Big Idea:

Big Idea 3

Functions can be represented in multiple, equivalent ways.

1 week

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

 

  • 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

 

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

Core Resource
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