In Vayikra 12:2-5 we learn about the Biblical periods of impurity after a woman gives birth. We learn that after giving birth to a son, she is impure for one week (7 days) and she may not touch holy items or partake in eating the terumah for an additional 33 days. At the end of the 40 day period (7 + 33 = 40), she brings sacrifices. After giving birth to a daughter, she is impure for 2 weeks (14 days) and she may not touch holy items or partake in eating the terumah for an additional 66 days. At the end of the 80 day period (14 + 66 = 80), she brings sacrifices.
Doubling Numbers & The Sums of Numbers:
If we look at the timeline for a woman's post-delivery impurity and offering of sacrifices, we can see that the timeline after the delivery of a daughter is double the timeline after the delivery of a son. Let's take a minute to break it down piece by piece:
Post delivery impurity:
Son- 1 week (7 days)
Daughter- 2 weeks (14 days)
Additional time before bringing sacrifices:
Son- 33 days
Daughter- 66 days
Total time post-delivery until sacrifices are brought:
Son- 7 days + 33 days = 40 days
Daughter- 14 days + 66 days = 80 days
As a teacher, I have seen students many times find a pattern in the way numbers work together and automatically assume that the pattern will apply to all numbers. Sometimes their assumption is correct and they have found an accurate pattern in number theory; other times students stumble upon a neat trick that works with specific types of numbers but cannot be extrapolated to other numbers. Without thinking about and testing their pattern, students may inadvertently apply a neat trick as a greater application in number theory.
With this in mind, I propose the following investigation for students:
If you double two numbers, will the sum of the doubled numbers always be double the sum of the original numbers? (Note that this investigation is applicable for students of any age who aren't yet certain of the answer and explanation of why.)
Students can test this by picking a variety of different numbers and checking what happens when they double the numbers and compare the sums of different numbers- original and then doubled. Students can work in partners or individually and compare their findings with their classmates. It's important for students to consider that, while they can't test every number, if enough numbers follow their pattern, they can feel confident that their pattern holds true for most numbers.
With enough testing, students should develop the basic premise of the theorem:
If a + b = c, then 2a + 2b = 2c
Through their testing, at least some students (at least by grade 5+) should develop enough of a thought process about their testing to begin to explain why this is true.
Some follow-up investigations:
Math related-
*Does this hold true when you add more addends to your original addition statement? i.e. if you add three numbers, will the sum of double those 3 numbers be double the original sum? 4? 5? etc. Why?
*Does this hold true for subtracting numbers?
*Does this hold true for multiplication? division?
*Does this hold true for negative numbers? fractions & decimals?
The more scenarios and number sets that they test, the stronger theory they can develop for use in their future work.
Math & Parsha related-
*Specifically related to this week's parsha, when you convert 33 days and 66 days into time measured in weeks & days, will they still appear to be doubled at first glance? Can you explain your findings? Based on your findings, do you think there's a reason that the Torah may have listed the time periods in the way that they are listed?
Showing posts with label Tazria. Show all posts
Showing posts with label Tazria. Show all posts
Thursday, April 23, 2015
Friday, March 28, 2014
Tazria- Conditional Statements and Flow Charts
"Hashem spoke to Moshe and Aaron, saying: If a person will have on the skin of his flesh a s'eit, or a sepachat, or a baheret, and it will become a tzara'at affliction on the skin of his flesh; he shall be brought to Aaron the Kohen, or to one of his sons the Kohanim. The Kohen shall look at the affliction on the skin of his flesh: If hair in the affliction has turned white, and the affliction's appearance is deeper than the skin of his flesh-it is a tzara'at affliction; the Kohen shall look at it and make him impure.
If it is a white baheret on the skin of his flesh and its appearance is not deeper than the skin, and the hair has not turned white, then the Kohen shall close off the affliction for a seven-day period. The Kohen shall look at it on the seventh day, and behold!- the affliction remained in its appearance, and the affliction did not spread on the skin, then the Kohen shall close him off a second time for a seven-day period. The Kohen shall look at it again on the seventh day, and behold!- if the affliction has dimmed and the affliction has not spread on the skin, then the Kohen shall declare him pure, it is a mispachat; he shall immerse his garments and become pure. But if the mispachat should spread on the skin after it had been shown to the Kohen for its purification, it should be shown to the Kohen again. The Kohen shall look, and behold!- the mispachat has spread on the skin; the Kohen shall make him impure; it is tzara'at." ~Vayikra 13;1-8
In continuation of our study of understanding information and organization of information using graphic organizers, this week we'll look at two new ideas: 1) conditional statements and 2) flow charts.
Conditional Statements:
Conditional statements are statements in "If..., then..." form that give you a piece of information that is based on whether or not the other part is true. For example, "If it rains, I will need my umbrella." This statement tells me that I may or may not need an umbrella, and the way to determine if I do is based on whether or not it rains. If it rains, yes, I do; if it doesn't rain, no, I don't. Conditional statements are used in math to organize information, and often students will work with conditional statements to determine whether they are true or false. "If a shape has four sides, then it's a square." This statement could be true, but is not always true, since there are other shapes that also have four sides, and our statement is not specific enough about the shape. Sometimes, switching the first and second clauses can make a false statement true- "If a shape is a square, then it has four sides." We just took a statement that is not always true and made it into one that is always true, since a square does always have four sides. Rearranging the order of clauses and adding or removing negatives in clauses of conditional statements can be a whole exercise on its own, and is typically studied in conjunction with beginning algebra concepts. For our purposes this week, we just need to understand what a conditional statement is.
Flow Charts:
Flow charts are an organizational tool that can be used to make sense of a process or "flow" of information. You start at one point and determine what that information leads you into. Often, there are two or more options that come out of one point and the flow chart helps you separate what happens in case 1 of this situation from what happens in case 2 of this situation. The flow chart offers a visual representation of the process in the situation with which you are working.
Parsha Connection:
In this week's parsha, we are told about the process that the Kohen must go through to determine whether or not a person has tzara'at. Using a flow chart to map out the conditional statements that are given, we can create a visual aid for understanding when a person is diagnosed with tzara'at (impure) and when they are ok (pure).
We begin by charting the initial situation along with any possible first step outcomes from the situation.
Next, we take each of those outcomes and see if a final decision is made or if there is a follow-up step that occurs as part of the outcome. In our case, if the person is determined to be either pure or impure then that path has ended; if a determination has not yet been made, then the path will continue.
Now we take the follow-up step and chart the possible outcomes from that step.
From here, we continue, as before, and look to see if a final decision was made and each path has ended, or if follow-up steps are required based on the outcomes. We chart each path until all paths end at either a pure or impure status.
This is just one situation that lends itself to being graphed in a flow chart in this week's parsha. Try your hand at flow charts by mapping out another situation.
If it is a white baheret on the skin of his flesh and its appearance is not deeper than the skin, and the hair has not turned white, then the Kohen shall close off the affliction for a seven-day period. The Kohen shall look at it on the seventh day, and behold!- the affliction remained in its appearance, and the affliction did not spread on the skin, then the Kohen shall close him off a second time for a seven-day period. The Kohen shall look at it again on the seventh day, and behold!- if the affliction has dimmed and the affliction has not spread on the skin, then the Kohen shall declare him pure, it is a mispachat; he shall immerse his garments and become pure. But if the mispachat should spread on the skin after it had been shown to the Kohen for its purification, it should be shown to the Kohen again. The Kohen shall look, and behold!- the mispachat has spread on the skin; the Kohen shall make him impure; it is tzara'at." ~Vayikra 13;1-8
In continuation of our study of understanding information and organization of information using graphic organizers, this week we'll look at two new ideas: 1) conditional statements and 2) flow charts.
Conditional Statements:
Conditional statements are statements in "If..., then..." form that give you a piece of information that is based on whether or not the other part is true. For example, "If it rains, I will need my umbrella." This statement tells me that I may or may not need an umbrella, and the way to determine if I do is based on whether or not it rains. If it rains, yes, I do; if it doesn't rain, no, I don't. Conditional statements are used in math to organize information, and often students will work with conditional statements to determine whether they are true or false. "If a shape has four sides, then it's a square." This statement could be true, but is not always true, since there are other shapes that also have four sides, and our statement is not specific enough about the shape. Sometimes, switching the first and second clauses can make a false statement true- "If a shape is a square, then it has four sides." We just took a statement that is not always true and made it into one that is always true, since a square does always have four sides. Rearranging the order of clauses and adding or removing negatives in clauses of conditional statements can be a whole exercise on its own, and is typically studied in conjunction with beginning algebra concepts. For our purposes this week, we just need to understand what a conditional statement is.
Flow Charts:
Flow charts are an organizational tool that can be used to make sense of a process or "flow" of information. You start at one point and determine what that information leads you into. Often, there are two or more options that come out of one point and the flow chart helps you separate what happens in case 1 of this situation from what happens in case 2 of this situation. The flow chart offers a visual representation of the process in the situation with which you are working.
Parsha Connection:
In this week's parsha, we are told about the process that the Kohen must go through to determine whether or not a person has tzara'at. Using a flow chart to map out the conditional statements that are given, we can create a visual aid for understanding when a person is diagnosed with tzara'at (impure) and when they are ok (pure).
We begin by charting the initial situation along with any possible first step outcomes from the situation.
Next, we take each of those outcomes and see if a final decision is made or if there is a follow-up step that occurs as part of the outcome. In our case, if the person is determined to be either pure or impure then that path has ended; if a determination has not yet been made, then the path will continue.
Now we take the follow-up step and chart the possible outcomes from that step.
From here, we continue, as before, and look to see if a final decision was made and each path has ended, or if follow-up steps are required based on the outcomes. We chart each path until all paths end at either a pure or impure status.
This is just one situation that lends itself to being graphed in a flow chart in this week's parsha. Try your hand at flow charts by mapping out another situation.