Technology Infused Lesson Plan

PRESENTED BY: JESSIE GARABEDIAN

Technology Infused Lesson Plan

Conic Sections: Investigating the Circle, Ellipse, Hyperbola, and Parabola!

Grade Level: 10Subject Area: Math 2Topic Addressed: ConicsTools Used:

Geometer’s Sketchpad, Conic Flyer, Smartboard, TI-Smartview, TI-84 Plus

Web 2.0 Tools Used: ToonDoo, Make Beliefs Comix

Description of Project

Purpose: Provide students with a means to discover the rules

associated with the center and intercepts of conics Differentiate between circles, ellipses, hyperbolas,

and parabolas. Facilitate collaboration between students and the use

of technology Practice effective communication of mathematical

concepts


Task: Students will be asked to use Conic Flyer and Geometer’s

Sketchpad to manipulate the different conic sections: Circles Ellipses Hyperbolas Parabolas

Students will reveal the rules associated with defining the center and intercepts associated with each conic.

Students will practice using the rules given several examples.

Students will use TI-84 calculator applications to reinforce their learning from the previous day.

Students will express their understanding of each conic section through the creation of a comic strip.


Procedures:Day 1

Students will meet in the computer lab: Room 120 Students will pick up a worksheet that instructs them to

do the following: Go to the following website:

http://www.shodor.org/interactivate/activities/ConicFlyer/?version=1.5.0_10&browser=MSIE&vendor=Sun_Microsystems_Inc

* The website can also be found by using Google to search “conic flyer”. (It is the first result of the search)

Description of the Project

Procedure: (continued) Students will be required to manipulate each conic by

using the drop down menu on the website On their worksheets, students will work collaboratively

to: List the general formula for the conic at their

respective station. Answer all questions at the station involving the

conic they are manipulating. Create an example as a group for each conic: circle,

ellipse, hyperbola, parabola. Justify the validity of the conic by providing a

complete explanation of the solution for the given example.


Procedure (continued)Day 2

Teacher will set up TI-Smartview and Smartboard Teacher will guide students to conic applications on

the calculator Students will engage in a Think-Pair-Share to review

what they learned the previous day about the different conic sections

Teacher will facilitate a “Share-Out” of how the radius, center, and intercepts of a conic determine the format of the equation.


Procedure (continued)Day 2

Students will work with partners to create a comic strip that demonstrates their understanding of an assigned conic section.

Students will collaborate with other groups of partners to check for validity and understanding of the comic strips.

Teacher will post the comic strips around the room for students to comment on and learn from.


Resources: Conic Flyer: Interactive Activity Geometer’s Sketchpad Smartboard TI- Smartview TI-84 Plus Graphing Calculator ToonDoo Make Beliefs Comix


Evaluation: Rubric to Assess Objectives Evidence of Technology As a Means to Problem Solve

Student Ability to Answer Questions in Stations via the Discovery/Manipulation Format of Conic Flyer/Geometer’s Sketchpad

Student Operation of the TI-84+ APPS Program on Conic Sections

Student Creation and Critique of Comic Strips Related to Conic Sections

Evidence of All Levels of Learning Questions and Tasks Formatted to Support Bloom’s

Taxonomy Variety of Tasks/Activities Support Different Learning Styles

of Students

NYS Curriculum Standards

G.G.71 Write the equation of a circle, given its center and radius or given the endpoints of a diameter

G.G.72 Write the equation of a circle, given its graph

G.G.73 Find the center and radius of a circle, given the equation of the circle in center-radius form

G.G.74 Graph circles that are not centered at the origin


G.PS.2 Observe and explain patterns to formulate generalizations and conjectures

G.PS.3 Use multiple representations to represent and explain problem situations (e.g., spatial, geometric, verbal, numeric, algebraic, and graphical representations)

G.RP.4 Provide correct mathematical arguments in response to other students’ conjectures, reasoning, and arguments

G.RP.5 Present correct mathematical arguments in a variety of forms

G.RP.6 Evaluate written arguments for validityG.CM.4 Explain relationships among different

representations of a problem


A2.A.47 Determine the center-radius form for the equation of a circle in standard form

A2.A.48 Write the equation of a circle, given its center and a point on the circle

A2.A.49 Write the equation of a circle from its graph

*NYS is currently undergoing a transition from Math A/B to Sequential 1/2/3. These standards reflect the most recent Core Curriculum of March 2005. They will be updated when the transition is completed.

ISTE Technology Standards

Basic operations and concepts Students demonstrate a sound understanding of the nature

and operation of technology systems. Students are proficient in the use of technology.

Social, ethical, and human issues Students understand the societal issues related to technology. Students practice responsible use of technology systems,

information, and software. Students develop positive attitudes toward technology uses

that support lifelong learning, collaboration, personal pursuits, and productivity.

Technology productivity tools Students use technology tools to enhance learning, increase

productivity, and promote creativity. Students use productivity tools to collaborate in constructing

technology-enhanced models and producing other creative works.

ISTE Technology Standards

Technology communications tools Students use telecommunications to collaborate and interact

with peers, and other audiences. Students use a variety of media and formats to communicate

information and ideas effectively to multiple audiences. Technology research tools

Students use technology to locate, evaluate, and collect information from a variety of sources.

Students use technology tools to report results. Students evaluate and select new information resources based

on the appropriateness for specific tasks. Technology problem-solving and decision-making tools

Students use technology resources for solving problems and making informed decisions.

Students employ technology in the development of strategies for solving problems in the real world. (Inverse Variation)

Technology Used

Students: Geometer’s Sketchpad Conic Flyer Web 2.0: Comic Strip TI-84 Plus Graphing Calculator Smartboard ToonDoo Make Belief Comix

Teacher: Conic Flyer TI- Smartview Smartboard

Teacher Preparation

Ensure that the computer lab has GSP 4.0 installed and computers are Java compatible

Create Stations Worksheets and Questions * I suggest laminating the stations on cardstock to allow for

reuse of the stations each year*

Set up Smartboard to demonstrate interactively what is expected of students at each station

Connect Smartboard to TI-Smartview to illustrate to students where the APPS they will be using are located

Investigate ToonDoo and Make Belief Comix and create an example for students to reference

Timeline of Activities

Day 1: Teacher Demonstration of Conic Flyer and Overview of

Expectations: 5 Minutes Conic Flyer Stations Activity: 35 Minutes

Day 2: TI-Smartview Demonstration of APPS for Conics using

the Smartboard: 5 Minutes Applications Activity: 5 Minutes Teacher Overview of Comic Strip Expectations: 5

Minutes Comic Strip Creation: 15-2o Minutes Share-Out of Several Comic Strips: 5 Minutes Teacher Posting of Comic Strips: 5 Minutes

Learning Activities That Will Occur

Cooperative Group Work: Stations Activity: Day 1

Think-Pair-Share: TI-84 Applications: Day 2Group Creation of Comic Strips: Day 2“Share-out” of Comic Strips: Day 2Group Evaluation of Comic Strips: Day 2

Students will work in pairs/groups of three to critique the comic strips for correctness, creativity, and effectiveness.

Higher Order Thinking Skills Addressed

Analysis Can you make a distinction between each of the

conics you learned about today? How can you list and distinguish between each of the

parts of a conic section? How would you categorize conics based on their given

equations and/or graphs? What is the function of the x and y intercepts? What ideas justify the reason a hyperbola does not

intercept the x and y axes?


Synthesis Can you formulate a theorem on how the equation of a

given conic is determined? How would you modify the equation of a circle to

change the location of the center? Can you propose an alternative format for writing the

equation of an ellipse? What facts can you compile about the equation of an

inverse variation hyperbola? How would you test a conic for x and y intercepts?


Evaluation: How would you assess the impact of changing the

radius of a circle on the equation for that circle? What judgment could you make about a circle not

centered at the origin? How would you compare the equations of circles to

those of ellipses, hyperbolas, and parabolas? Differentiate between vertical and horizontal

parabolas. How can you assess the value of the x and y intercepts

of an ellipse?

Technology: Promotion of Student Learning

Increases Motivation Students are motivated to learn as all activities are

interactive and completed cooperatively in groups.

Promotes Classroom Management Students who are interested in their learning are far

more likely to maintain on-task behavior.

Discovery Learning Students are not listening to lecture. Rather, students

are discovering and making meaning of their learning through several interactive activities. These activities utilize technology that students are familiar with and have become accustomed to using.