The importance of knowing how sets are the same, and how two or more sets can be used together to make new sets.
Using Sets for Problem Solving
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Addition and Subtraction of Whole Numbers
The Set Model of Whole-Number Addition
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A set model is used for adding and subtracting whole numbers. When asking basic math questions such as, Michael has 3 pieces of candy, his mom gives him 4 more. How many candies does he have now? We can use a set model to model this exercise.
The Number Line Model of Addition
Properties of Whole Number Addition
Subtraction of Whole Numbers
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Subtracting whole numbers is the opposite operation of adding whole numbers.
Take-Away Model
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Example:
Start with 8 objects
Take 3 objects away
How many objects are left?
Comparison Model
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Number-Line Model
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Use hops on a number line to model subtraction of whole numbers. When subtracting a positive number, move to the left on the number line. If subtracting a negative number, move to the right.
Sets, Counting, and Whole Numbers
One to One Correspondence
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Being able to match one object to one other object or person. This can be used in pairing elements between two sets.
The Whole Numbers
Ordering the Whole Numbers
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When a=n(A) and b= n(B) and they are whole numbers and finite sets, If A matches a subset of B, then a
Problem Solving with Whole Numbers and Venn Diagrams
Multiplication and Division of Whole Numbers
Multiplication of Whole Numbers
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Multiplication as Repeated Addition
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Example: 5x3=5+5+5
How many is 3 groups of 5 fish?
The Multiplication Tree Model
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Division of Whole Numbers
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When dividing numbers you may not always get a whole number, unlike multiplying. When you divide, you separate into parts.
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The Partition Model of Division
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This model can be used with physical objects. Sometimes called division by sharing, or partitive division.
Division with Remainders
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When the set of whole numbers is not closed when using division. The remainder is the integer left over.
