ADVANCED MATHEMATICS II
(SECONDARY)
SELECTIVE UNIT 1 (S01)
(Vectors (9.1-9.6))
(July 2013)
Unit Statement: This unit is intended to introduce the student to vectors and applications in
relationship to forces and work. The student will learn to break vectors into component form
and basic algebraic and geometric operations with vectors. Additionally, the student will
learn to write parametric equations of lines and utilize a normal vector to find the equation of
a plane. This selective unit is recommended for the student going into IB SL/HL
Mathematics or for students planning to pursue higher mathematics in university as concepts
are relevant to Calculus in three dimensions.
Essential Outcomes: (must be assessed for mastery)
1. The Student Will write a vector in component form given its initial and terminal points
and a student will write a vector in terms of it’s horizontal and vertical components, i, j
and k. [9.1, 9.4, pp. 580, 603]
2. TSW add and subtract vectors and multiply by a scalar quantity in component form
algebraically and graphically and find the resultant force when multiple forces act on
an object. [9.1, 9.4, pp. 580, 603]
3. TSW find the magnitude and direction of a vector. [9.1, 9.4, pp. 580, 603]
4. TSW calculate the dot product of two vectors in component form and utilize the dot
product to calculate work. [9.2, 9.4, pp. 589, 603]
5. TSW utilize the dot product to calculate the angle between two vectors and to determine if
two vectors are orthogonal. [9.2, pp. 589]
6. TSW calculate the projection of u onto v. [9.2, pp. 589]
7. TSW plot points and surfaces on a three-dimensional rectangular coordinate system [9.3,
pp. 597]
8. TSW use the distance formula to find the distance between two points in three dimensions.
[9.3, pp. 597]
9. TSW find the cross product of two vectors and use the cross product to find an orthogonal
vector and the area of a parallelogram. [9.5, pp. 610]
10. TSW find the parametric equation for a line in three dimensions. [9.6, pp. 616]
11. TSW Find the equation of a plane. [9.6, pp. 616]
12. TSW engage in one or more interactive activities or projects that requires inquiry, analysis,
application and/or interpretation of unit objectives (TSWs).
Introduced and Practiced Outcomes:
1. The Student Will find the volume of a parallelepiped. [9.5, pp. 610]
QSI ADV MATHEMATICS II S01
Copyright © 1988-2013
37
Suggested Assessment Tools and Strategies:


Attached Rubric or teacher generated rubric that assesses ALL essential outcomes
(TSWs)
o Warm up practice (Formative Assessment)
o Group quizzes to practice TSW’s (Formative Assessment)
o Unit assessments (Interim Assessment)
*TSW 16: Projects/Group Work (Interim and/or Summative Assessment)
o Group Work 2: Section 9.1: Where do they Point (Instructor’s Guide)
o Group Work 3: Section 9.1: Cones in General (Instructors Guide)
o Group Work 3: Section 9.2: The Regular Hexagon (Instructor’s Guide)
o Group Work 3: Section 9.3: Fun with Visualization (Instructor’s Guide)
o Group Work: Section 9.4: A Rectangular Solid
o Group Work 2: Section 9.5: A Matter of Shading
o Group Work 1: Section 9.6: The Match Game
Suggested Resources:
(See Course Outcomes for more detailed descriptions.)
 Geogebra graphing software
o Free to download at www.geogebra.org
 TI-Smartview Emulator Software for TI-84 Plus to enable a class display.
o Purchasable at http://education.ti.com
 Graphics Display Calculator for every student. Texas Instruments, TI-84 Plus is
recommended.
 Student Solutions Manual
 Complete Solutions Manual
 Study Guide
 Instructor’s Guide
 Solution Builder
(http://www.stewartmath.com/media/5_inside_supplements.php)
Additional Resources:
These materials will not be provided automatically but schools are encouraged to purchase
them when possible.



Enhanced WebAssign
Text-Specific DVDs
PowerLecture with ExamView CD-ROM
(http://www.stewartmath.com/media/5_inside_supplements.php)
Technology Links:
www.explorelearning.com
www.quia.com
www.stewartmath.com
QSI ADV MATHEMATICS II S01
Copyright © 1988-2013
www.nctm.org
www.geogebra.org
38
SUGGESTED RUBRIC ADVANCED MATH II S01
Student Name: __________________________ Date: _______________________
 To receive a ‘B’, the student must show ‘B’ level mastery on all essential outcomes (TSWs).
 The teacher’s discretion on the student’s holistic performance on the unit, including such items as: the above ‘A’ level rubric, the unit project, group work
and class discussions will determine ‘A’ level mastery.
1.
2.
3.
4.
5.
6.
7.
TSW
TSW write a vector in component
form given its initial and terminal
points and a student will write a vector
in terms of it’s horizontal and vertical
components, i, j and k.
TSW add and subtract vectors and
multiply by a scalar quantity in
component form algebraically and
graphically and find the resultant force
when multiple forces act on an object.
TSW find the magnitude and direction
of a vector.
TSW utilize vectors to model velocity
and force.
TSW calculate the dot product of two
vectors in component form and utilize
the dot product to calculate work.
TSW utilize the dot product to
calculate the angle between two vectors
and to determine if two vectors are
orthogonal.
TSW calculate the projection of u onto
v.
QSI ADV MATHEMATICS II S01
Copyright © 1988-2013
‘A’* LEVEL
TSW analyze how two or more vectors
can be adjusted to reach equilibrium;
justify your answers
TSW solve applied problems related to
velocity and force utilizing vectors.
TSW create a diagram that justifies the
vector formula for work.
TSW use their knowledge of the dot
product, angle between vectors and
magnitude to make conjectures on parallel
vectors and unit vectors.
‘B’ LEVEL
TSW write a vector in component form
given its initial and terminal points and a
student will write a vector in terms of it’s
horizontal and vertical components, i, j
and k.
TSW add and subtract vectors and multiply by
a scalar quantity in component form
algebraically and graphically and find the
resultant force when multiple forces act on an
object.
TSW find the magnitude and direction of
a vector.
TSW utilize vectors to model velocity
and force.
TSW calculate the dot product of two
vectors in component form and utilize the
dot product to calculate work.
TSW utilize the dot product to calculate
the angle between two vectors and to
determine if two vectors are orthogonal.
TSW calculate the projection of u onto v.
39
Comments
8. TSW plot points and surfaces on a
three-dimensional rectangular
coordinate system
9. TSW use the distance formula to find
the distance between two points in
three dimensions.
10. TSW find the cross product of two
vectors and use the cross product to
find an orthogonal vector (using the
Right-hand rule to determine its
direction) and the area of a
parallelogram.
11. TSW find the parametric equation for a
line in three dimensions.
12. TSW find the equation of a plane
utilizing a normal vector.
13. TSW engage in one or more interactive
activities or projects that requires
inquiry, analysis, application and/or
interpretation of unit objectives
(TSWs).
QSI ADV MATHEMATICS II S01
Copyright © 1988-2013
TSW draw conclusions by visualizing
three-dimensional space such as “How
many regions can be formed by two
planes?” (See Instructor’s Guide, Section
9.3: Fun with Visualization.)
TSW formulate a strategy for finding the
distance between a point and a line.
TSW plot points and surfaces on a threedimensional rectangular coordinate system
TSW plot points and surfaces on a threedimensional rectangular coordinate system
TSW find the cross product of two
vectors and use the cross product to find
an orthogonal vector and the area of a
parallelogram.
TSW analyze if there is more than one
way to write a parametric equation of a
line and justify their reasoning.
TSW find the intersection of a line and a
plane.
TSW find the parametric equation for a
line in three dimensions
TSW find the equation of a plane utilizing
a normal vector.
The teacher should assess for mastery with an individualized rubric for the assignment.
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