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Common Core High School Number and Quantity Teaching and Learning Resources

Domain: VM: Vector and Matrix Quantities

Common Core Math

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VM-A: Represent and model with vector quantities.

Standards:

 

Technology-enhanced investigations:

Mathwords.com: Math Dictionary: Key vocabulary for this domain.  Use with VM-A, VM-B, VM-C:

additive inverse of a matrix dimensions of a matrix matrix addition scalar
argument of a vector distribute matrix inverse square matrix
associative operation identity matrix matrix multiplication vector
commutative operation magnitude of a vector matrix subtraction velocity
determinant matrix model zero matrix

 

CK-12 Flexbook: Trigonometry Concepts: Ch. 5: Triangles and Vectors: concepts, practice problems for learners, and videos included.  Complete the following sections:

GeoGebra: Vector Addition applet for viewing 2D vectors and their sum.

Mathispower4u: Trigonometry Videos is an extensive collection on nearly every topic in trig from James Sousa and includes a section on vectors and their operations.  Aligns with VM-A and VM-B.

PhET Interactive Simulations: Vector Addition and Vector Addition: Equations.  Aligns with VM-A.1, VM-A.2, VM-B.4, and VM-B.5.

PhysicsClassroom.com: Vectors -- Motion and Forces in Two Dimensions includes three lessons, each with multiple sections, animations, and embedded problems for learners to test their understanding.  Lesson 1: Vector fundamentals and operations; Lesson 2: Projectile motion; and Lesson 3: Forces in two dimensions.  Aligns with VM-A and VM-B.

TED-Ed Lessons: What is a vector? In this YouTube video (approx. 5 minutes), educator David Huynh "explains how vectors are a prime example of the elegance, beauty, and fundamental usefulness of mathematics" and begins by reminding viewers that "Physicists, air traffic controllers, and video game creators all have at least one thing in common: vectors."  Learn what vectors are and why they matter.  Aligns with VM-A.

Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives.  Note: Within the Wolfram Demonstration Project are 13 manipulatives addressing VM-A.1, 8 manipulatives addressing VM-A.2, and 4 manipulatives addressing VM-A.3. Among those are:

Multiple Choice:

Khan Academy: Precalculus Vectors unit. Practice questions with videos.

Constructed-response:

Algebra Lab:

Khan Academy: Precalculus Vectors unit. Practice questions with videos.

Performance tasks:

Georgia Standards of Excellence Framework: Pre-Calculus Unit 7: Vectors.  This unit contains ten tasks, including a culminating task: Putting It All Together. Tasks align with VM-A.1, VM-A.2, VM-A.3, VM-B.4, VM-B.5, and VM-C.11 and number standards CN-A.3, CN-B.4, CN-B.5, CN-B.6.

 

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VM-B: Perform operations on vectors

Standards:

Technology-enhanced investigations:

A. Dendane: Analyze Math:

Academo.org: 3D Vector Plotter.  Enter two vectors of the form (x, y, z) and see the sum, difference, and cross-product of the vectors.  Clicking on the end of a vector will reveal its components.  You can rotate the diagram and zoom in and out.  When z=0, the interactive is useful for viewing vectors in 2D.  Aligns with VM-B.4.

CK-12 Flexbook: Trigonometry Concepts: Ch. 5: Triangles and Vectors: concepts, practice problems for learners, and videos included.  Complete the following sections:

Interactive Mathematics: Introduction to Vectors includes 1-D, 2-D, and 3-D vector exploration.  Aligns with VM-B.4.

Mathinsight.org: Introduction to Vectors, including operations on vectors( +, -, scalar multiplication) and applets to explore magnitude and direction, vector addition.  Aligns with VM-B.4 and VM-B.5.

Mathispower4u: Trigonometry Videos is an extensive collection on nearly every topic in trig from James Sousa and includes a section on vectors and their operations.  Aligns with VM-A and VM-B.

PhET Interactive Simulations:

PhysicsClassroom.com: Vectors -- Motion and Forces in Two Dimensions includes three lessons, each with multiple sections, animations, and embedded problems for learners to test their understanding.  Lesson 1: Vector fundamentals and operations; Lesson 2: Projectile motion; and Lesson 3: Forces in two dimensions.  Aligns with VM-A and VM-B.

Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives.  Note: Within the Wolfram Demonstration Project are 12 manipulatives addressing VM-B.4. Among those are:

Multiple Choice:

Khan Academy: Linear-algebra: Vectors and spaces unit and Precalculus Vectors unit.  Two units with practice questions with videos.

Constructed-response:

Algebra Lab:

Khan Academy: Linear-algebra: Vectors and spaces unit and Precalculus Vectors unit.  Two units with Practice questions with videos.

Performance tasks:

Georgia Standards of Excellence Framework: Pre-Calculus Unit 7: Vectors.  This unit contains ten tasks, including a culminating task: Putting It All Together. Tasks align with VM-A.1, VM-A.2, VM-A.3, VM-B.4, VM-B.5, and VM-C.11 and number standards CN-A.3, CN-B.4, CN-B.5, CN-B.6.

 

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VM-C: Perform operations on matrices and use matrices in applications

Standards:

 

Technology-enhanced investigations:

A. Dendane: Analyze Math:

Calcul: Matrix Arithmetic Calculator (Solver).  This calculator with add, subtract, or multiply matrices.  You can input arbitrary matrices sizes (as long as they are correct).  Details for solutions are presented.  Aligns with VM-C.8.

CK-12: Algebra: Matrices The unit in algebra for matrices begins with Introduction to Matrices: concepts, practice problems for learners, and videos included, which aligns with VM-C.6.  The unit proceeds with matrix algebra, adding/subtracting/multiplying matrices including multiplying by a scalar and limitations of matrix multiplication, determinants, Cramer's Rule, matrix equations and solving those, solving systems  of linear equations with matrices, inverse matrices, and applications of matrices.  Unit aligns with VM-C.

CK-12 Flexbook: Algebra II with Trigonometry: Ch. 4: Matrices.  This chapter includes operations on matrices, multiplying matrices, determinants and Cramer's rule, identity and inverse matrices, and solving linear systems using inverse matrices.  Content also includes practice exercises for learners and videos.  Aligns with VM-C.

Mathinsight.org: Introduction to Matrices is comprehensive, including multiplying matrices and vectors with examples, how to transpose a matrix, matrices and determinants, the relationship between determinants and area or volume, determinants and linear transformations, and more.  Aligns with VM-C.

TED-Ed Lessons: How to organize, add and multiply matrices.  In this YouTube video (approx. 5 minutes), educator Bill Shillito introduces the concept of matrices.  He shows how to work with matrices, including tips for adding, subtracting, and multiplying them.  He begins by noting that matrices date back to ancient China.  They are everywhere, used in business, economics, physics, cryptography, electronics, and 3D graphics.  The video is followed by an six question quiz.  Aligns with VM-C.

Interactive Mathematics: The following align with VM-C.7 and VM-C.8:

Math is Fun: Matrix Calculator enables the user to work with matrices up to 10 x 10.  Operations include addition, subtraction, multiplication, finding a determinant, an inverse, squaring a matrix, and more.  Aligns with VM-C.8.

MatrixCalc.org: Matrix Calculator helps the user to find the determinant of a matrix, the rank, raise a matrix to a power, find sum and multiplication of matrices, calculate the inverse matrix.  Enter the matrix elements and click a button.  You can also solve systems of equations using matrices.  Aligns with VM-C.8.

Matrixcalculator.com logo Matrix Calculator developed by PJ in Belgium enables the user to work with matrices up to 10 x 10.  The calculator will add, subtract, multiply, divide, transpose, find an inverse, find a determinant, and raise to a power.  The beauty of this calculator is that each answer comes with a step-by-step, easy to understand, solution.  Users can show instructions for each operation, which are clearly written and help to understand the math.  Aligns with VM-C.8.

Meta-Calculator.com: With the Matrix Calculator you can add, subtract, multiply, transpose, find the inverse, determinant, and more.  Aligns with VM-C.8.

Purple Math:

Stat Trek: Tutorials: Matrix Algebra.  Lessons delve into matrix types, operations (addition, multiplication, vector multiplication, elementary operations), Echelon matrices, properties (vector dependence, matrix rank, determinants), the matrix inverse, applications, matrix theorems, notations.  Most lessons include sample problems.  Aligns with VM-C.

Study.com: Common Core HS Math: What is a Matrix? and How to Take the Determinant of a Matrix.  These video lessons also include sample problems and a short quiz.  Aligns with VM-C.6.

YouTube videos: Videos on solving systems with matrices and working with matrices.

Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives.  Note: Within the Wolfram Demonstration Project are 1 manipulative addressing VM-C.8, 4 manipulatives addressing VM-C.11, and 8 manipulatives addressing VM-C.12. Among those are:

Multiple Choice:

Khan Academy: Practice questions with videos.

Constructed-response:

Khan Academy: Precalculus Matrices unit.  Practice questions with videos.

Zweigmedia.com:  Tutorials and examples using fill-in or multiple choice to test understanding.  Application examples of concepts are included, as well as additional review exercises and topic true-false quizzes.  Learners can also choose to do game versions of some topics.  Use with VM-C:

Performance tasks:

Georgia Standards of Excellence Framework:

 

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