Printed by the Document Publishing Centre
Design: Strategic Marketing and Graphic Design
2004
04ED10-10204
Acknowledgments
The creation of this curriculum guide has become a reality due to the efforts of the Transitions
Mathematics Curriculum Committee and the Pilot Teachers. Their efforts are acknowledged with
sincere thanks from the Prince Edward Island Department of Education.
Transitions Mathematics Curriculum Committee
George Aiken
- Kensington Intermediate Senior High School
John Dunsford
- Bluefield High School
Edwin Hughes
- Westisle Composite High School
Dawn MacFadyen
- Three Oaks Senior High School
Carrie Watters
- Three Oaks Senior High School
Betsy O’Brien
- Holland College Adult and Community Education
Doug Kelly
- Holland College
Eric Gallant
- Department of Education
Brenda Millar
- Department of Education
Pilot Teachers
Carrie Watters
Elmer Arsenault
Edwin Hughes
Lorne Acorn
Scott MacCormack
- Three Oaks Senior High School
- Westisle Composite High School
- Westisle Composite High School
- Kinkora Regional High School
- Charlottetown Rural High School
Table of Contents
1.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
a.
b.
c.
d.
Environment for Learning and Teaching Mathematics . . . . . . . . . . . . 3
Teaching Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Assessment and Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Adapting to the Needs of All Learners . . . . . . . . . . . . . . . . . . . . . 6
2.
Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.
Estimates of Instructional Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.
Curriculum Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
a.
b.
c.
d.
e.
f.
g.
h.
i.
5.
Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Chapter 1 - Income and Debt . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Chapter 2 - Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Chapter 3 - Owning and Operating a Vehicle . . . . . . . . . . . . . . . .
Chapter 4 - Measurement Technology . . . . . . . . . . . . . . . . . . . . .
Chapter 5 - Relations and Formulas . . . . . . . . . . . . . . . . . . . . . . .
Chapter 6 - Applications of Probability . . . . . . . . . . . . . . . . . . . .
Chapter 7 - Personal Income Tax . . . . . . . . . . . . . . . . . . . . . . . . .
Chapter 8 - Preparing a Business Plan . . . . . . . . . . . . . . . . . . . . .
Appendix
9
11
31
43
63
77
93
105
111
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
1
2
Introduction
According to the 1999 Report of the Senior High School Transitions Advisory
Committee, the goal of the Transitions initiative is “to encourage and foster an increase
in the education attainment of students and to provide students with the opportunity to
obtain academic, personal, social and experiential foundations that will sustain life long
learning, the ability to access further training (either on the job or continuing their
education) and to equip them in their role as citizens in our society.”
It is the purpose of this Mathematics 531A Curriculum Guide to support this goal. It is a
major commitment of the Department of Education.
Environment for Learning and Teaching Mathematics
It is recognized that the teacher is a key element to the success of this initiative.
The information in this guide has been created by teachers for teachers with practical
suggestions to support the delivery of this curriculum. The learning environment for
grades 10-12 is:
participatory, interactive, and collaborative
inclusive, caring, safe, challenging
inquiry based, issues oriented
a place where resource-based learning which includes and encourages the
multiple uses of technology, the media, and other visual texts as pathways to
learning and as avenues for representing knowledge.
The teacher structures the learning situation and organizes necessary resources. In
assessing the nature of the task, the teacher may find that the situation calls for teacherdirected activities with the whole class, small groups of students, or individual students.
Such activities include direct instruction in concepts and strategies and brief mini-lessons
to create and maintain a focus.
As students develop a focus for their learning, the teacher moves to the perimeter to
monitor learning experiences and to encourage flexibility and risk taking in the ways
students approach learning tasks. The teacher intervenes, when appropriate, to provide
support. In such environments, students will feel central in the learning process.
As the students accept more and more responsibility for learning, the teacher’s role
changes. The teacher notes what the students are learning and what they need to learn,
and helps them to accomplish their tasks. The teacher can be a coach, a facilitator, an
editor, a resource person, and a fellow learner. The teacher is a model whom students
can emulate, a guide who assists, encourages, and instructs the student as needed during
3
the learning process. Through the whole process, the teacher is also an evaluator,
assessing students’ growth while helping them to recognize their achievements and their
future needs.
Learning environments are places where teachers:
•
integrate new ways of teaching and learning with established effective practices
•
have an extensive repertoire of strategies from which to select the one most
appropriate for the specific learning task
•
value the place of dialogue in the learning process
•
recognize students as being intelligent in a number of different ways and
encourage them to explore other ways of knowing by examining their strengths
and working on their weaknesses
•
value the inclusive classroom and engage all learners in meaningful activities
•
acknowledge the ways in which gender, race, ethnicity, and culture shape
particular ways of viewing and knowing the world
•
structure repeated opportunities for reflection so that reflection becomes an
integral part of the learning process
The physical learning environment should not be restricted to one classroom. There
should be ample physical space for students to use cooperative learning techniques as
well as other learning styles. There should be access to other learning centers in the
school building such as labs and gymnasiums. Learning should be extended to
community facilities, allowing field trips and guest speakers to expand the learning
environment, while appreciating the focus of the community in their education.
The learning environment will be one in which students and teachers make use of
manipulative materials and technology. In addition, they will actively participate in
discussing, verifying, reasoning, and sharing solutions. This environment will be one in
which respect is given to all ideas, and reasoning and sense-making are valued above
“getting the right answer”. Students will have access to a variety of procedural skills,
such as estimating routinely to verify the reasonableness of their work and computing in
a variety of ways while continuing to place emphasis on basic mental computation skills.
Teaching Strategies
Learning theory research clearly indicates that teachers need to employ a wide variety of
instructional strategies to address the learning styles of all learners. Moreover, the nature
of certain content or processes can only be taught effectively if specific instructional
strategies are employed. In order to achieve this objective, students must have an
opportunity to co-operatively brainstorm, discuss, evaluate information and make
informed decisions. Students often point to experiential activities as the best part of a
program as they have the chance to work cooperatively and be actively involved in the
learning process.
4
Teachers are ultimately responsible for determining the best teaching methods for their
students, the best way of grouping them, and the best way to present material to make it
relevant and interesting. Exemplary teachers use a variety of instructional strategies and
have the flexibility to call upon several different strategies both within one period and
during a unit of study. Adolescent learners need a balance between practical work,
listening, discussing, and problem-solving.
The Mathematics 531 course should provide students with an activity-based, meaningful
math course. The key is not what we teach, but how we teach. Content is important, but
not as important as having students engaged in relevant learning. It is our belief that a
motivated student who is actively learning will be more likely to stay on task, be less
disruptive, and attend more regularly. Establishing a classroom climate that is student
centered is of utmost importance for the success of this program.
Assessment and Evaluation
The terms “assessment” and “evaluation” are often used interchangeably. However, they
are not exactly the same. “Assessment” refers to the process of collecting and gathering
information about student performance as it relates to the achievement of curriculum
outcomes. “Evaluation” refers to the systematic process of analyzing and interpreting
information gathered through the process of assessment. Its purpose is to make
judgements and decisions about student learning. Assessment provides the data.
Evaluation brings meaning to the data. Assessment must reflect the intended outcomes,
be ongoing, and take place in authentic contexts.
Meaningful learning involves reflection, construction, and self-regulation. Students are
seen as creators of their own unique knowledge structures, not as mere recorders of
factual information. Knowing is not just receiving information but interpreting and
relating the information to previously acquired knowledge. In addition, students need to
recognize the importance of knowing not just how to perform, but when to perform and
how to adapt that performance to new situations. Thus, the presence or absence of
discrete bits of information - which has been the traditional focus of testing is no longer
the focus of assessment of meaningful learning. Rather, what is important is how and
whether students organize, structure, and use that information in context to solve
problems.
Evaluation may take different forms depending on its purpose. Diagnostic evaluation
will identify individual problems and suggest appropriate corrective action. Evaluation
may be formative in that it is used during the instructional process to monitor progress
and to make necessary adjustments in instructional strategies. Summative evaluation is
intended to report the degree to which the intended curriculum outcomes have been
achieved. It is completed at the end of a particular instructional unit.
5
Adapting to the Needs of All Learners
The Foundation for the Atlantic Canada Mathematics Curriculum stresses the need to
deal successfully with a wide variety of equity and diversity issues. Not only must
teachers be aware of and adapt instruction to account for differences in student readiness
as they enter the senior high setting and as they progress, but they must also remain
aware of avoiding gender and cultural biases in their teaching. Ideally, every student
should find his or her learning opportunities maximized in the mathematics classroom.
The reality of individual student differences must not be ignored when making
instructional decisions. While this curriculum guide presents specific curriculum
outcomes, it must be acknowledged that all students will not progress at the same pace
and will not be equally positioned with respect to attaining any given outcome at any
given time. The specific curriculum outcomes represent, at best, a reasonable framework
for assisting students to ultimately achieve the key-stage and general curriculum
outcomes.
As well, teachers must understand and design instruction to accommodate differences in
student learning styles. Different instructional modes are clearly appropriate, for
example, for those students who are primarily visual learners versus those who learn best
by doing. Further, the practice of designing classroom activities to support a variety of
learning styles must be extended to the use of a wide variety of assessment techniques,
including:
6.
journal writing/portfolios
7.
projects
8.
presentations
9.
structured interviews
10.
performance
11.
paper and pencil
12.
research
13.
investigation
14.
technology
Students will be expected to address routine and/or non-routine mathematical problems
on a daily basis. Over time, numerous problem-solving strategies should be modeled for
students, and students should be encouraged to employ various strategies in many
problem-solving situations. While choices with respect to the timing of the introduction
of any given strategy will vary, strategies such as:
•
guess and check
•
make assumptions
•
use a data bank
•
look for a pattern
•
use logic
•
work backwards
•
use a formula
6
•
interpret graphs
•
use a diagram or flow chart
•
solve a simpler problem
•
use algebra
•
use a table or spreadsheet
•
use estimation
should all become familiar to students.
Opportunities should be created frequently to link mathematics and career opportunities.
During these important transitional years, students need to become aware of the
importance of mathematics and the need for mathematics in many career paths. This
realization will help maximize the number of students who strive to develop and maintain
the mathematical abilities required for success in future areas of study.
The unifying ideas of the mathematics curriculum suggest quite clearly that the
mathematics classroom needs to be one in which students are actively engaged each day
in the doing of mathematics. No longer is it sufficient or proper to view mathematics as a
set of concepts and algorithms for the teacher to transmit to students. Instead, students
must come to see mathematics as a vibrant and useful tool for helping them understand
their world and as a discipline which lends itself to multiple strategies, student
innovation, and quite often, multiple solutions.
Resources:
Mathematics 531A Curriculum Guide
Essentials of Mathematics 11 - Student text
Essentials of Mathematics 11 - Teacher Resource Book
Choices and Decisions - Taking Charge of Your Financial Life - VISA Canada
Teaching Taxes Program - Canada Customs and Revenue Agency
Numeracy at Work - BC Construction Industry Skills Improvement Council
Algebra To Go - Teacher Resource and Handbook
Tools:
TI-30X Scientific Calculators - one class set per school
Vernier Calipers - one class set per school
7
Estimates Instructional Time
The following chart shows the estimated instructional time for each chapter expressed as a
percentage of total time available to teach the course. Teachers should aim to spend no more
than 2 ½ weeks per chapter.
Chapter
Problem Solving
pages in guide
integrated throughout
% of Time
Weeks
integrated throughout
1 - Income and Debt
12-27
15 - 25
3- 4
2 - Data Analysis
28-37
10 - 15
2
10 - 15
3-4
3 - Owning and Operating a Vehicle
38-55
56-67
5- 10
1
5 - Relations and Formulas
68-81
10 - 15
2
6 - Applications of Probability
82-91
10 - 15
2
7 - Personal Income Tax
92-95
10- 15
2- 3
8 - Business Plan (Optional)
96-109
15 - 20
1-2
8
4 - Measurement Technology
Curriculum Content
Problem Solving is a key aspect of any mathematics course. Working on problems
involving estimation, measurement, and constructing can give students a sense of the
excitement involved in creative and logical thinking. It can also help students develop
transferable real-life skills and attitudes. Multi-strand and interdisciplinary problems
should be included throughout Essentials of Mathematics 10.
Reinforce the concept that "problem solving" is more than just word problems and
includes other aspects of mathematics.
Introduce new types of problems directly to students (without demonstration) and play
the role of facilitator as they attempt to solve such problems.
Recognize when students use a variety of approaches; avoid becoming prescriptive about
approaches to problem solving.
Reiterate that problems might not be solved in one sitting and that "playing around" with
the problem—revisiting it and trying again—is sometimes needed.
Frequently engage small groups of students (two to five) in co-operative problem solving
when introducing new types of problems.
Have students or groups discuss their thought processes as they attempt a problem. Point
out the strategies inherent in their thinking (e.g., guess and check, look for a pattern,
make and use a drawing or model).
Ask leading questions such as:
a. What are you being asked to find out?
b. What do you already know?
c. Do you need additional information?
d. Have you ever seen similar problems?
e. What else can you try?
Once students have arrived at solutions to particular problems, encourage them to
generalize or extend the problem situation.
Assessment Strategies for Problem Solving:
Observe
Have students present solutions to the class individually, in pairs, or in small groups.
Note the extent to which they clarify their problems and how succinctly they describe the
processes used.
9
Question
To check the approaches students use when solving problems, ask questions that prompt
them to:
a. paraphrase or describe the problem in their own words
b. explain the processes used to derive an answer
c. describe alternative methods to solve a problem
d. relate the strategies used in new situations
e. link mathematics to other subjects and to the world of work
Collect
On selected problems, have students annotate their work to describe the processes they
used. Alternatively, have them provide brief descriptions of what worked and what did
not work as they solved particular problems.
Self-Assessment
Ask students to keep journals to describe the processes they used in dealing with
problems. Have them include descriptions of strategies that worked and those that did
not.
10
UNIT 1
INCOME AND DEBT
11
General Curriculum Outcome: Students will be able to demonstrate an awareness of the
different functions of a calculator.
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
•
•
12
demonstrate selected
functions of the TI-30X
calculator
Reset the calculator
Functions
• fix button
( 2nd ) ( FIX )
• bracket buttons ( )
• replay button
• delete button
( DEL )
• insert button
( 2nd ) ( INS )
• percent
• exponent
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
The matching of keys with functions should be
completed in this section.
Internet Resource:
˜ Users Resource Guide
Texas Instruments
www.ti.com/calc
˜ Overview of the TI30X IIS
scientific calculator
http://education.ti.com/us/pr
oduct/tech/30xiss/features/fe
atures.html
˜ TI-30X IIS Quick Reference
Guide (5 pages)
http://education.ti.com/us/pr
oduct/tech/30xiis/guide/30xii
sguideqgus.html
˜ TI-30X IIS Guide for Teachers
(118 pages)
http://education.ti.com/us/pr
oduct/tech/30xiis/guide/30xii
sguideus.html
˜ Free download of
Graphing Calculator to
Computer
http://www.geocities.com/the
sciencefiles/graphcalc/graph
calc.html
˜ Free download of Trig and
Geometry Calculators
http://www.wcsscience.com/c
alculators/page.html
The TI-30X IIS Guide for Teachers has a large number
of worksheets to allow students to practice using
functions.
Graphing calculator (TI-83) with
screen for demonstration
In-school Resource:
- Poster for graphing calculator
- Class set of TI-30X calculators
13
General Curriculum Outcome: The student will be able to demonstrate an awareness of
selected forms of personal income and debt.
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
solve problems involving:
•
Straight Commission
Straight Commission
Straight Commission = (Total Sales) x ( %)
Demonstrate steps using TI-83 calculator and overhead
screen.
•
Salary Plus Commission
Salary Plus Commission
Salary Plus Commission = (Salary) + (Total Sales) x (%)
Demonstrate steps using TI-83 calculator and overhead
screen.
•
Graduated Commission
Graduated Commission
Graduated Commission is a sales incentive program using
increased commission.
(Level 1) x (%) + (Level 2) x (%) + (Level 3) x (%)
Use a test tube with coloured layers to demonstrate the
change in commission amount.
Picture:
(Amount in Level 2) x (% rate)
(Amount in Level 1) x (% rate)
14
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Straight Commission
Straight Commission
Essentials of Mathematics 11
P. 14, Example 1
Notebook Assignment P. 18 # 1-3
Brainstorm careers/jobs using Straight Commission.
Salary Plus Commission
Brainstorm careers/job using Salary Plus Commissions.
Graduated Commission
Use the following example to teach this commission.
$20,000 in Area x 6%
$ 20,000
$10,000 in Area x 4%
$10,000
Amount in Area x 2%
A person sells $40,000 worth of goods:
SOLUTION
$10,000 x 2% = $200.00
$10,000 x 4% = $400.00
$20,000 x 6% = $1,200.00
Graduated Commission is $ 1, 800.00
Other Questions
1) What are commissions?
Possible Answer: A percent of sales that is paid to the
salesperson.
2) Which jobs include commissions?
Some Possibilities: real-estate agent, car salesperson, appliance
salesperson, clothing salesperson, insurance salesperson
3) Why pay with a commission rather than an hourly wage or
salary?
Possible Answer: To encourage salespeople to work harder to
sell the merchandise.
In-school Resource:
- Numeracy at Work P. 68
Activity # 1-3
Salary Plus Commission
Essentials of Mathematics 11
P. 14, Example 2
Notebook Assignment
P. 18-19, # 4-6
' OMIT
Text P. 19 # 8
Graduated Commission
Essentials of Mathematics 11
P. 15, Example 3
Notebook Assignment
P. 19-20, # 7, # 9-11
Chapter Project begins on P. 12
Students can complete the “Earning Commission”
worksheet. See Appendix 1
Use small group discussion in Essentials of Mathematics
11 P. 16
15
SCO: By the end of grade 11
students will:
•
solve problems using
performance-based income
Elaboration - Instructional Strategies/Suggestions
Performance-Based Income
Performance-based Income = (Units) x ($ per Unit)
Example: A seamstress gets paid by the number of logos
she sews on jackets. At 20¢ per logo, it is expected she will
sew 100 logos per hour. What is her hourly rate?
(100 units) x (.20¢ per unit) = $20.00
Discussion from newspapers:
• Make $1,000.00 stuffing envelopes
• Tree Planters pay rate is by $ per trees planted
• Newspaper carriers
16
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Brainstorm careers/jobs based on this income.
Essentials of Mathematics 11
P. 23-24 Example 1-3
Notebook Assignment
P. 25-27 # 1-12
Use for discussion Notebook Assignment P. 25
# 1-2
Students can complete ‘Weekly Wages for Piecework’
worksheet. See Appendix 2.
In-school Resource:
- Numeracy at Work P. 122
Activity 1- 4
' OMIT
Essentials of Mathematics 11
P. 25, # 4
17
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
Simple Interest
I = Prt
I = Interest, P = principal, r = rate, t = time
Note: Rate can be entered as % or converted to decimal.
TI -30X - review conversion.
Time is always expressed in years, so students must
multiply by 12 to calculate the number of months and
multiply by 365 to calculate the number of days.
solve problems using
simple interest
A neat way of finding one unknown with this formula is to
use the following diagram:
To find the formula for I, just cover
the I with a finger and because the
P, r, and t are lined up horizontally,
they are multiplied. To find P,
cover it, and the I is over the r and
t, so I is divided by r times t. Be
careful to use brackets around the r
x t! To find r, cover it and the
resulting formula is I divided by P times t. And finally, to
find t, the resulting formula is t =
I
( P × r)
.
If using a calculator to do Example 3 on page 30, have
I
P=
students express the formula as:
(r × t )
using the triangle method above. Then replace the values
$300
for I, r, and t and get: P =
remembering that
(6% × 4)
both the 6% and the 4 are divided into $300.
This can be done differently, depending on the type of
calculator used. (ie: Press 300 ÷ 6 % ÷ 4 = 1250 for any
type of calculator or if using a scientific calculator, press
300 ÷ ( 6 % × 4 ) = 1250.)
Note: 6% can be replaced by 0.06, anytime.
Invite a guest speaker (ie: accountant, banker, financial
planner) to address topics related to credit and borrowing.
Students should prepare questions to focus on the
underlying mathematics involved.
18
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Students can complete “Calculating Simple Interest”
worksheet. See Appendix 3.
Essentials of Mathematics 11
P. 29-31 Example 1 -5
Notebook Assignment P.32 - 33
#1-7
Worksheets to help students convert;
•
•
•
•
•
•
months to years
6 months ÷ 12 = 0.5 years
years to month
0.5 years x 12 = 6 months
weeks to years
13 weeks ÷ 52 = 0.25 years
years to weeks
0.25 years x 52 = 13 weeks
days to years
30 days ÷ 365 = 0.08 years
years to days
0.08 years x 365 = 30 days
Teachers may wish to introduce students to using
spreadsheets to calculate interest. Students who had
Essentials of Mathematics 10 possibly had some practice
in using spreadsheets already. A review, as a minimum,
would be necessary.
Quattro Pro is a tool for spreadsheets. The website cited
gives an excellent tutor to teach the use of this
spreadsheet program. It takes about one hour to complete
the tutorial.
Internet Resource:
˜ http://electron.cs.uwindsor.c
a/60-104/quattro.html#top
Example for spreadsheet
What rate does Phoebe have to get if she has $5000 to
invest and she wants to get $5500 back after five years?
Solution
r = I / (Pt)
I = $5500 – $5000= $500, P = $5000 , t = 5,
r = 500 ÷ (5000 x 5) thus r = 500 ÷25 000
r = 0.02 = 2%
Demonstrate other problems involving principal, time,
and the interest as the variable.
19
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
solve problems using
compound interest
Compound Interest is a simple interest with a changing
principal at the end of each interest period.
•
Compound Interest
Formula
Discuss the formula:
⎡ r⎤
A = P ⎢1 + ⎥
⎣ n⎦
( nt )
where: A = total amount, including principal and
interest
P = the amount of principal, loan, or deposit
r = rate expressed as a decimal
n = number of compounding periods per year
t = time in years
* Formula is shortcut for Text P. 35 Example 1
• Rule of 72
Introduce the Rule of 72 as a quick way to estimate the time
it takes for an investment to double in value for a specific
rate of interest. To calculate the doubling time, divide 72 by
the rate given.
72
r
where r must not be entered as a decimal.
The Math 431A curriculum contains a chapter on the use of
spreadsheets, so students may recall their use and apply it to
compound interest problems.
Students need to understand the terms:
• Annually
ie: (n = 1)
• Semi -annually ie: (n = 2)
• Quarterly
ie: (n = 4)
• Daily
ie: (n = 365)
20
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Compound Interest
Compound Interest
Essentials of Mathematics 11
P. 35 Example 1
Notebook Assignment P. 38 # 1
Provide students with descriptions of various
financial situations (e.g., inheritance in trust,
retirement plans, appreciating assets, a first
vehicle purchase).
To show the difference between Simple Interest and
Compound Interest use Essentials of Mathematics 11,
P. 35, Example 1.
Spreadsheets could be used to find answers for any
Compound interest calculation but recommended for
Notebook Assignment P. 39 # 10.
Formula:
Essentials of Mathematics 11
P. 36 Example 2
Notebook Assignment P. 38 # 1
Rule of 72:
Essentials of Mathematics 11
P. 37 Example 3
Notebook Assignment
P. 38-39, # 7 -8
' OMIT
Essentials of Mathematics 11
P. 39
Notebook Assignment # 10
(if no computer access)
21
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
Students should understand:
• the difference between cash or debit versus credit
• how to read a monthly statement
• how to convert between annual and daily interest rates
Annual = (daily interest rate) x (365)
Daily = (annual interest rate) ÷ (365)
• how to calculate minimum monthly payments
• the benefits and drawbacks of using a credit card
solve consumer problems
involving credit cards
•
•
22
how to use them
calculate the costs
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Cash or Debit versus Credit
Cash or Debit versus Credit
CIBC has trained employees to
discuss banking topics
•
•
discuss actual cost of item when using cash or debit
versus credit
discuss difference between credit cards
(ie. frequent-flyer miles or points, dividends, low
interest rates, purchase insurance)
Monthly Statement
•
a good sample statement is provided in Choices and
Decisions Binder CH. 8
Internet Resource:
˜ http://www.cba.ca/en/viewD
ocument.asp?fl=6&s1=111&
tl=&docid=246&pg=1
Monthly Statement
Essentials of Mathematics 11
Notebook Assignment
P.44 #1-2 and p. 46 # 6
In-school Resource:
- Choices and Decisions Binder
CH. 8 “Credit Cards”
Converting Interest Rates
•
use samples from the Text
Note:
Periodic interest is the same as monthly interest
rate if using Choices and Decisions Binder.
Minimum Monthly Payments
•
mmp = ( balance ) x ( % )
Benefits and Drawbacks
•
use overhead in the Choices and Decisions Binder
Converting Interest Rates
Essentials of Mathematics 11
P. 41- 42, Example #1- 2
Notebook Assignment P. 45
# 3- 4
In-school Resource:
- Choices and Decisions Binder
CH. 8 “Credit Cards”
Minimum Monthly Payments
Essentials of Mathematics 11
P. 43 Example 4- 5
Notebook Assignment
P. 46, # 6- 7
Benefits and Drawbacks
In-school Resource:
- Choices and Decisions Binder
CH. 7 “About Credit”
23
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
calculate the actual costs of
in-store promotions
Students should understand the difference between
• installment buying
• deferred payments
•
calculate taxes from
different provinces
Actual Costs include:
• List price
• GST = (list price) x (province % )
• PST = (list price ) x (province %)
• HST = (list price) x (15 % )
• In P.E.I. - PST = (list price) + (GST) x (10 %)
Example
Jane is buying new golf clubs at the list price of $ 456.78
Solution (If purchased in PEI)
($ 456.78) x (7%) = $ 31.97
($ 456.78 + 31.97) x (10 %) = $ 48.88
($ 456.78) + ($ 31.97) + ($ 48.88) = $ 537.63
Solution (If purchased in Ontario)
($ 456.78) x (7%) = $ 31.97
($ 456.78) x (8%) = $ 36.54
($ 456.78) + ($ 31.97) + ($ 36.54) = $ 525.29
Solution (If purchased in Nova Scotia)
($ 456.78) x (15 %) = $ 68.52
($ 456.78) + ($ 68.52) = $ 525 30
Hidden Costs include:
• Administration fees
• Delivery fees
Note: PEI has exemptions for PST
(ie. clothing, groceries)
Web Site for PEI exemptions is on Section16 or page 16.
http://www.gov.pe.ca/law/statutes/pdf/r-14.pdf
24
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Anita Chesterfield wants a new couch. Deon’s Furniture
offers one for $899.99. (Anita lives in PEI )
• Using the Pay-Now Plan
S she must pay the $899.99
S GST
S PST
S a delivery charge of $25 (taxes included)
•
Using the Pay-Later Plan
S she must pay the taxes
S a delivery charge of $25 (taxes included)
S a $49.99 (plus taxes) administration fee
S and $899.99 one year later.
a) Calculate Anita’s Pay-Now price.
b) Calculate Anita’s total Pay-Later price.
c) How much more would she pay with the pay-later
price?
d) Express the difference as a percent rate of the total
pay-now price.
Solution
a) Pay-now price: = $899.99
GST: $899.99 x 7% = $63.00
PST: ($899.99 + 63.00) x 10% = $96.30
Delivery = $25.00
Total pay-now price = $1084.29
Installment buying
Essentials of Mathematics 11
P. 52- 53 Example 1
Notebook Assignment
P. 56, # 2
b) Pay-later price: = $899.99
GST: $899.99 x 7% = $63.00
PST: ($899.99 + 63.00) x 10% = $96.30
Delivery = $25.00
Administration fee (including taxes) = $58.84
Total pay-later price: = $1143.13
Deferred payment
Essentials of Mathematics 11
P. 54 Example 2
Notebook Assignment
P. 56, # 3-4
In-School Resource:
- Choices and Decisions Binder
CH. 11 “Consumer
Awareness”
c)$ 1143.13 – $ 1084.29 = $ 58.84
d)
$58.84
× 100% = 5.43%
$1084.29
Taxes different in Provinces:
• Have students calculate the cost of a laptop, list
price = $ 3500.00, purchased in several provinces
Taxes different in Provinces:
Essentials of Mathematics 11
P. 51
Notebook Assignment P. 56 #1
25
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
Students should be familiar with:
• car loans
• personal loans
• personal line of credit
• mortgages
calculate the interest to pay
on a loan
Student should understand the terminology in Essentials of
Mathematics 11, P. 58:
• amortization period
• cost of borrowing
• fixed rate
• prime lending rate
• term
• variable rate
Note:
The Personal Loan Payment calculator in Essentials of
Mathematics 11, P. 59 uses Compound Interest !Monthly
Payment per $1000.00.
Important:
Use samples # 1 - 2 in Essentials of Mathematics 11 P. 60
as your guide.
26
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Personal Loans
Invite a guest speaker from a financial institution.
Personal Loans
Essentials of Mathematics 11
P. 60- 61 Example 1- 2
Notebook Assignment
P. 62- 63 # 1- 5
Loan Application
Students complete a loan application.
Personal Loan Payment Calculator
Use suggested resources.
Loan Application
Teachers Resource Book
Blackline Master # 2
Personal Loan Payment
Essentials of Mathematics 11
P. 59 (Overhead)
TI - 83 - TVM Solver
Internet Resource:
˜ www.ti.com/calc
27
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
convert Canadian money
into a foreign currency
Students should understand:
• Selling Rate:
(bank selling rate) x (foreign currency) = Canadian $
•
convert foreign currency
into Canadian dollars
•
Buying Rate:
(bank buying rate) x (foreign currency) = Canadian $
•
Exchange Rate:
• daily
• different institutions
Note:
Buying and Selling Rates are from the Bank’s perspective.
28
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Students could investigate the rate of exchange between
Canadian Dollars and three countries they could visit.
Essentials of Mathematics 11
P. 66- 68, Example 1- 4
Notebook Assignment
P. 69- 70, # 1- 7
Selling Rate
Have students take an amount of Canadian $’s to the
bank and use this formula:
(Canadian $) ÷ (bank selling rate) = foreign currency
(C$) ÷ (bsr) = fc
If you know the amount of foreign currency you want to
purchase, the band uses this formula to calculate your
cost.
(foreign currency) x (bank selling rate) = Canadian $
(fc) x (bsr) = C$
Buying Rate
Have students take an amount of foreign currency to the
bank and use this formula;
(foreign currency) x (bank buying rate) = Canadian $
(fc) x (bbr) = C$
r = Buying or Selling Rate
29
30
UNIT 2
DATA ANALYSIS
31
General Curriculum Outcome: The student will be able to analyse data with a focus on the
validity of its presentation and the inferences made.
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
The study of statistics enables students to extend and
integrate previous knowledge by collecting and analysing
data from real-life situations.
A line plot is a means of displaying data one-dimensionally
on a horizontal line.
•
construct and display line
plots
•
analyse data
32
Students will:
• construct an accurate line plot
• display an accurate line plot
Student will:
• identify any cluster
• identify any outliers
• identify any gaps
• state the range
• decide if the line plot is appropriate for graphing
this data
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Construct and Display
Essentials of Mathematics 11
P. 82-85
Notebook Assignment
P. 86-89, # 1, 2
Step 1. Draw a horizontal line with a ruler.
Step 2. Using your ruler, put a scale below the line. To
do this, find the smallest and largest values and
determine a suitable scale.
Step 3. Plot each value by placing an X above the line at
the appropriate location.
Note:
For values that are approximately the same, you may
want to place the Xs directly above each other in order to
avoid cramming. From the plotted data, it is now possible
to see features that were not apparent from the table.
Chapter Project begins on P. 86
Step 4. Continue until you have plotted all the data.
Example
Analyse Data (above example)
•
•
•
•
•
Clusters - 74 and 75
Outliers - 68
Gaps 69 through to 73
Range - 9
What does this line plot tell us about our data?
ie: Which golfer’s score is questionable?
Suggested pair activity in Essentials of Mathematics 11
P. 85.
33
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
Mean
Students often use the term average when referring to the
mean of a group of numbers. Average and mean are
interchangeable terms, though mathematicians use
arithmetic mean as the measure of central tendency found
by adding the set of data and then dividing by the number
of values in the set. (Note: when “arithmetic” is used as an
adjective, it is pronounced “a-rith-met’-tic” accent is on the
“met”)
calculate the three measures
of central tendency
• mean
• median, and
• mode
Median
The median, another measure of central tendency, is the
middle value in a set if the values are arranged in order
from smallest to largest. When there is an odd number of
values, the median is the middle number. When there is an
even number of values, then there are two middle numbers.
In this case you need to find the mean of the two middle
numbers.
Mode
It is possible that the mode is not necessarily a measure of
central tendency. It is simply the value that occurs most
often and could coincidently be near the centre. Sometimes
there is more than one mode. If two values occur the same
number of times, then there are two modes. If all the values
occur the same number of times, then there is no mode.
•
34
use each of these measures
appropriately
The measure that you use depends on the data and your
purpose.
• mean for sets of data with no unusually high or low
numbers
• median for sets of data with some points that are
much higher or lower than most of the others
• mode for sets of data with many data points that are
the same
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Example
On your first five math tests, you received the following
scores: 70%, 94%, 82%, 96%, 70%
Essentials of Mathematics 11
P. 90-93
Notebook Assignment
P. 93-95, # 1- 8
a) Find the mean score of your test results.
(70% + 94% + 82% + 96% +70%) ÷ 5 = 82.4%
b) Find the median score of your test results.
70%
70% 82%
94% 96%
c) Find the mode of your test results.
70%
d) Suppose you wrote a sixth test and scored 5%. Calculate
the new mean, median, and mode. How does this low mark
affect the mean, median, and mode?
Mean:(70% + 94% + 82% + 96% + 70% + 5%) ÷ 6 = 69.5%
Median: 5%
70% 70% 80% 94% 96%
(70% + 82%) ÷ 2 = 76%
Mode: 70
Both the mean and the median dropped in value, but a lower
outlier caused the mean to drop more than the median. The
mode was unaffected.
In-school Resource:
- Algebra To Go, A
Mathematics Handbook,
pages 333-338
- Algebra To Go, Teacher’s
Resource Book, pages 190196
Internet Resource:
˜ www.ti.com
The hockey players salary or math test results in the Appendix
of this guide is a sample that students can use to answer
questions like:
• compute the mean time in minutes
• compute the median
• compute the mode
Students can complete “Mean / Median / Mode” worksheet.
See Appendix 4.
Pencil/Paper
A survey of weekly television viewing time of 25 female and
26 male teenagers produced the following data:
a) Find the measures of central tendency (mean, median and
mode).
b) What types of
conclusions can you
make about the survey?
Note: Students might enjoy
using the IT-83 after doing
the problem by hand.
35
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
The major focus of this section is on how different
individuals or groups use mean, median, or mode to
represent a particular point of view. There should be some
exploration of the factors that influence these three
measures of central tendency.
solve problems involving
mean, median, and mode
In solving problems involving mean, median, and mode,
you will look at adjusting data, predicting or calculating
values, and identifying questionable values.
The opportunity to use spreadsheets to find mean, median,
and mode would bring technology into the math class.
36
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Use examples 1, 2, and 3 as best worthwhile tasks.
Essentials of Mathematics 11
P. 96-99
Notebook Assignment
P. 100-101, # 1- 5
Internet Resource:
˜ http://www.edu.pe.ca/journe
yon/student_files.html
37
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
Statistics can be used by advertisers, the media, and
governments to give information. They can also be used to
influence. Graphs can be drawn and statements made to
create false impressions. Students should know that when
stats are used to support an opinion or to influence a
decision, then they should study the data and the graph
carefully so that they are not misled.
•
construct and analyse bar
graphs
Students are expected to be able to manipulate a bar or line
graph to represent a particular point of view. These
manipulations could include changing the horizontal scale,
changing the vertical scale, or changing the starting point of
the scale.
•
construct and analyse
misleading bar graphs
The data described in Essentials of Mathematics 11 P. 105 108, Examples 1, 2, and 3 is the same but presented
differently to create different impressions. Manipulation of
the vertical axis on bar graphs allows for the change in
appearance of the information displayed.
While students are working with data, circulate, ask
questions, observe, and check to see how effectively they
are able to:
• design and collect data from simple surveys
• represent data effectively using tables, charts, plots, and
graphs
• make predictions and inferences based on graphs
• identify, analyse, and explain the misuse of statistics
• use appropriate terminology
Students may use their spreadsheet programs to produce bar
graphs. Some students become very good at using
spreadsheets and can be a good resource to teach others.
38
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Research
Have students find examples of advertising that try to
convince consumers to buy their products.
Essentials of Mathematics 11
P. 105-109
Notebook Assignment
P. 110-112, # 1- 4
Pencil/Paper
1)
This graph displays
the result of a taste
test between Popsie
and Slurpie soft
drinks given to 300
consumers.
In-school Resource:
- Algebra To Go, A
Mathematics Handbook
P. 339-349
a) Looking only at the heights of the bars, how many
times more popular does Popsie seem to be over
Slurpie?
b) Which company appeared to have created the graph?
What three techniques were used to create a false
impression?
c) Create a new graph that would more fairly compare
consumer differences.
2) In a school, 200 out of 400 grade 12 students and 100
out of 150 grade 11 students attended the musical.
Draw a graph to give the impression that
a) Grade 12 students are better supporters of the
musical.
b) Grade 11 students are better supporters of the
musical.
39
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
A circle graph shows how a whole is broken into parts. It
makes it easier to see how the size of each part compares to
the whole.
construct and analyse circle
graphs
Some students refer to circle graphs as “pie charts”. Each
“piece of the pie” is called a sector.
Each sector of the circle represents the part belonging to a
certain category.
Use a protractor to help draw a central angle with the
degree measure assigned to each category. Students will
need a review in the use of a protractor.
When using a protractor, students need to review changing
from degree measure to % of the circle and vice versa.
40
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Example
A sector with a central angle measure of 126° on the
protractor represents 35% of the circle. This is found by
dividing 126 by 360 and multiplying by 100 to get the
Essentials of Mathematics 11
P. 114-119
Notebook Assignment
P. 120-122, #1- 3
percentage.
126
× 100 = 35%
360
In-school Resource:
- Numeracy at Work P. 285
If the problem asks you to convert a percentage to degrees
ie: 35% of 360° to get 126° 0.35 x 360° = 126°
If the problem states that 40% of the data is to be
represented by a sector, then the central angle should
measure 144° . Found by taking 40% of 360° to get 144°.
0.40 x 360° = 144°
Example
Four pizza companies operate in the city. The percentage
of business for each company is shown below.
Grecoo
35%
Piizzaa Deeliight 30%
Doomiinoos
20%
Piizzaa Huuut
15%
Piizzaa Huuut (15.00%)
Grecoo (35.00%)
Doomiinoos (20.00%)
Piizzaa Deeliight (30.00%)
•
Survey your class to get data on a topic (ie: type of
vehicle they drive, brand of sneakers they wear, etc.)
and create a circle graph.
41
42
UNIT 3
OWNING AND OPERATING A VEHICLE
43
General Curriculum Outcome: The student will learn the costs involved in owning and
operating a vehicle.
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
New Vehicle
In PEI, to find the total cost of a vehicle after taxes the GST
must be added to the price before you calculate the PST.
Most questions ask for the taxes separately, but the easiest
way to find the total cost is:
price × 1.177 = total cost
calculate GST and PST
when purchasing a vehicle
The 1 in 1.177 represents 100% of the cost and the 1.177
represents the GST and PST combined.
Note: When students check their answers for Essentials of
Mathematics 11, P. 139 - 140 questions 5-10, taxes are
calculated differently for PEI, so if teachers choose to use
PEI sales, then answers need to be adjusted accordingly.
These answers are provided on the next page of this guide.
A reoccurring theme should be for students to calculate the
monthly income required for various purchases.
ie: Total Monthly Debt Repayment, Essentials of
Mathematics 11, P. 136 Example 1.
Used Vehicle
In PEI, if trucks up to but not including one ton or cars are
purchased privately, then the buyer must pay 12.5% PST
when registering it, but no GST. Motorcycles, ATV’s,
snowmobiles, and trucks one ton or greater purchased
privately, have a 10% PST. All vehicles purchased
privately, have a 10% PST. All vehicles purchased from a
dealer have PST (10%) and GST (7%) when registering.
Note:
GST and PST must be paid on a newer or used vehicle
purchased from a dealer. In Manitoba and British
Columbia, a vehicle purchased privately requires payment
of only PST. GST is 7% for all provinces and territories in
Canada. Refer to Essentials of Mathematics 11, P. 52 for
the map to find the PST rates for the provinces and
territories.
44
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Examples
New Vehicle
A new car total purchase price is $32, 000.00.
Essentials of Mathematics 11
P. 136-137
Notebook Assignment
P. 139-140, # 1- 9
Solution
In Ont:
GST = 7%, PST = 8% Total = 15%
15% of $32,000
0.15 x 32,000 = $ 4,800
Total cost = $32,000.00 + $4,800.00 = $36,800.00
In BC:
GST = 7%, PST = 7.5% Total = 14.5%
14.5% of $32,000
0.145 x 32,000 = $4,640
Total cost = $32,000.00 + $ 4,640.00 = $ 36,640.00
In PEI:
GST = 7%, PST = (GST + Price) x 10%
7% of $32,000 = $ 32,000 X 0.07 = $2,240
$ 32,000 + $ 2,240 = $ 34,240
$34,240 x .10 = $ 3,424
Total cost = $32,000.00 + $2,240.00 + $ 3,424.00 =
$37,664.00
Used Vehicle
A privately sold used vehicle total purchase price is
$ 15,000.00
In PEI:
PST = 12.5%
12.5% of 15,000.00 = 15,000 x .125 = $1,875
Total Cost = $15,000 + $ 1,875 = $16,875.00
Chapter Project begins on P. 134
The following are Answers for
PEI purchases in the
Essentials of Mathematics 11
P. 139-140 questions 5-9 for PEI
purchases:
5) GST= $27480×0.07=$1923.60
PST= (1923.60+27480)×0.10
= $2940.36
Total taxes = $1923.60+$2940.36
= $4863.96
Total cost = $27480+$4863.96
=$32343.96
6) GST = $8500×0.07=$595.00
PST = (595+8500)×0.10
= $909.50
Total taxes = $595.00 +$909.50
= $1504.50
Total cost = $1504.50+$8500
= $10004.50
7) No GST, therefore
PST= $25500×0.125
= $3187.50
Total cost = $3187.50+$25500
= $28687.50
8) PST= $8300×0.10 = $830
Total cost = $9130
9) GST = $32500×0.07 = $2275
PST = ($2275+$32500)×0.10
= $3477.50
Total cost = $38252.50
45
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
Discussion Questions
1. Discuss what expenses there are to keep a car on the
road:
• licence
• tires
• insurance
• repairs
• gasoline
• routine maintenance
calculate fuel costs for
operating a vehicle.
b) How much does it cost to buy 30 litres of gas at 78.4¢
per litre?
Solution 30 x $0.784 = $23.52
c) The bill for a tank of gas is $52.50. If the cost is 68.9¢
per litre, how many litres did you buy?
Solution $52.50 ÷ $0.689 = 76.2 litres
d) You buy 39.25 litres of gas for $23.51. How much does
each litre cost?
Solution $23.51 ÷ 39.25 = 59.9¢
Fuel economy is expressed as the number of litres of fuel
required to travel 100 kilometres.
fuel economy =
litres of fuel used × 100
kilometres driven
Students need to understand the difference between fuel
economy and litres of fuel used when doing the Notebook
Assignment on pages 146-148.
This formula can be used to find the number of litres of fuel
used.
litres of fuel used =
fuel economy × km driven
100
These formulas can convert litres of fuel used to mpg.
US Gallons
Imperial Gallons
235.2
= mpg
L / 100km
46
282.5
= mpg
L / 100km
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Example
Jane travels 567 km and then fills up her car with 40 litres
of gas. The cost per litre is 68.4¢.
Find:
a) the cost of filling the tank
b) the fuel economy
c) the cost per 100 km driven
Essentials of Mathematics 11
P. 142-143
Notebook Assignment
P. 146-148
Solution
a) 40 x $0.684 = $27.36
b) (40 ÷ 567) x 100 = 7.05 litres/100km
40 × $0.684
× 100 = $4.83 or FE x cost per litre
c)
567
7.05 x 68.4 = 482.2¢ or $4.82
In-school Resource:
- Choices and Decisions
Binder Lesson 9 “Cars and
Loans”
Note:
Car Dealers will provide the following information when
purchasing a car.
City
Highway
Litres / 100 km
12.9
8.8
Miles / gal.
22
32
For fuel economy (litres/km), less is better.
For mileage (miles/gal), more is better.
Pencil/Paper
Have students set up a spreadsheet to calculate fuel
economy.
47
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
Learning to make sound decisions about acquiring a motor
vehicle helps students to make connections between needs
and personal budgets.
understand the cost of
maintaining a vehicle
Acquiring and operating a vehicle involves costs that will
have an impact on the present and future budgets of
students.
In PEI, when calculating the total costs for maintaining a
vehicle, GST and PST are charged to all parts and labour.
Note:
PST is a provincial tax and in other provinces may not
apply to labour.
All cars at one time or another have to go into a garage,
either for maintenance or for fixing something that is
wrong.
At this point, the class could discuss the different prices for
a foreign car versus a North American model. In general,
costs would be more for a foreign car than for a North
American car.
48
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Example
Ann takes her car in for servicing. She needs two new
tires plus her transmission needs some work. Each tire
will cost $87.50 and the parts to fix her transmission will
cost $226.75. What will her total bill be if labour costs
$61 per hour and the work requires 3.2 hours? There is an
environmental levy of $2.80 per tire.
Solution
In PEI:
Parts
Tires
2 @ $87.50
$175.00
Tire Valves
2 x $2.80
5.80
Transmission
226.75
Total Parts
407.35
Labour
$61 x 3.2
195.20
Subtotal
602.55
Tax — GST
$602.55 x 0.07
42.18
Tax — PST
($602.55 + 42.18 ) x 0.10
64.47
Total
709.20
In Nunavit:
Parts
Tires
2 @ $87.50
$175.00
Tire Valves
2 x $2.80
5.80
Transmission
226.75
Total Parts
407.35
Labour
$61 x 3.2
195.20
Subtotal
602.55
Tax — GST
$602.55 x 0.07
42.18
Total
$647.73
Essentials of Mathematics 11
P. 149-150
Notebook Assignment
P. 152-153, # 1-6
Note:
#6 - suggest replace BC with PEI
Students can complete the “Vehicle Expenses” worksheet
for practice maintenance, operating, and repair costs.
See Appendix 5.
Pencil/Paper
Have students find out how much it would cost to repair
or replace a door in the following cars:
• Sunfire
• Dodge Dakota
• Subaru Outback
49
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
Invite a local insurance agent to speak to students about
insurance for vehicles.
understand how vehicle
insurance works
Understanding the costs of vehicle acquisition and
operation can help students make rational economic
decisions.
•
calculate the costs for
insuring and registering
your vehicle
Discuss the meaning of the new terms Essentials of
Mathematics 11, P. 155 - 156:
• at fault claims
• basic coverage
• collision insurance
• comprehensive insurance
• premium
• rate class
• rate group
• third part liability
• deductible
• safe driver discount
Discuss why it is important to have car insurance.
Discuss the following issues that have an impact on car
insurance:
• age
• gender
• driving record
• years of experience
• type and age of vehicle
• daily average driving distance
• security features on vehicle
• geographics
• driver’s education
• number of claims
Contact Motor Vehicle Registration office or website for
registration and licence plates costs.
50
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Have students contact insurance agents to determine costs
of insurance for various classes of vehicle and types of
driver (e.g., age of vehicle, age of driver, and type of
vehicle).
Essentials of Mathematics 11
P. 154-158
Notebook Assignment
P. 158-159, #1-9
Assessment should focus on students’ abilities to
estimate, predict, research, calculate (using appropriate
technology), and compare costs in the acquisition and
operation of a vehicle. Students should be able to verify
the reasonableness of their conclusions.
In-school Resource:
- Teacher Resource Book,
Appendix C, Blackline
Masters #4- 10
Have students research the cost of operating a vehicle for
a year. Ask students to prepare a report suitable for class
presentation that includes all anticipated costs (e.g., fuel,
oil, tires, tune-ups, registration, and insurance). Have
students convert the overall cost to cost per kilometre.
Internet Resource:
˜ https://www.gov.pe.ca/mvr/i
ndex.php3
˜ Insurance quotes available.
A PEI location will not be
accepted so it is suggested
using a NB or NS Postal
Code.
Moncton’s is E1A 3A1
http://www.kanetix.com
Note:
Copies of Teacher Resource Blackline Masters are
needed for the above exercises.
51
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
Discuss new terms on P. 160:
• basic price
• documentation fee
• freight charges
• optional equipment
• preferred equipment
• package
• sticker price
• trade-in allowance
calculate the total costs for
purchasing a new vehicle
Provide students with newspapers or other advertisements
that show the price of purchasing a new vehicle.
Contact individual dealers to acquire fact sheets on new
vehicle costs (base price + options) or visit web sites for
various makes of cars.
52
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Pencil/Paper
Find the cost of a new car when trading in your current
vehicle. Erwin wishes to buy a Dodge Ram truck. The
price is $29,600. He wants an option package for $3000
that includes A/C; freight is $685. The dealership is
willing to give him a trade-in allowance of $5500 for his
old car. What is the total price for this new vehicle
purchased on PEI?
Essentials of Mathematics 11
P.160-162
Notebook Assignment
P. 163-164, #1 - 7
Solution
Price
$29 600.00
Option Pkg.
$ 3 000.00
Freight
$ 685.00
Tire Tax
$
14.00
A/C Tax
$ 100.00
Administration Fee $ 195.00
Sticker Price
$33 594.00
Trade-in
$ 5 500.00
Subtotal
$28 094.00
GST
$ 1 966.58 = $28 094 x 7%
PST
$
3006.06=(28094+1966.58)x10%
Total Price
$33066.64=28094.00+1966.58+3006.06
Have students select a new vehicle of their choice and
calculate the cost to:
• purchase (with options)
• insure
• licence
• register
53
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
Most vehicles depreciate in value every year.
calculate the resale value of
a vehicle after depreciation
Note:
Cars, trucks, SUV’s, etc. depreciate at different rates. If a
vehicle is in demand, even when it is older it will not
depreciate as fast as a less desirable vehicle. When
unknown, the 20% rule of depreciation is suggested. Each
year, the vehicle depreciates by 20% of its value.
Example
How much is a $20,000 car worth after three years?
Solution 1
Year 1:
Depreciation $20,000 x 20% = $4000
Value:
$20,000 – $4000 = $16,000
Year 2:
Depreciation $16,000 x 20% = $3200
Value
$16,000 – $3200 = $12,800
Year 3:
Depreciation $12,800 x 20% = $2560
Value
$12,800 – $2560 = $10,240
Total worth after 3 years is $10,240
• Car worth is now 51% of the original purchase price.
Note:
Total depreciation after 3 years is
$4000 + $3200 + $2560 = $9760.
Solution 2
Extension formula for the same problem:
Purchase Price x 0.8t (where t = # of years)
20,000 x 0.83 = $10,240
54
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Pencil/Paper
Have students create a spreadsheet to calculate a car’s
value each year.
Essentials of Mathematics 11
P. 166-168
Notebook Assignment
P. 168-169, # 1- 4
Essentials of Mathematics 11
P. 170-171
The “Problem Analysis” offers
students a break from the content
in this chapter.
Have students calculate the resale value of their
personal/family vehicle.
55
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
In PEI, if trucks up to but not including one ton or cars are
purchased privately, then the buyer must pay 12.5% PST
when registering it, but no GST. Motorcycles, ATV’s
snowmobiles, and trucks one ton or greater purchased
privately, have a 10% PST. All vehicles purchased from a
dealer have PST (10%) and GST (7%) when registering.
calculate the total costs of
buying a used vehicle from
a dealer and privately
Note:
GST and PST must be paid on a new or used vehicle
purchased from a dealer. In Manitoba and British
Columbia, a vehicle purchased privately requires payment
only of PST. GST is 7% for all provinces and territories in
Canada. Refer to map on p. 51 to find the PST rates for the
provinces and territories.
Note:
Six Step Approach to buying a used vehicle privately on
P. 173 of Essentials of Mathematics 11.
Note:
The history of all used vehicles can be researched by using
the VIN (Vehicle Identification Number) at the following
web site: www.carfax.com.
Purchasers can check red book values at the Provincial
Library or Access PEI.
56
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Pencil/Paper
Have students calculate the cost of purchasing a used
vehicle by gathering information from the newspaper or
Auto Trader Magazine, etc.
Essentials of Mathematics 11
P. 172-174
Notebook Assignment
P. 175-177, #1 - 11
Internet Resource:
˜ www.carfax.com
57
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
In Essentials of Mathematics 11, P. 179-180, Examples 12 should be used.
58
calculate the monthly
payment, the total paid, and
the finance charge when
purchasing a vehicle
Personal Loan Payment Calculator chart needed for this
SCO is in the Essentials of Mathematics 11, P. 59.
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Students can complete the “Buying Cars” worksheet to
gain practice in buying new and used vehicles.
See Appendix 6.
Essentials of Mathematics 11
P. 178-180
Notebook Assignment
P. 182-183, # 1- 9
Note:
Must use Personal Loan Payment Calculator on
Essentials of Mathematics 11 P. 59
In-school Resource:
- Numeracy at Work P. 8
59
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
understand the concept of
leasing
Advantages of Leasing:
• lower monthly payments
• new vehicle more often
•
calculate the cost of leasing
a vehicle
•
60
compare the cost of buying
to the cost of leasing
Disadvantages of Leasing:
• never owning vehicle (renting)
• buying out the lease, pay more for the vehicle
• restrictions on mileage
• extra costs for interior and exterior appearance at the
end of the lease
• stipulations regarding insurance
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Pencil/Paper
Have students calculate the costs of owning and of
leasing a vehicle of a given price using information from
newspapers, dealerships, web sites, etc.
Essentials of Mathematics 11
P. 184-186
Notebook Assignment
P.187-188, # 1 - 8
In-school Resource:
- Numeracy at Work
P. 9-11 and P. 14-15
Internet Resource:
˜ Information on whether to
lease or buy a vehicle is
accompanied by a
questionnaire.
http://www.learner.org/exhi
bits/dailymath/car/
61
62
UNIT 4
MEASUREMENT TECHNOLOGY
63
General Curriculum Outcome: to make measurements in both the metric and imperial
systems.
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
Measurement experiences are a powerful application
of mathematical theory to everyday phenomena.
explore the history of
measurement systems
Take time to discuss the development of measurement
systems. Students should realize that there are more
systems than the SI and imperial. However, this unit will
focus on these two.
64
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Have students complete the Classroom Activity from
Essentials of Mathematics 11 P. 196.
Essentials of Mathematics 11
P. 195-197
Introduce students to measurements by using the “Earth
Facts” worksheet. See Appendix 7.
Notebook Assignment P. 198-200
#1 - 7
Students can complete the “ Metric Prefixes” worksheet
for practice. See Appendix 8.
In-school Resource:
- Numeracy at Work P. 155
- Numeracy at Work P. 156
In groups, students give a situation in which using one
particular measuring device is preferable to another. They
should give examples of situations in which a most
appropriate device for measurement exists (ie: ruler vs
odometer to measure the distance from North Cape to
East point).
Chapter Project begins on P. 194
Pencil/Paper
Identify suitable units of linear measure in the SI and
imperial systems.
Item
Metric–SI
Imperial
length of a pen
distance from
Souris to
Tignish
thickness of a
coin
diameter of a
car tire
dimensions of
a duotang
Line measurements to emphasize include:
1. SI: mm, cm, m, km
2. Imperial: inches, feet, yards, miles
65
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
Emphasis should be placed on the rationale of the SI system
(multiples of 10 to match our number system) and its
advantages over other systems.
measure lengths in both
the metric and imperial
systems and solve
problems
Advantages of SI system are:
• multiples of 10 for easier conversion within the
system
• consistent terminology
• universal use
Note:
It may be necessary to review the basic units of linear
measure in both systems by using the Chart in Essentials of
Mathematics 11 P. 209 as your guide.
Adding, subtracting, multiplying, and dividing fractions are
skills that are used in this chapter. These skills can be
b
simplified using the A
button on the TI-30X Scientific
c
Calculator.
The opportunity is here to review and introduce perimeter,
area, and volume of geometric shapes.
Note:
Volume is not covered in this section. There is a small
section in Exploration 4 that deals with volume.
66
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Students can practice using a ruler to complete the
following worksheets:
•
“SI Measure”
See Appendix 9.
•
“ Imperial Measure”
See Appendix 10.
Essentials of Mathematics 11
P. 201-204
Divide the class into small groups and provide students
with a ruler, measuring tapes, and/or metre sticks.
Assign objects to be measured to each group and have
students report to the class their choice of measuring
device, the ease or difficulty of measurement, and the
precision of the resulting measurement.
Notebook Assignment P. 205-208
# 1- 8
In-school Resource:
- Teacher Resource Book
Blackline Master 13.
rulers can be produced by
photocopying on overheads
- Numeracy at Work P. 331
Have students check each other’s work using appropriate
measuring systems.
Review students’ written work in using measurement
technology for evidence that they can:
•
give a situation in which using one particular
measuring device is preferable to another
•
give examples of situations in which a most
appropriate device for measurement exists
Pencil/Paper
1. Estimate the height of a door in both SI and imperial
units.
2. Identify an object that measures approximately:
a) 15 inches
b) 6 cm
3. Give three examples of where you use the imperial
system of measurement in your daily life.
Possible Answers
1. 2 m; 6.5 ft.
2. a) length of a long file folder
b) diameter of a soft-drink can
3. a) height (e.g., 5' 8" tall)
b) weight (e.g., 125 pounds)
c) baking (2½ cups of flour)
67
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
Use the sentence below to help teach students to remember
the metric system.
perform conversions within
both imperial and metric
systems of measurement
King Henry Drank My
kilo
hecto deca
Delicious Chocolate Milk
metre deci
centi
milli
Each word in the sentence represents one decimal place.
For example, 57.3 hectometres = 573000 centimetres
because centi is four spaces to the right, therefore you move
the decimal four places to the right.
Note:
Decametre is dam and decimetre is dm.
68
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Have students create posters that display conversion
factors or simple instructions for conversions within each
measurement system. Have students use the posters to
practice conversion problems.
Essentials of Mathematics 11
P. 209-212
Have students demonstrate their knowledge of
measurement concepts by generalizing about strategies
and performing basic conversions.
While students are working on measurement activities,
circulate and provide feedback on:
• their abilities to use the correct measuring devices and
measurement units
• the extent to which they consider the reasonableness
of their answers
• their overall understanding of measurement concepts
in solving problems
Notebook Assignment P. 213-214
#1-9
Internet Resource:
˜ Conversion tool
http://www.onlineconversio
n.com/
˜ Conversion tool
http://ts.nist.gov/ts/htdocs/2
00/202/conv.htm
Pencil/Paper
Convert each of the following units of linear measure as
indicated.
a) 3m =
________ cm b) 53 cm =
________ mm
c) 25 mm =
________ cm d) 450 cm =
________ m
e) 0.65 m =
________ mm f) 7.4 mm =
________ cm
g) 3.5 km =
________ m
h) 560 m =
________ km
Solutions
a) 300 cm
e) 650 mm
b) 530 mm
f) 0.74 cm
c) 2.5 cm
g) 3500 m
d) 4.50 m
h) 0.560 km
Convert each of the following units of linear measure as
indicated.
a) 5 ft. = ________ in.
b) 3 yd. = ________ ft.
c) 2 ft. = ________ in.
d) 36 in. = ________ ft.
e) 18 in.= ________ ft.
f) 27 in. = ____ ft. +_____ in.
g) 4 ft. 4 in. = ________ in.
h) 2 yd. 8 in. = ________ in.
Solutions
a) 60 in. b) 9 ft.
e) 1.5 ft. f) 2 ft. + 3 in.
c) 30 in.
d) 3 ft.
g) 52 in. h) 80 in.
69
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
The skill to convert units of linear measure from SI to
Imperial and vice versa is one that can be difficult for
students.
convert units from the
metric system to the
imperial system, and from
the imperial system to the
metric system of
measurement
Conversions between SI and imperial are extremely
important for students interested in a trade career.
The use of the Conversion Table is a must.
70
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Have students measure the diameter of a round table in
metres. Have them convert the distance to feet, then
measure again in feet to check their work.
Essentials of Mathematics 11
P. 215 - 217
Again students can create posters this time that display
conversion factors or simple instructions for conversions
between Imperial measures and corresponding SI
measures.
Using rulers and tape measures, students should measure
various objects to the nearest millimetre and to the nearest
1/16th inch. For some objects, it may be appropriate to
use either one of the systems (SI or imperial), or both.
Notebook Assignment P.218-219
#1-6
In-school Resource:
- Teachers Resource Book
Blackline Master 14.
- Numeracy at Work P. 158
Pencil/Paper
Estimate, in both SI and imperial units, the length and
width of each of the following objects. Use a metre stick,
ruler, tape measure, or any other suitable device, to
determine the actual measure of each object (rounded to
the nearest mm or 1/16th of an inch).
Item
SI
Estimate
Imperial
Estimate
Actual
SI
Actual
Imperial
desktop
textbook
classroom
window
door
For introducing the need to understand conversion
between systems in Trade Careers use the “Changing
Units Between The Metric and Customary Systems
Charts”. See Appendix 11.
71
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
It takes a little practice using Vernier calipers. Schools have
been provided a class set of 30 calipers for student use.
use Vernier calipers to make
accurate measurements
Thickness
Separate the outside jaws and place object between the
teeth and tighten the teeth just enough to firmly hold the
object. The thickness is read on either the metric scale as
3
5mm or the imperial scale as
inch. Be careful not to
16
confuse the two scales as the numbers are close to each
other.
Inside diameter
Use the inside jaws of the calipers and read scale the same
way.
Depth
The depth gauge (wire that comes out the end of calipers) is
pushed out and placed on the bottom of the object and the
foot of the calipers is pushed down until it touches the top
of the object. The depth is read where the outside jaws are
separated the same way the thickness was measured.
Note:
A good way to demonstrate difficulty of accurate
measurement is in Essentials of Mathematics 11 P. 225,
Example 2 as the solution is 4.61 cm NOT 4.68 cm as
given.
72
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Divide the class into small groups and provide students
with Vernier calipers to measure the thickness of a variety
of objects, such as pencils, books, desk tops, desk legs,
door knobs, hand rails, marbles, dice, etc.
Essentials of Mathematics 11
P. 222-225
Use the calipers to measure the inside diameter of
different sized pipes, paper cups (tops and bottoms),
rings, washers, and other similar objects.
Use the calipers to measure the depth of test-tubes, desk
drawers, paper cups, etc.
Have students use this Vernier caliper applet that can be
found at Westminister College web site. This java applet
helps students learn to read a vernier caliper.
Pencil / Paper
1. Give a situation in which using a ruler would be
preferable to using a vernier caliper and vice versa.
Notebook Assignment P. 227-229
#1-4
In-school Resource:
- A class set of 20 Vernier
calipers
- Numeracy at Work P. 211215
Internet Resource:
˜ http://www.people.westmins
tercollege.edu/faculty/ccline/
vernier/vernier.html
˜ http://www.wcsscience.com/
vernier/caliper.html
2. State the following vernier caliper measurement. Be
sure to include the units.
Solution
3.9 cm or 39 mm
73
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
Micrometers are more precise than Vernier calipers because
they can measure to a smaller unit (one hundredth of a
mm). They could be used to measure thickness or diameter
of small objects such as coins, paper, a washer, the wall of a
pipe, a dime, rings, etc.
read a micrometer
Note:
The physics lab at your school may have micrometers that
may be borrowed for this section.
74
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Have students use the suggested website which shows an
applet of the measurement scale of a micrometer.
Essentials of Mathematics 11
P. 230-234
Pencil/Paper
1. State the following micrometer measurement. Be sure
to include the units.
Notebook Assignment P. 235-237
#1-5
Solution
10.23 mm
Internet Resource:
˜ http://members.shaw.ca/ron
.blond/Micrometer.APPLE
T
2. Give examples of situations in which the most
appropriate device for measurement is:
a) a micrometer
b) vernier caliper
c) a ruler
Justify your choice.
75
76
UNIT 5
RELATIONS AND FORMULAS
77
General Curriculum Outcome: The student will examine linear relations by expressing them in
words, with a table of values, as a graph, and as a formula.
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
Using graphs of linear relations to represent real-life
situations, and interpreting graphs of relations are key
components of many problem solving situations. It is
important for students to be able to make appropriate
conclusions and interpretations based on graphical data.
•
examine linear relations
whose graphs pass through
the origin (y = mx form) by
expressing them in words,
as a table of values, as a
graph, and as a formula
Be familiar with the following terms:
• Relation is simply a mathematical sentence describing
how quantities are related.
• Variables are the quantities.
• Graphs are convenient ways to visualize the relation.
• Table of values gives several numerical examples that
satisfy the mathematical sentence.
All three are ways of showing how variables are related.
For our purposes, only linear relations will be studied.
When introducing the terms dependent variable and
independent variable, the vertical axis (y-axis) contains
the dependent variable because the “y” values “depend on”
the “x” values, represented on the horizontal axis.
Note:
Most often time is on the horizontal axis and distance is on
the vertical axis.
•
interpolate and extrapolate
values from the graph of a
linear relation
Finding unknown values between points you already know
is called interpolation. If your graph shows a trend, then
you may be able to predict values beyond your graph. This
is called extrapolation.
It is assumed that students know how to plot points on a
coordinate plane. A review would be appropriate.
78
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
A trucker charges a rate of $10.50/km when transporting
goods. (Fractions of a kilometre are rounded to the next
whole number.)
1. Create a table of values showing number of kilometres
driven and amount of money paid to the driver. (If
being done in the classroom discuss with students
some mental math strategies such as “add $21.00 for
every 2 km.)
2. State the dependent and independent variables, then
plot points to represent the relationship.
3. Explain why you should or should not join the points
Essentials of Mathematics 11
P. 247-251
Notebook Assignment P. 254-255
#1-7
Chapter Project begins on P. 246
plotted on the graph.
4. Ask students to describe in writing a pattern in the
table that they would use to predict the answer to the
cost of travelling 9km, 21km, and 30km.
5. Represent the relationship given with an equation.
6. Use the equation to predict the cost for a 25km taxi
ride; a 5.5 km ride.
7. What is the rate of increase in cost as you travel?
Note:
Keep tables of values simple and easy to read. All graphs
should have labels on both axes. Make sure the dependent
variable is on the vertical axis and the independent
variable on the horizontal (comes from horizon) axis.
Identify the dependent variable:
a) distance walked versus calories burned
b) gas consumed versus distance driven
c) test marks versus hours of studying
d) driving speed versus value of ticket received
A copy of the above “Graph Paper” is available for
photocopying or making an overhead. See Appendix 12.
79
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
learn to calculate the slope
of a line
The slope of a line can be described in several ways. It is
described as the “steepness” or the “rate of incline” of the
line.
•
describe the slope in words
and interpret its meaning in
a problem context
•
•
80
interpret the graph of a
relation and describe it in
words
construct a graph of a
relation from its description
in words
slope =
rise
run
The slope may be expressed as a fraction, a whole number,
or a decimal.
For purposes of this curriculum, only graphs that are in the
first quadrant will be studied.
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Pencil/Paper
Provide students with graphs showing the wages earned
versus hours worked for jobs typically held by young
temporary workers (e.g., cashier, server). Ask students the
following questions:
Essentials of Mathematics 11
P. 256-261
Notebook Assignment P. 262-264
#1-5
1. What is the hourly wage?
2. Can the wages earned be predicted for a point on the
graph?
3. How would the graph change if a raise were
incorporated into the hourly wage?
Example Slope
Daily Earnings
Hourly Wage
300
Dollars ($)
250
200
150
100
50
0
0
5
10
Time (hrs.)
15
20
81
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
It makes sense that if the line passes through the origin, the
y-intercept must be 0. All linear equations that pass through
the origin have the equation y = mx , where m is the slope
of the line.
determine the formula of the
linear relation if a line
passes through the origin
So, the line with equation y = 7.5x has a slope of 7.5.
•
evaluate formulas
The dependent variable is y and the independent variable
is x.
The general formula is:
dependent variable = (slope) x ( independent variable).
Just by looking at this graph,
the equation can be found by
finding the slope using rise
over run. Choosing any two
points of convenience, the rise
is 4 and the run is 3, therefore
4
the equation is y = x
3
82
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Pencil/Paper
State the slope of each line using rise over run.
Essentials of Mathematics 11
P. 265-271
Notebook Assignment P. 273-275
# 1-5
Questions
a) Which car uses more fuel?
b) State the slope of both lines?
Solutions
1. Car B uses more fuel than Car A. The line on the
graph is much steeper.
b) For Car A, the rise (vertical change) from the origin
(0,0) to the first data point is 10, and the run
(horizontal change) is 200.
10
1
or
The slope is
200
20
For Car B, the rise from the origin to the first data
point is 20, and the run is 100.
20
1
or
The slope (rise/run) is
100
5
83
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
The y-intercept touches the vertical axis and the symbol for
the y-intercept is “b”. The y-intercept or “b” represents the
fixed value.
graph lines that do not pass
through the origin
The equation of a line that does not pass through the origin
looks like y = mx + b where “b” is the y-intercept and
“m” is the slope.
The following formula should be used:
dependent variable =
(slope) x (independent variable) + fixed value
•
express a linear relation of
the form: y = mx +b
Example
Cost + (rate per hour) x (number of hours) + service fee
Formula is C = mx + b
A repairman works for 2 hours at $20.00 per hour fixing
your plumbing. He charges a service fee of $50.00.
What is the cost of the repair before taxes?
m= $20.00, x = 2 hours, b= $50.00
Cost = ($20.00) x (2) + $50.00 = $90.00
84
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Pencil/Paper
Many situations in life involve “fixed” costs, plus a
constant amount per item (hours, people, etc.). Renting a
car usually costs a fixed amount per day, plus a constant
amount per kilometre driven. This graph shows the cost
of renting a hall. The fixed amount is $500, plus $2.50 per
person.
Essentials of Mathematics 11
P. 278-281
Notebook Assignment P. 282-284
Questions
a) What is the cost to rent the hall if nobody shows up?
b) Determine the slope?
c) What does the slope represent?
Solutions
a) $500.00
b) $2.50 ÷ 100 = 2.5
c) cost per person
Example: Slope and y-intercept
Daily Earnings
Dollars ($)
Salary Plus Hourly Wage
350
300
250
200
150
100
50
0
0
5
10
Time (hrs.)
15
20
Students may complete the “Slope” worksheet.
See Appendix 13.
85
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
Two graphs can be drawn on the same coordinate plane for
the purpose of comparing two sets of data.
•
•
86
understand the real-world
relationships depicted by
graphs, tables of values,
and/or written descriptions
determine the slope of a
linear relation and describe
it in words and interpret its
meaning in a problem
context
interpolate and extrapolate
values from the graph of a
linear relation
Different slopes and y-intercepts allow for comparing two
companies offering the same service. For example,
comparing two taxi companies offering different flat rates
and different rates per km travelled will show two graphs
with different slopes and y-intercepts.
Note:
Keep in mind the point of intersection represents where the
costs for both companies are equal.
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
When students are solving problems involving real-life
applications, note whether they:
1. choose appropriate axes for given quantities
2. scale and label axes appropriately, and title the graph
3. plot data correctly and determine the slopes of linear
relationships
4. can make predictions (e.g. extrapolate or interpolate)
about other values based on their equations or graphs
5. correctly interpret the graph of a relation and describe
its intent in words
6. make appropriate conclusions and interpretations of
slope and y-intercept in problem situations (e.g. car
rental problems where there is an initial cost and a rate
charge)
Essentials of Mathematics 11
P. 285-289
Notebook Assignment P. 290-291
# 1- 4
Pencil/Paper
The Griswald family arrived in Europe for their holiday.
At the car rental agency, they are offered two options:
Option 1: $25/day plus $0.05 per kilometer
Option 2: $60/day with unlimited number of kilometers
Ask students to use graph paper or a spreadsheet to
examine the costs of two options for various driving
distances.
1) At what distance per day would option 2 become a
better option?
2) If the rate per kilometer was $0.12 and they planned to
travel an average of 450 km every other day for 5
days, which option should the family choose?
Explain.
As a review, have students research in newspapers, trade
reports, and the Internet to collect graphs or tables of data
for graphing. Ask them to define the variables, determine
the appropriate scaling of axis, plot the data, and draw
conclusions.
87
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
This exploration does not get into the equations of nonlinear relations. It simply expects students to interpret nonlinear graphs and describe it in words.
interpret graphs that are not
linear
Students will also be expected to draw a graph given its
word statement.
Example
Draw a graph of the following situations. Be sure to
identify the dependent and independent variables and label
the axes appropriately. Independent variable is time and the
dependent variable is height.
1. The height of a rose bush over time.
Solution
2. The height of a particular seat on a ferris wheel for three
revolutions.
Solution
88
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
By extracting meaning from linear relations, graphical representations
and using graphs to represent data, students can use these skills
throughout their lives.
Essentials of Mathematics 11
P. 293-297
Assessment in this area should focus on the real-world applications of
these skills.
Notebook Assignment p. 299-304
# 1- 6
1. Erica saves $2 in one week, $4 the following week, $6 the next
week, and so on for a number of successive weeks. Ask students
to:
a) complete the table
b) d
Savings (t) versus Week (w).
c)
In-school Resource:
- TI-83 Ranger from MAT
421A course.
raw the graph of Total
Determine if the graph is linear and explain why or why not?
Graphs should include labels, appropriate scales, and data points.
2. Write a scenario for the following graph. Be sure to identify the
independent and dependent variables.
Students may complete the “Distance-Time Graphs” worksheets.
See Appendix 14.
Students may complete the “Hot Air Balloon” worksheet.
See Appendix 15.
Using the TI-83 Ranger (motion detector) will demonstrate the
distance versus time relationship for students.
See Appendix 16.
89
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
Students are expected to use formulas to answer questions.
They will not be expected to manipulate formulas to have
the unknown part isolated. All exercises have the unknown
already isolated.
evaluate formulas
Evaluate formulas by substituting known values into the
right-hand side of the formula, and determine the value for
the unknown value on the left-hand side.
90
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Example
Find the area of a trapezoid with bases of 8 cm and 12
cm, and a height of 7 cm.
Essentials of Mathematics 11
P. 305-306
Notebook Assignment P. 307-310
# 1 - 6, 8 - 9
1) OMIT Question # 7
Solution
a=8, b=12, & h=7
Example
The amount of energy required to separate charges depends on the
voltage developed and the amount of charge moved. If W is the
energy in joules (J), Q is the charge in coulombs (C), and V is the
resulting voltage in volts (V), then
If it takes 35 J of energy to move a charge of 5 C from one point to
another, what is the voltage between the two points?
Solution
91
92
UNIT 6
APPLICATIONS OF PROBABILITY
93
General Curriculum Outcome: The student will demonstrate an understanding of the
applications of probability in real world situations and learn how to calculate probability, odds,
and how to use probabilities to calculate expected gains and losses.
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
Applications of probability that connect the real
world with students’ mathematical knowledge will
help students understand the importance of
probability. The study of applications of probability
enables students to explore how probability affects
our daily decision making.
For example:
• A weather forecaster says there’s a 60% chance of rain.
• A sports reporter says that a team has a 50-50 chance of
winning the championship.
express probabilities as
ratios, fractions, decimals,
percent, and in words
The above statements are about probability and odds.
Know the following terms:
• Probability and odds are ways of telling how likely it is
that an event or series of events will or won’t happen.
• An event is something that may or may not happen. The
probability of an event can be any number 0 through 1.
• Probability is a measure of likelihood. It is the ratio of
favourable outcomes to all possible equally-likely
outcomes.
Probability can be written as a fraction, decimal, percent or
in words.
There are many real-life applications of probability:
• science
• medicine
• commerce
• sports
94
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
At the start of the unit, have students note in their journals
what they already know about this field of mathematics
and what else they would like to know.
Essentials of Mathematics 11
P. 322-323
Example
If a die is a fair one, it is equally likely that one of six
possibilities will turn up when it is rolled. The probability
that a 5 would be rolled can be expressed in many ways:
P(5):
1
Fraction:
6
Decimal:
0.1666.
.17%
Percent:
In words:
“One out of six”
Notebook Assignment P. 324-325
#1 - 8
Chapter Project begins on P. 321
Pencil/Paper
Fraction
Decimal
Percent
In Words
0.75
25%
1. Fill in the table above.
2. One out of three students went to the movies last
weekend. In a class of 24 students, how many went to
the movies?
95
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
If an event is impossible, it has a probability of 0. If an
event is certain, its probability is 1.
use probability to predict
the result in a given
situation
The more unlikely an event is, the closer its probability is
to 1.
A probability cannot be greater than 1 because an event
can’t be more likely than certain.
Examples
1. Elvis Presley died in 1977. So it’s impossible for Elvis
Presley to give a concert at your school. The
probability of the original Elvis Presley performing at
your school is 0.
2. The weather forecaster says that there’s a 10% chance
of rain today in Souris, PEI. This means that it is
unlikely to rain. It doesn’t mean it won’t rain today in
Souris or that it will rain for 10% of the day.
3. When you toss a quarter, the chance of tossing heads is
½ or 50%. Tossing heads is as likely as unlikely.
4. In a deck of playing cards, there are 52 cards: 36
number cards, 12 face cards, and four aces. The chance
36
of picking a number card is
, or about 69%. This
52
means that if you pick a card at random from a full
deck, picking a number card is more likely than picking
a card that is not a number card.
5. Every week, it is certain that Monday will follow
Sunday. The probability of Monday following Sunday
is 1, or 100%.
96
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Pencil/Paper
Students may complete the “Chances of a Shark Attack”
worksheet. See Appendix 17.
Essentials of Mathematics 11
P. 326-330
Presently, if you are living in Canada, suppose the
probabilities for having a certain hair colour are given in
the following chart.
Colour
Fractions
Brown
7/10
Blonde
1/7
Black
1/10
Red
1/17
Decimal
Notebook Assignment P. 331-333
#1-8
Percent
Complete the chart by calculating the probabilities as
decimals and percent. Given the population of Canada is
32 million, theoretically how many people should have
the following hair colour:
• Brown
• Blonde
• Black
• Red
97
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
Odds and probability are two different ways of expressing
the same thing, likelihood.
The important difference between probability and odds is:
a) Probability is always expressed as a fraction, percent or
decimal.
b) Odds are expressed as a ratio.
determine the odds for and
against a particular event
occurring
The probability of the spinner stopping on “B” is
1
because, out of four possible events, there is one
4
favourable event.
The odds in favour of the spinner stopping on “B” are
1 to 3 (1:3) because of the four things that can happen, one
is favourable and three are unfavourable.
The odds against the spinner stopping on “B”are 3 to1
(3:1) because of the four things that can happen, three are
unfavourable and one is favourable.
The odds in favour of an event and the odds against an
event are reversed: 1:3, 3:1.
1
When an event has a probability of , it has odds of 1:1.
2
odds in favour = favourable outcomes:unfavourable
outcomes
odds against = unfavourable outcomes:favourable
outcomes
probability = (# of desired outcomes) ÷ (total possible
outcomes)
Note:
Total # of outcomes = (# of favourable outcomes) + (# of
unfavourable outcomes)
98
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Pencil/Paper
Essentials of Mathematics 11
P. 334-336
“If you are like most Islanders,
you eat a hamburger every eight
meals”.
Notebook Assignment P. 337-339
#1 - 10
1.
Suppose the claim is true. Find the odds in favour of
eating a hamburger at your next meal.
2. Find the odds against eating a hamburger at your next
meal.
Hint
For each eight meals, there is one meal with hamburger.
So, there are seven meals that have no hamburger. The
odds in favour of eating a hamburger at your next meal
is1:7 or 1 to 7.
Question
A random survey shows that 7 out of 10 voters will vote
for Lewis as Premier. Find the odds against a voter
voting for Lewis.
Solution
odds against = unfavourable outcomes: favourable outcomes
odds against = 3:7
Question
There are 50 people at a sports registration evening.
Fifteen people registered for basketball, 23 people
registered for volleyball, and the rest registered for
badminton. One person is chosen at random, find the
following:
a) the odds against the person playing badminton
b) the odds in favour of the person playing basketball
c) the odds against the person playing either volleyball
or basketball
99
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
Know the following terms:
• Theoretical probability is when you find the
probability of an event without doing an experiment or
analysing data.
compare experimental
observations with
theoretical predictions
Theoretical probability is used to predict the results of a
probability experiment. Usually, as the number of attempts
in an experiment increase, experimental probability gets
closer to theoretical probability.
Suppose you toss a die. The theoretical probability of the
die landing on four is
P ( 4) =
therefore,
•
# of sides with four
# of sides
P(4) =
1
6
Experimental probability is when you do an
experiment or collect data and analyse data to find
probability.
Experimental probability =
100
# of favourable outcomes in exp eriment
# of trials
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Pencil/Paper
Students should be able to complete experiments and
record results.
Essentials of Mathematics 11
P. 340-345
Students may complete the “ Shove A Coin” worksheet.
See Appendix 18.
Notebook Assignment P. 345
#1-3
Have students complete the 7 station “ Applications of
Probability: Theoretical and Experimental Probability”
project. This project activity will take 2 days to complete.
See Appendix 19.
101
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
Expected value is an estimate of the average return (or loss)
one would have in along series of trials.
use probabilities to
calculate expected gains
and losses
Expected value = (probability of winning) x (gain) (probability of losing) x (loss)
In general, the following statements are true:
• If you play a game for money with an expected value <
0 (less than 0), you can expect to lose.
• If you play a game for money with an expected value =
0 (equal to 0), you can expect to break even.
• If you play a game for money with an expected value >
0 (greater than 0), you can expect to win.
Example
A bag contains 10 marbles. There are five red, three black,
and two white. The game costs $2.00 to play. You draw one
marble from the bag. If it is red you win $1.00, black you
win $2.00, and white you win $5.00. Calculate the expected
value.
Solution
EV = 0.5(–$1.00) + 0.3($0.00) + 0.2($3.00) = $0.10 or a gain
of 10¢.
In a series of plays of this game, you could expect to win an
average of 10¢ for each time you play.
102
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Discuss how casinos are designed to make a profit.
Essentials of Mathematics 11
P. 348-352
Discuss gaming and lottery expected values.
Discuss advantages and disadvantages of all the above.
Notebook Assignment P. 353-354
#1-7
103
104
UNIT 7
PERSONAL INCOME TAX
105
General Curriculum Outcome: The student will learn how to prepare an income tax return for
a single, employed person with no dependents.
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
It is recommended teachers use the following free program:
The Teaching Taxes Program includes the following:
• Teacher’s Manual
• Student Workbook (class set)
• General Income Tax and Benefit Guide (class set)
• T1 Special Form (class set)
• T1 General Prince Edward Island Forms (double class
set)
All forms may be ordered at:
•
www.ccra.gc.ca
• 1-800 -959-2221 (toll free number)
• Client Services Directorate
400 Cumberland,
Room 2014
Ottawa, ON K1A 0L5
Fax: 613 -941 -5100
Note:
Order in June for delivery in September, or mid-October for
delivery by January.
•
gain an understanding of
the Canadian Taxation
System
Discuss the following:
• what is income tax
• what do taxes fund
• how does the government distribute the money
• why should people prepare their own income tax return
•
consider the effect of
marginal tax rate on the
amount of income tax paid
When students calculate the amount of provincial (PEI)
taxes to be paid, they must be careful to multiply the tax
rate by the first $30,574 and then any earnings above
$30,574 and up to $59,180 has a rate of 13.8%, and all
amounts greater than $61,510 has a rate of 16.7%.
Note: Rates will change yearly.
106
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Pencil/Paper
Joanne works in a PEI seafood processing plant for
$14.80 per hour. She works 40 hours per week and gets
paid time and a half for hours worked above that. She
works 47 weeks each year.
1. What are her earnings at regular pay?
2. What are her overtime earnings if she averages 4
hours of overtime each week?
3. What is her total earnings?
4. What taxes would she pay without her overtime
earnings?
5. What taxes does she pay on her total earnings?
6. Calculate her actual pay per hour after taxes.
Teaching Taxes Program
Chapter Project begins on P. 363
Internet Resource:
˜ www.ccra.gc.ca
Solution
1. Regular earnings = $14.50 × 40 × 47 = $27824.00
2. Overtime earnings = 1.5 × $14.50 × 4 × 47 = $4089
3. $27824.00 + $4089.00 = $31930.00
4. PEI taxes = $27824.00 × 0.098 = $2726.75
Federal taxes = $27824.00 × .16 = $4451.84
5. She pays PEI taxes of 0.098 × $30574.00 =
$2996.25 on the first $30574 earned and federal taxes
of $30754 × 0.16 = $4920.64 on the first $30754
earned. She pays PEI taxes of 0.138 × ($31930 $30574) = $187.13 and federal taxes of 0.22
× ($31930 - $30754) = $298.32 on the remainder
because her tax rate jumped from 9.8% to 13.8%
provincially and from 16% to 22% federally on
earning above $30574 and $30754, respectively. This
gives a total of $2996.25 + $4920.64 + $187.13 +
$298.32 = $8402.47 paid in taxes.
6. Pay after taxes = $31930.00 - $8402.47 = $23527.53,
so to calculate actual pay per hour, you divide this
amount by 40 and then by 47 to get
$23527.53
= $12.51 per hour.
40 × 47
Students may complete the Income Tax” worksheet.
See Appendix 20.
107
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
Examine a sample T4 slip and review the following
deductions:
• CPP
• El
• income tax
• union dues
• pension
Discuss the purpose of these deductions.
complete simple income tax
return
Recommended
Use the outline below as a guide for teaching this Unit.
1) Highlight and use examples in Essentials of
Mathematics 11 P. 364-367, Complete Notebook
Assignments P. 367 - 368, # 1 - 9
2) Highlight and use examples in Essentials of
Mathematics 11 P. 369-380 Use the T4 and Tax
return found here. Complete Notebook Assignment P.
381, # 1 on an overhead.
Note:
Use a TI-Special Form as it is a simplified version of the
TI -General.
•
evaluate tax implications
and lifestyle choices
3) Complete the Notebook Assignment P. 385 , # 1 - 8.
Divide students into grous of 2 - 3 and have them
complete 4 - 5 questions per group as assigned by you
from the Teaching Taxes Student Workbook P. 8 - 11,
Exercises A, B, C, and D.
4) Complete the Teaching Taxes Student Workbook 6
returns using information on P. 12 - 21.
Note:
Overheads of all forms you are teaching is recommended.
108
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Have student report on the effects of the levels of taxation
if:
• a given income is increased or decreased
substantially
• a change in marital status
• dependents versus no dependents
• living in a northern community
Essentials of Mathematics 11
P. 364-367
Notebook Assignment
P. 367-368 # 1 - 8
Pencil/Paper
Give students job descriptions, including wages, and have
them choose an occupation and complete an income tax
form for a single individual without dependents.
OR
Ask students to research their dream job and prepare an
income tax return for this job.
OR
Have students bring in their own tax information and
complete their own income tax return.
Essentials of Mathematics 11
P. 369-380
Notebook Assignment
P. 385 #1
Essentials of Mathematics 11
P. 384
Notebook Assignment
P. 385, #1 - 8
Note:
This activity could be their final assessment for this unit.
109
110
UNIT 8
PREPARING A BUSINESS PLAN
111
General Curriculum Outcome: The student will prepare a business plan.
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
Realistic activities involving the research and design of a
business plan enable students to recognize the connections
between mathematical skills they have learned and the
concrete situations these skills represent. An understanding
of procedures and applications of mathematics can help
students make reasonable business decisions.
•
develop an understanding
of the importance of a
business plan
Discuss with students the characteristics needed to be an
entrepreneur. Students may investigate if they are an
Entrepreneurial Type. See Internet Resource Site.
Discuss why a Business Plan is an important first step to
starting a business.
Explain the following terms:
• Retail industry sells goods to the general public.
• Service industry provides services to customers.
• Manufacturing industry make a product to sell to
businesses.
Brainstorm business in your area which fit the above three
industry sectors.
•
select and name a business;
determine product/services
and customer base
Recommended
Use examples # 1-3.
Note:
As a teaching tool for this Unit, it is recommended that you
use the Project Activity in each of the Explorations. Keep
in mind you may wish to do selected Notebook
Assignments as a lead-in for the Project Activity work.
112
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Project Activity
After covering the three industry sectors, assign students
the Project Activity in Essentials of Mathematics 11,
P. 398.
Essentials of Mathematics 11
P. 394-397
Notebook Assignment P. 399
# 1-5
Note:
Students may wish to work as individuals or small groups
throughout this Unit.
Internet Resource:
˜ Canadian Bankers
Association which gives an
excellent template for a
business plan
http://www.cba.ca/en/view
Pub.asp?fl=6&sl=23&doci
d=40&pg=7
˜ Canada Business Service
Centres has information
specific to PEI
http://bsa.cbsc.org/gol/bsa/
interface.nsf/engdoc/0.htm
l
˜ Junior Achievement
Program
http://www.ja.org/progra
ms/programs_high_overvi
ew.shtml
˜ Background information for
teachers
http://www.entreworld.org
/
Pencil/Paper
Have students choose a business in their community where
they might like to work, and complete the “Interview with
a Entrepreneur” worksheet with the owner or manager.
See Appendix 21.
˜ Am I the Entrepreneurial
Type?
www.potentielentreprene
ur.ca/client/questionnaire
section1en.asp
113
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
Discuss with the students the need for selecting the correct
space for their business. This will provide a good
understanding of the costs associated with renting or
leasing space.
develop a space plan for
the business and research
leasing costs
Contact local mall manager or real estate agent to get local
costs on the rental of space.
114
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Project Activity
Students should visualize a room in the school equal to
the space they feel would be needed for their business
(including Inventory Space). Ask students to measure
this room and determine the square footage.
Essentials of Mathematics 11
P. 400-402
Notebook Assignment
P. 403-404, # 1 - 9
Upon returning to the classroom, students should
determine the monthly cost of the space.
Complete Project Activity in
Essentials of Mathematics 11,
P. 403
Note:
May use your information or the Chart in Essentials of
Mathematics 11, P. 401.
115
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
Discuss the importance of Market Share and demand for
their business.
evaluate existing
competition; research and
prepare a collage of
competitor’s ads
Discuss the different types of customers that would use the
services of a typical business.
Discuss the different types of fast food restaurants in their
community. Make the point that not all competition is bad
for business.
116
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Project Activity
Use the yellow pages from the telephone book to identify
competition for the students’ selected businesses.
Essentials of Mathematics 11
P. 405-407
Notebook Assignment
P. 408-409, # 1- 5
Complete Project Activity in
Essentials of Mathematics 11,
P. 408
117
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
Discuss the advantages of advertising.
describe marketing
activities and distribution
Discuss the techniques used in a Marketing campaign.
Use Essentials of Mathematics 11, P. 411 - 414, examples
# 1 - 4 to examine the costs of various marketing
techniques.
•
118
develop an advertisement
strategy
Bring in examples of different media advertisements:
• TV
• radio
• flyers
• newspaper ads
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Project Activity
After students develop their advertisement campaign,
have students perform, present, or display their
advertisement in the class.
Essentials of Mathematics 11
P. 410-415
Notebook Assignment
P. 416-417, # 1 - 6, 8
Note:
Story boarding is an excellent technique to teach
students for this activity.
Complete Project Activity in
Essentials of Mathematics 11,
P. 415
In-school Resource:
- Choices and Decisions Binder
Lesson 10 “ The Influence of
Advertising”
119
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
Discuss staffing, work schedules, and payroll
responsibilities.
develop a staffing plan
Use examples #1 - 2.
120
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Students may complete the “Problem Analysis” activity
in Essentials of Mathematics 11, P. 424 as a warm-up
for their Project Activity.
Essentials of Mathematics 11
P. 418-420
Notebook Assignment
P. 422- 423, # 1 - 6
Project Activity
Have students examine the staffing needs for their
business. They should prepare a work schedule for their
employees with a brief job description. Also, they
should research the wages they would be expected to pay
their employees based on their job description.
Complete Project Activity in
Essentials of Mathematics 11,
P. 421
Invite a business owner and/or operator to discuss with
the class how he or she manages the business. Have
students prepare questions related to the topic
beforehand.
121
SCO: By the end of grade 11
students will:
Elaboration - Instructional Strategies/Suggestions
•
Explain to students that the purpose of establishing a
business is to generate revenues that are greater than
expenses, creating a profit.
develop a financial plan
Students should be familiar with the following terms:
• Operating expenses are the expenses incurred
regardless of sales (ie; leasing, insurance and wages).
• Overhead costs are the general operating costs of a
business.
• Capital expenses are long term expenses such as,
buying buildings, tools, or equipment.
• Financial charges are charges to repay loans.
• Gross profit is the difference between what a business
pays for the products or services it sells and what it
charges in return.
• Net profit is the profit remaining after all operating
costs is deducted from their gross profit.
Use examples # 1 - 4.
122
Worthwhile Tasks for Instruction and/or Assessment
Suggested Resources
Project Activity
Have students prepare a monthly statement of expected
revenue and expenses to show if they expect to make a
profit.
Essentials of Mathematics 11
P. 426-431
Notebook Assignment
P. 432-434 # 1 - 8
Note:
The use of spreadsheets may be useful in organizing a
financial plan.
Recommended
The completed Business Plan based on the Project
Activity assignments may be the assessment tool for this
Unit.
In closing, discuss the following questions as a class:
• What are the advantages and disadvantages of
operating your own business?
• What are the advantages and disadvantages of
working for others?
• What mathematical skills do you need to operate your
own business?
Have students investigate real-world situations by
comparing their business plans with the plans of
established businesses.
123
124
APPENDIX
125
126
Appendix
1.
Earning Commission Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
2)
Weekly Wages for Piecework Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . 132
Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
3)
Calculating Simple Interest Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
4)
Mean /Median / Mode Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
5)
Vehicle Expenses Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
6)
Buying Cars Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
7)
Earth Facts Information Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
8)
Metric Prefixes Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
9)
SI Measure Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
10)
Imperial Measure Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
11)
Changing Units Between the Metric and Customary Systems Chart . . . . . 148
12)
Graph Paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
13)
Slope Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
14)
Distance Time Graphs Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
15)
Hot Air Balloon Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
16)
T1 - 83 Ranger Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
17)
Chances of Shark Attack! Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
18)
Shove a Coin Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
127
128
19)
Applications of Probability: Theoretical & Experimental Probability
Stations 19-1 through 19-7 Project Activity . . . . . . . . . . . . . . . . . . . . . . . 163
20)
Income Tax Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
21)
Interview with an Entrepreneur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
Note: All Appendix are on the Mathematics 531A CD for teachers use.
129
Appendix 1
Example:
Earning Commission
Sandra sells furniture. She earns 10% commission on her sales up to her quota of
$2,500. She earns a 14% commission on all sales beyond $2,500. Last week her
sales were $4,966. How much did Sandra earn?
Quota
$2,500
Step 1:
Step 2:
Step 3:
Step 4:
Rate
Sales
Bonus Rate
10%
$4,966
14%
Regular Commission - $2,500 x .10 = $250
Amount for Bonus Commission - $4,966 - $2,500 = $2,466
Bonus Commission - $2,466 x .14 = $345.24
Regular Commission + Bonus Commission = Total Commission
$250.00
+
$345.24
=
$595.24
So, Sandra earned $ 595.24
Compute the total commission for each example below. Add the Bonus Commission to the
Regular Commission.
Quota
Rate
Sales
1) $5300
11%
$5783
21%
2) $8700
6%
$14536
17%
3) $1600
11%
$1889
13%
4) $5600
8%
$9490
15%
5) $9400
10%
$11447
14%
6) $4500
5%
$7730
13%
7) $8800
4%
$10317
7%
8) $4600
2%
$7377
4%
9) $2500
8%
$1795
10%
10) $1900
8%
$2021
10%
11) $4600
9%
$8365
15%
12) $8800
3%
$3848
10%
13) $4400
5%
$8161
11%
14) $7000
9%
$9471
13%
15) $7800
8%
$7754
11%
130
Regular
Commission
Bonus
Rate
Bonus
Commission
Total
Commission
Answers
Earning Commission
Quota
Rate
Sales
Regular
Commission
Bonus
Rate
Bonus
Commission
Total
Commission
1) $5300
11%
$5783
$583
21%
$101.43
$684.43
2) $8700
6%
$14536
$522
17%
$992.12
$1514.12
3) $1600
11%
$1889
$176
13%
$37.57
$213.57
4) $5600
8%
$9490
$448
15%
$583.50
$1031.50
5) $9400
10%
$11447
$940
14%
$286.58
$1226.58
6) $4500
5%
$7730
$225
13%
$419.90
$644.90
7) $8800
4%
$10317
$352
7%
$106.19
$458.19
8) $4600
2%
$7377
$92
4%
$111.08
$295.08
9) $2500
8%
$1795
$143.60
10%
$0.00
$143.60
10) $1900
8%
$2021
$152
10%
$12.10
$164.10
11) $4600
9%
$8365
$414
15%
$564.75
$978.75
12) $8800
3%
$3848
$115.44
10%
$0.00
$115.44
13) $4400
5%
$8161
$220
11%
$413.71
$633.71
14) $7000
9%
$9471
$630
13%
$321.23
$951.23
15) $7800
8%
$7754
$620.32
11%
$0.00
$620.32
131
Appendix 2
Weekly Wages for Piecework
Compute the Weekly Wages for each example below:
Daily Production
Monday
Tuesday
Wednesday
Thursday
Friday
1)
37
38
34
38
35
$1.00
2)
10
11
11
9
12
$3.12
3)
16
14
15
14
14
$3.01
4)
31
32
33
34
34
$1.05
5)
9
10
10
8
8
$2.91
6)
8
6
7
6
9
$4.25
7)
19
18
18
18
15
$2.50
8)
13
14
11
13
11
$2.72
9)
14
13
13
12
14
$3.68
10)
17
20
21
19
20
$1.88
11)
12
16
17
16
15
$2.76
12)
6
7
6
7
7
$3.66
13)
22
20
19
21
17
$2.44
14)
15
16
14
17
17
$1.76
15)
28
29
26
28
25
$1.77
16)
16
14
16
16
13
$2.62
17)
54
49
45
46
48
$0.75
18)
101
97
106
100
110
$0.60
19)
83
80
85
86
88
$0.80
20)
95
98
90
91
89
$0.95
132
Piece
Rate
Wages
Answers
Weekly Wages for Piecework
Compute the Weekly Wages for each example below:
Daily Production
Monday
Tuesday
Wednesday
Thursday
Friday
Piece
Rate
Wages
1)
37
38
34
38
35
$1.00
$182.00
2)
10
11
11
9
12
$3.12
$165.36
3)
16
14
15
14
14
$3.01
$219.73
4)
31
32
33
34
34
$1.05
$172.20
5)
9
10
10
8
8
$2.91
$130.95
6)
8
6
7
6
9
$4.25
$153.00
7)
19
18
18
18
15
$2.50
$220.00
8)
13
14
11
13
11
$2.72
$168.64
9)
14
13
13
12
14
$3.68
$242.88
10)
17
20
21
19
20
$1.88
$180.48
11)
12
16
17
16
15
$2.76
$209.76
12)
6
7
6
7
7
$3.66
$120.78
13)
22
20
19
21
17
$2.44
$241.56
14)
15
16
14
17
17
$1.76
$139.04
15)
28
29
26
28
25
$1.77
$240.72
16)
16
14
16
16
13
$2.62
$196.50
17)
54
49
45
46
48
$0.75
$181.50
18)
101
97
106
100
110
$0.60
$308.40
19)
83
80
85
86
88
$0.80
$337.60
20)
95
98
90
91
89
$0.95
$439.85
133
Appendix 3
1)
2)
Calculating Simple Interest
Calculate the interest paid on each of the following:
Principal
Rate per year
Time
$400.00
8 1/2%
3 years
$1,200.00
400.00%
7 months
$650.00
5 3/4%
115 days
$7,000.00
9.00%
90 days
$425.00
7.50%
5 years
$3,400.00
1.04%
9 months
$6,500.00
3 1/4%
230 days
Find the unknown quantities for each of the following:
Principal
Rate per year
Time
$900.00
5 1/2%
$700.00
8%
days
$40.04
$4,000.00
9%
months
$658.00
$1,500.00
8%
11 1/4
$640.00
$2,400.00
10%
Interest Paid
60 days
$300.00
134
Interest Paid
2 years
$30.00
4 months
$55.00
200 days
$16.00
5
years
$250.00
days
$19.93
120 days
$98.63
Answers
1)
2)
Calculating Simple Interest
Calculate the interest paid on each of the following:
Principal
Rate per year
Time
Interest Paid
$400.00
8 1/2%
3 years
$102.00
$1,200.00
4%
7 months
$280.00
$650.00
5 3/4%
115 days
$11.78
$7,000.00
9%
90 days
$155.34
$425.00
8%
5 years
$170.00
$3,400.00
1%
9 months
$25.50
$6,500.00
3 1/4%
230 days
$133.12
Find the unknown quantities for each of the following:
Principal
Rate per year
Time
Interest Paid
$900.00
5 1/2%
60 days
$8.14
$700.00
8%
261 days
$40.04
$4,000.00
9%
22 months
$658.00
$300.00
5%
2 years
$30.00
$1,500.00
11%
4 months
$55.00
$365.00
8%
200 days
$16.00
$444.44
11 1/4
5 years
$250.00
$640.00
10%
114 days
$19.93
$2,400.00
13%
120 days
$98.63
135
Mean/Median/Mode
Appendix 4
The following table contains test results for the students in Mrs. Jones’
mathematics class. The test has a maximum of 30 marks and a passing grade
is 50%. Calculate the mean, median, and mode for the class.
Student
Mark
Student
Mark
Student
Mark
Susan Adams
19
Sara Wall
21
Adam Smith
28
Elliot White
15
Peter Williams
23
Sally Swanson
22
John Buchanan
19
Sarah Gaudet
15
Barbara Wilson
25
Dave Moore
25
Joe MacMillan
18
David Vincent
18
Jeff Black
26
Jason Profit
19
Basil Vessey
17
Dana Gallant
24
Melanie Taylor
20
Randall Tozer
23
Gloria Gillis
18
Lynden Stewart
27
Steven Simmons
18
Ross Hill
16
Bryon Sorrie
30
Jack Randall
19
Kim Walsh
12
Stan Peardon
2
Harvey Arsenault
16
136
Appendix 5
Vehicle Expenses
Use the information in the tables to answer the questions on the following page.
(The data in this table is invented for the purpose of this exercise)
Numbers are based on one year’s driving. Vehicle Maintenance, Operating, and Repair Information
Type of
Vehicle
# of
Type of Fuel
Fuel
Cylinders Used
Efficiency
regular
Moped
Oil
Efficiency
Tune-up
Costs
Lube &
Oil
Change
Repairs
per year
Depreciation
per year
Insurance
per year
57
km/L
1L/6500km
$22.50
$18.50
$65.00
12% of value
12% of value
Motorbike
regular
47
km/L
1L/4800km
$24.50
$19.50
$75.00
15% of value
12.8% of
value
Motorcycle
regular
40 km/L
1L/3200km
$26.50
$19.50
$100.00
22% of value
14.2% of
value
Subcompact car
4
regular
13 km/L
1L/1500km
$34.88
$21.88
$225.00
11.7% of value
12.9% of
value
Compact
car
6
supreme
11 km/L
1L/4000km
$39.88
$23.88
$325.00
16.2% of value
14.5% of
value
Intermediate
car
8
supreme
15 km/L
1L/8000km
$49.98
$25.88
$250.00
21.8% of value
18.0% of
value
Typical Fuel and Oil Costs
Gasoline Regular
Supreme
Oil
76.5¢ per litre
85.4¢ per litre
$2.90 per litre
137
Appendix 5
Vehicle Expenses
Student Name_________________
1. John drives his subcompact car about 12,000 km per year. How much gas will he use in an average
year? How much oil?
__________________________________________________________________________________
2. Cindy has purchased a compact car. What will it cost her for gasoline and oil to drive this car 8,300
km this year?
__________________________________________________________________________________
3. The intermediate car Warren has just bought will probably be driven 24,000 km in the next year. How
much will Warren have to spend on gasoline and oil for the car during this time?
__________________________________________________________________________________
4. The subcompact car M.J. drives runs about 15,000 km per year. What will be the cost of gasoline and
oil for the car during the year?
__________________________________________________________________________________
5. Damian wants to know the annual fuel and oil costs for three kinds of cars—a subcompact, a compact,
and an intermediate—if each car is to be driven a total of 32,000 km this year.
Subcompact________________________________________________________________________
Compact___________________________________________________________________________
Intermediate________________________________________________________________________
6. Tanya knows that she normally drives 25,000 km per year. What would be the cost of gasoline and oil
for each one of the three kinds of cars mentioned in question 5?
Subcompact________________________________________________________________________
Compact___________________________________________________________________________
Intermediate________________________________________________________________________
7. Tony wants to estimate the costs of driving his subcompact car for the coming year. He wants to
include the costs of gasoline, oil, tune-ups (one per year), and lube and oil changes (one per year).
What costs should Tony plan on if he expects to drive 17,000 km?
__________________________________________________________________________________
8. If Tony were to buy an intermediate car, what would be the costs of operating this car for one year?
Include the same costs as those mentioned in Question 7 for 17,000 km of driving.
__________________________________________________________________________________
9. Lori wants to know the total estimated cost of driving her intermediate car a total of 18,500 km in the
coming year. At the beginning of the year, the estimated value of her car was $6500.
__________________________________________________________________________________
10. A compact car will be driven 37,500 km in the coming year. Its current estimated value is $7250. What
are the total estimated costs for this car?
__________________________________________________________________________________
11. Gar’s older subcompact car is expected to have about three more years of good driving left. Its current
value is $4950. What expenses can he expect for this car for the coming 12 months? He expects to
drive the car 42,000 km in that time (12 months).
__________________________________________________________________________________
12. What are the total estimated driving expenses for each of these cars that will have to travel 42,500 km
in the coming year?
Subcompact (value is $4500)__________________________________________________________
Compact (value is $3600)_____________________________________________________________
Intermediate (value is $6550)__________________________________________________________
138
Answers
1. Gas = $706.15
Vehicle Expenses
2. Gas + Oil = $644.38 + $6.02 = $650.40
3. Gas + Oil = $1366.40 + $8.70 = $1375.10
4. Gas + Oil = $882.69 + $29.00 = $911.69
5. Subcompact:
Compact:
Intermediate
Gas + Oil = $1883.08 + $61.87 = $1244.95
Gas + Oil = $2484.36 + $23.20 = $2507.56
Gas + Oil = $1821.87 + $11.60 = $1833.47
6. Subcompact:
Compact:
Intermediate:
Gas + Oil = $1471.15 + $48.33 = $1519.48
Gas + Oil = $1940.91 + $18.15 = $1959.04
Gas + Oil = $1423.33 + $9.06 = $1437.39
7. Gas + Oil + Tune-up + Lube & Oil Change = $1000.38 + $32.87 + $34.88 + $21.88
=$1090.01
8. Gas + Oil + Tune-up + Lube & Oil Change = $967.87 + $6.16 + $49.98 + $25.88 =$1049.89
9. Gas + Oil + Tune-up + Lube & Oil Change + Repairs + Depreciation + Insurance
$1053.27 + $6.71 + $49.98 + $25.88 + $250.00 + $1417.00 + $1170.00 = $3972.84
10. Gas + Oil + Tune-up + Lube & Oil Change + Repairs + Depreciation + Insurance
$2911.36 + $13.59 + $39.98 + $23.88 + $325.00 + $1174.50 + $1051.25 = $5539.56
11. Gas + Oil + Tune-up + Lube & Oil Change + Repairs + Depreciation + Insurance
$2471.54 + $81.20 + $34.88 + $21.88 + $325.00 + $579.15 + $638.55 = $4152.20
12. Subcompact:
Gas + Oil + Tune-up + Lube & Oil Change + Repairs + Depreciation + Insurance
$2500.96 + $82.17 + $34.88 + $21.88 + $225.00 + $526.50 + $580.50 = $3971.89
Compact:
Gas + Oil + Tune-up + Lube & Oil Change + Repairs + Depreciation + Insurance
$3299.55 + $30.81 + $39.88 + $23.88 + $325.00 + $583.20 + $522.00 = $4824.36
Intermediate:
Gas + Oil + Tune-up + Lube & Oil Change + Repairs + Depreciation + Insurance
$2419.67 + $15.41 + $49.98 + $25.88 + $250.00 + $1427.90 + $1179.00 = $5367.74
139
Appendix 6
BUYING CARS
Note: Refer to Textbook P. 59
NAME:________________________
New Cars: The tax rate is_____________ Used Cars: The tax rate is ______________
1.
You wish to buy a new car for $45,000. You trade in your old car for $5,000. The
dealership offers a loan for 2% per year to be paid monthly over 4 years,
compounded semi-annually.
a. What is the tax on the new car? What is the cost of the new car?
b. What is the amount borrowed?
c. What is the monthly payment?
d. What is the total payment over 4 years?
e. What is the finance charge?
2.
You wish to buy a new car for $60,000. You trade in your old car for $10,000. The
dealership offers a loan for 1.5% per year to be paid monthly over 5 years,
compounded semi-annually.
a. What is the tax on the new car? What is the total cost of the new car?
b. What is the amount borrowed?
c. What is the monthly payment?
d. What is the total payment over 5 years?
e. What is the finance charge?
140
3.
You wish to buy a new car for $70,500. You trade in your old car for $12,000. The
dealership offers a loan for 0.9 % per year to be paid monthly over 4 years,
compounded semi-annually.
a. What is the tax on the new car? What is the total cost of the new car?
b. What is the amount borrowed?
c. What is the monthly payment?
d. What is the total payment over 4 years?
e. What is the finance charge?
4.
You wish to buy a new car for $120,000. You trade in your old car for $20,000. The
dealership offers a loan for 1.8% per year to be paid monthly over 3 years,
compounded semi-annually.
a. What is the tax on the new car? What is the total cost of the new car?
b. What is the amount borrowed?
c. What is the monthly payment?
d. What is the total payment over 3 years?
e. What is the finance charge?
141
5.
You wish to purchase a used car for $10,000. You have a $3,000 down-payment.
You borrow from the bank at 6.8% to be paid monthly over 5 years, compounded
semi-annually.
a. What is the tax on the car you wish to purchase? What is the total cost?
b. What is the amount borrowed?
c. What is the monthly payment?
d. What is the total payment over 5 years?
e. What is the finance charge?
6.
You wish to purchase a used car for $8,000. You have a $1,000 down-payment. You
borrow from the bank at 8.8% to be paid monthly over 3 years, compounded semiannually.
a. What is the tax on the car you wish to purchase? What is the total cost?
b. What is the amount borrowed?
c. What is the monthly payment?
d. What is the total payment over 3 years?
e. What is the finance charge?
142
7.
You wish to purchase a used car for $15,000. You have a $4,000 down-payment.
You borrow from the bank at 7.5% to be paid monthly over 4years, compounded
semi-annually.
a. What is the tax on the car you wish to purchase? What is the total cost?
b. What is the amount borrowed?
c. What is the monthly payment?
d. What is the total payment over 4 years?
e. What is the finance charge?
8.
You wish to purchase a used car for $6,000. You have no down-payment. You
borrow from the bank at 5.5% to be paid monthly over 2 years, compounded semiannually.
a. What is the tax on the car you wish to purchase? What is the total cost?
b. What is the amount borrowed?
c. What is the monthly payment?
d. What is the total payment over 2 years?
e. What is the finance charge?
143
Appendix 7
EARTH FACTS
Average Distance from Sun
About 150,000,000 kilometers (90,000,000 miles)
Diameter Through Equator
12,756.32 kilometers (7653.8 miles)
Circumference Around Equator
40,075.16 kilometers (24,045.1 miles)
PEI from outer space
Surface Area
Land area: about l48,300,000 sq. kilometers,
or about 30% of total surface area
Water area: about 361,800,000 sq. kilometers,
or about 70% of total surface area
Rotation Period
23 hours, 56 minutes, 4.09 seconds
Revolution Period Around Sun
365 days, 6 hours, 9 minutes, 9.54 seconds
Temperature
Highest: 58oC at Al Aziziyah, Libya
Lowest: –90oC at Vostok, Antarctica
Average surface temperature 14oC
Highest and Lowest Land Features
Highest: Mount Everest, 8848 meters above sea level
Lowest: shore of Dead Sea, 396 meters below sea level
Ocean Depths
Deepest: Mariana Trench in Pacific Ocean; 11,033 meters below surface
Average ocean depth, 3795 meters
144
Appendix 8
Metric Prefixes
Record the Metric Prefixes in the spaces provided. Below each, describe what the
prefix means. One prefix is done for you.
145
Appendix 9
146
Appendix 10
147
Appendix 11
148
Appendix 12
149
SLOPE ACTIVITY
Appendix 13
a) State the slope of each line using rise over run.
b) State the y-intercept
c) Determine the equation for each graph.
A
150
B
C
D
E
F
Appendix 14
Distance - Time Graphs
Each of the graphs in this exercise represents distance from an object as a function of time.
1. On the following graphs, distance, as labeled on the y-axis, refers to distance from an
amusement park. Which graph best matches the following sentence?
Hugo walked at a steady pace toward the amusement park.
A
B
C
D
2. Describe a situation involving distance and time that could match each of the graphs
that you did not choose as the answer to problem 1.
3. Each of the following graphs depicts the relationship between distance from a ride and
time elapsed for two people. Each person walks at a steady rate directly toward or away
from the ride or stands still. For each graph, describe the relationships and make
observations and comparisons.
A
B
C
D
In addition, answer the following questions for each example:
Which person is walking faster?
What is the significance of the x-intercept? The y-intercept?
151
4. The graphs below show motion away from the park for three different mothers. Jane
moves at a steady pace, Angela speeds up as she walks away, and Kathy slows down as
she moves away. Which graph matches which woman’s motion? Explain your
reasoning?
A
B
C
5. In the following two graphs, distance in metres from the main exit is graphed as a
function of time in seconds. Describe the motion using the coordinates shown as end
points of the line segments. Determine the rate at which the person walks for each
segment. Assume that the person is moving directly toward, or away from the exit, or is
standing still.
A
6. Which of the following tables best describes the graph?
152
B
7. Choose the sentence that best describes the following
table:
A Kirk walked away from the Water Slide at a rate of 6
feet per second.
B Kirk was 42 feet away from the Water Slide and
walked toward it at a rate of 7 feet per second.
C Kirk was 42 feet away from the Water Slide and
walked toward it at a rate pf 6 feet per second.
D Kirk walked away from the Water Slide at a rate of 7 feet per second.
8. For each answer that did not describe the table in question 7, make a table that could
correspond to it. Give entries for each second from 0 to 6.
9. Hugo was standing 9 feet from the hot-dog stand. He walked away, and after 3 seconds
he was 21 feet away. Which of the following graphs corresponds to this situation?
A
B
C
D
153
10.
154
Make tables that correspond to the graphs on question 9.
Answers
1.
2.
B
Answers can vary:
Distance - Time Graphs
A
C
D
standing still at a distance from the park
walking at a steady pace away from the park
walking to the park and then walking further away at a
steady pace in both directions, leaving a little faster
3. A Ann is farther from the ride and walks quickly to it, passing Bob on the way.
Bob is closer to the ride and walks slowly toward it but not all the way.
B Carl walks quickly toward the ride meeting Dianne on the way.
Dianne is closer to the ride than Carl, walks away from it at a slightly slower speed
than Carl.
C Both Elmer and Francis are walking toward the ride. Elmer is farther away and,
walking faster, arrives at the same time as Francis.
D George is standing still at a distance from the ride and Helen, being closer to the
ride, walks by him as she walks away from the ride.
The x-intercept indicates the time to reach the ride and the y-intercept the beginning
distance from the ride.
4. A is Jane as the graph is a line, indicating a steady pace
B is Kathy because the curve’s slope is decreasing indicating slowing down as she
moves away - the distance is less for more time
C is Angela because the increasing slope of the curve indicates speeding up - the
distance is greater for more time
5. A The person is 15 metres from the exit and is moving toward it at 3 metres per
second (it takes the person 5 seconds to cover 15 metres, thus, 3 metres per second),
then stands still for 6 seconds (5 seconds to 11 seconds), and finally moving away
from the exit at 2 metres per second (12 metres in 6 seconds).
B This person is 9 metres from the exit and takes 4 seconds to move 6 metres, so is
moving at 1.5 metres a second. Then walks toward the exit at 3 metres a second (3
seconds to cover 15 metres).
6. Table B best describes the graph. The line indicates the rate as being steady or
constant.
It decreases at 6 metres every 2 seconds on the table.
7. C describes Kirk’s movement best. Every second he moves 6 feet toward the Water
Slide, until he is at 0 distance from it.
155
8.
9. C because (0,9) indicates that Hugo is 9 feet from the hot-dog stand at 0 time and
(3,21) indicates that he is 21 feet away after 3 seconds.
10.
156
Appendix 15
Hot Air Balloon
The altimeter on a hot-air balloon recorded the following altitudes over a period of time.
a) State the dependent and independent variables in this problem.
b) Plot these points on the following grid.
c) Calculate the slopes of the line segments from (use a negative sign if necessary):
i) 12:00 – 15:00
ii) 15:00 – 17:00
iii) 17:00 – 20:00
d) In words, describe the flight of this hot-air balloon from 12:00 to 20:00.
e) Determine the formula that describes each of the following portions of the balloon’s
flight:
i) 12:00 – 15:00
ii) 15:00 – 17:00
iii) 17:00 – 20:00
f) Use the graph to determine the missing
information:
157
Appendix 16
T1 - 83 Ranger Activity
Use the ranger program (see Use of Ranger) to allow students to match their distance from
a wall to a given graph on the T1-83.
Example:
Press PGRM, choose Ranger, press enter and enter
Choose 2: Set Defaults
The following settings will be fine.
Real Time : Yes
Time(s):
15
Display:
Dist
Begin on:
Enter
Smoothing: None
Units:
Meters
Note:
Before a standard graph is shown, have someone do a walk in front of the CBR and have a
discussion analysing the graph. This could be done a number of times to see various types
of graphs.
To Get A Standard Graph
now cursor up to the top of the screen and over to MAIN MENU and press enter
now press 3: APPLICATIONS and 1: Meters 1: Dist Match now press enter and a graph is
displayed.
Set the CBR on a table and with the T1-83 connected to the view-screen and aim the CBR
directly at a wall. Position a student in front of the CBR, press enter and walk towards
and/or away from the CBR so it matches the graph shown.
To try again, press 2: New Match.
158
Appendix 16
Use of Ranger
A. Check to what programs are in your T1-83. PRGM, if RANGER is not displayed then
B. To enter the RANGER program
< connect the Ranger to the T1-83 using the cable provided
2) 2nd LINK press Enter
3) open the pivoting head on the Ranger (CBR) and press 82/83
calculator should display RECEIVING. When the transfer is complete, the green light
on the Ranger flashes once, the CBR beeps once and the calculator displays DONE
4) disconnect the cable
5) press 2nd quit
Transferring the Ranger Program to Other calculators
Use the short cords that came with the T1-83 to connect the calculator with the Ranger
Program to one that doesn’t have the program.
2nd LINK 3: PRGM and Ranger
then press 1: Transmit (enter)
For the second T1-83 that will be receiving the program:
2nd LINK, Receive, enter and it will say done when the program has been transferred.
Check to se if the Ranger Program is in the second calculator.
159
Appendix 17
CHANCES OF SHARK ATTACK!
The man who collects shark attack data from all over the world has messages for the
public. The odds of being attacked by a shark are 11 million to 1.
“Your chances of dying while driving from your house to the beach are a lot greater than
they are of being killed by a shark,” George Burgess, director of the International Shark
Attack File, said at a shark attack conference in Tampa.
“You’re also more likely to die of skin cancer than a shark attack,” he said.
Burgess calculated his 11 million-to-1 odds this way: In 2000, when 264 million people went
to beaches in the United states, 23 were attacked by a shark. Not one died.
Volusia County, on Florida’s east coast, has more shark attacks than any other place in the
world.
The deputy chief for the county’s beaches said 22 people were bitten by sharks in the
county last year. No one died, and most injuries were minor.
STUDENT EXERCISE
1. Without performing any calculations, do you think that the author’s odds of 11 million
to 1 were the “odds of being attacked by a shark”?
2. If 23 people out of 264 million were attacked by a shark in 2000, were the odds against
being attacked 11 million to 1?
3. Of the Volusia County shark-attack data were for 2000 also, what would have been the
probability that a US shark-attack victim in 2000, chosen at random, was attacked in
Volusia County?
4. To learn more about your risk of a shark attack, what questions might you ask?
5. Comment on the statement, “You are also more likely to die of skin cancer than a shark
attack.”
160
ANSWERS
SHARK ATTACKS!
1. Since shark attacks are relatively rare, the author probably meant the odds against
being attacked by a shark.
2. Actually the odds are somewhat higher:
264,000,000 − 23
= 11,478,259.87
23
So the odds are 11,478,259.87 to 1, or approximately 11.5 million to 1.
3. Almost certain—
22
, or about 96%.
23
4. Questions might include the following:
• What percent of US beaches could be expected to have sharks?
• What percent of the population frequents these beaches?
• How was the number 264 million obtained?
• The data for Volusia County was for 2001. What were the actual data for 2000?
5. The statement assumes that every person has an equal chance of getting skin cancer or
of being attacked by a shark. It does not consider other factors that increase an
individual’s risk, for example, spending time in the sun without protection or swimming
in shark-infested waters.
161
Appendix 18
Shove a Coin
Objective:
To determine experimentally whether a coin pushed on the chart will or will not stop on one
of the lines.
Game Setup:
Use a sheet of paper with lines 4 cm apart as the
game board. Line up the end of the game board with
the edge of the desk. Balance the coin on the desk
edge. Hit the coin with the butt of the hand. The
starting line is the end of the sheet where the coin is
balancing.
Starting the Game:
Hit the coin (start with a quarter) and record whether the coin stops between the lines or
touches a line. Repeat this procedure for at least twenty trials to establish an experimental
probability.
No score is recorded if the coin goes beyond the chart.
From the data recorded, predict the probability that the coin will stop between the lines if a
looney is used, and then if a dime is used. Experiment to find the experimental probability
using each coin.
exp erimental probability =
Coin
Quarter
Looney
Dime
162
# of times coin stops between lines
# of trials
# of trials
# of times coin
stopped between
lines
experimental
probability
Appendix 19-1
APPLICATIONS OF PROBABILITY
THEORETICAL AND EXPERIMENTAL PROBABILITY
BIRTHDAYS
In front of you, you have a bag containing numbers from 1 to 31, representing the 31
days in a month. Suppose one number is picked out of the bag. Before actually
selecting a number, find the probability that:
1) The number is 17.
2) The number is an odd number.
3) The number is a one-digit number.
Now draw a number from the container and write it down. Return the number to the
container, shake it up, and draw again. Repeat this process 20 times.
4) Find the fraction of odd numbers among the 20 numbers selected. Compare your
answer with your answer to question 2.
5) Find the fraction of one-digit numbers among the 20 numbers selected. Compare
your answer with your answer to question 3.
6) What is your birth month and birthday? For example, if your birthday is August
12, August is the month and 12 is the day of the month. What is the probability
that one number selected from the container matches your birthday?
163
APPLICATIONS OF PROBABILITY
Appendix 19-2
THEORETICAL AND EXPERIMENTAL PROBABILITY
TWO DICE DOUBLES
In this activity, you will determine the theoretical probability of rolling doubles with two
dice. Then you will conduct an experiment and compare your experimental probability with
the theoretical probability.
Use a chart such as the one below to record all possible outcomes for rolling a pair of dice.
Die 1
1
2
3
4
5
6
1
2
3
4
5
6
Circle all the combinations with doubles in your chart.
You should find a total possible number of doubles to be 6 out of a total of 36 possible
combinations. So, the theoretical probability is 1/6, or about 17%. This means, for every six
rolls, we can expect one set of doubles.
Now, conduct an experiment to determine the experimental probability.
1. Use a chart such as the one below to record your data. Roll the two dice a total of 20
times. Record “Yes” or “No” depending on whether you roll doubles or not.
Roll
Doubles
1
2
3
2. Count the total number of doubles rolled, and find the experimental probability of rolling
doubles.
3. Compare your results with the theoretical probability. Are they the same? Why? What
might happen if you roll the dice 600 times?
164
Appendix 19-3
APPLICATIONS OF PROBABILITY
THEORETICAL AND EXPERIMENTAL PROBABILITY
TOSSING TWO COINS
In front of you are two coins of different denominations.
S
Toss the two coins 50 times. Tally the results of each toss in a chart like the one
below.
Two Heads
One Head and One Tail
Two Tails
Total
S
In what fraction of the tosses did you obtain two heads? Two tails? One head and
one tail?
S
Were these results expected? Why or why not?
S
Using the results of this experiment, are the three events “two heads,” “two tails,”
and “one head and one tail” equally likely events?
S
What is your estimate of the probability of obtaining a head and a tail on the toss
of two coins?
165
Appendix 19-4
APPLICATIONS OF PROBABILITY
THEORETICAL AND EXPERIMENTAL PROBABILITY
STONE, SCISSORS, PAPER
In a fair game, each player has the same probability of winning. In an unfair game,
players do not have the same probability of winning.
Stone, Scissors, Paper is a game for two players. At the same time, each player uses
a hand to represent a stone, a pair of scissors, or a piece of paper.
For each possible pair of objects, points are scored using the following rules.
•
•
•
•
If player shows the same object, no points are scored.
Because stone breaks scissors, stone gets 1 point.
Because scissors cut paper, scissors gets 1 point.
Because paper covers stone, paper gets 1 point.
1. Play 15 rounds of Stone, Scissors, Paper. Record the points scored for each
player.
2. The table below shows two possible outcomes of the game.
3.
Player A
Player B
stone
stone
stone
paper
Copy the table. Complete it by including the other possible outcomes. How may
possible outcomes are there?
4. Use the table to find the probability that:
1. no points are scored
2. player A wins
3. player B wins
5. Is the game fair? Explain.
166
Appendix 19-5
APPLICATIONS OF PROBABILITY
THEORETICAL AND EXPERIMENTAL PROBABILITY
PENNY TOSS
In front of you are 10 pennies and a cup. One partner is to spill the pennies onto the
desktop, and the other will record the number of heads that show.
a) Using your knowledge of theoretical probability, how many heads should show when
you toss 100 pennies? Write this as a probability statement.
b) Use a table like the one below to record your data. Flip the 10 pennies and record
the number of heads you see. Repeat this activity 10 times.
Number of pennies tossed
Number of heads observed
1
2
3
4
c) Determine the number of heads when you tossed the 100 pennies. Write this as
an experimental probability statement.
d) Compare your experimental probability with the theoretical probability.
167
Appendix 19-6
APPLICATIONS OF PROBABILITY
THEORETICAL AND EXPERIMENTAL PROBABILITY
EXPERIMENT IN ESP
Do you have ESP (extrasensory perception)? Try this experiment and see.
In front of you are 40 cards of the same size with 4 different symbols.
A. Ask your partner to face away from you.
B. Mix the cards well.
C. Turn over a card and concentrate on the symbol it shows.
D. Ask your partner to read your mind and tell you what is written on the card.
E. Record the answer without telling him or her whether or not it is correct.
F. Repeat the procedure and tally the results until you have recorded a total of 20
answers.
Right Answer
Wrong Answer
Total
1. Do you think your partner has ESP? Why or why not?
2. If your partner is just guessing, what is the probability of his or her guessing
correctly on any one trial?
3. If you were to run this experiment again for 100 trials, about how many answers
do you predict would be correct?
168
APPLICATIONS OF PROBABILITY
THEORETICAL AND EXPERIMENTAL PROBABILITY
Appendix 19-7
PLAY YOUR CARDS RIGHT
In front of you is a deck of 52 playing cards. Mix them well and count out 25 cards (without
looking at them). Put aside the remaining cards. You are going to perform an experiment to
estimate the probability of drawing a club, a diamond, a heart, and a spade from your deck of
25 cards.
1. Mix the 25 cards well. Draw one card. Record its occurrence in the appropriate box below.
2. Replace the card and shuffle the deck of 25 cards.
3. Draw another card and record its suit.
4. Repeat the above steps until you have recorded a total of 25 draws.
Clubs
Diamonds
Hearts
Spades
Total
Use your data to answer the following questions.
1. What is your estimate of the probability of drawing a club from the deck of 25 cards?
2. What is your estimate of the probability of drawing a diamond from the deck of 25 cards?
3. What is your estimate of the probability of drawing a heart from the deck of 25 cards?
4. What is your estimate of the probability of drawing a spade from the deck of 25 cards?
5. Now look at your 25 cards. Count the number of cards in each suit.
6. What is the theoretical probability of obtaining a club? a diamond? a heart? a spade?
7. How do these theoretical probabilities compare with the estimated probabilities obtained
in the experiment?
8. Suppose you had recorded a total of 2,500 draws (instead of 25) in your experiment. How
would the estimated probabilities compare with the theoretical probabilities then?
169
Appendix 20
Income Tax Worksheet
Student Name_____________________
1. A student made $6000.00 last summer working at Lobster Suppers. She also collected $1100.00
in tips. What is her total income? Write the numbers of the lines where she would enter this
information.
2. Another student earned $7.00 per hour and worked 320 hours. He received $750.00 in tips. He
contributed $850.00 to his RRSP. Find his net income. Write the numbers of the lines where
he would enter this information.
170
Appendix 21
Interview With An Entrepreneur
Interview someone who has started a business, and, if possible, a member of the
entrepreneur’s family. Use the questions below to help you outline your interview.
1) Did your background influence your decision to start a business?
2) What motivated you to become an entrepreneur?
3) What risks and rewards did you consider before you began your venture?
4) Do you have the following entrepreneurial characteristics?
1)
2)
3)
4)
5)
6)
7)
8)
9)
the ability to take risks
total commitment and determination
patience
initiative
persistence
self-confidence
leadership abilities
creativity
reliability
5. Which of these characteristics are the most important?
171
6. What was the single biggest problem in starting your business?
7. In what ways did your family help you start your venture?
8. Outside of your family, who helped you the most? In what way?
9. How many hours a week do you presently work? How does this compare to the
start-up period of your business?
172