7.A.4.1 Use properties of operations (limited to associative, commutative, and distributive) to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents.
In a Nutshell
Numerical expressions are expressions containing only numbers and operations. Algebraic expressions contain numbers, operations, and variables. Equivalent expressions are expressions that have identical values but are written in different ways. Associative, commutative, and distributive properties allow for multiple equivalent representations of expressions.
Student Actions
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Teacher Actions
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- Develop a deep and flexible understanding by exploring tasks to discover when, why, and how to apply properties of operations.
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Develop accurate and appropriate procedural fluency in using properties of operations to generate and solve numerical expressions and algebraic expressions.
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Develop strategies for problem-solving by exploring a variety of expressions in order to discover the properties of operations.
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Pose purposeful questions to get students thinking about the benefits of using properties of operations and how and when to apply them.
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Explain how properties can be used when combining like terms.
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Implement tasks that create meaningful real-world opportunities for students to apply and analyze the properties of operations.
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Key Understandings
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Misconceptions
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Associative property is an extension of the commutative property, and the regrouping of values using parenthesis does not affect the value when used with the operations of addition and multiplication.
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The commutative property is changing order of values that are being added or multiplied.
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The distributive property is multiplying the same value by a set of values inside the parenthesis.
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The distributive property can also be used to separate a common factor from a set of values and write it succinctly using parenthesis.
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Students may ignore the order of operations in general, solving left to right at all times.
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Students may believe that you do everything inside the parentheses from left to right. (i.e. 3 + (4 - 1 x 5)). They do not realize that even within the parenthesis, you still must solve in the proper order.
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Students may think that when seeing an exponent on the outside of parentheses, they will only raise the last number to that power. (i.e. (3 + 2)^2 = 3 + 2^2).
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Students may believe that you do multiplication before division (i.e. 3+ (9 รท 3 x 2). They incorrectly apply the order of operations based on a mnemonic device they may have been taught (PEMDAS) whereas the updated mnemonic, GEMA (grouping symbols, exponents, multiplication (and it's inverse) and addition (and it's inverse)) may resolve this over-generalization.
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Students may not realize there are more than just parenthesis for grouping symbols, which might [include brackets] and {winged brackets} in most cases.
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Resources
OKMath Framework Introduction
7th Grade Introduction
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