Big Idea:

Big Idea 2

A solution makes a function rule true.

1 week

Evidence of Understanding

  • solve equations or inequalities in 1 variable using any method  
    • construct viable arguments to justify a solution method and articulating assumptions
      • describe the process for finding the solution (NOT proving why the solution is correct)
    • discuss advantages and disadvantages of different methods:  strategically guessing and checking, working backwards, zero product property, etc.
    • represent the solution to an equation or inequality using a number line
      • understand numbers can represent a point or a distance on a number line
      • use arrows to represent direction for positive and negative numbers
    • use a graph to solve linear or absolute value equations in 1 variable 
      • describe how the graph visually represents values that make the equation true
      • justify the intersection of f(x) = mx + b and f(x) = c as the solution to c = mx + b, Example: the solution to 14 = |3x + 5| is any x value when y = |3x + 5| meets the line y = 14
    • estimate and justify reasonable and unreasonable solution options
      • Example:  For 39 = 5x - 2, recognize -5, 0,  40, etc. are not reasonable solution options and quantities between 6 and 10 are reasonable

 

  • solve linear equations or inequalities in 1 variable using an algebraic method  
    • describe the operations and quantities that relate any input with its output
    • rewrite an equation or inequality by combining like terms and/or using the distributive property to represent equivalent parts
      • given the rate of change and a point on the line, convert an equation to standard form
      • Example: rewrite 60 = 5x + 10 as  50 + 10 = 5x + 10 or 5(12) = 5(x + 2), etc.   
    • analyze an equation or inequality and strategically use additive or multiplicative inverses, the zero product property, the distributive property, or combining like terms to identify a solution
      • justify how each step maintains the equation’s balance
    • determine the solution to an equation or inequality and justify its validity
      • decide whether a solution makes sense given the context of a situation
      • substitute the solution to show the equation or inequality is true

 

Develop conceptual understanding:

solution(s), solution set, simplify, solve, inverse operations, zero product property, additive inverse, multiplicative inverse, distributive property, distribute, combining like terms, balance, intersection, equivalent

Supporting terms to communicate:

expression, equation, inequality, variable, unknown, quantity, coefficient, constant, initial value, rate of change, factor, sum, difference, product, quotient, substitution, greater than, greater than or equal to, less than, less than or equal to, at least, at most, number line

Core Resource
A core resource supports multiple days of instruction. COMING SOON!
    Instructional Routine: Connecting Representations
    These tasks are embedded within the instructional routine called Connecting Representations.