1. Consider This… NAEP item: The two fair spinners shown below are part of a carnival game. A player wins a prize only when both arrows land on black after each spinner has been spun once. James thinks he has a 50-50 chance of winning. Do you agree?

2. Let’s Vote On a slip of paper to hand in write a “Yes” if you think James is correct or a “No” if you think he is wrong. Hand in your ballot.

3. Let’s Experiment How could we simulate this game? ◦ Using Spinners ◦ Using coins ◦ Using dice

4. What Are Your Findings? Share with the class the results of your experiment. As your classmates report their results, think about the vocabulary being used or that is needed to describe these results.

5. Language of Probability Experiments – actions that have distinct results Outcomes – the name for the results of an experiment Sample Space – the set of all outcomes of an experiment Event – any subset of a sample space Probability – a measure of the likelihood of an event

6. Language of Probability Six students Fran, Amber, Mike, Kevin, Rosa, and Jack had their names placed in a hat for a drawing for two prizes. What is the experiment? What is the sample space?

7. How did you find the likelihood? Talk with a partner – What is the probability that Fran will win a prize? What is the probability that Fran and Jack will win prizes? What is the probability that either Kevin or Jack wins a prize?

8. Predicting vs. Doing Talk with a partner – The probability that Fran and Jack will win prizes is 1 out of 15. So if the names are drawn, will they win? Rolling a fair, six-sided die, what is the likelihood you’ll roll a 5? How does the theoretical probability of rolling a 5 relate to the sample space {1, 1, 3, 3, 4, 4, 5, 5, 5, 6}?

9. Grading Rubric A grading rubric is used to show students exactly what the expectations are for a task that is being assessed. Rubrics help provide some credit for correct thinking even if the answer to the task is not exactly right. Typically, a rubric scores with points ranging from 0 to 4 and includes a description of the characteristics of a response that ranks at each levels.

10. Create Your Own Guidelines 4 (Everything was perfect and exceeds beyond just a correct answer) 3 2 (Something in between) 1 0 (No attempt was made or response was nonsensical)

11. Share Your Rubric Share your characteristics for each level beginning with level 0 Record each groups’ ideas in one list Decide upon a rubric for the whole class

12. How did you do? Assess the following student responses using our rubric. As you assess other student work, think about ◦ What constitutes a complete justification? ◦ Why would your instructor want you to justify a solution?

13. NAEP Scoring Guide Compare the rubric your class created to the scoring guide from NAEP Compare your scoring of student work to the score NAEP would assign

14. Now it’s your turn… If a person rolls two dice, what is the probability of getting a five as the sum? Justify your answer.

15. Extension: Not Equally Likely Suppose you are at the fair and you are playing a game for stuffed animal prizes. In this game you roll a dice and then spin a spinner and you will always win a prize. If you roll an even number, then you get to spin the spinner for a large stuffed animal. If you roll an odd number then you get to spin the spinner for a small stuffed animal (see spinners below). Determine the probability of winning a small animal, winning a large bear, and winning a pig.