread so that it would be one." ~Shemot 36:18 

Details of accountings of gold, silver, and copper that were collected:

"All the gold that was used for the work- for all the labor of the Sanctuary- the offered-up gold was twenty-nine kikar and seven hundred thirty shekel, in the shekel of the Sanctuary." ~Shemot 38:24

"The silver of the accountings of the assembly, a hundred kikar, one thousand shekel of the Sanctuary;" ~Shemot 38:25

"The hundred kikar of silver were to pour the sockets of the Sanctity and the sockets of the Parochet; a hundred sockets for a hundred kikar, a kikar per socket. And from the one thousand seven hundred seventy-five he made hooks for the pillars, and covered their tops and belted them." ~Shemot 38:27-28

"The offered-up copper was seventy kikar and two thousand four hundred shekel. With it he made the sockets of the entrance to the Tent of Meeting, and the copper Mizbe'ach, the copper lattice that was on it, and all the implements of the Mizbe'ach; the sockets of the Courtyard all around, the sockets of the gate of the Courtyard, all the pegs of the Mishkan, and all the pegs of the Courtyard, all around." ~Shemot 38:29-31

Explanations of Rashi:
On Shemot 38:27
Rashi itemizes the 100 silver sockets that are referred to. He explains that there were 48 beams, each with 2 sockets [48 x 2 = 96]. Then, there were 4 sockets on the parochet. 96 + 4 =100. Aside from these 100 silver sockets, the blueprints indicate that all other sockets were copper.

On Shemot 38:28 
Rashi explains that the remaining 1,775 shekalim of silver was used to cover the tops and bands of the pillars.

This week's double parsha begins with Parshat Vayakhel (link to last year's post) reviewing all the specifics of how the mishkan was built. This section is actually an exact review of the same blueprints that were given in Parshat Terumah. What's the difference between the two sections? In Terumah we are told that this is how the mishkan is to be built, and in Vayakhel we are told that this is how the mishkan was built. So, we are basically being told that Betzalel, Aholiav, and the other wise-hearted men who worked together built the mishkan according to the exact specifications that were given to Moshe.

Our double parsha continues with Parshat Pikudei, where we have an accounting of the gold, silver, and copper that was donated for the building of the mishkan. In last year's post, I first began by calculating the unit conversions to see how much gold, silver, and copper was collected when measuring with just the unit of shekel, rather than the mixed measure amounts that were given in Kikars and Shekels. At the end, I followed Rashi's example, and I finished off the post by working through the calculation to confirm that the amount of silver that was donated did indeed match up with the census population that was calculated. 

The two parshas come together to give us a complete view of the materials used, and how they were divided up to build the mishkan, down to the smallest details. 

Sometimes information is organized in one way for one purpose, but needs to be reorganized for another purpose. When the blueprints are given for the creation of the mishkan, the details are organized based on the way that the information would be most understandable when actually putting together each piece of each item that was being built. However, when figuring out how much of each material should be apportioned for each piece of the mishkan, the details from the blueprints should be reorganized according to the materials from which each item was to be made. 

This activity of reorganizing the given information in order to have a better vision of the breakdown based on materials used for the project fits well into the activity I have mentioned before, that of organizing, mapping, and creating a model mishkan based on the blueprints. 

This activity can be done on a larger scale, including the aspects of:
*a full start-to-finish organization of all the information related to building the mishkan
*creating blueprints from the information provided
*building a complete scale model mishkan

This activity could also be done on a smaller scale, by:
*choosing only a single item
*mapping out what materials would be needed for the chosen item
*creating blueprints for the chosen item
*possibly even building a scale model of the chosen item

Choosing as your activity to try to align the building information in Parshat Vayakhel directly with the detailed materials lists that are given in Parshat Pikudei would require organization of all the information given regarding building the mishkan, even if you're ultimately only interested in looking at the information for a constructing a single item. The reason for this is that the amount of gold, silver, and copper was to be divided based on what was donated to the construction. In order to divide up the materials to be used for the items, you need to account for all of the items and detailed pieces that needed to use each material. For example, from the pasuk and from Rashi above (38:27), we know that the 100 kikar of silver was used to make the 100 silver sockets, so there was 1 kikar of silver for each socket. For the remaining silver, however, there is a list of the remaining items amongst which it was to be divided, so additional calculation, thought, and possibly estimation would need to go into figuring out how many shekalim of silver went into each of the remaining items.

Real-Life Example:
Think about the sample situation of cooking for and hosting a dinner party. In order to host a dinner party, you will need to plan out your menu. When you plan a menu, you choose dishes to serve for each course. In order to plan the dishes that you are serving, you think about how the completed, cooked foods will go together, how they'll complement each other, and what order you will serve them in. At this point in the planning, you don't think about specific details of the ingredients, unless you are keeping in mind to specifically include or avoid certain individual ingredients. Even then, your focus is primarily on the final outcome of each cooked dish.

Once you have your menu planned, you need to start thinking about actually preparing and cooking the foods. In order to cook the foods, you need to go make sure that you have all of the ingredients. When you calculate to see what you have in stock and what you need to buy, it doesn't matter which 3 recipes call for orange juice, it only matters how much total orange juice you need in order to cook everything and whether or not you have that total amount of orange juice in stock. When you go to the store, it's not important how many carrots are in the soup and the side-dishes individually, or how many eggs you need first for the side-dishes and then for the desserts. When you walk into the store, you want to know how many carrots you need all together, and how many eggs you need all together.

The reorganization of information from individual recipes into a compilation of total ingredients needed in order to do all your cooking is exactly the same as the reorganization of information that I mention about in thinking about planning and dividing specific materials in order to build a model (or the real life) mishkan.

Mishpatim- Understanding and Applying a concept

Case #1: 

"When men will fight...if there will be a fatality, then you shall give a life for a life; an eye in place of an eye, a tooth in place of a tooth, a hand in place of a hand, a foot in place of a foot; a burn in place of a burn, a laceration in place of a laceration, a bruise in place of a bruise." ~Shemot 21:22-25

Case #2:

"When a man's ox will push his fellow's ox which dies, they shall sell the living ox and divide its money, and the carcass, too, shall they divide. Or if it was known that it was a goring ox from yesterday and the day before yesterday, but its owner did not guard it, he shall surely pay an ox in place of the ox, and the dead body shall be his." ~Shemot 21:35-36

Case #3:

"When a man will steal an ox, or a sheep or goat, and slaughter it or sell it, he shall pay five cattle in place of the ox, and four sheep in place of the sheep." ~Shemot 21:37

Understanding a Concept:
When learning a new concept, it is often difficult to have a full understanding just by reading an explanation or watching someone work out a single example. There are nuances, specifics of concepts that vary slightly based on given parameters. When learning a concept, there are levels to understanding what is meant. The base level is usually a straightforward understanding with an example that falls very neatly into the basic parameters. As you investigate and test out the way small changes effect the way the concept works, you are developing the complexity of your understanding of the concept. 

Let's look at a simple example first: a student learning the algorithm for subtraction (as they grow through elementary school)-

• First, the student will learn how to simply subtract a small single digit number from a slightly bigger single digit number (7 - 4 = ?)
• Next, they might start working with subtracting a smaller multi-digit number from a relatively slightly multi-digit number (395 - 273 = ?)
• Next, they would learn how to handle a situation where one of the place values doesn't have a large enough number, so they need to regroup (407 - 263 = ?)
• Next they would learn how to handle subtracting numbers with different place values (3,654 - 475 = ?)
• Finally, they start to transform their understanding of number sense by introducing subtracting a larger number from a smaller number (5 - 7 = ?). From here, they can also incorporate all their previously understood nuances of subtraction into this new framework of number sense based on the introduction of being allowed to take away more than you actually have (ie negative numbers).

The above example is a basic framework. Even here, there are other nuances that are incorporated which I have left out (how to handle numbers different types of numbers with decimal points, how to handle numbers with zeros in different place values, etc.)

Parsha Connection:
This week's parsha has many lists of various specific laws. Above we have 3 different specific cases where the laws related to valuation of damages are explained for us. Rashi also goes into lengthy, specific details in each of these cases to explain more clearly the nuances of each of these cases. 

Note that my summary of Rashi for each case below does not delve into specific details. Rashi, in these cases, actually goes through and explains methods for valuation of certain nuanced cases, which help give us a clearer picture. In order to really work with the problems presented in this post, it is important to look at Rashi's explanations in full to help develop the full understanding of valuation for each case.

For Case #1, Rashi on 21:24 and on 21:25 (note all Rashi links are in Hebrew) goes into detail about how the textual meaning is not literal. Rather, in essence, the restitution to be made should be based on valuation of loss of work time and cost of medical recovery. 

For Case #2, Rashi on 21:35 and on 21:36 goes into detail to explain what the division of money, animals, and profit from sale of animals should look like based on different potential specifics.

For Case #3, Rashi on 21:37 explains that the verse is specifically referring only to the animals that are stated in this case. This law is not generalizable to a larger group of other animals.

For a basic understanding of each case, we would look at cases that most closely match the exact situations that are presented. As we test out different changes or adjustments to the possible situations, we are learning the different nuances of each concept.

For students, after learning the specifics of each case, along with Rashi's nuanced explanations, appropriately leveled sample cases could be presented for them to work through and try to determine whether or not one of the case examples applies to the presented sample case, and, if so, what the valuation of damages would be for the case. More straightforward examples could be used with elementary level students, while more complex examples that involve more thought, dissection of information, or research, would be appropriate for middle or high school students.

Some example cases: (Do they apply to our sample cases? If so, what valuation can be made to settle the damages?)
For Case #1 
(Note: These cases would all be better for higher level students, as they all need research regarding valuation of medical damages and potential lost wages.)

1. Two men have an altercation and one of them has a tooth knocked out and a deep cut on his hand.
2. Two teenagers have an altercation and one of them has a baby tooth knocked out, while the other's eye is injured causing permanent blindness.
3. Two men are fighting. One is 40 years old and one is 60 years old. The 60 year old is killed. 

For Case #2

1. One man's $700 ox kills his friend's ox.
2. One man's $700 ox kills his friend's $300 ox.
3. One man's $400 ox kills his friend's $500 ox.
4. One man's ox is known for goring. The goring ox kills an ox worth $500.
5. One man's ox is known for goring. The goring ox is worth $300 and kills another ox.
6. One man's ox is known for goring. The goring ox, worth $600, kills an ox worth $300.

For Case #3

1. A man stole a $600 ox and killed it.
2. A man stole a goat and killed it.
3. A man stole a $300 sheep and it was found alive.
4. A man stole a $700 horse and killed it.
5. A man stole a $600 horse and it was found alive.

These are just a few possible examples. Working together with Rashi's complete explanations, examples can be created for multiple grade levels based on students concrete understanding and their level of inferential understanding of situations as they develop their understanding.

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.

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.

Nasso- Are the numbers useful?

From Parshat Bamidbar:

"...these are the Gershonite families- their counted ones according to the number of every male, from one month of age and up; their counted ones [were] seven thousand, five hundred." ~Bamidbar 3;21-22

"...these were the Kohathite families- the number of every male from one month of age and up [was] eight thousand, six hundred; the guardians of the charge of the sanctity." ~Bamidbar 3;27-28

"...these were the Merarite families- their counted ones according to the number of every male from one month of age and up [was] six thousand, two hundred." ~Bamidbar 3;33-34

From Parshat Nasso:
"From thirty years of age and up, until fifty years of age, everyone who comes to the legion for the work in the Tent of Meeting. Their counted ones according to their families were two thousand, seven hundred and fifty. These are the counted ones of the Kohathite families, all who work in the Tent of Meeting, whom Moshe and Aaron counted, at the word of Hashem, under the authority of Moshe." ~Bamidbar 4;35-37

"[F]rom thirty years of age and up, until fifty years of age, everyone who comes to the legion for the work in the Tent of Meeting. Their counted ones according to their families, according to their fathers' house were two thousand, six hundred and thirty. These are the counted ones of the families of the sons of Gershon, all who work in the Tent of Meeting, whom Moshe and Aaron counted, at the word of Hashem." ~Bamidbar 4;39-41

"[F]rom thirty years of age and up, until fifty years of age, everyone who comes to the legion, for the work in the Tent of Meeting. Their counted ones according to their families were three thousand, two hundred. These were the counted ones of the families of the sons of Merari, whom Moshe and Aaron counted, at the word of Hashem, through Moshe." ~Bamidbar 4;43-45

Math Connection:
Oftentimes, when children are learning a new skill and they see numbers in a problem, they just plug the numbers into the memorized algorithm that they were taught and they assume that the number that comes out of their calculation is the answer to whatever question is asked of them. Real life does not always work this way; just because the numbers are in front of you doesn't mean that the chosen calculation will answer your questions. Additionally, just because you have numbers in front of you, it doesn't mean that the information you want can be found in the information that you are given. It's important to always keep in mind the meaning of the numbers that you have and the meaning of the calculation or operation that you choose to employ in your problem solving process. 

Parsha Connection:
In last week's parsha, we are given the census numbers from the Levite males ages one month and older. The numbers from that census are (in the order listed in the parsha):

Gershon: 7,500 males

Kohath: 8,600 males
Merari: 6,200 males

In this week's parsha, we are given the census numbers from the all Levite males ages 30-50 who were to work in Holy service. The numbers from that census are (in the order listed in the parsha):
Kohath: 2,750 males
Gershon: 2,630 males
Merari: 3,200 males

Given these two sets of census numbers, we can compare the numbers from each category. It's important, though, to keep in mind exactly what information we are gaining from our comparison. 

If we know that there were 7,500 Gershonite males from one month and older, and 2,630 males ages 30-50, we can calculate that there's a difference of 7,500-2,630, or 4,870. From here, we know that there are 4,870 males who were not between the ages of 30-50. But, can we figure out how many of those 4,870 are younger than 30yo and/or how many of them are older than 50yo? 

We can make the same calculations for Kohath and Merari.
Kohath: 8,600-2,750 = 5,850
Merari: 6,200-3,200 = 3,000

And from these calculations, we know that there were 5,850 Kohathite males, and 3,000 Merarite males who were not between the ages of 30-50. But, again, we have no way of knowing how many of those 5,850 or 3,000 were between one month and 30 years, and how many were 50 years or older. 

Everyday Connection:
If the weather report tells you that Tuesday's morning temperature is 57° F and that the temperature rose 15°over the course of the day, no matter what calculation you use, you can't use the information in front of you to find out what the temperature was on Wednesday. A student who is asked to find the temperature by the end of the day Tuesday, would be able to add 57+15= 72°F. However, if a student is just given these two numbers and asked whether or not they know Wednesday's temperature, they might just assume that they should be adding the two numbers to find the sum. However, the information given does not tell us how much the temperature might have fallen or risen overnight from Tuesday evening until Wednesday morning. Thoughtfulness and understanding of both your information and your calculations are critical to finding meaning in the numbers that you use in every situation.