N VM 9 Understand that, unlike multiplication of numbers, matrix Teacher Moves: Desmos has a powerful matrix calculator, https://www desmos com/matrix ,
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Georgia Department of Education
December 2020
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Pre-Calculus
COMPREHENSIVE COURSE OVERVIEW
Big Idea(s)/ Topic(s)
solutions in context. and quadratic equation in two variables.Standard(s) Alignment
MGSE9-12.N.VM.9 Understand that, unlike multiplication of numbers, matrix multiplication for squarematrices is not a commutative operation, but still satisfies the associative and distributive properties.
MGSE9-12.N.VM.10 Understand that the zero and identity matrices play a role in matrix addition andmultiplication 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. MGSE9-12.N.VM.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.MGSE9-12.A.REI.7 Solve a simple system consisting of a linear equation and a quadratic equation in two
variables algebraically and graphically. For example, find the points of intersection between the line y = ş3x
and the circle x2 + y2 = 3.MGSE9-12.A.REI.8 Represent a system of linear equations as a single matrix equation in a vector variable.
MGSE9-12.A.REI.9 Find the inverse of a matrix if it exists and use it to solve systems of linear equations
(using technology for matrices of dimension 3 × 3 or greater).Sample Mathematics Learning Plan
Georgia Department of Education
December 2020
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Diagnostic Assessment
Directions: Determine the equation of both of these lines. Use an algebraic technique (elimination, substitution, etc.) to determine the solution to the system.Georgia Department of Education
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Instructional Design
Desmos Activity: Applying Matrices and Parabolas
Engage
Teacher Moves: Ŗ
probably not enough information for students to have a great understanding of how to solve it, but they
should develop a vague idea of how high the balls travel. This will hopefully engage the student into wanting
to know more about the situation. student responses. document or video. Allow students to share responses within the Desmos platform and provide feedback via the teacher dashboard. Additionally, students could use an audio/video to share. Provide feedback to individual student responses and highlight multiple strategies used by students. before engaging in the remaining sections.Georgia Department of Education
December 2020
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Explore
Teacher Moves: This activity will explore solving a system of equations using matrices. In this first example,
because c is actually known to be 14, students could solve the system using substitution or elimination
Georgia Department of Education
December 2020
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Ŗowns so encourage
Teacher Moves: Desmos has a powerful matrix calculator, https://www.desmos.com/matrix, where students can create matrices and perform operations on them. Teacher Moves: A common mistake students make is not realizing that matrix multiplication is not commutative. Using C = B*A-1 (Inverse) will not solve the equation properly.Georgia Department of Education
December 2020
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Teacher Moves: If this is the first time students have used matrices to solve a system, you will probably
want to talk again about how to set the equations up to solve A,B, and C. Students can use the first example
Teacher Moves: Ŗ
how to find the vertex of a quadratic. You can relate the x-coordinate of the vertex, x = -b/(2a) to the
quadratic formula. The x-coordinate of the vertex is always the same distance away from the two x- intercepts, which is what the quadratic solves for.Georgia Department of Education
December 2020
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Georgia Department of Education
December 2020
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Teacher Moves: Graphing the parabolas usually gives students a better visual of the balŖ can see the graph touching the x-axis which is height 0 meters above the ground.Georgia Department of Education
December 2020
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Teacher Moves: Both of these equations are factorable. Talk about what that would change about the solutions if they were not factorable.Georgia Department of Education
December 2020
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Teacher Moves: Students can drag the points to see the heights of both balls after t seconds. They are at
the same height at t = 1.Georgia Department of Education
December 2020
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Teacher Moves: A larger graph is provided so students can investigate the two heights over time. Teacher Moves: The previous screen (showing the same graph) may be more helpful since it displayed larger.Georgia Department of Education
December 2020
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blended. complete the screens and provide feedback. Ensure that enough time is provided for students to participate and respond to your feedback and edit responses as needed. screens 2 and 3. Allow students time to complete the work and submit through email/text or other means. Provide feedback and share with other students and provide access to Ŗ thinking. ApplyTeacher Moves: We could create a function for the difference in their heights D(t) = J(t) - B(t). We would
obtain D(t) = -4t + 4. However, we still would have to analyze using the graph because D(t) would not have a
maximum over the domain of real numbers. What it does provide us is that the difference between their
heights is always decreasing (slope is -Ŗ ŖŖ-4(7) + 4 = -24) at t = 7 seconds and then blended. complete the screens and provide feedback. Ensure that enough time is provided for students to participate and respond to your feedback and edit responses as needed. the questions presented on screens 4 through 9. Ask students to complete the questions and haveGeorgia Department of Education
December 2020
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them submit responses via email/text/phone. Provide feedback, share these responses with otherTeacher Moves: To investigate #4, a graph was placed on the next screen so students could slide values of
A, B, and C to see how the maximum would change.
Reflect
Georgia Department of Education
December 2020
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e-mail, text, etc.). The teacher can provide feedback to students on commonalities of what confused students and what students would want to see next time. the learning log to keep track of the main ideas of the lessons.Evidence of Student Success
Formative Assessment Questions:
Georgia Department of Education
December 2020
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Student Learning Supports
Establish mathematics goals to focus learning.
Facilitate meaningful mathematical discourse.
Pose purposeful questions.
the whole group. those variables (i.e., two equations with two unknown variables) Support productive struggle in learning mathematics.Elicit and use evidence of student thinking.
technology. Proactively address them with readily available and accessible resources. talk about the order of multiplication when using arrays to solve systems.Engaging Families
Students can deepen their understanding of systems of equations by completing the following activities.
With this interactive applet, the student can drag around the points on the lines and watch this interactive system and its solution in action. This is a super calculator that solves system of equations (with up to four unknown variables and four equations) This video shows several examples of solving nonlinear systems of equations. This video shows an intro to parabolas and their important characteristics (vertex, direction of opening, axis of symmetry, etc.)quotesdbs_dbs20.pdfusesText_26