11 Components
Big Ideas
Formative Assessment Lesson
End of Unit Assessments
Browse Components
Big Ideas
Formative Assessment Lesson
End of Unit Assessments
Big Idea:

### 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.

• Solving Equations
This Core Resource supports students in developing fluency in manipulating algebraic structures to solve equations.
Resource:
Solving Equations

This Core Resource supports students in developing fluency in manipulating algebraic structures to solve equations.

All Resources From:
• Unit 4

#### Rational and Polynomial Functions

Instructional Routine: Connecting Representations

These tasks are embedded within the instructional routine called Connecting Representations.

• Deriving a Parabola
Chunk a diagram, change the form of the diagram to add a right triangle, connect to what students know about the Pythagorean theorem to connect to derivations of the equation of a parabola.
Resource:
Deriving a Parabola

Chunk a diagram, change the form of the diagram to add a right triangle, connect to what students know about the Pythagorean theorem to connect to derivations of the equation of a parabola.

All Resources From:
• Unit 4