Round up lesson

Learning Goals:

In this lesson, students will:

• justify the validity of conditional statements used in chance experiments
• be able to explain and decipher common misconceptions of probability problems
• calculate probabilities of events where restrictions apply

Syllabus Outcomes:

• Use the language of 'if ... then', 'given', 'of', 'knowing that' to investigate conditional statements and to identify common mistakes in interpreting such language(ACMSP247)
• calculate probabilities of events where a condition is given that restricts the sample-space, eg given that a number less than 5 has been rolled on a fair six-sided die, calculate the probability that this number was a 3
• Critically evaluate conditional statements used in descriptions of chance situations

Syllabus Working Mathematically Indicators:

• describe the effect of a given condition on the sample space, eg in the above example, the sample space is reduced to {1,2,3,4} (Communicating, Problem Solving, Reasoning)
• identify and explain common misconceptions related to chance experiments, eg explain why the statement 'If you obtain a tail on each of four consecutive tosses of a coin, then there is a greater chance of obtaining a head on the next toss' is incorrect (Reasoning)

Prior Learning:

• Independent and dependent events
• Calculating probabilities of two to three step chance experiments
• With or without replacement
• P(A and B) = P(A) x P(B)
• P(A and B) = P(A) x P(B after A)
• Venn Diagrams

Teaching Strategies

• Literacy activities
• Group Work
• Consolidation of learning

Lesson Evaluation Questions

• Were able students able to use their prior knowledge and be able to use Venn diagrams to define conditional probability?
• Did breaking students into groups strongly promote discussion? Were there some students who struggled? How do you address those students?
• Was the conclusion and frayer model suitable enough to gauge students' understanding about probability?