Matrix And Determinant Lesson Plan for 8th Grade Example Students

Determinant

Topic: Transformations and their effect on the determinant of a matrix

Objectives & Outcomes

• Understand how transformations affect the determinant of a matrix
• Know how to use the determinant to determine whether a given transformation is possible or not

Materials

• Matrixes for practice
• Calculator
• Pen and paper to write down calculations and answers

Warm-up

• Ask students to give examples of different types of transformations they have seen in the context of math and geometry, such as translations, rotations, and reflections.
• Have them share their examples with the class and explain how each transformation affects the shape and size of the object being transformed.

Direct Instruction

• Introduce the concept of a matrix, and explain that it is a rectangular array of numbers, arranged in rows and columns.
• Show students some examples of matrices, and have them work with a matrix manipulator (such as the one provided in the resources section of this lesson) to create their own matrices.
• Explain the operation of multiplying matrices, and demonstrate how the resulting matrix is the result of applying a given set of transformations to the original matrix.
• Introduce the concept of the determinant of a matrix, and explain that it is a measure of the extent to which the matrix is reflected about its main diagonal.
• Show students how to calculate the determinant of a matrix using the formula, and explain the significance of the determinant in terms of the transformations applied to the matrix.

Guided Practice

• Have students work in pairs to create a set of matrices, each of which indicates a different set of transformations to be applied to the original matrix.
• Ask them to calculate the determinants of each of these matrices, and compare the results to see how they match up with the expected results.

Independent Practice

• Have students work in groups to create a set of matrices representing a sequence of transformations on a shape, and then use these matrices to create a new shape by applying the transformations in reverse order.
• Have them calculate the determinants of each of the matrices in the sequence, and use this to reconstruct the original shape from the sequence of matrices.

Closure

• Review the concept of a matrix and how to calculate its determinant.
• Ask students to share their results from the independent practice, and discuss any difficulties they encountered and ways to solve them.

Assessment

• Observe students during the guided practice and independent practice activities to assess their understanding of the concept of matrix closure and their ability to apply it to solve linear equations.
• Collect and review their solutions to the independent practice problems for accuracy and effective use of matrix closure to solve linear equations.