Big Idea:

Big Idea 1

Systems of Equations (or Inequalities) contain functions that share the same set of variables.

1 week

Evidence of Understanding

  • evaluate quantities in a system of equations or inequalities with a situation, table of values, or graph
    • describe how quantities from a situation, table or graph map to parts of the equations or inequalities in the system
    • analyze how variables of each function rule in the system are related
      • Example: Given a situation with nickels and dimes where n + d = 50 and .05n + .10d = 3.50. The first equation shows the number of dimes and nickels is 50 coins total. In the second equation, the total monetary value of the nickels and dimes is $3.50.  For the system the variables in both equations represent how many of each coin there is.  

 

  • solve a system of equations or inequalities using a graph or table of values
    • determine whether a given domain value corresponds to a range value that solves both equations or inequalities in the system
    • create and compare graphs and tables of values for each equation or inequality in the system
      • describe how the graph visually represents values that make each equation true
      • identify and justify the common set of solutions from the tables or graph
      • use a graphing calculator to determine or verify solutions from a table or graph
      • approximate and explain the intersection point(s) for linear-linear, linear-quadratic, linear-polynomial (degree > 2) linear-absolute value, and linear-exponential systems
    • compare the solution set for a system of equations and system of inequalities
      • distinguish when a system has one, none, many, or infinite solutions and use constraints from the given situation to justify reasoning
      • explain the meaning of each shaded portion of a system of inequalities
    • interpret domain and range pairs belonging to a system in the context of a situation

 

Develop conceptual understanding:

system, system of equations, system of inequalities

Supporting terms to communicate:

function, variable, domain, range, independent, dependent, input, output, coefficient, constant, initial value, rate of change

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