Big Idea:

Big Idea 4

Mathematical models illustrate the behavior of real-world situations.

1 week

Evidence of Understanding

  • solve polynomial functions in the context of a situation
    • build equations that model the relationship between two variables in a function
    • connect equivalent mathematical representations (an equation to a situation, etc.) and justify the connection
    • use multiple mathematical representations (equation, table, graph) to uncover solutions to a problem or answer questions for a given situation
  • solve systems with two or three variables in the context of a situation
    • algebraically solve systems containing a linear equation and either a polynomial equation or the equation of a circle
      • possible extension: solve a system containing a quadratic and the equation of a circle
    • graphically solve systems containing any two function types with the use of technology
    • solve 3x3 systems algebraically
    • build and combine functions by using the arithmetic operations of addition, subtraction, and multiplication
    • identify values in the solution set and describe solution(s) in the context of a situation  
  • apply geometric ideas to create and solve polynomial equations
    • recognize and apply polynomial identities describing numerical relationships
      • connect Pythagorean Triples to (x2 + y2)2 = (x2 - y2)2 + (2xy)2   
    • derive the equation of a parabola, the focus, or the directrix using information
    • derive the formula for the sum of a finite geometric series and use it to solve problems

Develop conceptual understanding:

polynomial identity, Pythagorean Triple, focus, directrix, geometric series

Supporting terms to communicate:

polynomial, linear, quadratic, cubic, zeros, roots, simultaneous solution, vertex, maximum/minimum point
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.