Assignment Three

ED637

Assignment Three

Project: Fair or Unfair

The Lesson Plan for this project can be found in my Week 12 Blog entry.

Students filled in a KWL chart listing things that they knew about:

·      theoretical probability

·      experimental probability

·      fair vs unfair

Students also did an activity at the end that showed what they learned about experimental and theoretical probabilities when applied to a situation.

And in addition to what they learned, had to create a blog or a glog

to communicate their results.  Student blogs and a glog can be found at the following sites.

http://probabilitygame.blogspot.com/

http://www.glogster.com/cuuyuk13/fair-or-unfair-by-student/g-6kq0rd0ql6ng2mpc2om2ga0

http://clayton32.blogspot.com/

Students in my class were first shown the blogs and glogs that I created to get an idea of the expected technological product for this project.  They chose which one their group would create.  We then went over the expectations and the rubric that I previously created.  Each group then filled in the what I know and want to learn columns in their KWL charts.  We then played the game described in the lesson plan and the groups made predictions about who would win each round.  They noticed that the person assigned to C, or the one who gets a head and a tail, won more than the others. I explained to the class that what they need to do is to step back and look at the big picture – so we listed all the possible outcomes.  We listed the four possible outcomes HH, TT, HT, and TH.  We went over the difference between experimental probability and theoretical probability.  From there, they had a good picture of why player C has an unfair advantage.  This reinforces how hands on activities play a big part in teaching mathematics.  I don’t think the teaching this concept would have gone as well if I gave them data to interpret.  I had fun with this activity and so did the class.  It was great to see them having fun and then focus their learning so that it was relevant to them at the time.  We figured the probability percentages for both the experimental and theoretical.  We had a good discussion about how the experimental probability will get closer and closer to the experimental probability if the experiment is done lots and lots of times.

As I reflect, I realize how many problems can arise with this sort of project as far as technology is concerned.  Students had fun creating blogs and glogs, but were frustrated with the Internet speed.  I did have the students fill out Permission to Publish forms that are available for LYSD, but was not sure if this was enough for the UAS course.  However, their work is now published online.  The permission slips allow documents and projects to be published on the World Wide Web and can include students’ first name, last name, photograph, and e-mail address.  Pictures that were taken and published were ones that students took of their own work and pictures I took of them working.  The glog required more work since it was not easy to learn how to use the tools for the students and for me, when I was first making a glog.  Another noticeable problem came with the writing to communicate results.  Students seemed to need more guidance than me just asking for them to compare the experimental and theoretical results.  Students were happy with their results and wanted to show their work to the Language Arts teacher so other standards could be marked off.

Week 12 Lesson Plan and Assessments

Lesson Plan: Fair or Unfair?

Date April 22-26, 2013

Grade Level:  10th (Students in Levels 6-9)

Number of Students: 11

Topic: Introduction to theoretical probability.

Standards:

new AK Math standard

Use probability to evaluate outcomes of decisions.

S‐MD.6. (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

LYSD Standard: The student demonstrates a conceptual understanding of probability and counting techniques by

M6.4.5 determining or comparing the experimental and/or theoretical probability of independent or dependent events

Technology Standard

Nets-C

2.g. Coach teachers in and model effective use of technology tools and resources to continuously assess student learning and technology literacy by applying a rich variety of formative and summative assessments aligned with content and student technology standards

Duration:  50 min classes for one week

Goals/Objectives:

Students will play a game to be able to determine that a game that seems fair is actually unfair after analyzing the game in a logical manner and find out why things happened as they did.  Students will also create either a glog, a blog, or a powerpoint presentation to communicate results and their conclusions.

Materials: pencil, index cards to keep score, 2 coins per group, and access to computers

Procedure:

• Explain to the group that they are going to play a game dealing with probability.
• Group the students into groups of three.
• Each group gets 3 index cards to keep score on.  Randomly assign players A,B, and C.
• The groups each get two coins to toss and are assigned points according to the following rules.
• Player A gets 1 point if the coin toss results in two heads, player B gets 1 point if the toss results in two tails, and player C gets 1 point if the coin toss results are mixed (one head and one tail).
• The game is over after 20 tosses.  The player who has the most points wins.
• The students play the game 3 times.  After each game they discuss whether they think the game is fair or unfair and make predictions about who will win the next game.
• As a class, have a discussion about the fairness of the game.  Challenge the students to make an argument not based on the data as whether the game is fair or unfair and why.
• Students will also create: a glog, a blog, or a powerpoint presentation to communicate results and their conclusions.

Assessment:

Pre-Assessment

KWL Chart

Topic: Experimental and Theoretical Probability	Topic: Fairness vs. Unfairness using probability
What I Know	What I Want to Know	What I Learned

Post-Assessment

Will take the form of filling in the What I Learned section of the KWL chart, and the Rubric for this lesson that is available in Week 10 blog posting, and final technology project.

Week 11 Technology and Management Considerations

Essential Question: What technology will I use to allow students to demonstrate they have met the standards targeted by my rubric? What are the classroom management considerations that I must address?

Technology for my project

Students in my class will play a game to be able to determine that a game that seems fair is actually unfair.  When they have determined the results and come to a conclusion, they will report their findings by creating: a glog using glogster, a group wiki, group blog, a recording using garageband to create a voice thread, a powerpoint presentation or any acceptable technology tool that they may already know.

I have 11 desktop iMacs in my classroom that are currently being reimaged and will have the latest OS on them.  Students can use their phones or cameras to take pictures if necessary.  Students can use any of the Microsoft Office applications for tables and graphs and written paragraphs.

My Rubric can be viewed through a link from my week 10 blog.  Students will know what is expected of them because they will have a copy of the rubric.  I will also do informal observations throughout the project.

Management

The group that will be working on this project is a group of eleven 10^th graders that range in ability levels.  This group is small enough that there are no major issues with classroom management or behavior problems.  It will also help with managing the project because we are able to communicate well.  Another management consideration will be time, since we only meet for one 50-minute period a day.  I will need to allocate enough time to work on both the hands on and the technology component.  More than likely, we may still be experiencing Internet connectivity problems, so I need to be ready to address this if the need arises.  I think I will resort to a PowerPoint if it comes down to this.

Week 10 Differentiate Through Student Product in my Classroom

Essential Question: How can I differentiate through student product in my classroom?

new AK Math standard

Use probability to evaluate outcomes of decisions.

S‐MD.6. (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

LYSD Standard: The student demonstrates a conceptual understanding of probability and counting techniques by

M6.4.5 determining or comparing the experimental and/or theoretical probability of independent or dependent events

Technology Standard

Nets-C

2.g. Coach teachers in and model effective use of technology tools and resources to continuously assess student learning and technology literacy by applying a rich variety of formative and summative assessments aligned with content and student technology standards

I will not do an in depth project with my students due to recent school wide computer problems and time constraints with the cultural week we are soon having.

Students will play a game to be able to determine that a game that seems fair is actually unfair after analyzing the game in a logical manner and find out why things happened as they did.  Students will also create either a glog, a blog, or a powerpoint presentation to communicate results and their conclusions.

Procedure:

• Explain to the group that they are going to play a game dealing with probability.
• Group the students into groups of three.
• Each group gets 3 index cards to keep score on.  Randomly assign players A,B, and C.
• The groups each get two coins to toss and are assigned points according to the following rules.
• Player A gets 1 point if the coin toss results in two heads, player B gets 1 point if the toss results in two tails, and player C gets 1 point if the coin toss results are mixed (one head and one tail).
• The game is over after 20 tosses.  The player who has the most points wins.
• The students play the game 3 times.  After each game they discuss whether they think the game is fair or unfair and make predictions about who will win the next game.
• As a class, have a discussion about the fairness of the game.  Challenge the students to make an argument not based on the data as whether the game is fair or unfair and why.

Unpacking the Standards

·      Make decisions based on expected values

·      Use expected values to compare long term benefits of several situations

·      Justify fairness/unfairness of the situation

·      Determine or compare the experimental and/or theoretical probability

·      Determine the probability of the outcomes

·      Determine how many options exist using counting techniques

·      Discuss the conclusions

·      Communicate the outcome in an age appropriate way

·      Create a product using technology to share outcome.

Students will be assessed based on the following rubric.

Rubric for Probability Experiment and Conclusions using a Technological Tool

Name:___________________________            Date:______________________________            Molly Hale’s Class

Category	High	Moderate	Developing	Needs Improvement
Probability Experiment	Experiment problem clearly stated.  Chart is set up with labels; data for 3 different sets of 20 tosses is neatly presented on a spreadsheet.  Calculations for theoretical probability and experimental probability are neat and correct.  A short paragraph reflecting results is accurate and typed.	Experiment problem clearly stated.  Chart is set up with labels; data for 3 different sets of 20 tosses presented on a spreadsheet or graph paper.  Calculations for theoretical probability and experimental probability are correct.  A short paragraph reflecting on the results is accurate.	Experiment problem stated but not clear.  Chart is set up with labels; data for 3 different sets of 20 tosses is presented on graph paper or on plain white paper. Calculations for theoretical probability or experimental probability contain a few errors.  A short paragraph reflecting on results contain a few errors.	Experiment problem not stated.  Chart is set up with no labels; data for 2 or fewer different sets of 20 tosses is presented on plain white paper.  Calculations for theoretical probability and experimental probability contain several errors.  No reflection paragraph on the results is given.
Communication	The student can represent work in a clear, organized manner.  Summary: the student uses appropriate mathematical language and symbols to explain how calculations were made and advised the class on the fairness or unfairness of the game.  Representations: the student has created an efficient system of tables or graphs to track the calculations for all the possible outcomes of the event, the results of the experimental probability experiment, and the results of the theoretical probability. Extension: the student includes a written rule, equation, generalization, and observation about their mathematical insights about their understanding of probability.	The student can represent work in a clear, organized manner.  Summary: the student uses appropriate mathematical language and symbols to explain how calculations were made and advised the class on the fairness or unfairness of the game.  Representations: the student has created an efficient system of tables or graphs to track the calculations for all the possible outcomes of the event, the results of the experimental probability experiment, and the results of the theoretical probability.	The student has communicated understanding of the task by labeling their work, but the task is not clearly organized and the student’s thinking is hard to follow. Summary: the student states final answer; and uses some mathematical knowledge and symbols to explain calculations and advised on the fairness or unfairness of the game.  Representations: the student has not established an accurate system of tables or graphs to track the calculations for all the possible outcomes of the event, the results of the experimental probability, and/or the results of the theoretical probability.	There is little or no communication, the student did not label the work, and/or their thinking is difficult to follow.  Summary: the student does not write final answer, and/or their thinking is difficult to follow.  Summary: the student does not writ final answer, and/or uses little or no mathematical language and symbols to explain how calculations were made and advised on the fairness or unfairness of the game. Representations: the student has no system of tables or graphs or charts to track calculations for all the possible outcomes of the event, the results of the experimental probability experiment, and/or the results of the theoretical probability.
Understanding	There is clear understanding of the topic in depth and it shows through the presentation of the information with a strong argument for the fairness or unfairness of the game.	There is clear understanding of the topic in depth and it shows through the presentation of the information with ease.	There seems to be understanding of the concept and the presentation is choppy.	There is an inadequate amount of understanding.
Oral Presentation	Holds attention of entire audience with the use of direct eye contact, seldom looking at notes.  Speaks with fluctuation in volume and inflection to maintain audience interest and emphasize key points.	Consistent use of direct eye contact with audience, but still returns to notes.  Speaks with satisfactory variation of volume and inflection.	• Displays minimal eye contact with audience, while reading mostly from the notes.  Speaks in uneven volume with little or no inflection.	• Holds no eye contact with audience, as entire report is read from notes.  Speaks in low volume and/or monotonous tone, which causes audience to disengage.
Final Product	Students create an original, accurate and interesting product using technology that adequately addresses the probability experiment.	Students create an accurate product using technology that adequately addresses the issue.	Students create an accurate product using technology but it does not adequately address the issue.	The product is not accurate and is incomplete.

References:

http://www.eed.state.ak.us/tls/assessment/standards/AKStandards_ELAandMath_080812.pdf