Unit Plan: Matrices (4 weeks or 20 instructional Days) Day 1: Review of Systems of Equations in 2 and 3 Variables Objectives: (M.4HS.CVM.18 )(CCSS.Math.Content.HSF-IF.B.6) Students will be able to solve systems of equations in two variables algebraically. Students will be able to solve systems of equations in three variables algebraically. Students will be able to determine whether a system of equations is consistent or inconsistent. Students will work with partners to solve systems of equations by the algebraic operations of substitution and elimination. Students will complete the guided practice problems at the chalk board. Student will complete the independent practice problems from the attached worksheet. Day 2: Introduction and Uses of Matrices Objectives: (M.4HS.CVM.10)(CCSS.Math.Content.HSN-VM.C.6(+)) Students will be able to define vocabulary such as matrix and dimension. Students will be able to determine the dimensions of a matrix. Students will be able to determine if two matrices are equal. Students will be able to determine the uses of matrices. Students will be able to see the use of a matrix to solve systems of equations with four or more variables. Students will fill in first part of unit vocabulary sheet. Students will brainstorm as a class what types of things matrices are used for. Students will be asked to create a matrix of a certain dimension and share with a partner to see if they are the same dimensions. They will then discuss as partners if the two matrices are equal and explain why or why not. Day 3: Matrix Addition and Subtraction Objectives: (CCSS.Math.Content.HSN-VM.C.8(+)) Students will be able to determine when two matrices can be added together and when they cannot be added together based on their dimensions.
Students will be able to determine when a matrix can subtract another matrix based on their dimensions. Students will be able to show that matrix addition is commutative. Students will be able to calculate the sum of two matrices. Students will fill in day 2 vocabulary in their vocabulary packet. Students will be asked to use vocabulary learned yesterday to explain when two matrices can be added. Students will create a 2X2 matrix individually then partner up and together find the sum of their matrices by adding their own matrix first. They should see that they both have the same answer and be able to conclude that matrix addition is commutative. Students will do independent practice problems from attached worksheet. Day 4: Scalar Multiplication Objectives: (M.4HS.CVM.11)(CCSS.Math.Content.HSN-VM.C.7(+)) Students will be able to multiply a matrix by a scalar. Students will be able to identify the identity matrix. Students will be able to add the product of a scalar and a matrix to another matrix. Students will be able to subtract the product of a scalar and a matrix from another matrix. Students will verbally define a scalar and be expected to multiply a matrix by a scalar out loud, at their seats, whilst anticipating to be randomly called upon. Students will complete the guided practice problems at the chalk board. Students will complete the independent practice problems on the attached worksheet. Days 5-7: Matrix Multiplication Objectives: (M.4HS.CVM.11)(CCSS.Math.Content.HSN-VM.C.7(+)) Students will be able to determine when two matrices can be multiplied and when they cannot by using the compatibility rule of matrix multiplication. Students will be able to determine that matrix multiplication is not commutative. Students will be able to determine what the dimensions of the product of two matrices will be. Students will be able to explain the process of multiplying matrices by showing their steps in their solutions.
Students will define matrix multiplication in their own words. There will be a couple of guided practice problems that the students work on with time to ask me questions. They will share their answers to the class. The students will partner up with the same student as yesterday and use the same matrices and method to see if multiplication is commutative. Students will complete the independent practice problems on the attached worksheet. Day 8: Solving Equations with Matrices Objectives: (M.4HS.CVM.17)(CCSS.Math.Content.HSF-IF.C.7) Students will be able to solve one step equations with matrices Students will be able to solve two step equations with matrices. Students will work on a warm up activity of multiplying matrices by a scalar. Students will use the result of their warm up activity to solve a one-step matrix equation. Students will solve two step matrix equations from guided practice problems from the board. Day 9: Determinant of 2x2 Matrix Objectives: (M.4HS.CVM.14)(CCSS.Math.Content.HSN-VM.C.10(+)) Students will be able to calculate the determinant of a 2x2 matrix. Students will be able to identify the uses of determinants. Students will calculate determinants of a 2x2 matrix at their seats for the teacher to check. Students will name at least one use of a determinant. Students will complete guided practice problems at the chalk board. Days 10-11: Inverse of a 2x2 Matrix Objectives: (M.4HS.CVM.14)(CCSS.Math.Content.HSN-VM.C.10(+)) Students will be able to use the determinant of a 2x2 matrix to find its inverse. Students will be able to solve equations involving the inverse of a 2x2 matrix.
Students will calculate determinants of 2x2 matrices as a warm up exercise. Students will use the determinants of those 2x2 matrices to find the inverse of each matrix. Students will use the inverse of 2x2 matrices to solve matrix equations at their seats. Days 12-14: Applications of Matrices and their Inverses Objectives: (M.4HS.CVM.10)(CCSS.Math.Content.HSN-VM.C.6(+)) Students will be able to identify at least three applications of matrices. Students will be able to use matrices to find area of irregular figures. Students will be able to use matrices and row operations to solve systems of equations. Students will be able to use Cramer s Rule to solve systems of equations. Students will use row operations to solve systems of equations with their partners. Students will find the determinant and inverse of a 2x2 matrix to find the area of an oblique triangle. Students will then come up with the coordinates of one acute triangle and one obtuse triangle and ask their partner to find its area. Students will discover Cramer s Rule and use it to solve a system of equations. Days 15-17: Transformational Matrices Objectives: (M.4HS.CVM.16)(CCSS.Math.Content.HSN-VM.C.12(+)) Students will be able to use a rotational matrix to find the image or pre image of a matrix before or after a rotation. Students will be able to use a reflection matrix to find the image or pre image of a matrix before or after a reflection. Students will be able to multiply a matrix by a scalar to find the image or pre image of a matrix before or after a dilation. Students will be able to add values to elements of a matrix to find the image or pre image of a matrix before or after a translation. Students will work in small groups to sketch four geometric figures of their choice. Students will then decide which figure they wish to rotate, reflect, dilate, and translate. Students will work with their groups to rotate one of the four figures and then cut out the
Students will work with their groups to reflect one of the four figures and then cut out the Students will work with their groups to dilate one of the four figures and then cut out the Students will work with their groups to translate one of the four figures and then cut out the Students will share their completed transformational figures with the class and turn it in to the teacher for a group grade. Days 18-19: Review of Matrices Objectives: Students will be able to exhibit mastery of the content on the unit from matrices. Students will be able to verbally explain each key concept of matrices to their partner and to the teacher as if said individuals were not familiar with the content. Students will complete the attached study guide as a group and share their answers with the class. Students will participate in the jeopardy review game with the winning group receiving extra credit on the unit test. Day 20: Unit Test on Matrices Objectives: Students will be able to exhibit mastery of the content by completing the unit test to the best of their ability. Students will complete the unit test in one class period (45 minutes).