### Course 2 Unit 1 - Matrix Models 1st Edition

Matrix Models is the first unit in Course 2 of the Contemporary Mathematics in Context program. Students beginning this course should have successfully completed Course 1 of the program or an algebra 1 course. (See the descriptions of Course 2 Units.) Note that there are seven units and a capstone unit for this course. Units vary in length but are typically completed in 3 to 6 weeks.

#### Unit Overview

Matrix Models extends student ability to use matrices and matrix operations to represent and solve problems from a variety of real-world settings while connecting important mathematical ideas from algebra, geometry, statistics, probability, and discrete mathematics.

 Unit Objectives To see the interconnectedness of mathematics through the use of matrices and to explore topics in algebra, geometry, statistics, probability, and discrete mathematics To use matrices for organizing and displaying data in a variety of real-world settings like brand switching, tracking pollution through an ecosystem, and tournament rankings To develop further the skill of mathematical modeling by building matrix models and then operating on them to solve problems To learn and apply matrix operations: row sums, scalar multiplication, addition, subtraction, and matrix multiplication To use matrices and inverse matrices to answer questions that involve systems of linear equations

#### Sample Overview

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.

#### Instructional Design

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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#### How the Discrete Mathematics Strand Continues

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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