1. 1 Understanding Mathematical Representations in the Media Mr. Emich 11/6/2008

2. 11/6/20082 Understanding Mathematical Representations in the Media Grade: 7 Grade: 7 Subject: Mathematics Subject: Mathematics Rationale: Rationale: Mathematical arguments are often made to support a position in the media. It is important as consumers of the media that we are able to look critically at the information presented and make informed decisions regarding its validity. In this project will we delve deeply into a real mathematical argument made in the media. Using math skills we have already developed we will analyze our findings for full understanding. We will look at the bias presented in the original argument and then use the same data to create a different argument. Mathematical arguments are often made to support a position in the media. It is important as consumers of the media that we are able to look critically at the information presented and make informed decisions regarding its validity. In this project will we delve deeply into a real mathematical argument made in the media. Using math skills we have already developed we will analyze our findings for full understanding. We will look at the bias presented in the original argument and then use the same data to create a different argument. Trivial Example: Trivial Example: Headline: “Phillies win the World Series in 5 Games” Headline: “Phillies win the World Series in 5 Games” Alternative Headline: “Tampa Bay Rays are the 2 nd best team in the world” Alternative Headline: “Tampa Bay Rays are the 2 nd best team in the world”

3. 11/6/20083 Understanding Mathematical Representations in the Media Objectives: Objectives: Understand that different mathematical representations of the same data and analysis can present a different message to the reader. Understand that different mathematical representations of the same data and analysis can present a different message to the reader. Understand that mathematical evidence needs to be critiqued in terms of its credibility and usefulness. Understand that mathematical evidence needs to be critiqued in terms of its credibility and usefulness. Understand the ways in which mathematics is used to represent bias in real world contexts. Understand the ways in which mathematics is used to represent bias in real world contexts.

4. 11/6/20084 Understanding Mathematical Representations in the Media Relevant NYS Learning Standards: Relevant NYS Learning Standards: Students will organize and consolidate their mathematical thinking through communication. Students will organize and consolidate their mathematical thinking through communication. Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others. Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others. Students will analyze and evaluate the mathematical thinking and strategies of others. Students will analyze and evaluate the mathematical thinking and strategies of others. Students will recognize and use connections among mathematical ideas. Students will recognize and use connections among mathematical ideas. Students will understand how mathematical ideas interconnect and build on one another to produce a coherent whole. Students will understand how mathematical ideas interconnect and build on one another to produce a coherent whole. Students will recognize and apply mathematics in contexts outside of mathematics. Students will recognize and apply mathematics in contexts outside of mathematics. Students will create and use representations to organize, record, and communicate mathematical ideas. Students will create and use representations to organize, record, and communicate mathematical ideas. Students will select, apply, and translate among mathematical representations to solve problems. Students will select, apply, and translate among mathematical representations to solve problems. Students will use representations to model and interpret physical, social, and mathematical phenomena. Students will use representations to model and interpret physical, social, and mathematical phenomena.

5. 11/6/20085 Understanding Mathematical Representations in the Media Materials: Materials: Poster board Poster board Color pens Color pens Copies of Word documents: Copies of Word documents: Ladder of Feedback Ladder of Feedback Final Presentation Rubric Final Presentation Rubric

6. 11/6/20086 Understanding Mathematical Representations in the Media Timing This project is a part of a portfolio of “Math Outside the Classroom” projects that students will work on throughout the year. This project is a part of a portfolio of “Math Outside the Classroom” projects that students will work on throughout the year.“Math Outside the Classroom” “Math Outside the Classroom” These projects extend the mathematical skills already obtained by the students into real world situations. These projects extend the mathematical skills already obtained by the students into real world situations. These projects typically run over the course of a week. These projects typically run over the course of a week. Students will be given the task of looking for mathematics in the media on a Monday. By the following Monday they need to have their media selection ready. Students will be given the task of looking for mathematics in the media on a Monday. By the following Monday they need to have their media selection ready. Groups will be formed on Monday. On Wednesday group peer review will occur. Groups will be formed on Monday. On Wednesday group peer review will occur. Class Presentations will take place on Friday. Class Presentations will take place on Friday.

7. 11/6/20087 Understanding Mathematical Representations in the Media Overall Project Procedures: Overall Project Procedures: Individually students will search the media for a mathematical argument, that they feel they can re-represent to support a different position. In class, students will team into groups of 3 and discuss the media items they discovered. As a group they will choose one item and develop a draft of a poster that shows the original argument and the new argument, using the same data. Pairs of groups will explain their posters to each other. The pairs of groups will give feedback to each other. Groups can incorporate feedback into their final poster. Finally groups will present their posters to the class. Individually students will search the media for a mathematical argument, that they feel they can re-represent to support a different position. In class, students will team into groups of 3 and discuss the media items they discovered. As a group they will choose one item and develop a draft of a poster that shows the original argument and the new argument, using the same data. Pairs of groups will explain their posters to each other. The pairs of groups will give feedback to each other. Groups can incorporate feedback into their final poster. Finally groups will present their posters to the class.

8. 11/6/20088 Lesson Procedures Day 1 Day 1 Introduction to Project Introduction to Project Work through example from: http://www.nytimes.com/2008/11/06/business/06pay.html?_r=1 &scp=1&sq=wall%20street%20bonus&st=cse&oref=slogin Work through example from: http://www.nytimes.com/2008/11/06/business/06pay.html?_r=1 &scp=1&sq=wall%20street%20bonus&st=cse&oref=slogin http://www.nytimes.com/2008/11/06/business/06pay.html?_r=1 &scp=1&sq=wall%20street%20bonus&st=cse&oref=slogin http://www.nytimes.com/2008/11/06/business/06pay.html?_r=1 &scp=1&sq=wall%20street%20bonus&st=cse&oref=slogin Headline “Wall Street Bonuses Plummet 70%” Headline “Wall Street Bonuses Plummet 70%” Work through details if bonus was $68.5 million, as reported in article (bonus is still over $20 million) Work through details if bonus was $68.5 million, as reported in article (bonus is still over $20 million) Introduce and review assessment rubric Introduce and review assessment rubric Questions from class Questions from class Form class into groups of three Form class into groups of three Groups meet to discuss their media findings Groups meet to discuss their media findings Groups need to select which media finding they will chose for their project by the end of the period Groups need to select which media finding they will chose for their project by the end of the period Exit slip: Write a brief description the strengths and weakness of your media selection. Exit slip: Write a brief description the strengths and weakness of your media selection.

9. 11/6/20089 Lesson Procedures Day 2 Day 2 Questions from class Questions from class Remind students that they will meet in pairs of groups tomorrow to peer assess posters Remind students that they will meet in pairs of groups tomorrow to peer assess posters Introduce and review Ladder of Feedback Introduce and review Ladder of Feedback Groups meet to work on developing their project Groups meet to work on developing their project Groups need to work out their mathematical argument by the end of the period Groups need to work out their mathematical argument by the end of the period Groups meet to work on developing a draft of their poster, keeping in mind the assessment rubric Groups meet to work on developing a draft of their poster, keeping in mind the assessment rubric Draft has to be ready for review tomorrow by the end of class Draft has to be ready for review tomorrow by the end of class

10. 11/6/200810 Lesson Procedures Day 3 Day 3 Questions from class Questions from class Pair up groups for peer assessment Pair up groups for peer assessment Remind students to use the Ladder of Feedback Remind students to use the Ladder of Feedback Pairs of groups meet to perform peer assessment, using the Ladder of Feedback Pairs of groups meet to perform peer assessment, using the Ladder of Feedback

11. 11/6/200811 Lesson Procedures Day 4 Day 4 Questions from class Questions from class Remind students tomorrow is presentation day Remind students tomorrow is presentation day Groups convene to produce final poster Groups convene to produce final poster Final poster must be completed by the end of the period Final poster must be completed by the end of the period

12. 11/6/200812 Lesson Procedures Day 5 Day 5 Questions from class Questions from class Groups present final posters to class Groups present final posters to class Students choose one project that is presented to assess using the rubric. Write up of assessment to be handed in at next class. Students choose one project that is presented to assess using the rubric. Write up of assessment to be handed in at next class.

13. 11/6/200813 Understanding Mathematical Representations in the Media Assessments: Assessments: Individually students will write a one to two page paper describing their media selection and their thoughts on the strengths and weaknesses of it for this assignment. Individually students will write a one to two page paper describing their media selection and their thoughts on the strengths and weaknesses of it for this assignment. After the groups make their math in the media selection each student will write a one to two page paper covering: After the groups make their math in the media selection each student will write a one to two page paper covering: What are the strengths of the argument you have to present? What are the strengths of the argument you have to present? What are the concerns you have about the argument you have to present? What are the concerns you have about the argument you have to present? These concerns must be discussed during the group work on the project. These concerns must be discussed during the group work on the project.

14. 11/6/200814 Understanding Mathematical Representations in the Media Assessments: Assessments: Students will be provided with “Ladder of Feedback” forms to be used during peer review. These forms are to be filled out and handed in. Students will be provided with “Ladder of Feedback” forms to be used during peer review. These forms are to be filled out and handed in. Before final presentations each student will be given copies of the rubric. Students will assess presentations and write up their assessment on one project to be handed. Before final presentations each student will be given copies of the rubric. Students will assess presentations and write up their assessment on one project to be handed. Final presentations will be evaluated by the teacher according to the rubric. Final presentations will be evaluated by the teacher according to the rubric.

15. 11/6/200815 Understanding Mathematical Representations in the Media Ladder of Feedback Form: Ladder of Feedback Form: Feedback For: 1. Clarify: Are there aspects that you don’t believe you have understood 2. Value: What do you see that you find to be particularly impressive, innovative, strong? 3. Offer Concerns: Do you detect some potential problems or challenges? Do you disagree with something? 4. Suggest: Do you have suggestions on how to address the concerns you identified during the last step?

16. 11/6/200816 Understanding Mathematical Representations in the Media Ladder of Feedback Form Explanation: 1. Clarify 1. Clarify Are there aspects that you don’t believe you have understood? Are there aspects that you don’t believe you have understood? Ensure that you're clear about what your colleague hopes to achieve by asking some questions or stating any assumptions you've made (i.e., “I wasn’t sure if you meant that …, but that’s what I assumed, so now you can understand where my feedback is coming from.”) Ensure that you're clear about what your colleague hopes to achieve by asking some questions or stating any assumptions you've made (i.e., “I wasn’t sure if you meant that …, but that’s what I assumed, so now you can understand where my feedback is coming from.”) 2. Value 2. Value What do you see that you find to be particularly impressive, innovative, strong? What do you see that you find to be particularly impressive, innovative, strong? Valuing builds a supportive culture of understanding and will help your colleague to identify strengths in their work that they might not have recognized otherwise Valuing builds a supportive culture of understanding and will help your colleague to identify strengths in their work that they might not have recognized otherwise Valuing reminds your colleague of the parts of his/her work that should be preserved when making improvements Valuing reminds your colleague of the parts of his/her work that should be preserved when making improvements Expressing your appreciation for others and their ideas is fundamental to the process of constructive feedback Expressing your appreciation for others and their ideas is fundamental to the process of constructive feedback Stressing the positive points of the work and offering honest compliments sets a supportive tone Stressing the positive points of the work and offering honest compliments sets a supportive tone 3. Offer Concerns 3. Offer Concerns Do you detect some potential problems or challenges? Do you disagree with something? Do you detect some potential problems or challenges? Do you disagree with something? Share your concerns, not as derisive accusations or abrasive criticisms, but as honest thoughts (i.e., "Have you considered..."; "What I wonder about is..."; "Perhaps you have thought about this, but...".) Share your concerns, not as derisive accusations or abrasive criticisms, but as honest thoughts (i.e., "Have you considered..."; "What I wonder about is..."; "Perhaps you have thought about this, but...".) 4. Suggest 4. Suggest Do you have suggestions on how to address the concerns you identified during the last step? Do you have suggestions on how to address the concerns you identified during the last step? Help your colleague make improvements by sharing your ideas on how he/she might revise their work (of course, there is no guarantee that your colleague will use the suggestions -- suggestions are not mandates, after all!) Help your colleague make improvements by sharing your ideas on how he/she might revise their work (of course, there is no guarantee that your colleague will use the suggestions -- suggestions are not mandates, after all!)

17. 11/6/200817 Understanding Mathematical Representations in the Media Final Presentation Rubric: Final Presentation Rubric: CATEGORY4321 Picked appropriate mathematical argument from media Picked an article which made a mathematically based argument. Can fully explain what position is being conveyed. Picked an appropriate article, but lacked some clarity about what position is being conveyed. Picked an appropriate article, but is unclear about what position is being conveyed. Did not pick an article with a mathematical argument. Understands mathematical concepts of original argument Able to articulate mathematical concepts used in argument Able to articulate data source of original argument Able to articulate mathematical concepts but is not totally clear on data source or vice versa. Partially able to articulate mathematical concepts used in argument Partially able to articulate data source of original argument Not able to articulate mathematical concepts used in argument Not able to articulate data source of original argument Made mathematical connections to reposition data into a different position. Able to create a convincing mathematical argument based on the same data as the original argument. Able to create a convincing mathematical argument but had to extend data. Used the same data, but mathematical argument while correct, did not support a different position. Not able to create a convincing mathematical argument based on the same data as the original argument.

18. 11/6/200818 Understanding Mathematical Representations in the Media Final Presentation Rubric (continued): Final Presentation Rubric (continued): CATEGORY4321 Group creates a poster that is accurate, clear and presents a convincing conclusion Explanation is detailed and clear. Grammar and spelling correct. Diagrams and/or sketches are clear and greatly add to the understanding. Explanation is clear. Minimal spelling and grammatical errors. Diagrams and/or sketches are clear and easy to understand. Explanation is a little difficult to understand, but includes critical components. Several spelling and grammatical errors. Diagrams and/or sketches are somewhat difficult to understand. Explanation is difficult to understand and is missing several components OR was not included. Many spelling and grammatical errors. Diagrams and/or sketches are difficult to understand or are not used. Mathematical Concepts Explanation shows complete understanding of the mathematical concepts used. Explanation shows substantial understanding of the mathematical concepts used. Explanation shows some understanding of the mathematical concepts. Explanation shows very limited understanding of the underlying concepts. Mathematical Reasoning Uses complex and refined mathematical reasoning. Uses effective mathematical reasoning Some evidence of mathematical reasoning. Little evidence of mathematical reasoning. Mathematical Errors 90-100% of the steps have no mathematical errors. Almost all (85-89%) of the steps have no mathematical errors. Most (75-84%) of the steps have no mathematical errors. More than 75% of the steps have mathematical errors.

19. 11/6/200819 Student Portfolio – Math Outside of the Classroom Statement of purpose: You will be developing a showcase portfolio over the course of this year. This portfolio will support your learning and demonstrate growth in the area of “Math Outside the Classroom.” The contents of this working portfolio will help you and your classmates answer the question: “When am I ever going to use this stuff?” There will be plenty of opportunity for you and your classmates to assess your portfolio work as we progress throughout the year. There will always be opportunity for you to modify and enhance your work, based on your feedback and feedback from your classmates. The contents of this portfolio will be used to develop a project at the end of the year that demonstrates what you learned and how your thinking changed regarding “Math Outside the Classroom”, throughout the year. The audience for your portfolio will be yourself, classmates, your teachers and your parents. Statement of purpose: You will be developing a showcase portfolio over the course of this year. This portfolio will support your learning and demonstrate growth in the area of “Math Outside the Classroom.” The contents of this working portfolio will help you and your classmates answer the question: “When am I ever going to use this stuff?” There will be plenty of opportunity for you and your classmates to assess your portfolio work as we progress throughout the year. There will always be opportunity for you to modify and enhance your work, based on your feedback and feedback from your classmates. The contents of this portfolio will be used to develop a project at the end of the year that demonstrates what you learned and how your thinking changed regarding “Math Outside the Classroom”, throughout the year. The audience for your portfolio will be yourself, classmates, your teachers and your parents. Go back to: Understanding Mathematical Representations in the Media Understanding Mathematical Representations in the MediaUnderstanding Mathematical Representations in the Media