My idea is to teach the math behind permutations through an investigation of the PA Lottery. Students will find the chance of winning many lottery games. First, by writing all the possible winning numbers then formulating an equation or process to find the number of possibilities with out writing them all out. Students will then find the chance of winning other games like box numbers or Mega Millions. Their presentations will vary depending on interest. Groups might use PowerPoint, Prezi, Keynote, Glogster, or Vuvox. A rubric will explicate key learning outcomes. I expect this project to last one week. Students will work on it three times in class and outside of class. The following one of two days will be presentation days. Framework 4. Q: Using one core concept, what real life contexts and other subjects can be incorporated? A: Permutations 5. Q: Incorporate Bloom’s Taxonomy to push past rote learning. A: Illustrate the number of outcomes possible. Justify the permutation method used. Invent a new lottery game. 6. Q: Authentic interactions and 21st century skills A: Collaboration within team. Use the internet to locate information on how lottery works. Watch the PA Lottery. Create a presentation with PowerPoint, Prezi, Keynote, Glogster, or Vuvox. Play classmates new lottery games. 7. Q: Students’ interests? A: Lottery is on nightly. Can win big bucks. 8. Q: Learning dispositions A: Curiosity, cooperation, persistence, motivation, self directedness, ambition NCTM Standards 1. Numbers and Operations Understand numbers, ways of representing numbers, relationships among numbers, and number systems develop a deeper understanding of very large and very small numbers and of various representations of them; Understand meanings of operations and how they relate to one another judge the effects of such operations as multiplication, division, and computing powers and roots on the magnitudes of quantities; develop an understanding of permutations and combinations as counting techniques Compute fluently and make reasonable estimatesdevelop fluency in operations with real numbers, vectors, and matrices, using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases. judge the reasonableness of numerical computations and their results. 2. Algebra Use mathematical models to represent and understand quantitative relationships draw reasonable conclusions about a situation being modeled 3. Problem Solving Instructional programs from prekindergarten through grade 12should 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

4. 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

5. 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.

6. 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

7. 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.

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 UnderstandingStudents will determine the number of possible winning numbers for multiple lottery games. Students will explain how to find the total number of possibilities and why it works. Students will invent a new lottery game that their class mates can play.

## Project Sketch #6 PA Lottery

11th grade Algebra 2 class

My idea is to teach the math behind permutations through an investigation of the PA Lottery. Students will find the chance of winning many lottery games. First, by writing all the possible winning numbers then formulating an equation or process to find the number of possibilities with out writing them all out. Students will then find the chance of winning other games like box numbers or Mega Millions.

Their presentations will vary depending on interest. Groups might use PowerPoint, Prezi, Keynote, Glogster, or Vuvox. A rubric will explicate key learning outcomes. I expect this project to last one week. Students will work on it three times in class and outside of class. The following one of two days will be presentation days.

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

A: Permutations

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

A: Illustrate the number of outcomes possible. Justify the permutation method used. Invent a new lottery game.

6. Q: Authentic interactions and 21st century skills

A: Collaboration within team. Use the internet to locate information on how lottery works. Watch the PA Lottery. Create a presentation with PowerPoint, Prezi, Keynote, Glogster, or Vuvox. Play classmates new lottery games.

7. Q: Students’ interests?

A: Lottery is on nightly. Can win big bucks.

8. Q: Learning dispositions

A: Curiosity, cooperation, persistence, motivation, self directedness, ambition

NCTM Standards1. Numbers and OperationsUnderstand numbers, ways of representing numbers, relationships among numbers, and number systemsdevelop a deeper understanding of very large and very small numbers and of various representations of them;

Understand meanings of operations and how they relate to one anotherjudge the effects of such operations as multiplication, division, and computing powers and roots on the magnitudes of quantities;

develop an understanding of permutations and combinations as counting techniques

Compute fluently and make reasonable estimatesdevelop fluency in operations with real numbers, vectors, and matrices, using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases.judge the reasonableness of numerical computations and their results.

2. AlgebraUse mathematical models to represent and understand quantitative relationshipsdraw reasonable conclusions about a situation being modeled

3. Problem SolvingInstructional programs from prekindergarten through grade 12should enable all students to—4. Reasoning and Proof5. Communication6. Connections7. Representationiste National Education Technology Standards for Students (NETS-S)1Creativity and Innovation2Communication and Collaboration3Research and Information Fluency4Critical Thinking, Problem Solving, and Decision Making5Digital Citizenship6Technology Operations and ConceptsEvidence of UnderstandingStudents will determine the number of possible winning numbers for multiple lottery games. Students will explain how to find the total number of possibilities and why it works. Students will invent a new lottery game that their class mates can play.Project Theme or ChallengePA LotteryIntroduction to ProjectMash-up Lottery video.