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Polynomial Functions Unit Plan

Polynomial Functions

Site: ARPDC
Course: ERLC Math 30-2, 2012-2014 - Candace Ketsa (Click to Enter)
Book: Polynomial Functions Unit Plan
Printed by: Guest user
Date: Sunday, 24 November 2024, 9:07 AM

Table of contents

Introduction to Polynomial Functions

General Outcome: Develop algebraic and graphical reasoning through the study of relations.

SO 7: Represent data, using polynomial functions (of degree ≤ 3), to solve problems. [C, CN, PS, V, T]

7.1.  Describe, orally and in written form, the characteristics of a polynomial function by analyzing its graph.
7.2.  Describe, orally and in written form, the characteristics of a polynomial function by analyzing its equation.
7.3.  Match equations in a given set to their corresponding graphs.
7.4.  Graph data, and determine the polynomial function that best approximates the data.
7.5.  Interpret the graph of a polynomial function that models a situation, and explain the reasoning.
7.6.  Solve, using technology, a contextual problem that involves data that is best represented by graphs of polynomial functions, and explain the reasoning.

Mathematical Processes

  • Communications [C]
  • Connections [CN]  Students are expected to make connections among mathematical ideas, other concepts in mathematics, everyday experiences and other disciplines
  • Problem Solving [PS]  Students are expected to develop and apply new mathematical knowledge through problem solving
  • Visualization [V]  Students are expected to develop visualization skills to assist in processing information, making connections and solving problems.
  • Technology [T] Students are expected to select and use technology as a tool for learning and for solving problems

Polynomials -- Real Life Applications

1. Click here to link to the website Everyday Use of Polynomials.

Connection:

1.  Organize students into groups of two. Have students search for data about sports, economics, science, or other topics of interest. Direct them to enter portions of the data on a graphing calculator to see if the data can be modeled in a reasonable way by a linear, quadratic, or cubic polynomial function. Students then record the equations for the models and sketch graphs of the data points and models. Have students classify their models by degree and number of terms.

Exploring the Graphs of Polynomial Functions

Achievement Indicators:

7.1.  Describe, orally and in written form, the characteristics of a polynomial function by analyzing its graph.

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Lesson Links: 

  • Click here for a Notebook version of ERLC Lesson Link.  Please use this lesson as a framework for your own teaching environment.
    • Click here for a pdf version of the same ERLC Lesson Link.

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Videos:

General video for this lesson (Youtube)


Discovery Based Learning Ideas:

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1.  MATHLab (Ketsa) -- Click here

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2.  Algebra 2: Exploring Polynomials: Factors, Roots, and Zeros (Nspired Math Classroom) -- Click here

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3.  Communication Idea: 

Have students associate the name of each polynomial with its degree. For example, a monomial relates to a monologue, or speech by one person; and a quartic relates to a quartet, or singing group with four people.

Advanced Learners:  Challenge students to explain why quad, meaning four, is the prefix in the word quadratic that describes a second-degree polynomial.

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4.  Technology Activity Graphs of Polynomial Functions (Ketsa) -- Click here for Word Document  and Click here for pdf copy of the activity

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5.  Polynomial Function Investigation -- Barry

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6. Building Connections -- Illumuniations 

This lesson focuses on having students make connections among different classes of polynomial functions by exploring the graphs of the functions. The questions in the activity sheets allow students to make connections between the x-intercepts of the graph of a polynomial and the polynomial's factors. This activity is designed for students who already have a strong understanding of linear functions, some knowledge of quadratic functions, and what is meant by a polynomial function.


Assessment For Learning

Characteristics of the Equations of Polynomial Functions

Achievement Indicators:

7.2.  Describe, orally and in written form, the characteristics of a polynomial function by analyzing its equation.
7.3.  Match equations in a given set to their corresponding graphs.


______________________________________________________________________

Lesson Links:

  • Click here for a Notebook version of ERLC Lesson Link.  Please use this lesson as a framework for your own teaching environment.
    • Click here for a pdf version of the same ERLC Lesson Link.

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Videos:

Characteristics of the Equations of Polynomial Functions -- (Youtube)


Discovery Based Learning Ideas:

Please feel free to share any ideas by emailing me at cketsa@gsacrd.ab.ca

Assessment For Learning

Games:

1.  Polynomial Match Up -- Barry

Open Ended Questions:

1. Write a third-degree polynomial function. Make a table of values and a graph. Find the x- and y-intercepts.

2.  Write a polynomial function with the following features: it has three distinct zeros; one of the zeros is 1; and it opens from lower right to upper left.

Communication:

1.  Explain how to describe the graph of a polynomial function.

2.  A cubic function of degree 3 can have three zeros.  Explain how to use this fact to graph the function.

3.  Explain why cubic functions are useful for interpolating between known data points.Why are they often not reliable for extrapolating data?


Modelling Data with a Line of Best Fit

Achievement Indicators:

7.4.  Graph data, and determine the polynomial function that best approximates the data.
7.5.  Interpret the graph of a polynomial function that models a situation, and explain the reasoning.
7.6.  Solve, using technology, a contextual problem that involves data that is best represented by graphs of polynomial functions, and explain the reasoning.


______________________________________________________________________

Lesson Links:

  • Click here for a Notebook version of ERLC Lesson Link.  Please use this lesson as a framework for your own teaching environment.
  • Click here for a pdf version of the same ERLC Lesson Link.

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Videos:

Modelling Data with a Line of Best Fit


Discovery Based Learning Ideas:


Assessment For Learning

Modelling Data with a Curve of Best Fit 

Achievement Indicators:

7.4.  Graph data, and determine the polynomial function that best approximates the data.
7.5.  Interpret the graph of a polynomial function that models a situation, and explain the reasoning.
7.6.  Solve, using technology, a contextual problem that involves data that is best represented by graphs of polynomial functions, and explain the reasoning.


______________________________________________________________________

Lesson Links:

  • Click here for a Notebook version of ERLC Lesson Link.  Please use this lesson as a framework for your own teaching environment.
    • Click here for a pdf version of the same ERLC Lesson Link.


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Videos:

Modelling Data with a Curve of Best Fit
Click here


Discovery Based Learning Ideas:

Assessment For Learning

Hands On Investigation:

1.  Drop Lab Lab -- Teacher Notes

Student Worksheet

2.  Holey Cub Lab -- Teacher Notes

Student Worksheet


Student Exemplars

Please feel free to share any student's work by emailing me at cketsa@gsacrd.ab.ca

Summative Assessments

Click here to assess the summative assessment area. You will need an enrolment key to access this portion of the site.  Please email cketsa@gsacrd.ab.ca for access.

Below is a list of what is available for the Unit.

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Assignments

1.  Unit Assignment with Answer Key -- Ketsa

2.  Assignment 1 Polynomials -- Williamson


Quizzes

1.  Chapter 5 Polynomial Quiz with Answer Key -- Williamson

2.  Quizzy 1 - Polynomials -- Andersen

Exams

1.  Unit Exam with Blueprint Answer Key -- Ketsa

2.  Polynomial Function Unit Test with Answer Key -- Crittenden