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Common Core: Math
CCLS  Math: N.VM.10
 Category
 Vector And Matrix Quantities
 SubCategory
 Perform Operations On Matrices And Use Matrices In Applications.
 State Standard:
 (+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
22 Results

 Student Outcomes Students will create a short animation in ALICE 3.1 using onestep procedures. Students will apply their understanding of the mathematics of projecting threedimensional images onto...

 Student Outcomes Students learn to project points in 3dimensional space onto a 2dimensional plane. Students learn how to simulate 3dimensional turning on a 2dimensional screen.

 Student Outcomes Through discovery, students will understand how challenging it is to project threedimensional objects onto a twodimensional space. Students will understand that vanishing points...

 In Topic E students apply the knowledge developed in this module to understand how firstperson video games use matrix operations to project threedimensional objects onto twodimensional screens and...

 Student Outcomes Students represent complicated systems of equations, including 4×4 and 5×5 systems of equations, using matrix equations in the form Ax = b, where A represents the coefficient matrix...

 Student Outcomes Students will represent systems of three or more simultaneous equations as a linear transformation in the form Ax = b, where A represents the linear transformation, x represents the...

 Student Outcomes Students will represent systems of equations as linear transformations of the form Lx = b, using matrix notation. Students will discover that the systems of equations written in the...

 Topic C provides a third context for the appearance of matrices via the study of systems of linear equations. Students see that a system of linear equations can be represented as a single matrix...

 Student Outcomes Students study and practice the properties of matrix multiplication. Students understand the role of the multiplicative identity matrix.

 Student Outcomes Students construct matrices so that the linear transformation has a desired geometric effect. Students identify the geometric effect of the linear transformation based on the...

 Topic B explores the geometric context for higherdimensional matrices. The geometric effect of matrix operations—matrix product, matrix sum, and scalar multiplication—are examined, and students...

 Student Outcomes Students understand that an inverse transformation, when represented by a 2 × 2 matrix, exists precisely when the determinant of that matrix is nonzero.

 Student Outcomes Students understand that an inverse transformation, when represented by a 2 × 2 matrix, exists precisely when the determinant of that matrix is nonzero.

 Student Outcomes Students determine inverse matrices using linear systems.

 Student Outcomes Students understand that 2 × 2 matrix transformations are linear transformations taking straight lines to straight lines. Students understand that the absolute value of the...

 Student Outcomes Students understand that the absolute value of the determinant of a 2 × 2 matrix is the area of the image of the unit square.

 Student Outcomes Students use matrix transformations to model circular motion. Students use coordinate transformations to represent a combination of motions.

 Student Outcomes Students use matrix transformations to represent motion along a straight line.

 Student Outcomes Students represent linear transformations of the form L(x,y) = (ax + by, cx + dy) by matrix multiplication Students recognize when a linear transformation of the form ...

 Topic C highlights the effectiveness of changing notations and the power provided by certain notations such as matrices. The study of vectors and matrices is introduced through a coherent connection...

 Module 2 extends the concept of matrices introduced in Module 1. Students look at incidence relationships in networks and encode information about them via highdimensional matrices. Matrix...

 Precalculus Module 1: Complex Numbers and Transformations Module 1 sets the stage for expanding students' understanding of transformations by exploring the notion of linearity. This leads to the...