The sample material from Matrix Models is the second and third investigations of Lesson 1, "Building and Using Matrix Models." Prior to Investigation 2, students will have recognized the usefulness of matrices to represent information. In the two investigations included in this sample material, students analyze the information available from the matrices using row sums, column sums, and the mean of a row and combine matrices using addition, subtraction, and scalar multiplication.
Throughout the curriculum, interesting problem contexts serve as the foundation for instruction. As lessons unfold around these problem situations, classroom instruction tends to follow a common pattern as elaborated under Instructional Design.
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In Course 2, Unit 2, Patterns in Location, Shape, and Size, matrices are utilized to represent and transform polygons identified by their coordinates. Unit 5, Network Optimization, extends student ability to use vertex-edge graphs to represent and analyze real-world situations involving network optimization, optimal spanning networks, and shortest routes.
Unit 2, Modeling Public Opinion, in Course 3, develops student understanding of how public opinion can be measured using vote analysis methods, surveys, sampling distributions, the relationship between a sample and a population, confidence intervals, and margin of error. Also in Course 3, students study Discrete Models of Change which extends their ability to represent, analyze, and solve problems in situations involving sequential change and recursive change.
In Course 4, the Counting Models unit extends student ability to count systematically and solve enumeration problems, and develops understanding of, and ability to do, proof by mathematical induction.
Many of the mathematical concepts developed in the discrete mathematics strand are revisited in the other mathematical strands, thus enabling students to develop a robust, connected understanding of mathematics.
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