Probability and Statistics (Grades 3-5) Workshop DAY 1 Dr. Leah Shilling-Traina

1. Probability and Statistics (Grades 3-5) WorkshopDAY 1Dr. Leah Shilling-Traina

2. Community of Learners • Complete 3 X 5 notecard: • Name • Email • Where do you teach? • Number of years teaching & grade levels • Favorite mathematics topic • Why are you here? • Introductions – Introduce another person in our class to everyone!

3. Books Used in Workshop • Navigating through Data Analysis and Probability in grades 3-5 by Chapin, Koziol, MacPherson, Rezba (ISBN 978-0-87353-521-2) published by NCTM • Exploring Statistics in Elementary Grades Book 1 by Bereska, Bolster, Bolster, Schaffer (ISBN 1-57232-344-2) published by Dale Seymore in 1998

4. Books Used in Workshop • Math By All Means by Marilyn Burns (ISBN 0-941355-12-8) • Mathematics for Elementary Teachers Activity Manual by Sybilla Beckman (ISBN 978-0-321-64696-5) published by Addison-Wesley

5. Virginia Department of Education Resources • Probability and Statistics for Elementary and Middle School Teachers: A Staff Development Training to Implement the 2001 Virginia Standards of Learning (PSEMT) (http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/2001/resources/elementary/probability_module/mprobstatentire.pdf)

6. Virginia Department of Education Resources • 2009 Mathematics Standards of Learning (SOL) (http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/2009/stds_math.pdf) • Mathematics Curriculum Framework for grades 3 - 5

7. Manipulatives for You • Set of blank dice • Overhead dice • Overhead color tiles • Overhead circle spinners

8. Extras for You—Put in Your Binder! • The packet of print-out materials include: • Documents and materials related to the NCTM Standards and VA SOLs • VDOE’s Mathematics Word Wall Vocabulary Cards for Grades 3-5 Probability and Statistics (all cards can be found at http://www.doe.virginia.gov/instruction/mathematics/resources/vocab_cards/index.shtml) • A copy of activities from Exploring Statistics in the Elementary Grades by Bereska, Bolster, Bolster, and Schaeffer (ISBN 1-57232-344-2) • Some additional lesson plans and handouts • Copies of overheads/handouts for all activities in the NCTM and Burns texts • You should also take notes in your binder!

9. First…Let’s Take a Pre-Workshop Content Assessment! • Remember, you are not be graded during this workshop! • Please answer the questions to the best of your ability. • At the end of our third day together, you will take a post-workshop assessment to see how this workshop has impacted your knowledge of Grades 3-5 probability and statistics!

10. Standards in Mathematics Standards in mathematics education represent the goals we set for our students. They are value judgments about what we would like our students to know and be able to do. They are chosen through a complex process that is fed by societal expectations, past practice, research information, and visions of the professionals in the field… They represent our priorities. --- Hiebert, J. (2003). What Research Says About the NCTM Standards

11. 2009 VA SOL: Grade 3

12. 2009 VA SOL: Grade 4

13. 2009 VA SOL: Grade 5

14. VA SOL: Probability or Statistics? • In small groups, review the VA probability and Statistics Stands for grades 3-5. Classify each as addressing probability OR statistics. • Why did you make your choices? In your own words, what is probability? What is statistics? How do you distinguish them in your mind?

15. VA Statistics SOL (Gr. 3-5) • 3.17 The student will a) collect and organize data, using observations, measurements, surveys, or experiments; b) construct a line plot, a picture graph, or a bar graph to represent the data; and c) read and interpret the data represented in line plots, bar graphs, and picture graphs and write a sentence analyzing the data. • 4.14 The student will collect, organize, display, and interpret data from a variety of graphs. • 5.15 The student, given a problem situation, will collect, organize, and interpret data in a variety of forms, using stem-and-leaf plots and line graphs. • 5.16 The student will a) describe mean, median, and mode as measures of center; b) describe mean as fair share; c) find the mean, median, mode, and range of a set of data; and d) describe the range of a set of data as a measure of variation.

16. VA Probability SOL (Gr. 3-5) 3.18 The student will investigate and describe the concept of probability as chance and list possible results of a given situation. 4.13 The student will a) predict the likelihood of an outcome of a simple event; and b) represent probability as a number between 0 and 1, inclusive. 5.14 The student will make predictions and determine the probability of an outcome by constructing a sample space.

17. NCTM Data Analysis and Probability Standards (Gr. 3-5)

18. NCTM Data Analysis and Probability Standards

19. The VA SOL vs. The NCTM Standards • The NCTM Standards tell us what the government is expecting us to do in the classroom—how do the SOL compare? • What aren’t we doing that we SHOLD be doing? Where should we be going? • Together, can we list the NCTM’s 5 Process Standards? How do they relate to probability and statistics?

20. NCTM Expectations: By Grade-Level • Although our focus is on the probability and statistics learned in Grades 3-5, as teachers it is important to know what has come before and what will come after! • Let’s look at these expectations together—PSEMT, pages 15-18.

21. Big Ideas Focusing on the big ideas also means that teachers use strategies for advancing all students’ mathematical thinking (Fraivillig, 2001) by: • eliciting from students a variety of solution methods through appropriate prompts, collaborative learning, and a positive, supportive classroom environment; • helping students develop conceptual understanding by attending to relationships among concepts; • extending students’ mathematical thinking by (a) encouraging them to try alternative ways of finding solutions and to generalize, and (b) setting high standards of mathematical performance for all students.

22. Probability AND Statistics • Probability and statistics are NOT THE SAME…but they are closely related and each depends on the other in a number of different ways. They have been traditionally studied together (stochastics) and justifiably so. • The relationship cuts both ways – statistical analyses makes use of probability and probability calculations makes use of statistical analyses.

23. Activity: What is Statistics? • Break into small groups of 3 or 4; each group should get one piece of chart paper and a marker. • Come up with a list of words and phrases that you (and potentially, your students) associate with the term statistics. • When you’re done, hang them in front of the room? What commonalities do we see? Can we agree on some of the BIG IDEAS of statistics?

24. Statistics is… • A problem-solving process that has 4 major components: • Ask a question • Collect the appropriate data • Analyze the data. • Interpret the results. • In short, using data to answer questions!

25. Big Ideas of Statistics (from GAISE*)—Look Familiar?  • GAISE offers as a central part of their framework 4 components of statistical problem-solving that include: 1. formulating questions 2. collecting data 3. analyzing data 4. interpreting results *Guidelines for Assessment and Instruction in Statistics Education for Pre K-12 Education

27. Activity: Questions, Please? (NCTM, p. 13) • In statistics, it all begins with THE QUESTION! It’s always where the process begins. Think of a question that you would like to know the answer to! Write it on your post-it! • Let’s think about the purposes/reasons for conducting an investigation, as well practice formulating questions that have meaning related to those purposes.

28. Summary of Reasons to Conduct an Investigation • To describe or summarize what was learned from a set of data • To determine preferences or opinions from a set of data • To compare and contrast two or more sets of data • To generalize or make predictions from a set of data

29. Activity: How Long is the Classroom? • In attempts to answer this question, let’s break into small groups. Use 3 different measuring tools to collect your data: (1) a ruler, (2) a shoe, and (3) an arm span (stretch arms out like a “T” and it’s the length from fingertip to fingertip). • Once collected, add your data to the whole class data at the front of the room. • Which tool was best? Why? What happened with the other tools? • What is the lesson here?

30. What is Random Sampling? • Question: What TV shows do Americans watch the most? • In most circumstances, collecting information from every member of a population is impossible. Therefore, we collect data from a sample of the population and use the sample to make inferences about the population. • Samples can be very accurate in describing the population characteristics. However, for samples to be accurate, they must represent the population. • If the sample is not representative of the entire population, the sample is considered biased because it does not accurately reflect the population being studied.

31. Activity: Ice Cream Preferences (Bereska, p. 2) • It’s summertime, and there is really only one snack to help beat the heat—ice cream! Before you start dreaming about your favorite flavor, let’s do an activity together. As I pass out some papers, read over the description. Don’t turn over your paper until I say to! • Let’s answer some questions! • Now…what is YOUR favorite flavor?? Let’s collect data, and then think of some ways to represent it!

32. Activity: What Color are Your Eyes? What Month Were You Born? • I want to know the eye colors of the students in the classroom-how can we figure this out? • Now, suppose you can’t use any written communication—how can we organize our data? • My curiosity is unbounded! Now I want to know during what month you were born! Let’s get data from the whole class and make some graphs and observations! • What do these questions have in common?

33. Categorical Data • The past two activities have used categorical data-values that correspond to a particular category or label. Can we think of other questions that would require the use of categorical data to answer? • Graphical representations of categorical data include: • Pictograph-- uses a picture or symbol to represent an object. If there is more than one of the objects, multiple representations of the symbol are used. A key should be included that states the value of the symbol. • Bar graph -- uses parallel horizontal or vertical bars to represent counts for several categories. One bar is used for each category, with the length of the bar representing the count for that category • Circle graph -- shows the relationship of the parts to the whole

34. Examples of Graphs

35. Activity: Interpreting Graphs (Bereska, p. 10) • Together, let’s interpret these graphs representing categorical data. • For each graph we discuss, let’s also identify the graph type!

36. Activity: What’s Wrong with This Graph?

37. Activity: If the Shoe Fits (Bereska, p. 34) • I’m still curious about you all! You can tell a lot about a person from their shoes…everyone take off your right shoe and put it on the table. In small groups, first come up with some questions we could ask about the shoes worn by people in the class. • Which questions will we answer using categorical data? What graphs could you use to organize this data? • What kind of data is needed to answer the other questions? • Let’s look at some of these other kinds of questions together….

38. Numerical Data • The last activity elicited some questions that used numerical data- data that consist of numerical measures or counts. Can we think of other questions that would require the use of numerical data to answer? • Graphical representations of numerical data include: • Line plot-- uses stacked x ’s to show the distribution of values in a data set. • Line graph-- uses a line to show how data changes over time. • Stem-and-leaf plot-- a table showing the distribution of values in a data set by splitting each value into a “stem” and a “leaf”; this is a useful way to display data that range over several tens (or hundreds).

39. Why Don’t We Have an Activity to Create a Line Graph? • Is it because we just don’t like it as much as the other graphs?  • VDOE’s Enhanced Scope and Sequence Sample Lesson Plans: http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/index.shtml • Hot or Cold Lesson and www.weather.com!

40. Examples of Graphs

41. Activity: What’s Wrong with This Graph? (Part 2)

42. Activity: If the Shoe Fits (Part 2) • Let’s try to determine the typical length of shoe worn by people in this class! There are a couple ways we could do this…suggestions? • For now, let’s all just measure our shoe. What kind of questions do we need to consider first? • Put your name and measurement on a post-it. How can we organize and display this data? • How would this activity be different if we asked about the typical shoe size of students in the class?

43. Activity: Counting on You (Bereska, p. 22) • Look at the “Can We Count on You” Survey—what do you notice? • Would you like to add any questions? • Break into small groups; each of you are responsible for answering 1-2 of these survey questions! • Display your data in a way that makes sense based upon your data type to share with the class.

44. End of Day 1 Grade-Band Break Out! • For the last 30 minutes (or so) of our day, let’s break up into small groups according to the grade we teach! Where are the 3rd grade teachers? 4th grade? 5th grade? • Reflect on the different activities in which you engaged today. Which activities could/would you do with your students? How would you implement those activities? Be sure to refer to all of the documents (i.e. the Curriculum Framework)!

45. Probability and Statistics (Grades 3-5) WorkshopDAY 2Dr. Leah Shilling-Traina

46. Welcome Back!  • How are you feeling today? What kind of graph could we use to represent our data if we asked for responses to be “happy,” “sad,” “angry,” or “indifferent”? What kind of data is this? • Any questions/comments about what we’ve done so far? • Let’s begin where we left off…

47. Quick Review: Categorical or Numerical Data? • Think about possible responses to the following questions and decide which responses will provide categorical data and which will provide numerical data: • How many pets do students in our class have? • How many hours a week do we spend watching TV? • What is the typical monthly rainfall in Seattle? • What kind of music do we like best? • How many hours a week do we talk on the phone? • What kinds of snacks do we like? • How many kids eat in the cafeteria each day? • How much candy do we eat each week? • What kind(s) of graphs would you use to display each data set?

48. Quick Review: Name that Graph!

49. Activity: Graph Detective (PSEMT, p.97) • Look at the three graphs and conclusions. In your group, discuss whether the conclusion is accurate and what factors about the graph may have lead to inaccurate conclusions. • Be prepared to discuss your thoughts with the whole class!

50. Thinking back… • We answered questions like “How many colors are you wearing?” , “What is the length of your foot?” and “How tall are you?”and looked at how to display the data for the entire class. • What other questions might we ask about the different colors we are all wearing, or the length of our feet, or how tall we are? What else might be good to know?