For younger students:
"Hashem spoke to Moshe, saying, 'Send forth for yourself men, and let them spy out the Land of Canaan that I give to the Children of Israel; one man each from his fathers' tribe shall you send, every one a leader among them.'" ~Bamidbar 13:1-2
"...Your children will roam in the wilderness for forty years and bear your guilt, until your carcasses shall cease to be, in the wilderness. Like the number of the days that you spied out the land, forty days, a day for a year, a day for a year, shall you bear your iniquities- forty years- and you shall know what parting from me [is]." ~Bamidbar 14:33-34
I've addressed the idea of one-to-one correspondence a couple of times in the past (see Parshat Haazinu and Parshat Ki Tisa). In this week's parsha, we have 2 instances that deal directly with this idea.
At the beginning of the parsha, Hashem instructs Moshe to have one leader from each tribe assigned to go out and visit the land of Canaan to see what the Children of Israel were to expect upon entering the land.
- If there is one man from each tribe, how many men were sent? Since we know that there are 12 tribes, if each tribe sends one man, there will also be 12 men.
- Acting it out- Students can be separated into 4 or 5 groups ("tribes"). Within each group, a "leader" can be chosen. Students can count how many groups/tribes there are. Based on this, ask students how many leaders there will be. Have the leaders come to a separate area in the room and have the class count the leaders. Were there predictions correct? Are the students all making the one-to-one connection?
In the middle of the parsha, Hashem becomes upset with the spies' report of Canaan, which led to fear-mongering amongst the Children of Israel. As punishment, Hashem decides that the Children of Israel will wander in the desert one year for each day that the spies were out in Canaan.
- If we know that the spies were in Canaan for 40 days, how many years would the Children of Israel wander the desert? If the spies were there for 40 days, then 1 year for each day would mean that they would wander the desert for 40 years.
- Extrapolation discussion- [Sample questions] If you received one present for every birthday that you've had, how many presents would you have now? (5yo would have 5, 6yo would have 6, etc.); If there are 10 classes in school, and each class makes a poster to put in the hallway, how many posters will be in the hallway? (10 classes = 10 posters)
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Multi-level:
"Hashem spoke to Moshe, saying, 'Speak to the Children of Israel and say to them: When you will come to the land of your dwelling places that I give you, and you perform a fire-offering service to Hashem- an olah-offering or a [peace-offering] sacrifice by articulating a vow or a free-will offering, or on your festivals, to produce a pleasing fragrance to Hashem, from the cattle or from the flock- the one who brings his offering to Hashem shall bring a meal-offering of a tenth [of an ephah] fine flour, mixed with a quarter-hin of oil; and a quarter-hin of wine for a libation shall you prepare for the olah-offering or the [peace-offering] sacrifice for each sheep. If it is a ram- you shall prepare a meal-offering, two-tenths [of an ephah] fine flour mixed with a third-hin of oil; and a third-hin of wine for a libation shall you bring as a satisfying aroma to Hashem. When you prepare a young bull as an olah-offering or a [peace-offering] sacrifice, because of an articulated vow, or a peace-offering to Hashem, one shall bring with the young bull a meal-offering: three tenths [of an ephah] fine flour mixed with a half-hin of oil. You shall bring a half-hin of wine for a libation, a fire-offering, a pleasing fragrance to Hashem...'" ~Bamidbar 15:1-10
At the end of this week's parsha there is a list of information regarding different sacrifices. In this section, depending on the animal offered as part of the sacrifice, the specifications of the meal-offering ingredients differ. There are a number of activities that can be arranged around this information.
- The first step is to organize the information- I recommend charting the information based on the animal that each different meal-offering is assigned to. For younger students, you can have the information pre-charted for them, including pictures of ingredients for pre-readers.
- Comparing information:
- Which sacrifice has the most flour? Which has the most oil? Which has the most wine?
- Order them from least to greatest (or greatest to least) amounts of flour. Order by amounts of oil. Order by amounts of wine.
- Are there any patterns that you see? Between the different sacrifices? When they are ordered by amounts?
- Conversions- Using current day equivalencies for ephah and hin, how much of each ingredient would be used for each sacrifice?
- Note: For conversion reference, I posted a chart with conversions including ephah for Parshat Beshalach and Wikipedia has a page with Biblical measurements, including hin under liquid measures; as I wrote in Parshat Shelach last year, a se'ah is usually calculated between 2.25 and 4 gallons in current measurements.
- Interesting conceptual thought:
- For younger students- When you convert from Biblical units to modern day units, does the amount that you have change? Another way of thinking about it- if you measure a table using inches and then using feet, does the size of the table change, or just the measurement you're using to think about the item?
- For older students- When you convert the measurements, will they still compare in the same ways when you order them? What about patterns? If there is a relationship between the measurements, will the relationships remain the same when you have converted into modern day measurements?
"Hashem spoke to Moshe, saying: 'When you will take a census of the Children of Israel according to their counts, every man shall give Hashem an atonement for his soul when counting them, and there will be no plague among them when counting them. This is what they shall give- everyone who passes among the counted- half of the shekel, by the holy shekel, the shekel is twenty geirah, half of the shekel as a portion to Hashem. Everyone who passes among the counted, from the age of twenty years and up, shall give the portion of Hashem. The wealthy shall not increase and the destitute shall not decrease from half of the shekel- to give the portion of Hashem, to atone for your souls. You shall take the silver of the atonements from the Children of Israel and give it for the work of the Tent of Meeting; and it shall be a remembrance before Hashem for the Children of Israel, to atone for your souls.'" ~Shemot 30:11-16
One-to-One Correspondence Activity:
[K-2 concept]
In this week's parsha, we learn of Hashem telling Moshe that at such time as he chooses to take a census- a counting of the number of people, either total Children of Israel or a portion of the population- he should not just count the people. Rather, he should have each person being counted give a half-shekel as a donation to the Holy Tabernacle. It explicitly states that a rich person should not give more, and a poor person should not give less; any person being counted must give exactly a half-shekel.
Socially, an important message about the value of human life can be embedded into this lesson- each person is equally as important; a rich person's life isn't worth more, and a poor person's life isn't worth less.
Mathematically, if each half-shekel is representative of a person in the given community, it is important for each person to give exactly a half-shekel (no more, no less). Children can discuss what would happen if someone put in an extra half-shekel, or if other people gave less than a half-shekel.
An activity of playing out taking a census in the classroom with a given token can help students understand the one-to-one correspondence of each person giving in one specific coin to represent their presence as part of the community. Together, they can look at the coins collected to see that the number of coins matches exactly to the number of people in the class.
A follow-up activity would be to have some students with extra coins and some students with fewer coins (or no coins). Children could be allowed to give as many coins as they want. Then go back, as a class, to look at how many coins were collected and see if they can figure out how many people are in the class based on the coins collected. How does the number of coins compare to the actual number of students in the class? Students will be able to see the confusion caused by the discrepancy- the missing aspect of the one-to-one correspondence.
Base-10 Connection:
[3-5 concept]
Students can also talk about the idea that, in Judaism, we don't count out individual people. If we need to know how many people are in a group, we use another method of tallying the number of people in the group. Rather than counting people, for example, we could count people by their shirts (17 shirts in a room means 17 people who are wearing those shirts). If you do need to "point and count" people in a group, there is a custom to use the passage:
"הושיע את עמך וברך את נחלתך ורעם ונשאם עד עולם"
"Save Your people, and bless Your inheritance; And tend them, and carry them forever"
~Tehillim 28:9
Mathematically, using this Hebrew phrase from Tehillim works out very nicely, since there are 10 words in the phrase. Each word represents one person, so every full phrase represents 10 people. Students can discuss different example situations of how many full passages and a number of extra words represents how many people in a group. For example, if I'm counting people in a crowd, and I go through the full passage 3 times and then begin the passage again, ending on the word "וברך", that would mean that there are 34 people in the crowd.
"When the Supreme One gave nations their portion, when He separated the children of man, He set the borders of peoples according to the number of the Children of Israel." ~Devarim 32;8
Rashi on 32;8 makes reference to 70 languages which correspond to the 70 nations enumerated in Bereishit chapter 10, which developed from the descendants of Noah.
One to One Correspondence:
Have you ever heard a young child count pictures in a book and watched as they accurately count up to 13, only to see that there are actually only 5 pictures on the page? Have you watched a small child try to count items in front of them, trying to figure out which ones were already counted?
One to One Correspondence is one of the first concepts that young children need to understand in order to understand what numbers actually mean. One to one correspondence is the idea that each counting number correlates to one item that is being counted. The way to assign a number to an entire group is to have each item represented by a single number; we can then say that the size of the group is that of the largest counting number used to count the items. If I have 12 marbles, for example, I would be able to know this by counting each individual marble once, and identifying that when I've counted the last marble, the number that I used to count it was number 12. Since I ran out of marbles at number 12, that means that I have 12 marbles in my group.
Once children know the proper order of the counting numbers, the biggest confusion for them when learning to count is how to keep track of what they have already counted. The best strategy for teaching tracking while you're counting is to move the counted items to the side, out of the way, so that they can easily identify which items have already been counted and which items still need to be counted. So how can you help children practice counting when they are given pictures or drawings of items? The best thing to do in that situation is to line up or organize the drawings on the paper in such a way that children can methodically move through each section of the picture in a way that they can keep track of what has already been counted. Organized rows and columns work very well in this type of situation. The fancy books with dynamic types of designs tend to be more confusing and leave children less successful in their counting.
Parsha Connection:
When Rashi references the 70 languages which correspond to the 70 nations that came from the descendants of Noah, this is a perfect example of one to one correspondence. In this case, we have 70 descendants- each of those 70 descendants developed into their own nation, resulting in 70 nations (one descendant for each nation)- and each of the 70 nations had its own language, resulting in 70 languages (one nation for each language).
Another, year-long exercise in one to one correspondence is matching each parsha (or double-parsha) with each shabbat. There is a specific order to the parshiot readings, and there are certain parshiot that are specifically read at certain times. For example, Devarim is always read the week before Tisha B'Av, and Va'etchanan is always read the week the week after Tisha B'Av; V'Zot Ha'Bracha is always read on Simchat Torah. Using these placeholders in the calendar, we can go through the year of parshiot and match them up to the shabbatot in which they will be read. This process of matching one to one is an exercise in one to one correspondence.
Everyday Connection:
The mere fact that we are each able to count items successfully on a daily basis for day-to-day activities shows that we have each internalized and successfully rely on our understanding of one-to-one correspondence. Interestingly, as we grow and our brains develop, we can start to automatically, accurately identify the quantities of small groups of items. Visually organizing items makes it easier for our brains to automatically, accurately identify the quantities of larger groups of items.
For a different example, musicians who play the harp need to identify the notes of the strings. As identification, the C note strings are all red, and the F note strings are all blue. Using these placeholders, musicians are able to identify which strings are which notes and what their finger placements need to be- 2 examples of one to one correspondence- matching strings to notes and matching fingers to strings.
What examples are in your daily life?
