# Matthew Fay's Portfolio

Design Project: Using Real World Data to Teach Statistics and Probability

## Project Topic

Getting students to understand statistics can be a challenge. Many students are able to get through by just going through the motions and copying the steps in a process without truly understanding why they are doing it. This project will be for students at the end of a unit in statistics. They already know how to create many statistical graphs and calculations, now they will tie it together.

## Intent of Project

The purpose of this project is for students to bring together an entire unit worth of study in the topic of statistics. They will have learned how to create different types of graphs and perform calculations using graphing calculators as well as Microsoft Excel. The purpose of this project is to show that they can interpret the data they collected.

**At the completion of this project students will have been able to:**

- Create a frequency table and frequency histogram
- Create analyse and interpret a stem and leaf diagram
- Calculate the 5 number summary of a data set
- Create analyse and interpret a box and whisker diagram
- Using Miscrosoft Excel or a graphing calculator, calculate the correlation coefficient
- Create a Scatterplot along with a corresponding linear equation with which to predict future values

## Needs Assessment

**Instructional Problem**
This project is focused on understanding and communications more than calculations. Students will have already performed most of the work required of them but now are focusing on analysis and understanding of how statistics can be used. The following are standards that reflect this intent.

- A.CM.2 Use mathematical representations to communicate with appropriate accuracy, including numerical tables, formulas, functions, equations, charts, graphs, Venn diagrams, and other diagrams
- A.CM.5 Communicate logical arguments clearly, showing why a result makes sense and why the reasoning is valid
- A.CN.3 Model situations mathematically, using representations to draw conclusions and formulate new situations
- A.CN.6 Recognize and apply mathematics to situations in the outside world

**What is to be learned**
Students will create, analyze and interpret calculations and various statistical graphs.

**About the learners and instructional context**
This Project is designed for an Applied Mathematics Course. The students are generally juniors and seniors in their third and final math course required for graduation. Overall, the course is made up of a variety of different ability levels. Some student are here because they lack the ability to go into geometry or AlgebraII/Trigonometry. Other students have tried and been unsuccesful in AlgebraII/Trig. Many of the students have still yet to pass the Algebra Regents exam. Throughout the course students will be working in a cooperative setting, as well as utilise technology in the class. There is a laptop card available, a class set of graphing calculators, and a Promethean Activeboard(smartboard) in the room.

## Performance Objectives

- Given raw data, students will be able to generate a frequency table along with the associated histogram and Stem and leaf diagram by drawing them on graph paper with fewer than 2 errors each.

- Given raw data, students will be able to demonstrate how to calculate a five number summary using a graphing calculator or Miscrosoft Word with fewer than 2 errors.

- Given a five number summary, demonstrate how to calculate if a data set has outliers using a graphing calculator with fewer than two computation errors.

- Given a five number summary and calculated outliers, generate a box and whisker diagram on graph paper with fewer than 2 errors.

- Given a list of raw data, Generate a Scatterplot with a line of best fit by drawing it on graph paper with fewer than three errors.

- Given a list of raw data, Execute the calculation of correlation using a graphing calculator or Microsoft Excel with fewer than two errors.

- Given Data and graphs, adopt opinions of the data provided by justifications through sound reasoning and calculations.

## Task Analysis

**Objective**Given raw data, students will ba able to generate a frequency table along with the associated histogram and Stem and leaf diagram by drawing them on graph paper with fewer than 2 errors each.

*Enabling Prerequisites*

- Determine the appropriate number of intervals to use
- What is a "Stem" and a "Leaf"
- Proper labeling needed

*Supporting Prerequisites*

- Univariate vs. Bivariate Data
- Qualitative vs. Quantitative

**Objective**Given raw data, students will be able to demonstrate how to calculate a five number summary using a graphing calculator or Miscrosoft Word with fewer than 2 errors.

*Enabling Prerequisites*

- Calculate Median
- Proper use of Graphing Calculator or Excel

*Supporting Prerequisites*

- Different measures of central tendency
- Percentiles

**Objective**Given a five number summary, demonstrate how to calculate if a data set has outliers using a graphing calculator with fewer than two computation errors.

*Enabling Prerequisites*

- Calculate Interquartile Range
- Quartiles 1st, 2nd, etc...

*Supporting Prerequisites*

- Percentiles

**Objective**Given a five number summary and calculated outliers, generate a box and whisker diagram on graph paper with fewer than 2 errors.

*Enabling Prerequisites*

- Drawing a scale appropriate to the data
- Quartiles
- Proper labeling of box and whisker and outliers

*Supporting Prerequisites*

- Percentiles
- Range

**Objective**Given a list of raw data, Generate a Scatterplot with a line of best fit by drawing it on graph paper with fewer than three errors.

*Enabling Prerequisites*

- Bivariate Data
- How to generate a scale appropriate to data
- How to create a line of best fit

*Supporting Prerequisites*

- Correlation
- Linear equations

**Objective**Given a list of raw data, Execute the calculation of correlation using a graphing calculator or Microsoft Excel with fewer than two errors.

*Enabling Prerequisites*

- Proper use of graphing calculator or Excel
- Meaning of Correlation

*Supporting Prerequisites*

- Difference between Correlation and Causation
- Bias

**Objective**Given Data and graphs, adopt opinions of the data provided by justifications through sound reasoning and calculations.

*Enabling Prerequisites*

- Understanding of different graphs and what information can be obtained from them
- How to generate the graphs listed above

*Supporting Prerequisites*

- Bias
- Sampling
- Univariate vs Bivariate data
- Correlation vs. Causation