Additive Identity Property of Zero: a+ 0= 0+ a=

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1 MA 118: Section 2.3 Addition and Subtraction of Whole Numbers Examples: Addition and Subtraction with Cuisenaire Rods; Adding with two color counters Research: Count All Count On Strategies (group 10s, estimate etc.) The teaching goal for learners is automaticity or fluency, the ability to quickly recall basic facts. I. Whole Number Addition Definition: Addition of Whole Numbers If A and B are any two disjoint sets for which a= n( A) and b= n( B) then the sum of a and b, written a+ b, is given by a+ b= n( A B). Vocabulary (for you and your students): 1) a and b are called the addends or summands. 2) Addition is a binary operation (requires two operators). Properties of Whole Number Addition If a and b are any whole numbers, then Closure Property: a+ b is a unique whole number. Commutative Property: a+ b= b+ a. Associative Property: a+ ( b+ c) = ( a+ b) + c. Additive Identity Property of Zero: a+ 0= 0+ a= a 1

2 Section 2.3 Addition and Subtraction of Whole Numbers Mathematics arises from human activity. People want to keep track of stuff, or make predictions. Context: Real life or meaningful situations from which the mathematical situation arises. Model: A concrete representation or a pictorial representation of a mathematical situation or process. Models should clarify the situation. Addition: Join Context - Set Model Example: Jill has 4 pencils. Her mother gives her 3 more pencils. How many pencils does Jill have? = Addition: Join Context Number Line (Measurement) Model Example: Jill walks 4 miles to Sacha s house. Together they walk 3 more miles to Pedro s house. How far did Jill walk? = 2

3 II. Whole Number Subtraction Set Definition of Subtraction: Subtraction of Whole Numbers If A and B are any two sets for which B A and a= n( A) and b= n( B) then the difference of a and b, written a b, is given by a b= n( A B) = n( A\ B). Addition and subtraction are inverse operations, different perspectives of the same situation. Subtraction of Whole Numbers If a and b are any whole numbers, their difference, written a b, is the unique whole number c such that a= b+ c. That is, a b= c if and only if there is a whole number c such that a= b+ c. Vocabulary you should know: 1) a is the minuend, b is the subtrahend, c is the difference. 2) Subtraction is a binary operation. Properties of Whole Number Subtraction? Closure Property? Commutative Property? Associative Property? Identity Property of Zero? The lack of properties makes subtraction difficult for children. 3

4 Subtraction: Take-Away Context Set Model Example: Joe had 5.00, then he spent 3.00 on candy. How much does Joe have left? 5 3 = Subtraction: Comparison Context Set Model Example: Joe has Sue has How much more does Joe have than Sue? 4

5 Subtraction: Missing Addend Context Set Model Example: Joe has He needs 5.00 to buy a book. How much more does he need? 5? + 2 = = Subtraction: Missing Subtrahend Context, Number line model Example: Clara has 5 feet of ribbon. She leaves the room and comes back. Only 2 feet are left. How many feet are missing? 5? = = 5

6 Subtraction: Missing Minuend Context Set model Fred has some cookies. He gives his sister 2 of his cookies. Now he has 3 cookies. How many cookies does Joe have to begin with?? * * * * * 2 = = Fact families: What is the fact family for = 9? What is the importance of fact families? Representing addition and subtraction on the number line (measurement model): Represent each member of the fact family on a number line. What is the importance of number line representation? 6