HSN-VM.C.12

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- HSN-VM.C.6(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
- HSN-VM.C.7(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
- HSN-VM.C.8(+) Add, subtract, and multiply matrices of appropriate dimensions.
- HSN-VM.C.9(+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
- HSN-VM.C.10(+) 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.
- HSN-VM.C.11(+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.
- HSN-VM.C.12(+) Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.

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## HSN-VM.C.12

## (+) Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.

8 Lesson(s)

### Final Exam Review Stations (Day 1 of 3)

12th Grade Math »
Unit: Review

12th Grade Math »
Unit: Review

Big Idea:

#### Students review by working through various stations at their own pace and receive immediate feedback on their work.

Standards:

Favorites
(5)

Resources
(23)

Reflections
(1)

Big Idea:

#### Students employ the transformation matrices they discovered yesterday to manipulate figures in the plane.

Standards:

Resources
(19)

Reflections
(1)

Big Idea:

#### Students answer questions on their personal response systems to guide the review for the test.

Standards:

Resources
(6)

### Determinants and Area of a Triangle (Day 2 of 2)

12th Grade Math »
Unit: Matrices

12th Grade Math »
Unit: Matrices

Big Idea:

#### Students struggle to find the area of a variety of triangles; they learn a quick way to find the area using determinants.

Standards:

Resources
(16)

### Determinants and Area of a Triangle (Day 1 of 2)

12th Grade Math »
Unit: Matrices

12th Grade Math »
Unit: Matrices

Big Idea:

#### Students discover a method to calculate the determinant of a 2x2 matrix and practice using an inner-outer circles activity.

Standards:

Favorites
(1)

Resources
(15)

### Determining the Matrix for Transformations

12th Grade Math »
Unit: Matrices

12th Grade Math »
Unit: Matrices

Big Idea:

#### Students use manipulatives to discover the matrices that perform various transformations.

Standards:

Favorites
(1)

Resources
(21)

Reflections
(1)

### Using Matrices to Find the Area of a Triangle

12th Grade Math »
Unit: Matrices

12th Grade Math »
Unit: Matrices

Big Idea:

#### When the determinant of the matrix used to find area of a triangle is zero the 3 points are collinear.

Standards:

Resources
(17)

Big Idea:

#### Students will demonstrate their learning of Matrices in this formal assessment.

Standards:

Resources
(3)

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