Generating Equivalent Expressions

Students generate equivalent expressions using the fact that addition and multiplication can be done in any order (commutative property) and any grouping (associative property). Students recognize how any order, any grouping can be applied in a subtraction problem by using additive inverse relationships (adding the opposite) to form a sum and likewise with division problems by using the multiplicative inverse relationships (multiplying by the reciprocal) to form a product. Students recognize that any order does not apply to expressions mixing addition and multiplication, leading to the need to follow the order of operations. The any order, any grouping property introduced in this lesson combines the commutative and associative properties of both addition and multiplication.