**Lesson Plan**

Unit: Designing Our World Using

Algebraic Functions

Pre-Assessment Strategies

Pre-Test to determine mastery of:

Graphing the basic functions: constant, linear and quadratic

Transformations and translations of those basic functions

Domain and range of basic, transformed, and translated functions

Relative extrema of basic, transformed, and translated functions

Manipulation of functions on the TI-84 graphing calculator to affect zeros, domain, range and extrema

Piecewise defined functions

Essential Questions

1. How can algebraic functions be used to model roller coaster pathways?

2. What do domain and range represent in this scenario?

3. What domain and range values are reasonable in this scenario?

4. What do extreme values represent in this scenario?

5. What other real-world phenomena can be modeled by algebraic functions?

6. How do algebraic functions create limitations when used to model roller coaster pathways?

Content

Intermediate algebra

Functions: constant, linear, quadratic

Function features: zeros,domain, range, extrema

Function translations and transformations

Manipulation of functions using a graphing calculator

Piecewise defined functions

Technology for research and presentations

Gifted and Talented Goals and

Culminating Objectives

GOAL TWO: To develop understanding of concept, skills and issues which are fundamental to the disciplines as well as society and to develop an appreciation for interrelationships among the disciplines.

CULMINATING OBJECTIVE: A. Demonstrate comprehension of a discipline as a system of knowledge. C. Analyze a concept, theme, problem or issue within and across disciplines by using different perspectives of those disciplines.

GOAL FOUR: To develop the skills of critical and creative thinking, problem solving, and decision making at a level of complexity, abstractness and depth appropriate for gifted learners.

CULMINATING OBJECTIVE: A. Demonstrate effective use of critical and creative thinking skills. 1. Apply the cognitive processes of application, analysis, synthesis and evaluation. 3. Reason logically.

GOAL FIVE: To develop proficiency in communicating abstract and complex ideas, relationships, and issues.

CULMINATING OBJECTIVE: A. Synthesize knowledge and skills to communicate ideas, relationships and issues effectively through products and presentations.

**Mary Ann Brady**

EDU 592

Spring 2015

EDU 592

Spring 2015

Pre-Test: Functions Mastery I

Enduring Understanding: Algebraic functions are represented in our world in a variety of contexts. Exploring these relationships will connect algebra to real world phenomena.

Purpose: The purpose of this lesson is to connect the real world of roller coasters to the algebraic functions that can be used to model them.

Value for the Student: The student will recognize how algebraic functions can model real world phenomena.

Learning Environments

Grouping Arrangements

Differentiation for Gifted and Talented Students

Differentiaiton within Gifted and Talented

Instructional Phase

Set/Hook

Teacher Input

Student Activity

Technology Integration

Product or Presentation

Questions

Lesson Closure

Evaluation/Post Assessment

Standards

Objectives

Thinking and Inquiry Strategies

Ask for input from class members on their roller coaster experiences.

Ask class members to describe what they saw in the first 3 segments of the Fury 325 ride.

Show students the 2nd video and ask for class members to identify algebraic functions they observe.

Tell students to break into their discussion/project groups.

IA-1.1 Communicate knowledge of algebraic relationships using mathematical terminology appropriately.

IA-1.3 Apply algebraic methods to solve problems in real world contexts.

IA-1.4 Judge the reasonableness of solutions.

IA-1.5 Understand algebraic relationships using a variety of representations, including verbal, graphical, numerical and symbolic.

IA-1.6 Understand how algebraic relationships can be represented in concrete models, pictorial models, and diagrams.

IA-1.7 Understand how to represent algebraic relationships using tools such as hand-held computing devices.

IA-2.10 Carry out a procedure to determine the domain and range of discontinuous functions, including piecewise functions.

IA-4.2 Carry out a procedure to determine specified points (including zeros, maximums and minimums) of polynomial functions.

The student will use knowledge of algebraic functions to sketch a graph of the pathway of the Fury 325 roller coaster, using reasonable values for zeros, domain, range, and extrema.

The student will use a graphing calculator and manipulate algebraic functions to create a model of the Fury 325.

The student will collaborate with group members to create a roller coaster and represent the roller coaster using a variety of models: pictorial, graphical, symbolic, and numeric.

The student will make a presentation of the roller coaster, using appropriate terminology and technology.

Classroom with video capability.

Classroom with group dynamics for discussion and graphing calculator work.

Computer lab for design and research.

Computer lab for creating the presentation, using a presentation tool (i,e, Prezi, PowerPoint, Animoto and Vuvox).

Classroom with technology, for project presentations.

The class, as a whole, will view the videos of the Fury 325 and students will share thoughts and ideas with the class.

The class will be divided into homogeneous groups for discussion, sketching and graphing calculator work.

Each group will design a roller coaster and create a presentation of the group findings.

Each group will present a project, with all members demonstrating participation.

SMARTBoard technology

YouTube videos

Handout for graph sketching

Graphing calculators

Handout for calculator work

Project instruction handout

Computers with Internet access

Presentation tools

Materials List

The teacher will encourage class members to share thoughts and experiences of roller coaster rides.

Group discussions will help determine the best functions to represent the roller coaster pathway.

Calculator strategies will be discussed to construct an accurate, graphic model.

Teacher will act as a facilitator for group discussions and will answer questions and pose new questions, promoting deeper thinking.

Group members will carry out design and research, and select technology, based on the best outcome for the project.

Class members will be observers and questioners of the group presentations.

Teacher will pose questions after group presentations to assess understanding and to determine whether or not objectives are met.

Teacher will provide feedback and facilitate whole class discussions after presentations.

Students will use higher-degree functions (i.e. cubic and quartic) and non-functions (i.e. conic sections and parametric equations) to depict roller coaster pathways.

Students will focus on more complex roller coaster designs.

Students will use technology, other than graphing calculators (i.e. computer algebra systems), to create roller coaster pathways.

In addition to domain and range, students will add the parameter of time, when representing the roller coaster pathway.

Students will research the principles of physics inherent in roller coaster design and include their findings in the presentation.

Students will research and present other real world phenomena that can be modeled using algebraic functions.

Students will write a calculator program to determine specific graphic features, such as zeros and extrema.

Students will use technology to depict the graphic model of the roller coaster pathway in 3-dimensional, rather than 2-dimensional, format.

Students will build a 3-dimensional scale model of the group's roller coaster and present it to the class.

Lesson #3: Roller Coasters and the Paths They Take

FURY 325

at

CAROWINDS

Day 1

Students will watch the 2 videos of the Fury 325 roller coaster and respond to teacher questions and contribute to the whole class discussion.

Students will work with group members to discuss, plan, and sketch the first 3 sections of the ride.

Students will discuss, create, and manipulate constant, linear and quadratic functions in the graphing calculator to create a calculator model of the first 3 sections of the ride.

Day 2

Students will design a roller coaster, determine the piecewise defined function, and create multiple representations of the path.

Students will create a presentation of the design and the piecewise defined function using presentation tools.

Day 3 (one week after Day 1)

Students will present the final project to the class and answer questions from class members and the teacher, about the final project.

SMARTBoard technology for YouTube videos and project presentations

Graphing calculators for function manipulation

Graphing calculators for Gifted and Talented students to create programs

Computers, with Internet access, for design and research

Presentation tools and software, for projects

3-D computer software for Gifted and Talented students

Groups of students will use presentation software to create and present the results of their design and research.

If the design, research and presentation cannot be completed in one class period, group members must complete the assignment outside the classroom.

Presentations will begin 1 week after the viewing the YouTube videos, and will be in random order.

The presentation should be 3 - 5 minutes in length.

The question and answer session following the presentation will be monitored and managed by the teacher, for length and content.

All group members must participate in the presentation.

All group members must be able to accurately answer questions and provide feedback to class mates and to the teacher.

For whole class discussion after videos:

What functions do you recognize in the second video?

What features of the ride are we NOT considering in our scenario? Why?

For small group discussion:

What issues do you have creating your sketch, with respect to domain and range?

What algebraic manipulations did you find most helpful when working with the calculator?

What limitations do you find with your calculator?

For group presentations:

What functions would be impossible with regards to a roller coaster ride?

What functions would create a boring ride? a thrilling ride?

What other real world phenomena could be modeled by algebraic functions?

Consider the statement: Piecewise defined functions make better models for real world phenomena than single functions. Why?

Additional Explorations

http://www.learner.org/interactives/parkphysics/coaster/

http://faculty.sunydutchess.edu/reda/simulation.htm

http://www.nolimitscoaster.com/

http://www.funderstanding.com/educators/coaster/

Classmates will vote for the best design and the best presentation.

The teacher will address how other disciplines (with STEAM emphasis) relate to roller coaster design and ask for input from class members.

The teacher will share the following sites and encourage class members to explore the options.

Informal evaluation: observation and assessing answers to questions in group work.

Formal evaluation: Fury 325 graph and piecewise defined function, domain, range and scale.

Informal evaluation: Observation of group dynamics in computer lab.

Formal evaluation: Assessment of presentation and group participation using the rubric.

Ongoing evaluation: Depth of understanding judged by responses, and questions asked and answered.

Additional evaluation: products of exploration of coaster websites.