Evidence of Understanding

**analyze expressions, equations or inequalities and justify whether they are equivalent**- substitute specific values into both equations, evaluate the equations, and justify equivalency
- consider how many input and output pairs suffice to show equivalency

- create diagrams or visual models to show that two equations are equivalent
- algebraically prove equivalency by representing each equation identically
*Example: show how 3(x + 2) and 3x + 6 are equivalent*

- create equivalent algebraic expressions, equations, or inequalities
- solve for one variable in terms of another variable (x in terms of y, etc.)
- fluently add or subtract polynomial expressions

- recognize and describe a quantitative relationship between variables and use
**substitution**to write one variable in terms of another*Example: is there are 5 times as many apples (A) as bananas (B), A can be written in terms of B as 5B, consecutive numbers can be represented in terms of the first number in the sequence as x, x + 1, x + 2*

- substitute specific values into both equations, evaluate the equations, and justify equivalency

**solve equations or inequalities with a variable on both sides of the equation or inequality**- express an equation with a variable on both sides as two linear functions
*Example: given 2x +3 = 5x - 1, understand how to create y = 2x + 3 and y = 5x - 1*

- graphically solve an equation with a common variable on both sides of the equation
- create a table of values for each side of the equation and identify the common solution
- graph each equation and explain how the intersection point represents the solution

- algebraically solve an equation or inequality with a common variable on both sides
- analyze an equation or inequality and strategically use additive or multiplicative inverses, the zero product property, or the distributive property to identify a solution
- verify the solution is valid using substitution

- express an equation with a variable on both sides as two linear functions

Develop conceptual understanding:

substitution

Supporting terms to communicate:

expression, equation, inequality, equivalent, equal, balance, solution(s), solution set, solve, simplify, distribute, like terms, zero product property, sum, difference, product, quotient, variable, quantity, coefficient, constant, initial value, rate of change, dependent, independent, linear