Big Idea:

Big Idea 1

Linear functions are characterized by a constant rate of change.

1 week

Evidence of Understanding

  • create a linear equation or inequality in 2 variables from a situation, table of values, or graph
    • explain the difference between an expression, an equation, and an inequality
    • understand the difference between variables and fixed quantities in a function rule
    • given f(x) = mx + b, compare how the constant (b) and the lead coefficient (m) relate to the graph, table, or situation
      • Ex: explain how y = 2x + 5 and y = 5x + 2 are different
         
  • write linear equations or inequalities in 1 variable from a situation
    • in the form px + q = r where p, q, and r are rational numbers, describe how r is one specific output value of the general function f(x) = px + q
      • describe the units of a variable or quantity and explain what each term/value in the equation represents
    • represent an equation or inequality in 1 variable using a visual diagram or model
    • recognize equations have a single valid input for a given output and inequalities have several possible inputs for a given output
    • articulate (p, r), (x, r), (q, r) as possible function relationships and understand why (p, q), (x, q), and (p, x) do not make sense as a function relationship (spiral back to Unit 1, Big Idea 1)
    • in the form px + q = r, describe how increasing or decreasing p, q, or r impacts x

Develop conceptual understanding:

expression, equation, inequality, variable, fixed quantity, coefficient, constant, rational, equality, equal, reasonable

Supporting terms to communicate:

function, function rule, initial value, rate of change, domain, range, dependent, independent, linear equation, greater than, greater than or equal to, less than, less than or equal to, at least, at most

Core Resource
A core resource supports multiple days of instruction.