Course Information:
Instructor _Dean S. Conis_________ Course_Geometry___________________
Grade Level _10________________ Class Length_45min__________________
Unit __What is a Vector? Topic_How can we add (subtract) Vectors?_day4
Rationale:
We live in a multidimensional world full of multivariate phenomena. This unit is
a gentle introduction to Vector Algebra which is a gateway to Linear Algebra and
an introduction to working with bound quantities.
Vector addition and subtraction give real world problems of travel, force and
statics a mathematical method of formulation.
Prior Knowledge Required:
The student should be familiar with coordinate geometry, geometric transforms ,
the Pythagorean Theorem and simple Trigonometry. Having been introduced to
vectors and the zero vector and additive inverses, addition becomes consistent with
the addition of real numbers the student is familiar with.
Previous Activity:
Scalar multiplication introduced the student to the zero vector and additive
inverses.
Specific Goals/Objectives for Today’s Lesson(in terms of student learning):
> The student will know how to add and subtract two vectors graphically.
> The student will know how to add two vector component wise.
> The student will understand that vector subtraction involves additive inverses.
> The student will see that vector addition obeys Associative and Commutative
Laws.
> The student will understand adding the Zero Vector to any vector does not
change that vector.
>The student will worked some problems using vectors.
> The student will become familiar with notation.
State Standards( or city standards, when relevant):
>ISBE 6.A.5
>ISBE 7.B.4
>ISBE 8.C.4b
>ISBE 9.A.5, 9.B.4, 9.C.5b
Materials and Equipment:
Pencil, paper and calculator.
On-Task Start-up and Transition from Previous Activity(e.g. bell-ringers):
On the board both the Pythagorean Theorem and the Law of Cosines, with the
instruction to note the modification when the angle is not a right triangle.
Activities to Cover/Objectives(and time needed, in bold type):
1.(5 minutes)Bell Ringer
2.(5 minutes)Homework Review and Q&A.
3.(30 minutes)Lesson on Vector Addition and Subtraction
Graphical and Algebraic representation and calculation
4.(5 minutes)Homework passed out and discussed.
Checking to assess Student Mastery/Learning:
Does the student have the understanding that the distance between connected vectors
is the resultant?
Do Inverse Vectors have meaning?
Technology Inclusion:
Calculators may be used
Differentiating Instruction for Individual Student Needs:
The video from The Kahn Academy on vectors may give another introduction ( see
http://www.youtube.com/watch?v=FaF3v-ezbSk&feature=youtube_gdata_player).
Vector addition can also be performed with thin tape laid straight and a ruler.
One on one tutoring is available after school.
Review of Day’s Objectives:
Vector addition is given meaning graphically and algebraically. Physical problems can
now be approached.
Homework Assignment:
Homework number four, titled “How Can We Add and Subtract Vectors”, has practice
problems.
Reflection on the Lesson (What do you anticipate will work well? Potential Problems?)
Vector addition is what most people find useful and when it seems to make sense. For
those that have difficulty the ruler addition is available.
How do we add or subtract Vectors? Name___________________________________
1)
2)
< -1 , -4 > + < -1 , 4 > = < _______ , ________ >
4j + i + ( -2)j = < ______ , ________ >
3)
< 1 , -2 > + < 0 , 4 > = _____i + _____ j
4)
< 3 , 2 > + { < 4 , 1 > + < 5 , 0 > } = < _____ , ______ >
5)
{ < 3 , 2 > + < 4 , 1 > } + < 5 , 0 > = < _____ , _____ >
6)
A = < 4 , 7 > , B = < -3 , 3 > what is A – B? answer A – B = ____i + _____ j
7)
Add these vectors graphically as neatly as possible, preserving magnitude and
direction. Show result in the same grid.
a)
b)
8)
Find the missing scalar. < 30 , -13 > + _____ * < 7 , 12 > = < 9 , - 52 >
9)
Find the missing vector. 2 * < 1 , 3 > - < _____ , _____> = < 1 , 1 >
10) Graphically add : A = < 2 , 3 >, B = < 0 , -6 >, C = < -4 , 0 >, - B and D = < 2 , 3 > .
What is the result?
answer < _____ , _____ >
11) You start at Lincoln Ave and Howard ( 0.0 , 0.0 )
and ride your bike East to Howard and Western ( 3.0 , 0.0 ), then
you turn South and travel South to Balmoral your destination ( 3.0 , 2.8 ).
You have traveled 5.8 miles. If you had taken Lincoln Ave, how far would the trip
been? Show your work.