Probability and Statistics

1. Probability and Statistics

2. Info Todd Smith Math Instructional Specialist todd_smith@boces.monroe.edu http://thinkmath.blog.monroe.edu/

3. Today’s Goals We will: • Explore the connection of concepts within a grade and the progression of concepts between grades • Discuss various teaching strategies • Engage in various activities that we might use in the classroom

4. Statistics and Probability Students view statistical reasoning as a 4 step process · Formulate questions that can be answered with data · Design and use a plan to collect relevant data · Analyze the data with appropriate methods · Interpret results and draw valid conclusions from the data that relate to the questions posed.

5. Statistics and Probability Students view statistical reasoning as a 4 step process · Formulate questions that can be answered with data · Design and use a plan to collect relevant data · Analyze the data with appropriate methods · Interpret results and draw valid conclusions from the data that relate to the questions posed.

6. Statistics and Probability Students view statistical reasoning as a 4 step process · Formulate questions that can be answered with data · Design and use a plan to collect relevant data · Analyze the data with appropriate methods · Interpret results and draw valid conclusions from the data that relate to the questions posed.

7. Statistics and Probability Students view statistical reasoning as a 4 step process · Formulate questions that can be answered with data · Design and use a plan to collect relevant data · Analyze the data with appropriate methods · Interpret results and draw valid conclusions from the data that relate to the questions posed.

8. Statistics and Probability Students view statistical reasoning as a 4 step process · Formulate questions that can be answered with data · Design and use a plan to collect relevant data · Analyze the data with appropriate methods · Interpret results and draw valid conclusions from the data that relate to the questions posed.

10. How much money does the President of the United States make in a Year?

11. How much money does the President of the United States Make in a Year? How much money does the Prime Minister of Sweden make?

12. How much money does the President of the United States Make in a Year? How much money does the Prime Minister of Sweden make? How much money does an American worker make?

13. How much money does the President of the United States Make in a Year? How much money does the Prime Minister of Sweden make? How much money does an American worker make? How much money does a Swedish worker make?

14. Statistical Question • Discuss what a statistical question is and give examples. • Discuss various examples and non examples • Have students work through a sorting activity in which they separate statistical and non-statistical questions • Have students come up with their own real life situations and create their own statistical and non statistical questions • Share out questions as a class and sort into the two categories

15. Statistical Question • Discuss what a statistical question is and give examples. • Discuss various examples and non examples • Have students work through a sorting activity in which they separate statistical and non-statistical questions • Have students come up with their own real life situations and create their own statistical and non statistical questions • Share out questions as a class and sort into the two categories

16. Statistical Question • Discuss what a statistical question is and give examples. • Discuss various examples and non examples • Have students work through a sorting activity in which they separate statistical and non-statistical questions • Have students come up with their own real life situations and create their own statistical and non statistical questions • Share out questions as a class and sort into the two categories

17. Statistical Question • Discuss what a statistical question is and give examples. • Discuss various examples and non examples • Have students work through a sorting activity in which they separate statistical and non-statistical questions • Have students come up with their own real life situations and create their own statistical and non statistical questions • Share out questions as a class and sort into the two categories

18. Statistical Question • Discuss what a statistical question is and give examples. • Discuss various examples and non examples • Have students work through a sorting activity in which they separate statistical and non-statistical questions • Have students come up with their own real life situations and create their own statistical and non statistical questions • Share out questions as a class and sort into the two categories

19. Statistical Question • Discuss what a statistical question is and give examples. • Discuss various examples and non examples • Have students work through a sorting activity in which they separate statistical and non-statistical questions • Have students come up with their own real life situations and create their own statistical and non statistical questions • Share out questions as a class and sort into the two categories

20. Describing Data Students can build on prior knowledge to describe the shape of a set of data by creating visuals

21. Describing Data Students can build on prior knowledge to describe the shape of a set of data by creating visuals Symetric

22. Describing Data Students can build on prior knowledge to describe the shape of a set of data by creating visuals Symetric Skewed left Negative Skew

23. Describing Data Students can build on prior knowledge to describe the shape of a set of data by creating visuals Symetric Skewed Right Positive Skew Skewed left Negative Skew

24. Introduce the need for measures of variability Two sets of grades on math tests Student A: 29, 45, 50, 70, 98, 99, 99 Student B: 64, 67, 69, 70, 72, 73, 75 Who is the better student?

25. Relating measure of center and variability to their context SituationMeanMad Diameter of a tire 17 in .01 in Number of chocolate chips 17 8 in a chocolate chip muffin Number of bb’s in a bb box 1000 8