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Unformatted text preview: Lecture 6. Logic II: Simple Sentences June 9, 2011 CCSS for Grade 6 (page 39) Students understand the use of variables in mathematical expressions. They write expressions and equations that correspond to given situations, evaluate expressions, and use expressions and formulas to solve problems. Students understand that expressions in different forms can be equivalent, and they use the properties of operations to rewrite expressions in equivalent forms. Students know that the solutions of an equation are the values of the variables that make the equation true. Students use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple onestep equations. Students construct and analyze tables, such as tables of quantities that are in equivalent ratios, and they use equations (such as 3 x = y ) to describe relationships between quantities. Equivalent expressions Arithmetic expressions denote numbers. Algebraic expressions, on the other hand, don’t denote any thing but they have the form of arithmetic expressions, and consequently if numerical values are assigned to the variables, then the result denotes a number. Two arithmetic expressions are said to be equivalent if they denote the same number. Two algebraic expressions are said to be equivalent if, whenever values are assigned to the variables in the two expressions in the same way, the resulting expressions denote the same number. Equivalence in this sense is called “equivalence in meaning.” There is another way to understand equivalence of expressions which is dependent upon rules such as the associative, commutative and distributive laws. Each of these laws gives us a rule for rewriting expressions—for example, using the commutative law, we may rewrite a + b as b + a . If one expression can....
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This note was uploaded on 11/23/2011 for the course MATH 6302 taught by Professor Madden during the Summer '11 term at LSU.
 Summer '11
 MADDEN
 Math, Logic, Equations

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