After a few basic lessons about quadratic functions and parabolas, the Angry Birds PBL will be introduced. My idea is to have students further investigate the properties of parabolas through the use of graphing technology in correspondence with the flight of an angry bird. My students will watch a video of a bird in flight that will freeze when it reaches maximum height. From there they will use Geogebra to match the flight path of the bird. Along the way, students will examine the potential path of the bird,
investigate the changing coefficients in the quadratic equation as they fit a curve to the bird’s path, and theorize how they can better predict if they will make a hit. Once a team has determined if the original bird on the video will hit the pig or not they will present their predictions and further findings through the use of a presentation tools. The presentation products may vary from group to group, but a rubric will clearly define key learning outcomes and guide their work. I expect this project to last one week, two in class work days, two days and nights out of class, and the third and fourth day will be presentation days.

Framework
4. Q: Using one core concept, what real life contexts and other subjects can be incorporated?
A: Parabolas, used in games

5. Q: Incorporate Bloom’s Taxonomy to push past rote learning.
A: Examine the potential path of the bird. Investigate the changing coefficients in the quadratic equation as you fit a curve to the bird’s path. Theorize how you can better predict if you will make a hit.

6. Q: Authentic interactions and 21st century skills
A: Students will play Angry Birds. Use graphing technology to match the parabolic path of the bird and find the equation for the path. Collaborate with team members to analyze changing coefficients, curve, and end point.

7. Q: Students’ interests?
A: Angry Birds is a game most students have played or at least heard of. The game shows how math (parabolas) are used in even simple games like Angry Birds. Learning about the arch of a projectile can help students become better at other games where something is shot or thrown.

NCTM Standards and Expectations 1. Number and Operations Standards Understand numbers, ways of representing numbers, relationships among numbers, and number systems

compare and contrast the properties of numbers and number systems, including the rational and real numbers, and understand complex numbers as solutions to quadratic equations that do not have real solutions;

Compute fluently and make reasonable estimates

judge the reasonableness of numerical computations and their results.

2. Algebra Standards Understand patterns, relations, and functions

interpret representations of functions of two variables

Use mathematical models to represent and understand quantitative relationships

identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships;

draw reasonable conclusions about a situation being modeled.

3. Geometry Standards Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them;

establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others;

Specify locations and describe spatial relationships using coordinate geometry and other representational systems

use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze geometric situations;

investigate conjectures and solve problems involving two- and three-dimensional objects represented with Cartesian coordinates.

4. Process Standards Problem Solving Instructional programs from prekindergarten through grade 12

should enable all students to—

Build new mathematical knowledge through problem solving

Solve problems that arise in mathematics and in other contexts

Apply and adapt a variety of appropriate strategies to solve problems

Monitor and reflect on the process of mathematical problem solving

Reasoning and Proof

Recognize reasoning and proof as fundamental aspects of mathematics

Make and investigate mathematical conjectures

Develop and evaluate mathematical arguments and proofs

Select and use various types of reasoning and methods of proof

Communication

Organize and consolidate their mathematical thinking through communication

Communicate their mathematical thinking coherently and clearly to peers, teachers, and others

Analyze and evaluate the mathematical thinking and strategies of others;

Use the language of mathematics to express mathematical ideas precisely.

Connections

Recognize and use connections among mathematical ideas

Understand how mathematical ideas interconnect and build on one another to produce a coherent whole

Recognize and apply mathematics in contexts outside of mathematics

Representation

Create and use representations to organize, record, and communicate mathematical ideas

Select, apply, and translate among mathematical representations to solve problems

Use representations to model and interpret physical, social, and mathematical phenomena

iste National Education Technology Standards for Students (NETS-S)

1

Creativity and Innovation

Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology. Students:

a. apply existing knowledge to generate new ideas, products, or processes. b. create original works as a means of personal or group expression. c. use models and simulations to explore complex systems and issues. d. identify trends and forecast possibilities.

2

Communication and Collaboration

Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others. Students:

a. interact, collaborate, and publish with peers, experts, or others employing a variety of digital environments and media. b. communicate information and ideas effectively to multiple audiences using a variety of media and formats. d.contribute to project teams to produce original works or solve problems.

3

Research and Information Fluency

Students apply digital tools to gather, evaluate, and use information. Students:

a. plan strategies to guide inquiry. b. locate, organize, analyze, evaluate, synthesize, and ethically use information from a variety of sources and media. c. evaluate and select information sources and digital tools based on the appropriateness to specific tasks. d. process data and report results.

4

Critical Thinking, Problem Solving, and Decision Making

Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources. Students:

a. identify and define authentic problems and significant questions for investigation. b. plan and manage activities to develop a solution or complete a project. c. collect and analyze data to identify solutions and/or make informed decisions. d. use multiple processes and diverse perspectives to explore alternative solutions.

5

Digital Citizenship

Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior. Students:

a. advocate and practice safe, legal, and responsible use of information and technology. b. exhibit a positive attitude toward using technology that supports collaboration, learning, and productivity. c. demonstrate personal responsibility for lifelong learning. d. exhibit leadership for digital citizenship.

6

Technology Operations and Concepts

Students demonstrate a sound understanding of technology concepts, systems, and operations. Students:

a. understand and use technology systems. b. select and use applications effectively and productively. c. troubleshoot systems and applications. d. transfer current knowledge to learning of new technologies.

Evidence of Understanding
Students will fit a parabola to the path of the inflight bird using a computer graphing tool.
Students will determine if the in flight bird will in fact hit a pig.
Students will find the equation of the bird in flight.
Students will predict future shots.

Project Theme or Challenge
Angry Birds

Introduction to Project
Students will watch a video where a bird is shot at a pig. The video will freeze when the bird reaches its maximum height.

11th grade Algebra 2 class

After a few basic lessons about quadratic functions and parabolas, the Angry Birds PBL will be introduced. My idea is to have students further investigate the properties of parabolas through the use of graphing technology in correspondence with the flight of an angry bird. My students will watch a video of a bird in flight that will freeze when it reaches maximum height. From there they will use Geogebra to match the flight path of the bird. Along the way, students will examine the potential path of the bird,

investigate the changing coefficients in the quadratic equation as they fit a curve to the bird’s path, and theorize how they can better predict if they will make a hit. Once a team has determined if the original bird on the video will hit the pig or not they will present their predictions and further findings through the use of a presentation tools. The presentation products may vary from group to group, but a rubric will clearly define key learning outcomes and guide their work. I expect this project to last one week, two in class work days, two days and nights out of class, and the third and fourth day will be presentation days.

Framework4. Q: Using one core concept, what real life contexts and other subjects can be incorporated?

A: Parabolas, used in games

5. Q: Incorporate Bloom’s Taxonomy to push past rote learning.

A:

Examinethe potential path of the bird.Investigatethe changing coefficients in the quadratic equation as you fit a curve to the bird’s path.Theorizehow you can better predict if you will make a hit.6. Q: Authentic interactions and 21st century skills

A: Students will play Angry Birds. Use graphing technology to match the parabolic path of the bird and find the equation for the path. Collaborate with team members to analyze changing coefficients, curve, and end point.

7. Q: Students’ interests?

A: Angry Birds is a game most students have played or at least heard of. The game shows how math (parabolas) are used in even simple games like Angry Birds. Learning about the arch of a projectile can help students become better at other games where something is shot or thrown.

8. Q: Learning dispositions

A: motivation, curiosity, cooperation, confidence

NCTM Standards and Expectations1. Number and Operations StandardsUnderstand numbers, ways of representing numbers, relationships among numbers, and number systemsCompute fluently and make reasonable estimates2. Algebra StandardsUnderstand patterns, relations, and functionsUse mathematical models to represent and understand quantitative relationships3. Geometry StandardsAnalyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationshipsSpecify locations and describe spatial relationships using coordinate geometry and other representational systems4. Process StandardsProblem SolvingInstructional programs from prekindergarten through grade 12should enable all students to—Reasoning and ProofCommunicationConnectionsRepresentationiste National Education Technology Standards for Students (NETS-S)1Creativity and Innovationb. create original works as a means of personal or group expression.

c. use models and simulations to explore complex systems and issues.

d. identify trends and forecast possibilities.

2Communication and Collaborationb. communicate information and ideas effectively to multiple audiences using a variety of media and formats.

d.contribute to project teams to produce original works or solve problems.

3Research and Information Fluencyb. locate, organize, analyze, evaluate, synthesize, and ethically use information from a variety of sources and media.

c. evaluate and select information sources and digital tools based on the appropriateness to specific tasks.

d. process data and report results.

4Critical Thinking, Problem Solving, and Decision Makingb. plan and manage activities to develop a solution or complete a project.

c. collect and analyze data to identify solutions and/or make informed decisions.

d. use multiple processes and diverse perspectives to explore alternative solutions.

5Digital Citizenshipb. exhibit a positive attitude toward using technology that supports collaboration, learning, and productivity.

c. demonstrate personal responsibility for lifelong learning.

d. exhibit leadership for digital citizenship.

6Technology Operations and Conceptsb. select and use applications effectively and productively.

c. troubleshoot systems and applications.

d. transfer current knowledge to learning of new technologies.

Evidence of UnderstandingStudents will fit a parabola to the path of the inflight bird using a computer graphing tool.

Students will determine if the in flight bird will in fact hit a pig.

Students will find the equation of the bird in flight.

Students will predict future shots.

Project Theme or ChallengeAngry Birds

Introduction to ProjectStudents will watch a video where a bird is shot at a pig. The video will freeze when the bird reaches its maximum height.

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