Big Idea:

Big Idea 3

The solution to a system of equations (or inequalities) can be represented in multiple, equivalent ways.

1 week

Evidence of Understanding

  • solve a system of equations or inequalities in 2 variables using any method
    • use at least two different methods to determine and confirm the solution set for the system and describe how each method conveys equivalent information
    • discuss advantages and disadvantages of different methods: strategically guessing and checking, graphing, analyzing tables of values, using substitution, etc.
      • identify conditions of a problem that make one solution method better than another and use it to solve the system
      • recognize that different approaches for solving a system can highlight different information about the situation that it models
      • Example: solving a system algebraically gives an exact solution and a graphic approach is limited to exact integer solutions, but graphs help estimate the solution to a system and it is difficult to predict a solution by looking at the equations or inequalities of a system
    • describe how each a table, graph, or algebraic approach convey equivalent information
      • Example: the intersection point of two equations on the graph match the coordinates in the table where an input has the same output for both equations in the system

 

  • construct a system of equations or inequalities and use it to solve problems
    • analyze the graph of a system and create the equations or inequalities that model it
      • use features of each inequality (shading, line type, etc.) to justify the rule that models it
    • express two linear functions in a system as an equation with a single variable on both sides
      • Example: create y = 2x + 3 and y = 5x - 1, and understand how to create 2x +3 = 5x - 1
    • create two equations or inequalities that model a situation and justify reasoning
      • distinguish when a system of equations or inequalities best models a situation

 

Develop conceptual understanding:

Supporting terms to communicate:

function, solution(s), solution set, simultaneous, intersection, equivalent, substitution, elimination, equation, inequality, system, variable, constant, coefficient, viable, integer, input, output, domain, range

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