Behar/Bechukotai- Graphs, Patterns, and Calculation Activities

"Hashem spoke to Moshe, saying: Speak to the Children of Israel and say to them: When a man will express a vow to Hashem regarding the valuation of souls, the valuation of a male shall be: for someone twenty years of age to sixty years of age, the valuation shall be fifty silver shekels, of the sacred shekel. If she is female, the valuation shall be thirty shekels. And if from five years of age to twenty years of age, the valuation of a male shall be twenty shekels and of a female ten shekels. And if from one month of age to five years of age, the valuation of a male shall be five silver shekels; and for a female, the valuation shall be three silver shekels. And if from sixty years of age and up, if for a male, the valuation shall be fifteen shekels; and for a female, ten shekels. But if he is destitute for the valuation, then he should have him stand before the Kohen, and the Kohen should set his valuation; according to what the hand of the person who makes the vow can attain should the Kohen set his evaluation." ~Vayikra 27:1-8

In this section of this week's parsha, we learn about the standard valuation for donations that are vowed to the Beit HaMikdash on behalf of family members. We have the standard valuations, and we are also told that if someone makes a vow but doesn't have the funds to meet the standard valuations, the Kohen can make a determination of an appropriate valuation for that person. This week I would like to look at some activities for students of varying levels based on the standard valuations that are listed.

To begin, let's organize the information (older students could be asked to chart this information for themselves by identifying and organizing the information in the passage):

Note that this could also be organized into two charts- one for males and one for females. This breakdown might be clearer for some students when trying to separate information on males and females in follow-up activities.

Related Activity Suggestions:

• Graph It!- A good way to compare data of this nature is by graphing it. This information lends itself well to a double bar graph, with a category for each age grouping, and two bars within each category (one for males and one for females). The left side of the bar graph (y-axis) would indicate the number of shekels donated. As always, grade levels recommended are an approximation, and individualization for students is necessary to meet their actual ability levels. K-2 students could fill in a pre-made class-sized graphing chart as a class activity, with older students also copying the information onto personal graphs. Grades 3-5 students could create individual graphs on pre-printed graph templates with spacing indicated for different levels of labeling, and then graphing the information. Students in grades 6+ could create their own double-bar graph from start to finish.

• Is there a pattern?- Looking at the table above and/or the double-bar graph created in the first activity, students can look for comparisons between males and females at each age group. They can also look for comparisons between the different age groups for males and then between the different age groups for females. 
• What trends do they see over a person's lifetime? Is this consistent for both men and women? Why do they think the valuations may have been set in the way that they were?
• After making note of comparisons, older students could look for specific numerical comparisons between males and females in each age group and then across the data for males and females at different age groups. Are any of the ratios between groups consistent in any way? Rashi's note on 27:7 is also relevant to these comparisons, as he specifically points out some differences in the ways that the valuations change between the different age groups.

• Problem Solving- Processing the information through sample family valuations- Using the valuations given, students could be provided with sample problems with different family groupings to calculate the valuation for each family. Students could also create their own sample families to calculate or switch with friends to calculate. What about students' own families? What would each student's personal family valuation be if they were donating to the Beit HaMikdash? Can older students come up with an algebraic formula for calculating the valuation for any given family scenario?

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.

Vayikra- Statistics part 1

About the Parsha:
In Parshat Vayikra we have 5 chapters that just list different types of sacrificial offerings that can be brought. Rather than quoting sections of the parsha, I've reduced the information into the summary below:

olah-offering-- male cattle
olah-offering--male sheep or goat
olah-offering--turtledoves or young doves
meal-offering--fine flour, oil, frankincense

meal-offering--first fruits

peace-offering--male or female cattle

peace-offering-- male or female from flock (sheep or goat)

Kohen's sin-offering-- young male cattle

Community sin-offering-- young bull (male cattle)

Ruler sin-offering-- male goat

individual sin-offering-- female goat or sheep

guilt-offering--female sheep or goat

guilt-offering-- two turtledoves or two young doves (if can't afford sheep/goat)

guilt-offering-- flour (if can't afford doves)

guilt-offering-- ram

What is a graph?
A graph is a visual representation of information in order to easily compare information in a given situation. There are many types of graphs- line graphs, bar graphs, pie charts, histograms, venn diagrams- each type of graph is suited to a certain type of information and a certain format. A pie chart, for example, gives information about the division of categories within a total group, or sectional percentages out of 100%.

For the next few weeks, I'd like to look at different types of graphs and statistical analysis of information that's given in the parshiot.

For this week, we'll look at bar graphs. Bar graphs are graphs that are used to compare categories. A vertical bar graph has the names of the categories on the bottom of the graph, and the left side of the graph has the number scale to show how much is measured in each category. A horizontal bar graph can display the same exact information, but the graph is turned sideways- the names of categories are on the left of the graph, and the number scale is along the bottom of the graph.

It's interesting to look at different ways that the same information can be graphed- each graph bringing out different aspects of the information.

Let's first make a graph showing how many options there are for each type of offering. First we'll organize our data:

*olah-offering: (3 options)
--cattle
--sheep/goat
--doves
*meal-offering: (2 options)
--fine flour mixture
--first fruits mixture
*peace-offering: (2 options)
--cattle
--sheep/goat
*sin-offering: (4 options)
--Kohen (cattle)
--community (cattle)
--ruler (goat/sheep)
--individual (goat/sheep)
*guilt-offering: (4 options)
--sheep/goat
--doves
--flour
--ram

Now that we have our data organized the way we want it, we can graph it (chart on top, graph underneath):

Number of Options for Sacrifice Types:

Now, what if we make a graph of how many must be male animals, must be female animals, could be either male or female, or are grain/fruit?

Again, let's first organize our data:

*male animals: (8 options)

--olah-offering (x3)
--sin-offerings (x3)
--guilt-offering (x2)
*female animals: (2 options)
--sin-offering (x1)
--guilt-offering (x1)
*male or female: (2 options)
--peace-offering (x2)
*grain/fruit: (3 options)
--meal-offering (x2)
--guilt-offering (x1)

Now that we have our data organized the way we want it, we can graph it (chart on top, graph underneath):

Number of Sacrifices by Animal Type:

So, here we have two very different graphs, both based on the same exact data set, but focusing on different aspects of the information; one looks at which sacrifices have the most options for what can be offered for that type of sacrifice, and the other looks at how many sacrifice types each animal can be used for. 

Some good questions for testing for understanding of graphs might be: Which category has the most options? Which category has the least? Are there any that have the same amount? How much difference is there between two given categories? These questions can be tailored for each specific graph that you're reading.