How can expressions support a generalized interpretation of number?

Students analyze expressions and solve algebraic equations.

Numerical expressions can include powers.

The conventional order of operations includes performing operations in parentheses, followed by evaluating powers before other operations.

Algebraic terms with exactly the same variable are like terms.

Constant terms are like terms.

Like terms can be combined through addition or subtraction.

The terms of an algebraic expression can be rearranged according to algebraic properties.

Algebraic properties include

• commutative property of addition: a + b = b + a, for any two numbers a and b

• commutative property of multiplication: ab = ba for any two numbers a and b

• associative property of addition: (a + b) + c = a + (b + c)

• associative property of multiplication: a(bc) = b(ac)

• distributive property: a(b + c) = ab + ac

All simplified forms of an equation have the same solution.

The conventional order of operations can be applied to simplify or evaluate expressions.

Algebraic properties ensure equivalence of algebraic expressions.

Algebraic expressions on each side of an equation can be simplified into equivalent expressions to facilitate equation solving.