Ch3 Notes (F09)

Ch3 Notes (F09) - Section 3-1 Addition and Subtraction of...

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1 Section 3-1 – Addition and Subtraction of Whole Numbers Addition of Whole Numbers Suppose A and B are disjoint finite sets. If n (A) = a and n (B) = b , then a + b = n (A B). a and b are called the addends and a + b is called the sum . Example : A = { m, n, p } B = { w, x, y, z } n (A) = n (B) = Then, n (A B) = Discrete Amounts – buttons, trucks, pets, etc. Continuous Amounts – ounces, inches, feet, etc. Examples : Model each of the following using a number line and determine if the amounts are discrete or continuous. a) Tommy has 4 balloons. Mike gives him 3 more balloons. How many balloons does Tommy have? 0 1 2 3 4 5 6 7 8 9 10 b) A recipe calls for 3 ounces of milk and 2 ounces of oil. How much liquid is needed for the recipe? 0 1 2 3 4 5 6 7 8 9 10
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2 The Properties of Addition of Whole Numbers: The Commutative Property : If a and b are whole numbers, then a + b = b + a The Associative Property : If a , b , and c are whole numbers, then ( a + b ) + c = a + ( b + c ) The Identity Property : If a is a whole number, then a + 0 = 0 + a = a 0 is called the “additive identity” The Closure Property : If a and b are whole numbers, then a + b is a whole number. (If you add two whole numbers, a unique sum will exist and it will be a whole number) Examples : Which property justifies each of the following? a) (1 + 2) + 4 = 1 + (2 + 4) b) 5 + 3 = 3 + 5 c) (8 + 2) + 9 = (2 + 8) + 9 Example: Show on a number line that 4 + 2 = 2 + 4 = 6. 0 1 2 3 4 5 6 7 8 9 10 Example : Fill in the blanks with the appropriate property that was used. (3 + 8) + (3 + 4) = (8 + 3) + (3 + 4) ____________________________________ = 8 + (3 + 3) + 4 ____________________________________
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3 Example: Are the following sets closed under addition? a) {1, 2, 3, 4, …} b) {0, 1, 2} c) {2, 4, 6, 8, …} d) {1, 3, 5, 7, …} See “Mastering Basic Addition Facts” on pg.118 1. Counting On 5 + 3 Start at 5, then count 6, 7, 8. 2. Doubles (Doubles +1; Doubles +2; Doubles – 1) 3. Making 10 8 + 5 = (8 + 2) + 3 4. Counting Back 9 + 7 = 10 + 7 – 1 Subtraction of Whole Numbers For any whole numbers a and b such that a b , a b is the unique whole number c such that a = b + c a = minuend, b = subtrahend, c = difference Every subtraction problem can be re-written as an addition problem: a – b = c iff c + b = a Examples : Rewrite the following subtraction problems as addition problems: a) 10 – 3 = x b) x – 9 = 20
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4 Types of Subtraction problems : 1. Take-away – A part is taken away from a whole 2. Comparison – Two amounts are being compared (either 2 parts of a whole, or 2 wholes) 3. Missing addend – One of the parts is missing from the whole (gives rise to algebraic thinking) = 7 – 3 = ____ ____ + 3 = 7 7 – 3 = ____ Examples : Determine the type of subtraction problem, then model it. 1. Amy has 5 apples. She gave 3 apples to her sister. How many does she have left? 2. Bob has 10 sheep. Billy has 6 sheep. How many more does Bob have?
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5 3. At the beginning of the week, Martha had 8 oranges in the refrigerator. During the week, she ate 5 oranges. How many oranges did Martha have at the end of the week?
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Ch3 Notes (F09) - Section 3-1 Addition and Subtraction of...

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