ALEX Classroom Resource

Students:

• Use the distributive property to write an equivalent expression for the sum of the two numbers as the product of the greatest common factor of the two numbers, and the sum of two whole numbers with no common factor. [if the two whole numbers are 36 and 8, 36+8 = 4(9+2)].

Students know:

• Distributive property of multiplication over addition.
• Strategies to express the sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor by decomposing the numbers.

Students are able to:

• Use and model the distributive property to express the sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor by decomposing the numbers.

Students understand that:

• Multiplication is distributive over addition.
• Composing and decomposing numbers provides insights into relationships among numbers.
• Quantities can be represented using a variety of equivalent expressions.

Learning Objectives:
M.6.7.1: Define greatest common factor, least common multiple, and the distributive property.
M.6.7.2: Design problems using greatest common factor and the distributive property.
M.6.7.3: Show an understanding of how to solve a problem using the distributive property, with or without the use of a calculator.

Students:

• Given contextual or mathematical problems which may be modeled by algebraic expressions, use properties of the operations to produce combined and re-written forms of the expressions that are useful in resolving the problem.

Students know:

• the properties of operations, including inverse, identity, commutative, associative, and distributive and their appropriate application to be able to generate equivalent algebraic expressions.

Students are able to:

• Accurately use the properties of operations on algebraic expressions to produce equivalent expressions useful in a problem solving context.

Students understand that:

• The properties of operations used with numerical expressions are valid to use with algebraic expressions and allow for alternate but still equivalent forms of expressions for use in problem solving situations.

Learning Objectives:
M.6.16.1:Define equivalent, simplify, term, distributive property, associative property of addition and multiplication, and the commutative property of addition and multiplication.
M.6.16.2: Simplify expressions with parentheses (Ex. 5(4 + x) = 20 + 5x).
M.6.16.3: Combine terms that are alike of a given expression.
M.6.16.4: Recognize the property demonstrated in a given expression.
M.6.16.5: Simplify an expression by dividing by the greatest common factor.
Example: 18x + 6y = 6(3x + y).
M.6.16.6: Determine the greatest common factor in an algebraic expression.