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Probability

Probability . By Michael Forbes and Natarlia Semple -Trinder . Declarative Knowledge. Declarative knowledge is what the learner knows and understands. For example a student might know the definition of an amoeba or the rules of basketball. . Procedural Knowledge.

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Probability

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  1. Probability By Michael Forbes and Natarlia Semple -Trinder

  2. Declarative Knowledge • Declarative knowledge is what the learner knows and understands. For example a student might know the definition of an amoeba or the rules of basketball.

  3. Procedural Knowledge • Procedural knowledge is when the learner is able to perform a certain skill or demonstrate a skill. For example, analyse an argument or apply a rule.

  4. Part A -The Learning Object The learning object that was chosen in this assignment was Dice Duels: Fair or Unfair.

  5. Declarative Knowledge for the Learning Object • Dice • Probability of a Result • Bias • Sample size • Frequency • Random Variation

  6. Procedural Knowledge for the Learning Object • Predict outcome • Compare the shape of distribution with experimental results • Analyse data distribution • Interpret frequency graph • Identify causes of variation • Draw conclusions about sample size

  7. Australian Maths Curriculum Year 9 Statistics and Probability: Chance Declarative Knowledge: • Two-step chance experiments • Tree diagrams • Arrays • Probability • Data • Frequency • Estimation

  8. Australian Maths Curriculum Year 9 Statistics and Probability: Chance Procedural Knowledge: • Calculate relative frequencies • Collect data • Estimate probabilities • Investigating reports of surveys • Estimate populations mean and median.

  9. Part B Other Digital Resources Three other digital resources were evaluated by the following criteria; • Ease of access • Clear objective • Interactive • Interest created for the Student • Relevance to Australian Curriculum

  10. Other Digital Resources Resource 1: Probability unit from Math Goodies. This digital resource has an interactive component where you can work out probabilities of different events. http://www.mathgoodies.com/lessons/vol6/intro_probability.html Resource 2: Probability calculator from Kids Zone. This digital resource calculates the probability of the outcome when rolling a certain number of dice. • http://nces.ed.gov/nceskids/chances/dice_handler.asp?NUMROLLS=5000 Resource 3: Probability Simulator from Subtangent. This digital resource rolls two dice as many times as you want and shows the numbers that have been rolled. • http://www.subtangent.com/maths/coindice.php

  11. Evaluation of Digital Resources

  12. Part C- The Learning Federation Object • Dice Duels – Fair of unfair is only relevant to an introduction to the year 9 Australian Curriculum in maths. • The Australian Curriculum requires a two step chance experiment. • The two step chance experiment: • If two dice are thrown, what is the chance of obtaining a total of 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. There are not even chances as demonstrated in following table. • http://econtent.thelearningfederation.edu.au/ec/viewing/L2635/index.html

  13. Array of a 2 step dice experiment The chances of getting a number between 2 and 12 are shown in the table on the left:

  14. Conclusion • The Learning object Dice Duels – Fair or Unfair is only an introductory experiment to learning about chance and probability where as the Australian Curriculum states that for a year 9 level a two step experiment is required. The learning object is not enough of a experiment to be learnt at a year 9 level hence the array of two step dice throwing was used..

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