day 5 - closure.notebook€¦ · day 5 closure.notebook 4 september 11, 2012 sep 143:50 pm do now...
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Day 5 Closure.notebook
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September 11, 2012
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ClosureSWBAT: • Determine if a given set of numbers is closed under a given operation.• Prove (support with an explanation) that a given set of numbers is or is not closed under a given operation.
Do Now: Worksheet
HW#6--Closure Practice WorksheetQuiz Thursday on BASIC Properties of operations NO CLOSURE / Sets Test Friday 9/21
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5X
2x
0
1
0
1
-1
03x
Distributive Property of Multiplication over Addition
Associative Property of Addition
Commutative Property of Addition
Additive Inverse Property
Multiplicative Identity Property
Multiplicative Property of Zero
Multiplicative Inverse Property
Multiplicative Property of -1
Additive Identity Property
0
1
Opposite
Reciprocal
Distributive Property of Multiplication over Subtraction
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Do Now Review:
Draw a graphic organizer to show the relationships among all the subsets of the set of Real Numbers
Venn DiagramTree Diagram
True/False (1-6)/ Answer 7 and 8:1. A whole number is an integer.5. If x is a positive integer then x≥0.2. Zero is a positive integer.6. If x is a negative integer then x<0.3. An integer is a whole number.7. What is the greatest negative integer?4. One-half is not an integer8. What is the smallest positive integer?
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September 11, 2012
Sep 143:52 PM
Property of Closure:A set is closed under an operation if whenever the operation (+, -, x, ÷) is performed within the set the answer is also a member of the set.
When you are asked about closure you will be given:a) A set of numbers <AND>b) An operation to be performed upon the set of numbers.
REMEMBER--Numbers can be OPERATED on with themselves.
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Example:
Given the set: {1, 2, 3 ...}
Is the set closed under:
Addition: Subtraction:
Multiplication: Division:
Not Closed--show one "counter example"Closed--show THREE cases that work.
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September 11, 2012
Sep 144:16 PM
Example:
Given the set: {0,1, 2, 3 ...}
Is the set closed under:
Addition: Subtraction:
Multiplication: Division:
Not Closed--show one "counter example"Closed--show THREE cases that work.
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Sep 144:19 PM
Example:
Given the set: {-1, 0, 1}
Is the set closed under:
Addition: Subtraction:
Multiplication: Division:
Not Closed--show one "counter example"Closed--show THREE cases that work.
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September 11, 2012
Sep 144:18 PM
Example:
Given the set: {Rational Numbers}
Is the set closed under:
Addition:Subtraction:
Multiplication:Division:
Not Closed--show one "counter example"Closed--show THREE cases that work.
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September 11, 2012
Sep 144:29 PM
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Question: Is the set of negative integers closed under the operation of SQUARING a number?
Why or Why not?
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x
x
x xx
**x x xx xx
*Division by zero is undefined. The set would beclosed under division if zero were excluded.
*
√ √ √√ √
√ √√√√√
√√√√√
√√
√√√√
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September 11, 2012
Sep 111:54 PM