Project #1: The Birthday Paradox

Title Page Project Lesson Plan Implementation Plan Project Website Synopsis

Project #2: Marshmallow Project

Title Page Project Lesson Plan Implementation Plan Project Website Synopsis

Table Of Contents

Table of Contents The Birthday Paradox Marshmallow Project

Information ExchangePooled Data Analysis

Implementation Date: April 1st - April 6th, 2010

Telecollaborative Structures:

The Birthday Paradox

Birthday Paradox Backwards Design Lesson Plan

Stage 1 – Desired Results Established Goals: S2C1 Draw inferences from graphs and data analysis S1C2 Solve simple percent problems S3C2 Use a graph to interpret data

Understandings: Students will understand that…

1. Graphs represent collected data 2. Data can be written as percentages 3. Graphs can display meaningful

information about collected data such as patterns, trends, or probability

Essential Questions:

1. Why is it important to analyze data? How do you think a graph aids in analyzing data?

2. Why is data typically shown as a percentage? What are the advantages and disadvantages to displaying data as a percentage?

3. How can you determine patterns, trends, and probability using a graph? Give examples to support your answer.

Students will know how to...

1. Collect, analyze, and graph data 2. Convert fractions into percents 3. Interpret data from a graph

Students will be able to…

1. Compare and contrast data collected and graphed

2. Calculate percentages for their data

3. Predict outcomes using collected data

Stage 2 – Assessment Evidence

Performance Tasks (Summative):

1. Answers to reflection questions posted to Birthday Paradox Discussion Group

2. Graph of data collected by the student

3. Data conversions into percentages 4. Presentation of findings to class

Other Evidence (Formative):

1. Self-evaluate data collection 2. Self-assess homework on

percentages 3. Peer-evaluation of data analysis

Stage 3 – Learning Plan Learning Activities (Building Blocks Towards Learning):

1. Collect birthday data from at least 23 people (not classmates) per student 2. Graph classmate birthday information as a class 3. Analyze classroom data by converting data into percentages 4. Students work with a partner to graph, convert, and analyze data each student

collected

Birthday Paradox Timeline Day 1:

1. Objective: • Introduce students to Birthday Paradox project • Students will be able to use a formula to calculate percents

2. Standards: Students can use proportions and percents 3. Anticipatory Set:

• Ask if any students have a birthday coming up in April • Ask if they know anyone else who has a birthday on the same

day • Ask the class what they think the odds of someone having the

same birthday as them is • Display/share Birthday Paradox statistics

4. Teaching Presentation:

• How to calculate percents: proportions and cross multiplying, which leads to formula (amount/whole x 100)

• Review proportions and cross multiplying • Show how proportions lead to percent formula

(amount/whole x 100)

5. Guided Practice: Complete problems in class related to statistics/percents

6. Closure: Review percents formula and project 7. Independent Work: Assign students the task of collecting the names

and birthdays of at least 23 people that are not in the class by Day 3

8. Resources: Birthday Paradox website, Algebra 1 text, template to

collect birthday data Day 2:

1. Objective: • Students will be able to graph a data set • Students will be able to use a formula to calculate percents

2. Standards: Students can use proportions and percents to graph data 3. Anticipatory Set:

• Have students line up around the room by birthday • Record birthdays on the board and note any repeats

4. Teaching Presentation:

• Explain the components of a graph and how to translate data into a graph

• Create a graph with the class of the class birthday data

5. Guided Practice: In teams, students calculate the percentage of students with similar birthdays and the probability of having two students in a class have the same birthday

6. Closure: Compare percentages calculated from the teams 7. Independent Work: Assign students homework on percentages 8. Resources: graph paper, Algebra 1 text, rulers, colored pencils

Day 3:

1. Objective: • Students will be able to graph a data set • Students will be able to use a formula to calculate percents

and peer evaluate

2. Standards: Students can use proportions and percents to graph real-life data collected

3. Anticipatory Set:

• Graphic organizer of tasks for the day

4. Teaching Presentation: • Observe student work and monitor progression through

activities • Students work with a partner to analyze their data,

calculating percentages and completing a graph of the data

• Students self-evaluate data collection by determining whether their data was sufficient, from a variety of sources, and accurately displayed

5. Guided Practice: • Students self-assess their homework • Students peer-evaluate their partner’s data analysis to see if it

was correct, accurate, and followed the requirements of the project

6. Closure: Have students preliminarily reflect on their findings; exit ticket 7. Independent Work: Check data and graph 8. Resources: graph paper, Algebra 1 text, rulers, colored pencils,

graphic organizer Day 4:

1. Objective: • Students will be able to graph a data set • Students will be able to use a formula to calculate percents

and peer evaluate • Students will be able to communicate findings to class

2. Standards: Students can use proportions and percents to graph real-

life data collected 3. Anticipatory Set:

• Students sign up for a time slot to present data

4. Teaching Presentation: • Students share their findings (data and graph) with the class,

including self-evaluation of their work

5. Guided Practice: • Students answer reflection questions from Discussion Group

and post to appropriate forum

6. Closure: Students write 3 things they learned, 2 things they liked, 1 thing they thought could be better about the project

7. Independent Work: none 8. Resources: timer, camera to photo student projects, computers,

reflection questions, website

About Me Who Am I? Blog About Me 2 Welcome 3

Welcome Welcome 2

Class

Mrs. Benson’s Period 7Number of Students

30

Our class data:

The Birthday Paradox was fun for students because they were able to poll their friends on birthdays. They analyzed the birthday data to see if it matched the project’s claim: 1 in 23 people will have the same birthday. In our own class of 30, 4 sets of 2 people shared a birthday!

Students enjoyed the independence of posting onto a forum. Many knew how to use a forum already. The disappointing part of this project was that we were the first class to participate and the only one. Still students published their work and were able to share it with their parents and friends they had polled.

Our class experience...

Synopsis

About Me Who Am I? Blog About Me 2 Welcome 3

Welcome Welcome 2

Analyzing Student Collected Data

Student Work

Student Reactions

Student Reactions

Student Reactions

Table of Contents The Birthday Paradox Marshmallow Project

Electronic PublishingPooled Data AnalysisInformation Exchange

Implementation Date:August 25-27 2010

Structures:

Marshmallow Project

Marshmallow Project Backwards Design Lesson Plan

Stage 1 – Desired Results Established Goals: Analyze data using mean, median, mode, and range Simplify algebraic expressions Use technology to create graphical representations of data

Understandings: Students will understand that…

1. Data represents real-life situations 2. Mean, median, mode, and range are

ways of analyzing data 3. Math is related to aspects of real-life

Essential Questions:

1. Why is it important to gather data? 2. How will you use mean, median,

mode, and range in your life? Give specific examples.

Students will know how to...

1. Calculate the mean, median, mode, and range for a data set

2. Simplify algebraic expressions using properties of real numbers

Students will be able to…

1. Create a graph that represents a data set

2. Analyze real life data

Stage 2 – Assessment Evidence

Performance Tasks (Summative):

1. Graphs of collected data

2. Marshmallow Question sheet/calculations from project

Other Evidence (Formative):

1. Independent practice 2. Online post

3. Class data analysis

Stage 3 – Learning Plan Learning Activities (Building Blocks Towards Learning):

1. Students estimate how many marshmallows can fit in their mouths. 2. Students learn about mean, median, mode, and range in class. 3. Students calculate the mean, median, mode, and range for class data. 4. Students collect data on marshmallow project. 5. Students analyze the data on Marshmallow Question sheet and create graphs. 6. Students reflect online.

Marshmallow Project Timeline Day 1:

1. Objective: • Introduce students to Marshmallow Project • Students will be able to calculate the mean, median, mode, and

range

2. Standards: Students can calculate the mean, median, mode, and range of a data set.

3. Anticipatory Set:

• Students estimate how many marshmallows they think they can fit in their mouths

• Introduce Project and Wiki

4. Teaching Presentation: • Notes on mean, median, mode, and range • Review AIMS questions (Arizona Instrument for Measuring

Standards) related to mean, median, mode, and range

5. Guided Practice: • Students calculate the mean, median, mode and range for a

variety of classroom data sets including hair color, eye color, etc. 6. Closure: Reflect on using mean, median, mode, and range in real life 7. Independent Work: Assign students homework on the mean, median,

mode and range 8. Resources: Wiki, notes, homework

Day 2:

1. Objective: • Students will be able to calculate the mean, median, mode, and

range • Students will be able to compare real life data

2. Standards: Students can calculate the mean, median, mode, and range

for a data set. Students can use addition and subtraction properties of real numbers.

3. Anticipatory Set:

• Marshmallow competition: Record students’ data as they see how many large marshmallows fit in their mouths at once

4. Teaching Presentation:

• Use data from marshmallow competition to calculate the mean, median, mode and range

5. Guided Practice:

• Students answer questions pertaining to mean, median, mode, and range as well as percentages and adding and subtracting integers

6. Closure: Students write reflections about the marshmallow project. 7. Resources: marshmallows, camera, marshmallow questions, student

volunteers, data collectors Day 3:

1. Objective: • Students will be able to compare and analyze real life data

2. Standards: Students can analyze data represented by a graph. 3. Anticipatory Set:

• Students review wiki for other school responses to marshmallow project

4. Teaching Presentation:

• Explain how to analyze the data on a graph and how to create a graph from a data set

5. Guided Practice:

• Students create graphs for the data presented • Students post graphs online

6. Closure: Students reflect on learnings from project 7. Resources: camera, colored pencils/markers, graph paper, data set,

computer/internet

Table of Contents The Birthday Paradox Marshmallow Project

About Me Welcome

We love marshmallows! Or at least we did before this project! The students loved the competition involved in this project. It really was entertaining to participate and the students will not stop talking about it in the classroom.

We were the first class to participate in this project for the year so we had to alter part of our lesson plan, which involved looking at the data from other classes and graphing it. Instead, we graphed our own data only. Next time, I would have students hold up a sign showing how many are in their mouth in the picture. I also would ask the project designer to add more of a global component as the students did not have to get on the computer during the project.

Our class experience...

Class

Mrs. Benson’s Period 3Number of Students

28

Our Class Data

19 marshmallows!!!

Synopsis

Table of Contents The Birthday Paradox Marshmallow Project

About Me Welcome

Mrs. Benson joined in with 8 marshmallows

Some of us did not like marshmallows afterwards!14 marshmallows

Student Work

Student Work

*Notice of Change* The Marshmallow Project replaces the original GLP in this eNotebook We Are Family!. I chose to change to the Marshmallow Project because it supported the focus of my math department this year, which is AIMS review (Arizona Instrument for Measuring Standards – state testing). I would like to try We Are Family! another time, especially now that I have experience implementing GLP’s in the classroom.