March 6, ) Summarizing Measurement Data 2) Analyzing Two Quantitative Variables

 Title your poster (say what you measured)  Create a line plot that displays your data  Complete the left-side column on the “Summarizing the Survey” sheet from last class

 Join with another group  Take turns sharing posters.  As your partner group shares their poster, complete the right side column of the “Summarizing the Survey” sheet  After both groups have shared, discuss your observations from the recording sheet

Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by marking a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters.

 MATH ◦ What prior knowledge and understandings do the students need for this lesson?  LANGUAGE: ◦ What were the demands on the receptive language of the students? ◦ How were they required to express their knowledge and understanding?

 SOCIAL SKILLS ◦ What did the students have to do to successfully participate? ◦ What were the expectations for movement and interactions?  ORGANIZATION ◦ What did students have to manage?

 Read the description of your student and identify: Challenges s/he may have with the lesson demands Aspects of this lesson that may actually support the student, given his/her challenges What else you may need to do to provide the support needed by this student

Kevin  Have him paraphrase the directions  Provide a peer buddy  Work with him to create a readable checklist of what to do.

Isabelle  Be selective about her group members  Have her paraphrase/repeat the directions  Consider a check-off sheet with “quality indicators” for tasks completed  Use a self-monitoring check-off sheet for listening to peers

Danny  Provide a social skills checklist for him to use to self-monitor  Rehearse how to ask questions when conducting survey  Rehearse how to participate in groups  Assign a partner  Provide templates to organize the data as he collects it  Have him verbalize each step  Use graph paper if data is categorical

Melissa  Address vocabulary  Consider terms to pre-teach  Be mindful of using terms consistently  Provide a chart with examples  Ask her to paraphrase directions  Consider rehearsal using sentence starters  That is a good idea because…..  That might not work because….  If we ask that question, people’s answers might be…

Would they profit from the teacher modeling his/her thinking and planning in each part of the process? Is there a way to break the task(s) down further? Could a peer help? Would they profit from checklists? Would they profit from strategy posters?

Distinguish between 2 variables: quantitative and categorical data Identify the independent and dependent variables Construct a scatterplot Identify positive, negative, or no association in a scatterplot.

Investigate patterns of association in bivariate data. 1. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

At your table make a list of the different types of data we have analyzed and what were some of the primary tools we used to analyze the data types. Be as specific as you can.

 Categorical One variable Bar or Circle Graph Two Variables Two way table Segmented bar Graph Association Examples: One Variable: favorite pizza topping or favorite candidate for governor Two variables: size of dog and pass obedience class or gender and roll tongue

Quantitative One variable dot plot, box plot, stem and leaf plot, histogram Two variable Scatterplot Examples: One variable: height, IQ, $ in bank Two variable: Height and weight, arm span and height

Statistical Questions: Is there a relationship between where a student sits in a classroom and how attentive the student is? Is there a relationship between the weight of a car and the number of miles per gallon the car gets?

Is there a relationship between the population of a state and the number of area codes? Is there a relationship between taking an aspirin and chances of a heart attack? Is there a relationship between number of TV sets per capita and life expectancy? Is there a relationship between taking vitamin C and getting a cold?

Overarching question: How can I determine if there is a relationship between 2 quantitative variables? Example: Is there a relationship between height and wingspan? What are the 2 variables?

Independent Variable (Explanatory Variable) The independent variable is typically the variable representing the value being manipulated or changed. Dependent Variable (Response Variable) The dependent variable is the observed result of the independent variable being manipulated.

Identify the independent and dependent variable in each pair: 1. Miles per gallon and weight of car 2. Age and height of a person 3. Minutes studied and test score 4. Years of schooling and lifetime earnings 5. Grams of fat and calories in fast food

As the population increases the number of state representatives increases

As the temp outside increases the age when a baby crawls decreases

As the running time of a movie increases the gross income is hard to predict. (scattered)

 For each of the following make a sketch of a scatterplot and describe the association 1. Miles per gallon and weight of car 2. Age and height of a person 3. Minutes studied and test score 4. Years of schooling and lifetime earnings 5. Grams of fat and calories in fast food 6. Marriage rate and divorce rate 7. Amount of sun and amount of rain/snow 8. Number of TV sets and life expectancy

Where were you (the more senior of our group) when the space shuttle challenger exploded on 1/28/86?

The 25th flight of the National Aeronautics and Space Administration (NASA) space shuttle program took off on January 20, Just after liftoff a puff of gray smoke could be seen coming from the right solid rocket booster. Seventy-three seconds into the flight, the space shuttle Challenger had climbed 10 miles into the air and then exploded into a fireball. All seven astronauts died.

The cause of the explosion was determined to be an O-ring failure in the right solid rocket booster. Cold weather was a contributing factor. The Shuttle solid rocket booster is assembled in three sections. Each joint between sections has a pair of rubber O-rings (a primary O- ring and a secondary O-ring) that are designed to seal the joint and prevent the escape of hot gasses.

The following table gives the temperature and the number of O-ring failures for each of the previous 24 shuttle flights. The term failure is used here in a very broad sense, and occurs whenever there is significant erosion of the O-rings at a joint or blow-by of the hot gasses at the joint. Since there are two rockets, each with three joints, the number of O-ring failures for a launch is between 0 and 6. Flight number 4 has a missing data point because the rockets were lost at sea.

1. Sketch a dot plot for the number of O-ring failures. What does this plot tell you about a possible relationship between temperature and O-ring failure? 1. Sketch a bar graph that shows the number of O-ring failures as a function of flight number. Does this graph given any useful information on the possible relationship between temperature and O-ring failure?

1. Construct a scatterplot for the two variables temperature and O-ring failures. Does this graph suggest a possible link between temperature and O-ring failures? Note: Independent is x and dependent is y Note: Kids have a difficult time with the scale for the x and y axis 2. Do you think that the relationship suggested in the scatterplot can be extrapolated (going beyond the data) to a temperature of 31º (the approximate temperature on the day that Challenger was launched)? Discuss the potential problems with such extrapolation.

Using the data number of TV sets and life expectancy: 1. Construct a scatterplot with TV sets as the independent variable. 2. Describe the association. 3. In your own words what is the relationship between TV sets and life expectancy. 4. Can we say more TV Sets increases life expectancy?

1. Describe a real life situation that would involve a positive association. 2. Describe a real life situation that would involve a negative association. 3. Describe a real life situation that would involve no association. For each clearly identify the independent and dependent variables and make a sketch of a possible scatterplot. Make sure both axis are labeled. 4. Complete the Area code worksheet. 5. Calories and Life expectancy worksheet.