Big Idea/Unit OverviewStudents will gather data, conduct investigations, and apply mathematical concepts and models to solve problems in mathematics and other disciples. Students will demonstrate reasoning skills in developing, explaining, and justifying sound mathematical arguments, and analyze the soundness of mathematical arguments of others and communicate with mathematics orally and in writing as part of independent and collaborative work, including making accurate and clear presentations of solutions to problems. The students will determine and interpret conditional probabilities and probabilities of compound events by constructing and analyzing representations, including tree diagrams, Venn diagrams, and area models, to make decisions in problem situations. The student use probabilities to make and justify decision about risks in everyday life and calculate expected value to analyze mathematical fairness, payoff, and risk. | Concepts and Key Understandings * Analyze and construct representations of events, including tree diagrams * Construct Venn diagrams and determine probabilities * Analyze and construct area models to determine probabilities * Explore the use of probabilities such as playing computer games or selecting classes * Explore and make decisions and justify their decisions about risk involved in a situation * Calculate expected values to analyze payoffs in variety of situations * Apply their understanding of expected values to determine the mathematical fairness of situations | Evidence of Student Learning | Formative Assessment(s)Unit 2 Section A Quiz SAS 2.C9: Extension 9 & 10 Quiz | Summative Assessment (Correlation between summative assessment and performance indicators/student expectations)Unit 2 Lesson 1 & 2 Test SAS 2C10 #13 Mini-project (Design a carnival game) | Academic Vocabulary (New - Direct Teach)Area model, probability, sample space, weighted probability, dependent events, independent events, expected value | Vocabulary ReviewTree diagram, Venn diagram, percentages, | Guiding Questions (2-3 overarching questions that students should be able to answer by the end of the unit)Describe a situation that could be modeled with a Venn diagram and create the diagram. Use the diagram to determine the probability of at least two events that are possible in the situation. Create a probability situation that uses compound events. Describe the outcomes for the situation. What type of model do you think will help you answer questions about the situation? List some advantages and disadvantages for each type of model: a tree diagram and Venn diagram. | Points of Integration (Cross-curricular connections and/or real-world applications)In Section 2 uses everyday decisions based on probabilities: section planning with probability in games, driving and risk, and choosing classes. | Reflection (What worked? What did not work? What could be done differently?) |