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1 WORK PROGRAM MQ 9 NSW 5.2 Pathway Chapter 13 Probability Strand: Number, Data Substrands and outcomes: Chance NS2.5 Describes and compares chance events in social and experimental contexts Chance NS3.5 Orders the likelihood of simple events on a number line from zero to one Probability NS4.4 Solves probability problems involving simple events Probability NS5.1.3 Determines relative frequencies and theoretical probabilities Data analysis and evaluation DS4.2 Collects statistical data using either a census or a sample, and analyses data using measures of location and range Section Are you ready? (page 452) GC tips, Investigations, History of mathematics, Maths Quest challenge, 10 Quick Questions, Code puzzles SkillSHEETS, WorkSHEETS, Interactive games, Test yourself, Topic tests (CD–ROM) SkillSHEETS (page 452) 13.1: Understanding chance words 13.2: Probability scale 13.3: Understanding a deck of playing cards 13.4: Listing the sample space 13.8: Theoretical probability Technology applications (CD–ROM) Learning outcomes NS2.5 using the language of chance in everyday contexts NS3.5 describing the likelihood of events and ordering the events on a number line NS4.4 listing all possible outcomes of a simple event using the term ‘sample space’ to denote all possible outcomes assigning probabilities to simple events by reasoning about equally likely 2 Introduction to probability (page 453) WE 1a-b, 2a-c, 3a-b Ex 13A Introduction to probability (page 455) SkillSHEET 13.1: Understanding chance words (page 455) SkillSHEET 13.2: Probability scale (page 456) SkillSHEET 13.3: Understanding a deck of playing cards (page 456) Mathcad: Probability scale (page 456) Sample space (page 457) WE 4a-b, 5a-b. 6a-b Ex 13B Sample space (page 459) SkillSHEET 13.4: Listing the sample space (page 459) Excel: Coin toss lister (page 460) SkillSHEET 13.5: Forming fractions (page 464) Excel: Simulating die roll (page 462) Relative frequency (page 461) Investigation: Investigating relative outcomes expressing the probability of a particular outcome as a fraction between 0 and 1 NS3.5 describing the likelihood of events as being more or less than a half (50% or 0.5) and ordering the events on a number line NS4.4 expressing the probability of a particular outcome as a fraction between 0 and 1 explaining the meaning of a probability of 0, 1 and 1 in 2 a given situation (Communicating, Reasoning) using language associated with chance events appropriately (Communicating) NS4.4 listing all possible outcomes of a simple event using the term ‘sample space’ to denote all possible outcomes NS5.1.3 repeating an experiment a 3 WE 7a-b, 8 frequency (page 462) Ex 13C Relative frequency 10 Quick Questions 1 (page 463) (page 465) Experimental probability (page 466) WE 9, 10a-b Ex 13D Experimental probability (page 468) Theoretical probability of an event (page 471) WE 11 Ex 13E Theoretical probability of an event (page 472) Maths Quest challenge: Q1-2 (page 474) 10 Quick Questions 2 (page 474) Code puzzle (page 475) SkillSHEET 13.6: Calculating relative frequency (page 465) SkillSHEET 13.7: Converting a fraction into a decimal (page 465) WorkSHEET 13.1 (page 465) Game time 001 (page 470) Excel: Frequency tables and relative frequency (page 464) SkillSHEET 13.8: Theoretical probability (page 472) SkillSHEET 13.9: Converting a fraction into a percentage (page 473) Game time 002 (page 473) WorkSHEET 13.2 (page 473) Mathcad: Theoretical probability (page 472) Mathcad: Experimental probability (page 468) number of times to determine the relative frequency of an event estimating the probability of an event from experimental data using relative frequencies NS5.1.3 estimating the probability of an event from experimental data using relative frequencies expressing the probability of an event from experimental data using relative frequencies applying relative frequency to predict future experimental outcomes (Applying strategies) NS5.1.3 expressing the probability of an event A given a finite number of equally likely outcomes as P(A) = number of favourable outcomes n where n is the total number of outcomes in the sample space 4 Estimating probability (page 476) WE 12, 13 Ex 13F Estimating probability (page 478) Investigation: Simulating days of the week (page 478) Investigation: Who’s watching (page 479) WorkSHEET 13.3 (page 479) Extension: How to generate random numbers (page 476) Excel: Generating random numbers (page 478) Excel: Generating random numbers (DIY) (page 478) GC program – Casio: Generating random numbers (page 378) GC program – TI: Generating random numbers (page 478) GC program – Casio: Rolling a die (page 479) GC program – TI: Rolling a die (page 479) Excel: Simulating die roll (page 479) using the formula to calculate probabilities for simple events NS5.1.3 repeating an experiment a number of times to determine the relative frequency of an event estimating the probability of an event from experimental data using relative frequencies simulating probability experiments using random number generators designing a device to produce a specified relative frequency e.g. a fourcoloured circular spinner (Applying strategies) recognising that probability estimates become more stable as the number of trials increases (Reasoning) DS4.2 formulating key questions to generate data for a problem of interest making predictions from a sample that may apply to the whole population consider the size of the 5 Summary (page 480) Chapter review (page 481) ‘Test yourself’ multiple choice questions (page 482) Topic tests (2) sample when making predictions about the population (Applying strategies) drawing conclusions based on the analysis of data (Applying strategies, Reasoning)