Objectives
Students should identify equivalent expressions and explain why they are equivalent using properties of multiplication and addition. They use a variety of strategies, including rewriting an expression and properties of operations, to develop equivalent expressions.
Vocabulary
expression
variable
constant
associative property
commutative property
distributive property
equivalent expressions
Two expressions are equivalent if they have the same value for every possible replacement for the variable or variables.
Some statements can be true for many values of a variable or variables but not true for others. For example, “multiplication” makes things larger is true if you are multiplying whole numbers greater than 1.
Which expression is equivalent to 8(x-2) + 4(3-x) - 2x?
Answer: 2x-4
Students consider how to verify that expressions are equivalent by using the associative and commutative properties of addition and multiplication as well as the distributive property.
Students reason about values produced by an expression as the variable x changes and look for relationships between the structure of the expression and its value.
Engage students in reasoning about the values produced by an expression as the variable x changes and in looking for patterns and relationships between the structure of the expression and its value.
