4C.NVM.4.5.12.7.11
2011
Domain: Number and Quantity
Cluster: Perform Operations on Matrices
Standard: 4. (+) Add and subtract vectors.
Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum
of two vectors is typically not the sum of the magnitudes.
Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude
as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the
appropriate order, and perform vector subtraction component-wise.
5. (+) Multiply a vector by a scalar.
Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform
scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).
Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when
|c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).
Essential Questions
Enduring Understandings
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How can we use
contextual situations
from a variety of
disciplines to model
vector addition and
subtraction?
How can scalar
multiplication be
connected to dilations
and similarity?
What real life examples
can be used to justify
vector addition and
scalar multiplication?
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The parallelogram rule is
used to find the sum of two
vectors.
Vectors are added using
components.
The magnitude of a sum of
two vectors is typically not
the sum of the magnitudes.
The resultant is the sum of
the horizontal and vertical
components of the vectors.
Activities, Investigation, and Student Experiences
1. Vector addition activities.
http://www.teacherlink.org/content/science/instruct
ional/activities/vectoraddition/Vectors-print.PDF
4C.NVM.4.5.12.7.11
Content Statements

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Students will add
vectors end-to-end,
component wise, and
by the parallelogram
rule.
Students will subtract
vectors and represent
subtraction
graphically.
Students will multiply
a vector by a scalar
and compute the
magnitude and
direction of a vector.
Assessments
1. Describe each resultant as an ordered pair
(example problems)
2. Open-ended question, such as:
Under what conditions is the scalar product of the
sum of two vectors the same as the sum of the
scalar products of the two vectors?
2. Classwork problems:
3. Finding the resultant vector:
2011
4C.NVM.4.5.12.7.11
2011
3. Under what conditions is the sum of the
magnitudes of two vectors be equal to the
magnitude of the sum?
Equipment Needed:
Smart board
Teacher Resources:

Calculators
Computer/Internet access
White boards
Overhead
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http://www.teacherlink.org/content/scien
ce/instructional/activities/vectoradditi
on/Vectors-print.PDF
http://mathworld.wolfram.com/VectorMultiplication.ht
ml
http://www.onlinemathlearning.com/vectormultiplication.html
http://mathworld.wolfram.com/DotProduct.html
http://www.netcomuk.co.uk/~jenolive/vect6.html
http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html
http://schools.utah.gov/CURR/mathsec/Com
mon-Core/Secondary-I/IHNVM.aspx
http://www.nhn.ou.edu/~walkup/demonstrations/WebTu
torials/HeadToTailMethod.htm