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56 Results
  • Curriculum Lesson
    Girl Studying

    Precalculus and Advanced Topics Module 1, Topic A, Lesson 4

    Jan 26, 2016 - Student Outcomes Students solve quadratic equations with complex solutions. Students understand the geometric origins of the imaginary unit i in terms of 90-degree rotations.  Students use this...
  • Curriculum Lesson
    Girl's Graduation Day

    Precalculus and Advanced Topics Module 3, Topic A, Lesson 3

    Jan 26, 2016 - Student Outcomes Students determine the complex roots of polynomial equations of the form xn = 1 and, more generally, equations of the form xn = k positive integers n and positive real numbers k....
  • Curriculum Lesson
    Lecture Hall

    Precalculus and Advanced Topics Module 3, Topic A, Lesson 2

    Jan 26, 2016 - Student Outcomes Students apply their understanding of polynomial identities that have been extended to the complex numbers to find the square roots of complex numbers.
  • Curriculum Lesson
    Boy Asking Question to Teacher

    Precalculus and Advanced Topics Module 3, Topic A, Lesson 1

    Jan 26, 2016 - Student Outcomes  Students determine all solutions of polynomial equations over the set of complex numbers and understand the implications of the fundamental theorem of algebra, especially for...
  • Curriculum Topic
    Students Commencement Ceremony

    Precalculus and Advanced Topics Module 3, Topic A, Overview

    Jan 26, 2016 - Topic A brings students back to the study of complex roots of polynomial functions.  Students briefly review quadratic and cubic functions and then extend familiar polynomial identities to both...
  • Curriculum Lesson
    Students Together

    Precalculus and Advanced Topics Module 2, Topic E Lesson 27

    Jan 26, 2016 - Student Outcomes Students will create a short animation in ALICE 3.1 using one-step procedures. Students will apply their understanding of the mathematics of projecting three-dimensional images onto...
  • Curriculum Lesson
    Students Studying in the Library

    Precalculus and Advanced Topics Module 2, Topic E, Lesson 26

    Jan 26, 2016 - Student Outcomes Students learn to project points in 3-dimensional space onto a 2-dimensional plane. Students learn how to simulate 3-dimensional turning on a 2-dimensional screen.
  • Curriculum Lesson
    Student Asking Teacher Question

    Precalculus and Advanced Topics Module 2, Topic E, Lesson 25

    Jan 26, 2016 - Student Outcomes Through discovery, students will understand how challenging it is to project three-dimensional objects onto a two-dimensional space. Students will understand that vanishing points...
  • Curriculum Topic
    Graduation Day

    Precalculus and Advanced Topics Module 2, Topic E, Overview

    Jan 26, 2016 - In Topic E students apply the knowledge developed in this module to understand how first-person video games use matrix operations to project three-dimensional objects onto two-dimensional screens and...
  • Curriculum Lesson
    High School Students Working in Library Together

    Precalculus and Advanced Topics Module 2, Topic D, Lesson 24

    Jan 26, 2016 - Student Outcomes   Students apply linear transformations and vectors to understand the conditions required for a sequence of transformations to preserve the solution set to the system of equations.
  • Curriculum Lesson
    Students Learning in Class

    Precalculus and Advanced Topics Module 2, Topic D, Lesson 22

    Jan 26, 2016 - Student Outcomes Students write parametric equations for a line through two points in ℝ2 and ℝ3 and for a line segment between two points in ℝ2 and ℝ3. Students write parametric equations for the...
  • Curriculum Lesson
    Students Reading Texts

    Precalculus and Advanced Topics Module 2, Topic D, Lesson 23

    Jan 26, 2016 - Student Outcomes Students solve problems involving physical phenomena that can be represented by vectors.
  • Curriculum Lesson
    Students Studying Together

    Precalculus and Advanced Topics Module 2, Topic D, Lesson 21

    Jan 26, 2016 - Student Outcomes Students write the equation for a line in ℝ2 or ℝ3 using vectors. Students write the parametric equations for a line in ℝ2 or ℝ3 . Students convert between parametric equations and...
  • Curriculum Lesson
    Students in the Library

    Precalculus and Advanced Topics Module 2,Topic D, Lesson 20

    Jan 26, 2016 - Student Outcomes Students understand the forces involved in constructing a stone arch. Students add and subtract vectors given in magnitude and direction form. Students solve problems that can be...
  • Curriculum Lesson

    nysed_playlist_no_item_0.jpg

    Precalculus and Advanced Topics Module 2, Topic D, Lesson 19

    Jan 26, 2016 - Student Outcomes Students find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. Students add vectors end-to-end using the...
  • Curriculum Lesson
    Students Learning Together

    Precalculus and Advanced Topics Module 2, Topic D, Lesson 18

    Jan 26, 2016 - Student Outcomes Students use vectors to define a translation map and translate geometric figures in ℝ and ℝ . Students represent and perform calculations with three-dimensional vectors and...
  • Curriculum Lesson
    Students Studying Together

    Precalculus and Advanced Topics Module 2, Topic D, Lesson 17

    Jan 26, 2016 - Student Outcomes Students add and subtract vectors and understand those operations geometrically and component-wise. Students understand scalar multiplication graphically and perform it component-...
  • Curriculum Topic
    Student on Compouter

    Precalculus and Advanced Topics Module 2, Topic D, Overview

    Jan 26, 2016 - Topic D opens with a formal definition of a vector.  The arithmetical work for vector addition, subtraction, scalar multiplication, and vector magnitude is explored along with the geometrical...
  • Curriculum Lesson
    Group Work

    Precalculus and Advanced Topics Module 2, Topic C, Lesson 16

    Jan 26, 2016 - Student Outcomes Students represent complicated systems of equations, including 4×4 and 5×5 systems of equations, using matrix equations in the form Ax = b, where A represents the coefficient matrix...
  • Curriculum Lesson

    nysed_playlist_no_item_0.jpg

    Precalculus and Advanced Topics Module 2, Topic C, Lesson 15

    Jan 26, 2016 - Student Outcomes Students will represent systems of three or more simultaneous equations as a linear transformation in the form Ax = b, where A represents the linear transformation, x represents the...
  • Curriculum Lesson
    Student in Library Reading

    Precalculus and Advanced Topics Module 2, Topic C, Lesson 14

    Jan 26, 2016 - Student Outcomes Students will represent systems of equations as linear transformations of the form Lx = b, using matrix notation. Students will discover that the systems of equations written in the...
  • Curriculum Topic
    Students Together

    Precalculus and Advanced Topics Module 2, Topic C, Overview

    Jan 26, 2016 - Topic C provides a third context for the appearance of matrices via the study of systems of linear equations.  Students see that a system of linear equations can be represented as a single matrix...
  • Curriculum Lesson
    Boy on Computer

    Precalculus and Advanced Topics Module 2, Topic B, Lesson 13

    Jan 26, 2016 - Student Outcomes Students study and practice the properties of matrix multiplication. Students understand the role of the multiplicative identity matrix.
  • Curriculum Lesson
    Students Learning in Library

    Precalculus and Advanced Topics Module 2, Topic B, Lesson 12

    Jan 26, 2016 - Student Outcomes Students discover and verify that matrix multiplication is distributive. Students discover and verify that matrix multiplication is associative.
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