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Overview
Overview
Although students have intuitive notions of how probability works, often their naive mathematical understandings miss critical nuances of probability in action. In this unit, the objective is to confront students with their misconceptions of how probability works and then extend their understanding of probability. This unit builds a foundation for working with probabilities. Basic rules of probability are discussed, including conditional probabilities. Extra care should be taken to develop the conceptual understanding of probability, rather than just memorizing a relationship. Instruction through the use of simulations will help build the necessary conceptual foundation for the successful study of probability. The idea of independence is important and often misunderstood. Being able to explain probability in everyday language as well as interpret everyday language into probability statements is a critical skill for mastering these standards. Students should be exposed to multiple representations of information and asked to calculate probabilities from them. Two-way tables, Venn diagrams, and probability trees should be common in this curriculum.
Although students have intuitive notions of how probability works, often their naive mathematical understandings miss critical nuances of probability in action. In this unit, the objective is to confront students with their misconceptions of how probability works and then extend their understanding of probability. This unit builds a foundation for working with probabilities. Basic rules of probability are discussed, including conditional probabilities. Extra care should be taken to develop the conceptual understanding of probability, rather than just memorizing a relationship. Instruction through the use of simulations will help build the necessary conceptual foundation for the successful study of probability. The idea of independence is important and often misunderstood. Being able to explain probability in everyday language as well as interpret everyday language into probability statements is a critical skill for mastering these standards. Students should be exposed to multiple representations of information and asked to calculate probabilities from them. Two-way tables, Venn diagrams, and probability trees should be common in this curriculum.
The purpose of this unit is for students to learn about how statistics are used and potentially misused. Students will need opportunities to actually carry out sampling processes for themselves and learn about how statistics are used to support conclusions. In this unit, students will explore the process of making inferences about populations. This unit relies heavily on vocabulary and conceptual understandings. Simulation is also a critical part of developing inferences. Students should spend time learning about the various data collection instruments by constructing and carrying them out for themselves. Comparisons between collected data and simulations will lend a real-life feel to this unit.
The purpose of this unit is for students to learn about how statistics are used and potentially misused. Students will need opportunities to actually carry out sampling processes for themselves and learn about how statistics are used to support conclusions. In this unit, students will explore the process of making inferences about populations. This unit relies heavily on vocabulary and conceptual understandings. Simulation is also a critical part of developing inferences. Students should spend time learning about the various data collection instruments by constructing and carrying them out for themselves. Comparisons between collected data and simulations will lend a real-life feel to this unit.
This unit contains three main ideas: interpreting data using measures of center and spread, modeling data using familiar functions, and making the connection between probability and statistics. Students make comparisons between graphs, lists, and tables of multiple data sets by describing the shape, center, spread, and extreme values. Students should develop a conceptual understanding of correlation and causation and recognize that correlation does not imply causation. Students should be able to use technology to find regression functions.
This unit contains three main ideas: interpreting data using measures of center and spread, modeling data using familiar functions, and making the connection between probability and statistics. Students make comparisons between graphs, lists, and tables of multiple data sets by describing the shape, center, spread, and extreme values. Students should develop a conceptual understanding of correlation and causation and recognize that correlation does not imply causation. Students should be able to use technology to find regression functions.
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