MATH 598: Statistics & Modeling for Teachers May 21, 2014

◦ Pretest ◦ Big Idea Warm-up ◦ Introduction ◦ M&Ms Activity

◦ Find someone with whom you did not work last week. ◦ Spend 5 minutes discussing the following with your partner. Be prepared to summarize your discussion for the larger group:  Which of the concepts included in Big Idea 1 do your students seem to understand well?  Which of the concepts included in Big Idea 1 are more of a challenge for your students?

 Formulate a question  Gather data accordingly ◦ Design: plan on how to obtain data to answer the question of interest  Analyze data accordingly ◦ Description: summarize and analyze the data that are obtained  Interpret results to answer the question ◦ Inference: make decisions and predictions based on the data for answering the statistical questions, typically we want to do this for a larger group than those directly in the study

 What proportion of students at your school prefer country music over rap, rock, and oldies?

 We typically work with and observe samples but we are actually interested in populations  A population is the set of ALL the subjects of interest  In practice, we have data for only some of the subjects in the population  A sample is a subset of the population for whom we have (or plan to have) data, hopefully they are randomly selected  Occasionally, data are available for the entire population (e.g., Census)

 Descriptive statistics: methods for summarizing the collected data  Typically either a numeric summary (e.g., the mean) or a graph (e.g., a histogram)

 A parameter is a numerical summary of the population  A statistic is a numerical summary of the sample  For example, suppose you are interested in the average grades of students at LMU and you take a sample of students to work with ◦ What is the population of interest? ◦ What is the parameter of interest? ◦ What is the sample statistic you would use?

 What proportion of students at your school state that country music is their favorite instead of rap, rock, and oldies? ◦ What is the population? ◦ What is the population parameter of interest? ◦ How could you investigate the population parameter of interest? ◦ Since the value of the sample statistic will vary for each sample, how can you answer the question?

 Problem: How can we describe how the percentage of candies that are blue varies from one bag of M&Ms to another?

Get into groups of 2. Spend a few minutes discussing answers to the following questions. 1. What is the specific question that needs to be addressed in the investigation? 2. How does this question relate to the background information at the beginning of the activity? Be sure to use some of the review terms in your answer. 3. What is the population of interest in the investigation? 4. What is the population parameter of interest in the investigation? 5. Why can we not realistically calculate the population parameter of interest directly? 6. How could the concept of random sampling be used to investigate the population parameter of interest?

 Each person will be given M&M bags.  Record the number of blue M&Ms and the total M&Ms in the bag for each of the bags.  Follow the activity sheet.

What are the important take-away ideas from this task?

How might you extend this activity to build students’ understanding of sampling distributions?

 Which GAISE level is the M&Ms Activity?  Which Common Core content standards are addressed in the M&Ms Activity?  Which Common Core mathematical practice standards are addressed in the M&Ms Activity?

 Take time to answer the set of in-class problems

 Bring your laptop to class.  HW 2: Valentines Day Marbles ◦ Keep in mind that your work will be scored and returned to you. So, please write out complete answers. In other words, answer the questions in the manner that you would hope your students would. ◦ You should work alone. ◦ Be prepared to share your answers with the rest of the class.  Read Big Idea 4 from 6-8 DEU