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Rolling Dice

Rolling Dice. Hansen and Michelle are taking turns rolling two six-sided die.   a) What are all of the possible outcomes when two die are rolled? b) Which sum is most likely to be rolled?   How do you know? c) Which sum is least likely to be rolled?   How do you know?

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Rolling Dice

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  1. Rolling Dice Hansen and Michelle are taking turns rolling two six-sided die.   a) What are all of the possible outcomes when two die are rolled? b) Which sum is most likely to be rolled?   How do you know? c) Which sum is least likely to be rolled?   How do you know? d) What is the chance that they will both roll a nine on consecutive turns?

  2. Probability: Concrete manipulatives • Certain, Impossible and Indeterminate • Connection to everyday life • Have students conduct experiments • Work with experimental and theoretical probabilities • Law of larger numbers • Manipulatives • Grab bag • Coin toss, Dice (one thrown at a time for concrete learners), spinners

  3. Probability:Representational Manipulatives • Combinations of independent events • Multiple coins, counters or dice • Tree Diagrams • Real-life events • Experiments

  4. Representational Manipulatives • Real-life events Susan has a blue shirt, a red shirt, and a yellow shirt in her closet. She wants to wear dress pants or a skirt. Susan owns both shoes and flip-flops. List all of the possible outfits that Susan can wear?

  5. Probability:Representational Manipulatives • Real-life events UNC-C’s cafeteria is serving pizza, hotdogs and cheeseburgers. You can get fries, an apple or chips. Your drink choices are sweet tea or water. If you must select a main dish, a side and a drink, what are the possible meals. Make a tree diagram.

  6. Representational Manipulatives • Fair vs. unfair games • Students should have the opportunity to experiment then unpack the mathematics content • A fair game: both players have an equal probability of winning the game. Chip game: Is it fair?

  7. Probability:Symbolic Activities • Determining the probability mathematically • Probability = Number of actual outcomes Number of possible outcomes • Look at your polyhedra dice • Number of possible outcomes? • Probability?

  8. Measures of Central Tendency • Mean- “fair share” • Median- the number centrally located in the data set • Mode- the one that appears the most Other statistical numbers Range: difference between the highest and lowest numbers Unusual data points- informal terminology for “outliers”

  9. Developmental Levels • Concrete • Unifix cubes, teddy bear counters, M&M’s • Representational • Unifix cubes, drawings • Symbolic • Algorithms for finding the mean

  10. Statistics: Representational Meisha and her friends all got summer jobs. What was the average amount of money earned? Which salary did most people get? What was the median amount earned?

  11. Symbolic • Mean • Sum of numbers divided by total number of addends • Do not teach the formula until • Students have been exposed to “fair shares” • Range • Largest - smallest • Median • Finding the number in the middle

  12. Stem and Leaf The test scores are: 78, 94,79, 91, 87, 89, 79, 93, 85, 87, 89, 91, 92, 93, 94, 62 Make a stem and leaf plot from the test scores above.

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