1. Assessment Task A – Learning Object RELATIVE FREQUENCY By Staceylee, Courtney & Heather

2. Today's Lesson Includes; Introduction of topic - What is relative frequency? Introduction of topic - What is relative frequency? Worked Example Worked Example Introduce Learning Object Introduce Learning Object Real Life Contexts Real Life Contexts 3 Digital Resources Explained & Evaluated using PMI (Plus Minus Interesting) 3 Digital Resources Explained & Evaluated using PMI (Plus Minus Interesting) Wrap Up Questions Wrap Up Questions

3. Relative Frequency What is Relative Frequency? (Experimental Probability) Probability based on an experiment which is written as a ratio (or fraction) comparing the number of times an event occurred to the number of trials. Probability based on an experiment which is written as a ratio (or fraction) comparing the number of times an event occurred to the number of trials. Relative Frequency formula Relative Frequency = number of times an event occurred Number of trials

4. When you gather data by observing a random event, you can calculate the Relative Frequency (experimental probability). In order to calculate the relative frequency of a random event, you use the following rule/ formula: (event) is the event P (event) = number of times an event occurs number of trials where P is the probability

5. Another way to write the rule for relative frequency is; Relative Frequency = f ∑ f ∑ f

6. Declarative and Procedural Knowledge Declarative KnowledgeProcedural Knowledge Decimal Fractions Analyse data to identify the key mathematical content in the generation of an equation Percentages Use mathematical interpretation and conclusions to generalise reasoning and make inferences Probability Calculate relative frequencies from given or collected data to estimate probabilities Frequency tables Substitute variables into formulas to determine an unknown Relative frequency formula Select appropriate data from the information given Terminology Investigate real life examples that demonstrate the use of relative frequency Data interpretation Evaluate the appropriateness of sampling methods and sample size Algebra – Variables and constants are represented using words and symbols when writing expressions and equations

7. EXAMPLE 1 A student flipped a coin 50 times. The coin landed on HEADS 28 times. Find the relative frequency (experimental probability) of having the coin land on HEADS. Think Write the number of times the coin landed on HEADS and the total number of coin flips Write the rule for relative frequency (experimental probability) Substitute the known values into the rule Answer the question Write Number of times coin landed on HEADS = 28 Total number of coin flips = 50 P(event) = number of times the event occurred Total number of trials Total number of trials P(HEADS) = 28 50 50 The experimental probability of the coin landing on HEADS is 28 = 0.56 = 56% 50 50

8. Marble Mania Learning Object.

9. 50 Marbles

10. Real life Contexts Apart from gambling, (mention Las Vegas) the theory of probability can help us make relatively reasonable choices in our daily lives. Apart from gambling, (mention Las Vegas) the theory of probability can help us make relatively reasonable choices in our daily lives. Students choose college courses which have a high probability of leading to employment after college. Students choose college courses which have a high probability of leading to employment after college. Many people have left New Orleans for good because there is a high probability of devastating hurricanes in that region. Many people have left New Orleans for good because there is a high probability of devastating hurricanes in that region. People don’t smoke because there is a high probability of their developing cancer as a result of smoking. People don’t smoke because there is a high probability of their developing cancer as a result of smoking.

11. Real Life Context cont. Probability has widespread use in business, science and industry. Its uses range from the determination of life insurance premiums Probability has widespread use in business, science and industry. Its uses range from the determination of life insurance premiums Sporting uses - in tennis the player knows his relative frequency of wins in relation to whether he serves or receives first. Sporting uses - in tennis the player knows his relative frequency of wins in relation to whether he serves or receives first. In cricket teams know the relative frequency of wins in relation to the pitch conditions In cricket teams know the relative frequency of wins in relation to the pitch conditions

13. Digital Resource 1 Websites Experimental Probability Digital Resource - Joseph L. Coffman (2010) http://www.jcoffman.com/Algebra2/ch1_6.htm Experimental Probability Digital Resource - Joseph L. Coffman (2010) http://www.jcoffman.com/Algebra2/ch1_6.htm http://www.jcoffman.com/Algebra2/ch1_6.htm Relative Frequency Quiz – Lesson 6 Quiz - Pearson Prentice Hall Mathematics: Prentice Hall’s online practice test (enter this web code to play: aga – 0106) http://www.phschool.com/webcodes10/index.cf m?wcprefix=aga&wcsuffix=0106&area=view&x =8&y=10 Relative Frequency Quiz – Lesson 6 Quiz - Pearson Prentice Hall Mathematics: Prentice Hall’s online practice test (enter this web code to play: aga – 0106) http://www.phschool.com/webcodes10/index.cf m?wcprefix=aga&wcsuffix=0106&area=view&x =8&y=10 http://www.phschool.com/webcodes10/index.cf m?wcprefix=aga&wcsuffix=0106&area=view&x =8&y=10 http://www.phschool.com/webcodes10/index.cf m?wcprefix=aga&wcsuffix=0106&area=view&x =8&y=10

14. PLUS,MINUS,INTERESTING (PMI) on Digital Resource 1 PLUSMINUSINTERESTING Offers a great definition on what relative frequency (experimental probability) is Offers an easy to follow example (procedural knowledge) on correct rules and correct setting out Has a quiz which opens in a new tab to allow you to test your skills and declarative knowledge It is named experimental probability – not relative frequency Only offers one easy example It offers an online quiz to test your knowledge on relative frequency (experimental probability)

15. http://www.zweigmedia.com/RealWorld/tutorialsf15e/frames6_2.html Digital Resource 2

16. Plus MinusInteresting Meets most of the DK and PK needed Calculate relative frequency from given or collected data Doesn’t use real life contexts Quiz page. Need certain points to go onto the next one. You get a smiley face when you get it right! Simple definitions, with examples Not many questions Gives you plenty of practice questions where you can help check you are on the right track before you put your answer in.

17. Digital Resource 3

18. DigitalResource3

20. PlusMinusInteresting It shows the DK needed for relative frequency : data tabulation; influence of sample size; formula for relative frequency It is too simpleIt leads well from one topic to another It is easily understood It gives examples and explanations

21. For more info go to... https://usingrealativefrequency. wikispaces.com/ StaceyleeCourtney Heather