Mathematics 11
Teacher and Student Support Resource
December 2013
DRAFT
Mathematics 11
Table of Contents
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
i
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
Teaching and Learning Guidelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Websites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
11
Planning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sample Lesson: Numeracy Games. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sample Lesson: Weather and the Environment . . . . . . . . . . . . . . . . . . . .
Sample Lesson: Wheel of Fortune . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sample Lesson: Puzzles, Games, and Measurement. . . . . . . . . . . . . . . .
Sample Lesson: Which Phone Would You Buy?. . . . . . . . . . . . . . . . . . . .
Sample Lesson: Healthy Eating. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
13
15
17
18
20
22
Theme Overviews and Suggestions for Teaching and Learning . . . . . . . . . . . . .
Concept Map of Themes and Outcomes . . . . . . . . . . . . . . . . . . . . . . . . .
Outcomes: Arithmetic Operations and Proportional Reasoning . . . . . . . .
Theme: Earning and Spending Money . . . . . . . . . . . . . . . . . . . . . . . . . . .
Theme: Home . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Theme: Recreation and Wellness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Theme: Travel and Transportation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Appendices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Appendix A: Arithmetic Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Appendix B: Proportional Reasoning. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Appendix C: Earning and Spending Money . . . . . . . . . . . . . . . . . . . . . . .
Appendix D: Home. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Appendix E: Recreation and Wellness. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Appendix F: Travel and Transportation . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Mathematics 11
These materials were created by writing partnerships of school boards and the
provincial government. This document reflects the views of the developers and not
necessarily those of the Ministry of Education. Permission is given to reproduce these
materials for any purpose except profit. Teachers are also encouraged to amend,
revise, edit, cut, paste, and otherwise adapt this material for educational purposes.
Any references in this document to particular commercial resources, learning materials,
equipment, or technology reflect only the opinions of the developers of this Mathematics
11 course overview, and do not reflect any official endorsement by the Ministry of
Education or by the partnership of school boards that supported the production of the
document.
Acknowledgments
Michelle Dament
Prairie Spirit School Division
Dalmeny, Saskatchewan
Samantha Olenick
Greater Saskatoon Catholic School Division
Saskatoon, Saskatchewan
Heather Granger
Prairie South School Division
Avonlea, Saskatchewan
Wanda Pihowich
Saskatoon Public School Division
Saskatoon, Saskatchewan
Shelda Hanlan Stroh
Greater Saskatoon Catholic School Division
Saskatoon, Saskatchewan
Kelly Russell
Lloydminster Catholic School Division
Lloydminster, Saskatchewan
Mathematics 11
Introduction
Recommended Prerequisite: Mathematics 9
This course is designed for theme-based instruction, which
should enable students to broaden their understanding of
mathematics as it is applied in important areas of
day-to-day living. There is a need for learning to be
meaningful in order to be transferable. Learning
mathematics should provide students an opportunity to
explore mathematics in their lives.
Earning
and Spending
Money
My
Life
In this course, emphasis is placed on
Travel and
making informed decisions about
Transportation
finances, home design and maintenance,
recreation and personal wellness, and
travel and transportation. All mathematics
relate to the themes: Earning and Spending
Money, Home, Recreation and Wellness, and Travel and
Transportation. Students can draw on their own or others
experiences in the workforce to develop and extend their
Recreation and
knowledge about earning and spending money. They will
Wellness
also apply mathematics for the purpose of designing,
building, and maintaining a home and yard. Students will
apply reasoning and problem solving skills to make predictions
and decisions in recreational and wellness activities. As well, they will investigate and
solve problems related to planning a trip.
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Mathematics 11
Home
Teaching and Learning Guidelines
The teacher of a Mathematics 11 course should:
 Choose themes and topics from the curriculum appropriate to student background,
interests, and motivation.
 Identify the appropriate teaching/learning and assessment/evaluation strategies to
help students achieve the outcomes.
 Use resources that best suit students’ competencies and interests, and include
both print and web-based resources.
 Plan the delivery of the themes, using the support materials as a guideline, to
provide students with a variety of learning experiences that focus on active
learning, understanding, and engagement.
Students in a modified course typically benefit from instruction that:
 Provides students with a clear overview of the course, each unit of study, and
expectations.
 Provides students with activities that involve developing critical thinking and
decision-making skills.
 Helps students organize new knowledge, understand the relationships among the
new knowledge, and connect it to knowledge already learned.
 Helps students understand where they have been, where they are now, and where
they are going in the learning process (Lenz, 2000).
 Diagnoses the students’ current understanding and skill level.
 Identifies and builds on student’s prior knowledge.
 Differentiates what students will learn in order to achieve the outcomes and
teaches the prerequisite skills if they are missing.
 Differentiates the instructional approach and instructional groups (alone, pairs,
small group, total group).
 Structures individual lessons in a systematic and organized manner, and presents
course content in a structured manner.
 Integrates technology and uses a variety of resources.
 Uses current and local information to promote relevance.
 Models and uses scaffolded instructional strategies.
 Teaches students strategies that are specific to particular learning tasks.
 Provides enough guidance and practice so that students can master the
strategies.
 Teaches students self-management, self-reflection, and self-regulation strategies
to assist students in accomplishing tasks.
 Provides timely and constructive feedback to students.
 Provides assessment criteria for tasks to students.
 Bases students’ assessment and evaluation on the knowledge, skills, and
strategies that help students achieve the outcomes.
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Mathematics 11
 Uses the information obtained from assessment and evaluation to individualize
and inform upcoming instruction.
 Shares assessment and evaluation information (e.g., rubrics, checklists, etc.) with
students before those items are used, to help students track personal growth and
set learning goals.
Strategies
Teachers use multiple teaching, learning, and assessment strategies to ensure that
students have had the opportunity to learn the curriculum content and improve skills
prior to evaluation. When deciding which strategy to use, consider the following
questions:

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Can all learners use this strategy to show thinking and learning?
Will this strategy inform my instruction and provide a way to give feedback to
students?
Will patterns of understanding or confusion emerge as a result of using this
strategy?
Is this strategy convenient to design, use, and administer?
(Cris Tovani, 2011, So What Do They Really Know?, p. 74)
The following is a partial list of strategies that could be used in the Mathematics 11
course to help students achieve the outcomes.
Strategy
Description
12 word
summary
In 12 words or less, have students summarize important aspects of a particular
chunk of instruction.
3-2-1
Students jot down 3 ideas, concepts, or issues presented.
Students jot down 2 examples or uses of the idea or concept.
Students write down 1 unresolved question or a possible misunderstanding.
60 second
think
Use in your classroom at any time as no equipment is required. Ask students to
stop, and have a 60-second think about how their learning is going right then.
Accurately “time” the 60-seconds to allow quiet thinking time.
Circular
check
In groups, students are each given a different problem with a definite answer.
The first student completes the first step without contribution from others in the
group and passes it to the next student. The second student corrects any
mistakes in the first step and completes the next step without input from the
group. The problem is passed to the next student and the process continues
until the group has the correct answer.
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Mathematics 11
Class vote
Present several possible answers or solutions to a question or problem and
have students vote on what they think is best.
Concept
circle
Ask students to quickly sketch a concept circle like this image (noting that any
number of spikes can be drawn). Students then do an “individual brainstorm”,
trying to recall the key concepts that are related to the work they are doing
now. Students then highlight or draw a box around, any concepts that they are
having trouble understanding. These concepts are then recorded by the
student in their learning logs for further examination or they can be discussed
with the teacher next time there is an opportunity to do so.
Enter/exit
slips
Ask students a specific question about the lesson (or refer to Phrases and
Prompts for ideas to respond to). Students respond on the slip and give it to
the teacher, either on their way out or on their way in the next day. Teacher
can then evaluate the need to re-teach or questions that need to be answered.
Feedback
sandwich
Good news “I did really well on … ”
Bad news “I think these parts need to be changed … because …”
Good News “Some ways I can improve it are …”
Flash cards After 10 minutes into a lecture or concept presentation, have students create a
flash card that contains the key concept or idea. Toward the end of the class,
have students work in pairs to exchange ideas and review the material.
Four
corners
Page 4
Teacher posts questions, concepts, or vocabulary words in each of the corners
of the room. Each student is assigned a corner. Once in the corner, the
students discuss the focus of the lesson in relation to the question, concept, or
words. Students may report out or move to another corner and repeat.
Mathematics 11
Frayer
model
Write a term in the middle (e.g. rational number). Complete the other four
boxes in regards to the term.
Definition
Facts
Term:
Examples
Give
one/Get
one
Non-Examples
Students are given papers and asked to list 3-5 ideas about the learning.
Students draw a line after their last idea to separate his/her ideas from their
classmate’s lists. Students get up and interact with one classmate at a time.
Exchange papers, read your partner’s list, and then ask questions about new
or confusing ideas.
Graphic
organizers
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Mathematics 11
ICE tactic
Students ask themselves:
What are the:
Ideas (basics, details, facts, terminology)?,
Connections (relationships, synthesis, patterns)?
Extensions (transfer, hypotheticals, creative adaptations, going beyond
the obvious)?
This is a simple way to keep students focused on the big picture even while
they are on the run, learning, during any lesson (Young and Wilson, 2000).
Idea wave
Each student lists 3-5 ideas about the assigned topic. One volunteer begins
the “idea wave” by sharing his idea. The student to the right of the volunteer
shares one idea; the next student to rights shares one idea. Teacher directs
the idea wave until several different ideas have been shared. At the end of the
formal idea wave, a few volunteers who were not included may contribute.
Jigsaw
Students first meet in their “expert group”, where each student has the identical
assignment. The students become a team of specialists, gathering and
synthesizing information, becoming experts on their topic, and rehearsing their
presentations. Then the students change groups to their jigsaw groups. Each
student in each group educates the whole group about her or his specialty.
Learning
cell
Students develop questions and answers on their own (possibly using the QMatrix). Working in pairs, the first student asks a question and the partner
answers and vice versa. Each student can correct the other until a satisfactory
answer is reached.
Learning
logs
Use learning logs or learning journals for students to reflect on their recent
work (perhaps at the end of their work each week). Refer to Phrases and
prompts for ideas.
Muddiest
point
Students are asked to write down the muddiest point (what was unclear) in the
lesson.
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Mathematics 11
Old school
Ipads
Give students whiteboards, paper plates, index cards, or large sheets of paper
when they enter. When asking a question have ALL students write the answer
and at your signal, have ALL students hold up the Ipad so that you can see
who/ how many got the answer. Discussion to elaborate can follow.
Phrases
and
prompts
What have I learnt?
What am I most pleased with about my work?
What did I find difficult?
How can I try to improve?
What did I learn today?
What did I do well?
What am I confused about?
What do I need help with?
What do I want to know more about?
What am I going to work on next?
(Weeden et al., 2002)
The part I liked best was…
The part I found confusing was…
Two things I learnt were…
One question I have is…
I was surprised that…
I already knew that…
One thing I know that wasn’t mentioned is…
I would like to know more about…
I would like to spend more time on…
Some questions I know how to do…
One thing I want to get better at is …
One word web card…
(Davies, 2012)
This week I have learned…
For next week I am focusing on…
I will know I am getting better when…
I feel confident when …
My strength today was …
I’m proud of this because…
I feel frustrated when …
I need to find out more about …
I need help with …
My highest priority learning goal is ..
Next time I do this I will …
When I wasn’t sure, I asked [my friend’s name] about …
When I wasn’t sure, I asked [my teacher’s name] about …
One thing I am still not sure about is …
I will work on this by …
(Office of Learning and Teaching, DE&T
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Mathematics 11
http://www.sofweb.vic.edu.au/blueprint/fs1/assessment.asp).
What is the most important point you learnt today?
What point remains least clear to you?
How is ___________ similar to/different from ____________ ?
What are the characteristics/parts of ____________ ?
In what other ways might we show/illustrate ____________ ?
How does ____________ relate to ____________ ?
Give an example of ____________ .
What approach/strategy could you use to ____________ ?
Provide three examples of ____________ and one non-example.
Explain to a student in grade X (or who was absent today) what you learned
about ____________ today.
Write about the work we did today. What was easy? What was hard? What do
you still have questions about?
If you got stuck today in solving a problem, where did you get stuck? Why do
you think you had trouble there? If you did not get stuck, what idea helped you
solve the problem?
The hardest part of this chapter so far is ….
I need help with ____________, because …
To me, ____________ (e.g. geometry) means …
____________ (e.g. measuring angles) can be useful for ….
____________ (e.g. fractions) are challenging when …
Place mat
Each group member writes ideas in a space around the centre of a large piece
of paper. Afterwards, the group compares what each member has written, and
common items are compiled in the centre of the paper.
Portfolio
In the process of selection and explanation as to why students have chosen
specific pieces for their portfolios there is already a self-assessment process in
place. However, this can be taken further by more specifically asking students
to respond to the following process and questions:
1. Arrange all your work from most to least effective
2. Reflecting on your two best works, and on a separate sheet(s) of
paper for each work, answering the following questions.
What makes this your best (second best) work?
How did you go about it?
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Mathematics 11
What problems did you encounter?
How did you solve them?
What goals did you set for yourself?
How did you go about accomplishing them?
3. Answering these two questions on a single sheet(s) of paper at the
front of your portfolio.
What makes your most effective work different from your least
effective work?
What are your goals for your future work?”
(http://www.ncrel.org/sdrs/areas/issues/students/learning/lr2port.htm)
Quick write
Students write for 2-3 minutes about what they learned or heard from the
explanation. Also it could be an open ended question from teacher (refer to
Phrases and prompts for ideas).
Studentgenerated
lists
Top 10 things I need to find out …
Questions I have about my work …
Strategies I can use to improve my work …
Think, Pair,
Share
Think about your answers and write them down, Pair with a partner to discuss
and add comments to your answers, Share your answers with the class.
Thumbs up
- thumbs
down
To check for understanding, have students hold up their thumb; thumb up
means “I got it”, thumb horizontal means “I’m not sure, maybe”, and thumb
down means “I’m lost. I have questions”.
Traffic
Lights
The traffic lights can be used in a range of different ways.
To check for understanding, during individual or group work, provide students
with a set of green, yellow, and red stacking cups. All students start with the
green cup displayed, stacked over the other two cups. As students work, they
can change the cup that is displayed to indicate to the teacher that their
progress is green (good understanding and do not need assistance), yellow
(partial understanding, getting answers, but with difficulty, minor errors, or have
a basic question), or red (no understanding, stalled, need an explanation
before moving forward).
For self-assessing their own work, students label their work green, yellow or
red according to whether they have good (“I got it”), partial (“I’m not sure,
maybe”), or little (“I’m lost, I have questions”) understanding.
(Black et al, 2003).
Examine your work and highlight where you feel
• Stopped
• Cautious
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Mathematics 11
• Going straight ahead.
Use a red marker or a pink highlighter to mark in the margins where you feel
“stopped” because you don’t understand. Write a learning goal about this. Use
an orange or yellow marker or highlighter to mark in the margins where you
feel “cautious” because you are unsure or don’t understand it very well. Use a
green marker or highlighter to mark in the margin where you feel you are
“going straight ahead” because you understand it well.
For assessing a peer’s oral presentation:
Green: better than I could have done/I learnt something from this
Yellow: about the same as I could have done/no major omissions or mistakes
Red: not as good as I could have done/some serious omission or mistakes”
Students could then go on and give their peers feedback on specific strengths
and weaknesses.
(Black et al., 2003)
Transfer
and apply
Students list what they have learned and how they might apply it to their lives.
Students list interesting ideas, strategies, concepts learned in class. They
write some possible ways to apply this learning in their lives, another class, or
in their community.
Wall
posters
Regular prompt questions can be made into wall posters. Refer to Phrases
and prompts for ideas.
Which
face?
3 boxes are labelled with:
put their work into.
and students choose which box to
(Unless otherwise referenced, the above strategies are from Office of Learning and
Teaching, DE&T http://www.sofweb.vic.edu.au/blueprint/fs1/assessment.asp).
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Mathematics 11
Resources
Each theme makes reference to the use of specific websites. Teachers need to consult
their board policies regarding use of any copyrighted materials. Before reproducing
materials for student use from printed publications, teachers need to ensure that their
board has a Can copy licence and that this licence covers the resources they wish to
use. Before screening videos/films with their students, teachers need to ensure that
their board/school has obtained the appropriate public performance licence. Teachers
are reminded that much of the material on the Internet is protected by copyright. The
copyright is usually owned by the person or organization that created the work.
Reproduction of any work or substantial part of any work on the Internet is not allowed
without the permission of the owner.
Websites
The URLs for the websites were verified by the developers prior to publication. Given
the frequency with which these designations change, teachers should always verify the
websites prior to assigning them for student use.
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Centre for Innovation in Mathematics Teaching http://www.cimt.plymouth.ac.uk/
Coolmath 4 Kids http://www.coolmath4kids.com/
Figure This! Math Challenges http://www.figurethis.org/index.html
Fun Math Lessons http://math.rice.edu/~lanius/Lessons/
Index of EARAT Manuals: The Apprenticeship Network
http://www.theapprenticeshipnetwork.com/earat/manuals/
Interactive Mathematics http://www.cut-the-knot.org/content.shtml
Intermath Online Mathematics Dictionary
http://intermath.coe.uga.edu/dictnary/homepg.asp
Math Central http://mathcentral.uregina.ca/
Math in Daily Life http://www.learner.org/interactives/dailymath/
Math is Fun http://www.mathisfun.com/
Math TV http://www.mathtv.com/
Math Worksheets http://www.math-aids.com/
Mudd Math Fun Facts http://www.math.hmc.edu/funfacts/
National Library of Virtual Manipulatives http://nlvm.usu.edu/en/nav/vlibrary.html
The Math Forum @ Drexel University http://mathforum.org/
Trades Math Workbook
http://www.hrsdc.gc.ca/eng/jobs/les/tools/support/trades_math_workbook.shtml
Virtual Math http://www.virtualmaths.org
Your Financial Toolkit http://www.fcac-acfc.gc.ca/ft-of/home-accueil-eng.html
Mathematics 11
Planning
Traditionally, teachers start unit planning with interesting activities and textbooks in
mind, rather than starting with the big ideas or concepts they want the students to
master. If learning is to be effective for the students, the teacher must begin with the
final destination in mind. Teachers should be clear about what learning outcome(s) and
goal(s) will be set for the students and what assessments will be used to provide
evidence that the students have mastered the learning outcome(s) and goal(s)
(Wiggins, G. and McTighe, J. (1998). Understanding by Design).
A concern with teaching any mathematics course is the time it takes to cover the
content. Employing a conceptual approach allows the teacher to become a facilitator or
guide to coach learners in building on what they already know. This constructivist
approach allows learners to:
 build on their prior knowledge
 place less emphasis on memorization and rote learning
 see mathematical skills as useful tools and processes
 build a depth of knowledge
 develop an understanding of the connections in mathematics
 build self-confidence and a positive disposition towards mathematics.
(ABE Level Three: Mathematics Curriculum Guide, pp. 128)
When a teacher uses a conceptual approach, instruction framed around context focuses
on concepts rather than content. According to the National Council of Teachers of
Mathematics (2000):
In planning individual lessons, instructors should strive to organize the mathematics
so that fundamental ideas form an integrated whole. Big ideas encountered in a
variety of contexts should be established carefully, with important elements such as
terminology, definitions, notation, concepts, and skills emerging in the process. (p.15)
As teachers design and plan their course, lessons should reinforce basic skills, include
a variety of instructional strategies and activities, and connect to the larger
mathematical concepts. Sample lessons have been included as examples that
incorporate overlapping outcomes, indicators, and themes and use a variety of
strategies, resources, and activities.
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Mathematics 11
Sample Lesson: Numeracy Games
Outcome(s):
M11.1 Extend understanding of arithmetic operations to rational numbers to solve
problems within the home, money, recreation, and travel themes.
M11.2 Demonstrate understanding of reasoning by analyzing puzzles and games.
Suggested Theme(s):
Recreation and Wellness
Resource(s):
Math Link. MathLinks 9
(2009). pp. 54, 62, 71
Material(s):
Deck of playing cards
Two dice
Coin
Game 1: Play the following game with a partner or in a
small group. You will need one deck of playing cards.
 Remove the jokers, aces, and face cards from the
deck.
 Red cards represent positive integers. Black cards
represent negative integers.
 In each round, the dealer shuffles the cards and deals
two cards to each player.
 Use your cards to make a fraction that is as close as
possible to zero.
 In each round, the player with the fraction closest to
zero wins two points. If there is a tie, each tied player
wins a point.
 The winner is the first player with ten points. If two or
more players reach ten points in the same round, keep
playing until one player is in the lead by at least two
points.
Game 2: Play this game with a partner or in a small group.
You will need two dice and one coin.
 For each turn, roll the two dice and toss the coin.
Then, repeat.
 Create numbers of the form
. from the result of
rolling the two dice.
 Tossing heads means the rational numbers are
positive. Tossing tails means the rational numbers are
negative.
 Record the two pairs of numbers.
 Choose one number from each pair so that the sum of
the chosen numbers is as close as possible to zero.
Record the sum of the chosen numbers.
 In each round, the player with the sum closest to zero
wins two points. If there is a tie, each tied player wins
one point.
 The winner is the first player with ten points. If two or
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Mathematics 11
more players reach ten points in the same round, keep
playing until one player is in the lead by at least two
points.
Game 3: Play this game with a partner or in a small group.
You will need a deck of playing cards.
 Remove the jokers, face cards, and 10s from the deck.
 Red cards represent positive integers. Black cards
represent negative integers. Aces represent 1 and -1.
 In each round, the dealer shuffles the cards and deals
four cards to each player.
 Use your four cards to make two fractions with a
product that is as far from zero as possible.
 In each round, the player with the product that is
furthest from zero wins two points. If there is a tie,
each tied player wins a point.
 The winner is the first player with ten points. If two or
more players reach ten points in the same round, keep
playing until one player is in the lead by a least two
points.
Game 4: In a magic square, the sum of each row, column,
and diagonal is the same. Try Magic Squares
(http://illuminations.nctm.org/LessonDetail.aspx?id=L263).
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Mathematics 11
Sample Lesson: Weather and The Environment
Outcome(s):
M11.1 Extend understanding of arithmetic operations to rational numbers to solve
problems within the home, money, recreation, and travel themes.
M11.3 Demonstrate understanding of data collection and analysis within the home,
recreation, and travel themes.
M11.4 Demonstrate understanding of measurement in the Système International
(metric) and Imperial System within the home and travel themes.
Suggested Theme(s):
Home
Recreation and Wellness
Travel and Transportation
Resource(s):
Data Analysis and
Probability
http://mdk12.org/instructio
n/clg/public_release/algebr
a_data_analysis/G3_E2_I
2.html
Skill Building: The most extreme change in temperature
in Canada took place in January 1962 in Pincher Creek,
AB. A warm, dry wind, known as a Chinook, raised the
temperature from -19°C to 22°C in one hour. How many
degrees did the temperature rise in Celsius? In
Fahrenheit? (MathLinks 9, p. 345).
Introduction: Wind makes the air feel colder than the
actual temperature. This is called wind chill. The graph
below shows the wind chill temperatures for various wind
speeds when the actual air temperature is 8° Celsius. A
curve of best fit has been drawn.
MathLinks 9 (2009)
Material(s):
Page 15
Mathematics 11
Questions:
 For what wind speed is the wind-chill temperature 0°
Celsius? Use mathematics to explain how you
determined your answer. Use words, symbols, or both
in your explanation.
 Use the graph to explain how the wind-chill
temperature changes in comparison to the wind speed.
Include an estimate of when the effect of the wind
levels off.
Activity
It’s Raining, It’s Pouring
http://www.glencoe.com/sec/math/t_resources/lab_m
anual/pdfs/mac1_04/scimath_lab21.pdf
Project
Global Warming
MathLinks 9 (2009). pp. 448
Page 16
Mathematics 11
Sample Lesson: Wheel of Fortune
Outcome(s):
M11.2 Demonstrate understanding of reasoning by analyzing puzzles and games.
M11.3 Demonstrate understanding of data collection and analysis within the home,
recreation, and travel themes.
Suggested Theme(s):
Recreation and Wellness
Resource(s):
Authentic Activities for
Connecting Mathematics
to the Real World: Wheel
of Fortune
http://www.wfu.edu/~mcco
y/mprojects.pdf
Material(s):
Wheel of Fortune episode
Page 17
Watch: an episode of Wheel of Fortune
Activity: Complete an analysis of the letters used in the
show. Make a list of all the letters of the alphabet and
chart the letters used on Wheel of Fortune using tally
marks. Do not count letters guessed but not found in the
phrase. Find the total for each letter and the grand total of
all letters in the entire show. For each letter, divide the
total for that letter by the grand total to find the percent of
each letter used. Create a circle graph displaying the letter
analysis.
Questions:
 Which are the top ten letters used (in order)?
 Which are the bottom five letters least used?
 How many vowels are in the top ten?
 Which consonants would be the most useful?
 Which vowel might be the least useful?
 What percentage of all the letters surveyed were
vowels?
 If you watched three different days of Wheel of Fortune,
do you think your results will be similar? Test and see.
Mathematics 11
Sample Lesson: Puzzles, Games, and Measurement
Outcome(s):
M11.2 Demonstrate understanding of reasoning by analyzing puzzles and games.
M11.4 Demonstrate understanding of measurement in the Système International
(metric) and Imperial System within the home and travel themes.
M11.6 Demonstrate understanding of the Pythagorean Theorem to solve problems
within the home theme.
Suggested Theme(s):
Recreation and Wellness
Introduction: Millions of Canadians enjoy the challenge
and fun of playing chess. Early versions of this game
existed in India over 1400 years ago. The modern version
of chess emerged from southern Europe over 500 years
ago.
Many Canadians also enjoy the challenge and fun of
completing Sudoku puzzles. Sudoku is a Japanese logic
puzzle completed on a 9-by-9 square grid. The grid
includes nine 3-by-3 sections.
Resource(s):
Problem Solving With
Games. MathLinks 9
(2009). pp. 45, 81
Material(s):
Chessboard and pieces
Ruler
Sudoku puzzle
Watch: How to Play Chess in 10 minutes
(http://www.youtube.com/watch?v=t-uwGvx4V_A)
Game: Play the game of chess. Describe strategies of
how you win the game. Award prizes for the student(s)
that win the most games.
Activity: Math is used to play, strategize, and win chess.
However, math is also used in the design of the game
board.
 If each of the small squares on a chessboard has a
side length of 3 cm, what is the total area of the dark
squares?
 Measure the chessboard you are using. Do the small
squares have side lengths of 3 cm? If not, what are the
side lengths? What is the total area of the dark
squares?
 If the total area of a chessboard is 1024 cm2. What is
the side length of each of the smallest squares? What
is the length of the diagonal of the board?
Compare your solutions with your classmates’ solutions.
Watch: How to Do a Sudoku
(http://www.youtube.com/watch?v=z6mGHf9bq3I)
Page 18
Mathematics 11
Puzzle: Complete a Sudoku puzzle. Describe strategies
used to complete the puzzle.
Activity:
 If the smallest squares on the grid have a side length of
1.1 cm, what is the area of the whole grid?
 Measure the Sudoku puzzle you completed. Do the
small squares have side lengths of 1.1 cm? If not, what
are the side lengths? What is the area of the whole
grid?
 If the whole grid has an area of 182.25 cm2, what are
the dimensions of each 3 by 3 section?
Page 19
Mathematics 11
Sample Lesson: Which Phone Would You Buy?
Outcome(s):
M11.3 Demonstrate understanding of data collection and analysis within the home,
recreation, and travel themes.
M11.4 Demonstrate understanding of measurement in the Système International
(metric) and Imperial System within the home and travel themes.
M11.7 Demonstrate understanding of proportional reasoning within the home, money,
recreation, and travel themes.
M11.9 Demonstrate understanding of responsible spending habits.
Suggested Theme(s):
Earning and Spending Money
Home
Recreation and Wellness
Resource(s):
Material(s):
Introduction: The market for mobile phones is ever
changing and ever expanding. Tech-savvy consumers are
continuously replacing their smart phones with a newer,
faster, and better model that has the latest technologies.
How does a consumer choose which phone they should
buy?
When shopping for a mobile phone, there are many
features to consider such as size, appearance,
ergonomics, robustness, screen size, display, and price.
Activity: One feature to consider when purchasing a
mobile phone is the size. Some consumers like a larger
phone which results in larger screen for displaying images
and videos. Others prefer a smaller phone that is more
Page 20
Mathematics 11
compact for fitting into pockets and purses. What is your
preference?
Have students choose four smart phones to compare and
contrast. They can compare and contrast current models
or phones from previous years with current models. Have
students research the dimensions to calculate the
perimeter and area of the phone and research dimensions
of the screen to calculate perimeter and area of the
screen. They can organize the information in a table.
Based on size, have students rank the phones in order of
their first through fourth choices.
Discuss: Use the following questions to generate
discussion:
 What affect does changing the dimensions have on the
size of the icons?
 How many icons fit on the screen?
 What are the trends of phones in regards to size?
 Have phones increased or decreased in size?
 Has screen size changed?
 How does adding a case affect the size of the phone?
Activity: Another consideration when purchasing a mobile
phone is the initial cost of the phone. Have students
research the cost of each of the phones. They can add
two more columns to their table and add the initial cost and
the length of the plan for each of the phones previously
researched. Based on the initial cost, have students rank
the phones in order of their first through fourth choices.
Discuss: Have a class discussion about cell phone
packages and what students deem as necessary. Group
the students according to their similar needs.
Activity: Have students research the cost of cell phone
plans for the four phones from at least three providers.
Based on the research and class discussion, have
students find the total cost to purchase each of the
phones. Ask students “Which phone would you purchase
and why?” Ask students to be prepared to share and
justify their answers with the class.
Page 21
Mathematics 11
Sample Lesson: Healthy Eating
Outcome(s):
M11.3 Demonstrate understanding of data collection and analysis within the home,
recreation, and travel themes.
M11.4 Demonstrate understanding of measurement in the Système International
(metric) and Imperial System within the home and travel themes.
M11.7 Demonstrate understanding of proportional reasoning within the home, money,
recreation, and travel themes.
M11.9 Demonstrate understanding of responsible spending habits.
Suggested Theme(s):
Recreation and Wellness
Resource(s):
Real-Life Math, Tables,
Charts and Graphs, Second
edition, Tom Campbell.
Food Labels.
http://classroom.kidshealth.
org/9to12/personal/nutrition/
food_labels.pdf
Material(s):
Food labels
20-oz. soft drink
Page 22
Introduction: When you drop your money into a vending
machine or onto a fast food counter, are you thinking
about the Nutrition Facts food labels of what you are
about to buy? Food companies spend a lot of time and
money marketing to teens, so it’s important that you learn
to think critically about what you eat. A balanced diet is
one of the keys to good health, physical and mental
development, and an active lifestyle. Making healthy
food choices requires knowledge of your nutritional needs
and of the nutrients found in foods. This project is meant
to analyze what one eats, what it costs, and use
mathematical applications of percent and reading and
interpreting data to better understand one’s own health
and nutrition.
Discussion: Use the following questions to generate
discussion:
 How often do you read Nutrition Facts food labels?
What information do you look for?
 Why is serving size such a crucial piece of information
on the food label? Do you pay attention to serving
size when you’re drinking a can of soda or eating a
bag of chips?
 Unless you grow all of your own food, you probably
eat food that’s been processed. What does
“processed” mean? How can you tell if a food is fresh,
minimally processed, or highly processed? Can you
think of an example of each?
 If nutrition information were available on restaurant
menus, would it affect what people order? Would it
make a difference to you?
 While food labels are helpful to everyone, why are
they necessary for people with food allergies or
Mathematics 11
certain health problems, like diabetes or heart
disease?
Activity:
1. Bring three nutrition labels (not a full bag of chips)
from three of your favorite foods or condiments
(ketchup, sour cream, granola bars, chips, Doritos,
etc.).
2. Read Deciphering Food Labels
(http://kidshealth.org/parent/nutrition_center/healthy_e
ating/food_labels.html) and Food Labels
(http://kidshealth.org/teen/food_fitness/nutrition/food_l
abels.html)
3. Look at the labels you brought and analyze what is in
that food. The guideline of 30% of calories from fat is
used for healthy living. Calculate the percentage of
fat in the foods using the three labels.
4. Notice the recommended serving size on your food
label. Is that the amount you would typically eat or
drink at one sitting? For most people it’s not — we eat
much larger portions, and therefore more calories,
sugar, and fat. Keep track of your portion sizes for 1
day. Are they over, under, or about even with the
recommended serving sizes?
Investigate: Bring in a 20-oz. soft drink. Note the grams
of sugar per serving (for example, some colas have as
much as 65 grams). If 4 grams of sugar is equal to 1
teaspoon, measure out the amount in the bottle into a
clear cup (16¼ teaspoons). What if you drank two of
those every day (32½ teaspoons)? Or three (48¾
teaspoons)? Discuss how empty calories really add up.
Research: Research the difference in fat content when
foods are labeled no fat, low fat, and fat free? What are
the differences when we are talking about calories from
fat? Read Figuring Out Fat and Calories
(http://kidshealth.org/teen/food_fitness/nutrition/fat_calori
es.html).
Activity:
1. In the table, you will record what you eat in one day.
Be as specific as possible with brands and record
information from the food labels in the table. Use the
applications My Fitness Pal, Lose It or other apps to
assist in collecting data.
Page 23
Mathematics 11
2. Do you take vitamins or minerals? Which ones? Keep
track of the vitamins and minerals you take. Read
Vitamins and Minerals
(http://kidshealth.org/teen/food_fitness/nutrition/vitami
ns_minerals.html)
3. How would you classify your diet? Check one.
 Super health freak!
 Healthy.
 Not too bad.
 Needs work.
 Cholesterol is hardening as we speak.
4. What modifications could you make to improve your
diet and reduce the calories from fat? Be very
specific in your plan.
Activity:
1. Using grocery store flyers and fast food or restaurant
menus, create a meal plan for one week of your
favourite or typical food choices. Determine the cost
of your food for the week.
2. Read The Food Guide Pyramid Becomes a Plate
(http://kidshealth.org/teen/food_fitness/dieting/myplate
.html).
3. Using Canada’s Food Guide (http://hc-sc.gc.ca/fnan/food-guide-aliment/index-eng.php), create a
healthy meal plan for one full week for you. Include
breakfast, lunch, supper and snacks. Ensure you are
getting the right number of servings every day in each
food group.
4. Read Supermarket Shopping
(http://kidshealth.org/teen/food_fitness/nutrition/grocer
y_shopping.html).
5. Using the store flyers again, make a grocery list and
price out the healthy meal plan items for you for that
week.
6. Compare your results from steps 1. and 3. Which is
more expensive? Why?
7. Compare your results from steps 1. and 3. with a
classmate. What similarities or differences do you
notice?
8. Adapt your meal plan and grocery list for your family.
How much would you have to budget for
food/groceries every month if you were responsible
for feeding your family?
Page 24
Mathematics 11
Food
Page 25
Total
Calories
Grams of
Fat
Calories
from Fat
% of
calories
from fat
Classification
Mathematics 11
Theme Overviews and Suggestions for Teaching and Learning
This resource was created as a teaching, learning, and assessment support to give
teachers an idea of how modified Mathematics 11 could be approached. Support
materials have been developed as a guideline and do not need to be followed precisely
or in a particular order.
Concept Map of Themes and Outcomes
The following concept map frames the themes and outcomes in Math 11.
Page 26
Mathematics 11
A Theme Overview chart for each of the themes offers a recommended clustering of
expectations and provides a starting point from which teachers can plan the course.
Following each theme overview are suggested teaching and learning experiences,
which may be used as a guideline for the teacher and may include:
Resources
Materials
Introduction
Pre-Assessment
Activities
Investigate
Assessment
Extension
Skill Building
Instruction
Practice
Questions
Interactive
Project
Problem
Connections
Game
Watch
Research
Terminology
Brainstorm
Discuss
Adaptations
Conclusion
The Arithmetic Operations (M11.1) and Proportional Reasoning (M11.7) outcomes
overlap in all four themes and the intent is that these outcomes may be taught in one or
more of the themes. However, if an outcome has been covered, it is not necessary to
revisit it in all four themes.
Arithmetic Operations Outcome
Proportional Reasoning Outcome
M11.1 Extend understanding of
arithmetic operations to rational numbers
to solve problems within the home,
money, recreation, and travel themes.
At a Glance
M11.7 Demonstrate understanding of
proportional reasoning within the home,
money, recreation, and travel themes.
At a Glance
Positive and negative numbers
Operations on whole numbers
Operations on integers
Operations on fractions
Operations on decimals
Operations on percents
Compare and convert fractions, decimals
and percents
Place value
Ratios
Rates
Unit rates
Unit costs
Currency conversions
Guiding Questions
Guiding Questions



What characteristics, patterns, and
properties of numerical values and
operations did your recognize?
Can you apply the meanings and
relationships of arithmetic operations to
Page 27


Where are proportions, ratios, and rates
used?
How are ratios and rates similar and
different?
Can you apply ratios, rates, and
proportions as a way to make
Mathematics 11









compute and make reasonable
estimations?
Can you compare and order positive and
negative numbers?
How can you identify opposite numbers?
How can you identify equivalent
numbers?
What is your understanding of arithmetic
operations and can you apply your
understanding to the context?
Do you understand that multiplication
makes numbers bigger, which is not
always the case with fractions?
Can the sum of two rational numbers be
less than both of the rational numbers?
Do you understand the relationship
between fractions, decimals, and
percents?
Do you understand place value?
Which successful and efficient strategies
did you use to answer questions with
rational numbers?







comparisons?
Do you recognize percent as a ratio
comparing a value to 100?
Can you identify when two ratios are
equivalent?
How can you identify if something is
proportional?
When you are shopping, how do you
determine which item is the better deal?
Why are unit costs necessary?
How can you calculate unit rate and unit
cost?
How do you convert from one unit to
another?
Sample Applications or Problems
Sample Applications or Problems






Work in the school canteen at noon or
during a school event.
Order numbers according to value by
listing or placing numbers on a number
line.
Bring in a set of measuring cups and
look to see which is larger: ¼, ⅓, or ¾.
(ABE Level Three: Mathematics
Curriculum Guide (2006). pp. 83).
Use examples of bank accounts in
overdraft, two under par versus three
under par, or temperature to compare
values. (ABE Level Three: Mathematics
Curriculum Guide (2006). pp. 80).
The temperature at 7:00am was
reported as -5° C. If the temperature
rose 10° C by noon, what was the
Page 28



If you make $11/hour, how long will you
have to work to make a purchase worth
$400?
Show that 3:6 represents the same ratio
as 2:4 by showing that a ramp with a
height of 3 m and a base of 6 m and a
ramp with a height of 2 m and a base of 4
m are equally steep.
You take 100 mL of a liquid vitamin
supplement every morning. You can buy a
100 mL size for $6.50 or a 500 mL size for
$25.00. If the supplement keeps in the
refrigerator for only 72 h, investigate which
size is the better buy. Explain your
reasoning.
Compare the cost of one bottle of juice
from a case of 12 versus the cost of one
Mathematics 11









temperature? (ABE Level Three:
Mathematics Curriculum Guide (2006).
pp. 82).
Find the difference of the average boiling
point of 98.5°C, found in the experiment,
and the accepted boiling point of 100°C.
(ABE Level Three: Mathematics
Curriculum Guide (2006). pp. 82).
Consider the numbering of houses. Can
you follow a pattern to determine the
order of the house numbers? Can you
predict the next house number?
Add 2⅛ + 3¼. Validate results using a
12-inch ruler.
Use skill testing questions from contests
to illustrate the order of operations.
Which is the better deal, ¼ off or 30%
off?
Use wrenches to compare and convert
fractions.
Determine a 15% discount on a
purchase already discounted 50%.
Estimate the change from a $20 bill if a
purchase of $12.87 is made.
Estimate the amount it will cost for the
groceries in your shopping cart.





bottle bought from a vending machine.
Age, gender, body mass, body chemistry,
and habits such as smoking are some
factors that can influence the
effectiveness of a medication. For which
of these factors might doctors use
proportional reasoning to adjust the
dosage of medication? What are some
possible consequences of making the
adjustments incorrectly?
Bring the label from a bag of chips to
class. Use the information on the label to
calculate how many calories and how
much fat you would consume if you ate
the whole bag. Then search out
information on a form of exercise you
could choose for burning all those
calories. For what length of time would
you need to exercise?
Use currency manipulatives to explain
why someone might offer $15.02, rather
than $15.00, to pay a charge of $13.87.
Use a collection of foreign currency to
convert to Canadian currency.
What are the various costs included in the
final total for purchasing a digital audio
player online from an American source?
Using an online calculator, calculate the
final cost, and describe how it compares
with the cost of the purchase from a major
retailer in Saskatchewan.
Activities and Resources
Activities and Resources
Understanding Arithmetic Operations
Appendix A.1.
How Many Students in the Class?
Appendix B.1.
Arithmetic Operations Choice Board
Appendix A.2.
What’s the Cost of Those Bananas?
Appendix B.2.
Basic Skills Choice Board
Appendix A.3.
Proportional Reasoning Choice Board
Appendix B.3.
Cut It
Appendix A.4.
Rate and Ratio
http://staff.argyll.epsb.ca/jreed/math7/stran
d1/1208.htm
Page 29
Mathematics 11
Using Integers
http://www.helpingwithmath.com/printable Equivalent Ratios
s/worksheets/numbers/int0601negative_
http://www.skwirk.com.au/p-c_s-12_u01.htm
208_t-573_c-2129/VIC/8/Equivalentratios/Ratios/Ratios-and-rates/Maths/
Comparing and Ordering Integers
http://www.helpingwithmath.com/by_subj Unit Rate
ect/integers/int_comparing.htm
http://www.icoachmath.com/math_dictionar
y/unit_rate.html
Comparing and Ordering Integers
http://www.helpingwithmath.com/printable
s/worksheets/numbers/int0601integers_0
1.htm
Comparing and Ordering Rational Numbers
MathLinks 9 (2009). pp. 46 - 54
Problem Solving With Rational Numbers in
Decimal Form
MathLinks 9 (2009). pp. 55 - 62
What’s a Fraction?
http://www.tv411.org/math/fractionsdecimals-percentages/whats-fraction
Fraction Division via Rectangles
http://fawnnguyen.com/2013/05/21/20130
518.aspx
Problem Solving With Rational Numbers in
Fraction Form
MathLinks 9 (2009). pp. 63 - 71
What’s a Percent?
http://www.tv411.org/math/fractionsdecimals-percentages/whats-percent
Using Percents
http://www.tv411.org/math/fractionsdecimals-percentages/using-percents
Multiple Percents
http://www.tv411.org/math/fractionsdecimals-percentages/multiple-percents
Counting and Making Change
Page 30
Mathematics 11
http://www.worksheetworks.com/math/mo
ney/change.html
Canadian Money Work Sheets
http://www.homeschoolmath.net/workshe
ets/canadian-money.php
Making Change
http://www.mathscore.com/math/practice/
Making%20Change/
Combining Percents
http://www.mcgrawhill.ca/school/learning
centres/file.php/9780070973381/olc2/dl/5
05863/4_4_Combining_Percents.pdf
Multiple Percents
http://www.tv411.org/math/fractionsdecimals-percentages/multiple-percents
Real World Applications
Real World Applications





















Redeeming coupons
Spending money
Paying bills
Taking inventory
Estimating amount spent when ordering
off a menu
Reconciling bank statements
Calculating amount of change due back
Calculating total of purchasing items
Calculating gross pay
Calculating net pay
Calculating pay deductions
Altering recipes
Evaluating the appreciation of property
and depreciation of a vehicle
Reading an odometer or a gauge
Recognizing values used in wrench and
socket measurements
Calculating the days left in a month or
minutes left in an hour
Comparing time in different time zones
Comparing temperatures
Keeping scores or running tallies in
Page 31











Rates of pay (hourly, weekly, or annually)
Price comparison through the purchase of
bulk items
Measurement conversions (100cm/km)
Currency conversions
Density in science (e.g. 1.00g/L)
Understanding recommended dosages for
medication (e.g. 1 tablet every 3 hours)
Adjusting recipes
Nutrition (labelling, serving size, calories
burned during certain activities, calories
from fat, recommended daily values of
nutrients)
Fitness (e.g. the number of repetitions per
set in weight training)
Calculating total time to travel
Speed (e.g. 100 m/ 8.2 s, 500 km/ 4.5 h)
Speed limits (e.g. 100 km/h)
Gasoline prices (e.g. $1.229/L)
(ABE Level Three: Mathematics
Curriculum Guide (2006). pp. 97 – 98,
100)
Mathematics 11
games (Yahtzee, Kaiser, Whist, Rummy)
 Recognizing the values used in sports
such as bowling, hockey, football,
baseball, soccer, and golf
(ABE Level Three: Mathematics
Curriculum Guide (2006). p. 86)
Page 32
Mathematics 11
Theme Overview: Earning and Spending Money
Theme Introduction
Some students may have already entered the workforce and will have some knowledge
about earning and spending money. The intent of this theme is to have students develop
a deeper understanding of different ways people earn money and spend responsibly by
exploring gross income, net income, and spending habits.
Outcomes that overlap in all four themes
M11.1 Extend understanding of arithmetic operations to rational numbers to solve
problems within the home, money, recreation, and travel themes.
M11.7 Demonstrate understanding of proportional reasoning within the home, money,
recreation, and travel themes.
Outcomes
M11.8 Demonstrate understanding of income.
M11.9 Demonstrate understanding of responsible spending habits.
At a Glance
Number sense
Estimation
Proportional reasoning
Time
Wages
Money
Currency
Guiding Questions












Page 33
What are the different ways that employees can be paid?
How often are you paid?
What is your understanding of net pay? Gross pay?
What deductions would you expect on your earnings?
How old do you have to be for the employer to begin to make deductions?
If you work part time, do you have the same deductions as someone who works full
time?
What are union dues?
What occupations have to pay union dues?
What other factors, besides amount of pay, are important to you when choosing a
job?
How much money do you spend in a week?
What are the advantages of tracking your spending?
What are tax exemptions and when do they apply?
Mathematics 11


What factors should you consider before making a purchase?
How does the value of your purchase change over time?
Career Connections
Cashier
Bank teller
Payroll clerk
TOPIC:
Server
Salesperson
Accountant
OUTCOME:
SUGGESTED TEACHING AND LEARNING:
EARNING MONEY
Methods of
Earning Income
M11.8
Activity
Does Money Grow On Trees?
Appendix C.1.
Resources
Wages and Salaries
MathWorks 10 (2010). pp. 54 – 78
Reading
Timesheets and
Pay Stubs
M11.8
Activity
Reading Timesheets
Appendix C.2.
Activity
Reading Pay Stubs
Appendix C.3.
Resources
Wages and Salaries, Additional Earnings
MathWorks 10 (2010). pp. 56, 61, 73
Timesheet Information: False Timesheets
http://www.brockport.edu/hr/payroll/timesheets.html
How to Check a Timesheet
http://www.ehow.com/how_2093546_checktimesheet.htmling
How to Calculate Total Hours from a Timesheet
http://www.ehow.com/how_5853052_calculate-totalhours-timesheet.html
Gross and Net
Income
Page 34
M11.8
Activity
Gross and Net Income
Appendix C.4
Mathematics 11
Calculating Gross Monthly Income
Appendix C.5.
Discussion
What other factors, besides amount of pay, are important
to you when choosing a job? (wages, hours, type of work,
location, distance from work, promotion, responsibility, job
security, unemployment, experience)
Resources
Wages and Salaries
MathWorks 10 (2010). pp. 54 – 63
Alternative Ways to Earn Money
MathWorks 10 (2010). pp. 64 – 71
Additional Earnings
MathWorks 10 (2010). pp. 72 - 91
Math at Work 10 (2011). pp. 147 – 148
Canadian Income Tax Rates for Individuals
http://www.cra-arc.gc.ca/tx/ndvdls/fq/txrts-eng.html
Calculating Deductions
http://www.craarc.gc.ca/tx/bsnss/tpcs/pyrll/clcltng/menu-eng.html
Payroll Deductions Tables
http://www.cra-arc.gc.ca/tx/bsnss/tpcs/pyrll/t4032/menueng.html
TOPIC:
OUTCOME:
SUGGESTED TEACHING AND LEARNING:
RESPONSIBLE
SPENDING HABITS
Spending
M11.9
Brainstorm
Brainstorm items and services that students spend their
money on. After brainstorming, organize the items into
categories (e.g. phone, transportation, dining out, snacks,
coffee, entertainment, clothing, etc.).
Activity
Spending Log
Appendix C.6.
Activity
Needs Versus Wants
Appendix C.7
Page 35
Mathematics 11
Activity
Online Need Versus Want Activity
http://web.extension.illinois.edu/money/needsVsWants.c
fm (has ideas for Math 21 credit and loans as well).
Purchasing and
Buying
M11.9
Activity
PST and GST
Appendix C.8
Activity
What are You Buying?
Appendix C.9
Resource
Canadian tax rates
http://www.watchbuys.net/kb/questions/159/What+are+t
he+GST%7B47%7DHST%7B47%7DPST+rates+for+Ca
nada%3F
Purchasing
Power
M11.9
Project
Research and report on the estimated costs involved in a
large expense from one of the three themes:
 HOME: Plan a home renovation/improvement. Include
the cost of contractors, equipment, supplies, etc.
 RECREATION and WELLNESS: Choose a leisure
activity or sport to participate in. Include the cost of
equipment, fees, uniform, travel, fundraising, etc.

Page 36
TRAVEL and TRANSPORTATION: Plan a trip. Include
the cost of gasoline, accommodations, food,
entertainment, car rental, etc.
Mathematics 11
Theme Overview: Home
Theme Introduction
The intent of this theme is to develop a deeper understanding of the applications of data
collection and analysis, measurement, and geometry for the purpose of designing,
building, and maintaining a home and yard.
Outcomes that overlap in all four themes
M11.1 Extend understanding of arithmetic operations to rational numbers to solve
problems within the home, money, recreation, and travel themes.
M11.7 Demonstrate understanding of proportional reasoning within the home, money,
recreation, and travel themes.
Outcomes
M11.3 Demonstrate understanding of data collection and analysis within the home,
recreation, and travel themes.
M11.4 Demonstrate understanding of measurement in the Système International
(metric) and Imperial System within the home and travel themes.
M11.5 Demonstrate understanding of angles to solve problems within the home theme.
M11.6 Demonstrate understanding of the Pythagorean Theorem to solve problems
within the home theme.
At a Glance
Number sense
Estimation
Proportional reasoning
Conversions
Measurement
Referents
Dimensions
Perimeter
Area
Angles
Pythagorean theorem
Guiding Questions

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Page 37
What is the purpose of collecting and analyzing data?
Why display data?
Can the data be presented in such a way to give a different message?
Which is the best way to display the data?
Can you make predictions from data?
Can you make decisions from data?
Can you identify trends?
What is the purpose of measurement?
What is the difference between counting and measuring?
What do you measure?
Mathematics 11
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


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What devices do you use to measure?
What kinds of measurements can a ruler give you?
If you didn’t have a standard measurement tool, what could you use instead?
What is metric measurement?
What is imperial measurement?
How are metric and imperial measurements the same?
How are metric and imperial measurements different?
How are length, height, and width different?
How are length, height, and width the same?
What is perimeter?
Does every shape have a perimeter?
How can you estimate the perimeter?
How can you calculate perimeter?
What is area?
Does every shape have an area?
How can you estimate the area?
How can you calculate area?
Why are the units for area always square units or units squared?
What is an angle?
Can you demonstrate replication of an angle?
When do angles need to be precisely measured and when are estimations
adequate?
How is the Pythagorean Theorem used?
How can you calculate the length of a diagonal?
What is a 3:4:5 ratio?
Career Connections
Framer
Surveyor
Landscaper
Lumber yard employee
Counter top installer
Window installer
Finishing carpenter
Kitchen designer
Appliance salesman
Electrician
Roofer
Mudder
Farmer
Page 38
Cabinet maker
Flooring buyer
Plumber
Painter
Buyer for lumber
Designer
Estimator
Business owner
Draftsperson
Dry Waller
Flooring installer
Rancher
Mathematics 11
TOPIC:
OUTCOME:
SUGGESTED TEACHING AND LEARNING:
DATA
COLLECTION AND
ANALYSIS
Read and
Interpret
Graphs
M11.3
Pre-Assessment (replicate in Recreation and Wellness and
Travel and Transportation)
Reading and Interpreting Graphs
Appendix D.1.
Collect and
Analyze Data
M11.3
Pre-Assessment (replicate in Recreation and Wellness and
Travel and Transportation)
Collect, Organize, and Analyze Data
Appendix D.2.
Activity: Explore the cost of a home renovation by collecting
data through reading newspapers, catalogues, and online
sources and create an organized list.
Activity: Graph the average house cost in your community for
the last 20 years.
Practice:
Data Analysis
MathLinks 9 (2009). pp. 410 – 429.
TOPIC:
OUTCOME:
SUGGESTIONS FOR TEACHING AND LEARNING:
M11.4
Activity
Throughout time, cultures have invented their own systems of
measurement – using the cycles of the moon, knots in a
string, the length of a hand or a foot, the observation of the
night sky, or other clues in nature. Have students research
units of measure and creatively present the information.
MEASUREMENT
History
Resource
The Math Teacher's Book of Lists: Grades 5-12, 2nd Edition
[Paperback] Judith A. Muschla
Robert Muschla
Systems of
Measurement
Page 39
M11.4
B001IQZOA6
B001H6RTNM
(Author), Gary
(Author)
Activity
Have students devise their own system of measurement and
Mathematics 11
explain it to others. Students can use an item with no
calibrations marked, for example the length of their arm or a
piece of string. This will reinforce the need for standardized
measures.
Activity
Examine and discuss what is measured and with what tools.
For example, time is measured with a clock and temperature
is measured with a thermometer.
Activity
Based on an estimate of the length of your foot, estimate the
dimensions of your bedroom, and compare your estimate with
the measurement you get using a tape measure.
Activity
Exploring the Relationship Between Metric and Imperial
Measures for Length
Appendix D.3.
Resource
Systems of Measurement
MathWorks 10 (2010). pp. 94 - 103
Conversions
M11.4
Activity
Use a ruler to draw and label lines for the following
measurements: 10 inches, 5 inches, 3 centimeters, 15
centimeters, 1 foot, 1 inch, 3 inches, and 10 centimeters.
Activity
Measure an object in your home and convert between SI and
Imperial units. What maximum size fridge/stove will fit in your
kitchen?
Resource
Converting Measurements
MathWorks 10 (2010). pp. 106 – 113
Perimeter
M11.1
M11.4
Activity
What is Perimeter?
Appendix D.4.
Application
Perimeter Measurement and Conversions
Appendix D.5.
Page 40
Mathematics 11
Area
M11.1
M11.4
Connections
Exponents and The Product and Quotient Laws
Appendix D.6.
Activity
What is Area?
Appendix D.7.
TOPIC:
ANGLES
Angles
OUTCOME:
M11.5
SUGGESTIONS FOR TEACHING AND LEARNING:
Activity
What is an Angle?
Appendix D.8.
Activity
Using Pattern and Fraction Blocks to Understand Angles
Appendix D.9.
Resource
Measuring, Drawing, and Estimating Angles
MathWorks 10 (2010). pp. 174 – 186
Angle
Construction
and Bisection
M11.5
Instruction
Construct and Bisect Angles
Appendix D.10.
Resource
Angle Bisectors and Perpendicular Lines
MathWorks 10 (2010). pp. 187 – 195
Complementary,
Supplementary,
and Vertically
Opposite
Angles
M11.1
M11.5
Investigate
Complementary, Supplementary and Vertically Opposite
Angles
Appendix D.11.
Game
Go Fish or Memory Card Game
Appendix D.12.
Angles in
Construction
Page 41
M11.5
Project
Consider the design of a shed, dog house, ice fishing shack,
etc. Describe the cutting angles for framing a window with
Mathematics 11
casing or a room with baseboards where mitre cuts are
required.
Resources
Draw a Floor Plan
MathWorks 10 (2010). p. 105
Basic Carpentry Framing Tips
http://www.carpentry-pro-framer.com/index.html
J & H Builders Window Measure Information Form:
http://www.jhbuilders.com/common/pdf/window_measure_f
orm042910.pdf
J & H Builders Door Measure Information Form:
http://www.jhbuilders.com/common/pdf/door_measure_for
m042910.pdf
TOPIC:
OUTCOME:
SUGGESTIONS FOR TEACHING AND LEARNING:
M11.6
Activity
Right Triangles And The Pythagorean Theorem
Appendix D.13.
PYTHAGOREAN
THEOREM
The Right
Triangle And
Pythagorean
Theorem
Activity
Pythagorean Theorem Choice Board
Appendix D.14.
Application
What is a 3:4:5 ratio? Find at least 5 sets of Pythagorean
triples that are not multiples of each other. Use the 3:4:5 ratio
to determine if objects in the classroom or your house are
square.
Resource
The Pythagorean Theorem
MathWorks 10 (2010). pp. 272 – 282
Irrational
Numbers
M11.6
Activity
Square Roots and Irrational Numbers
Appendix D.15.
Resource
MathLinks 9 (2009). pp. 72 – 81
Math Makes Sense 9 (2009), pp. 4 – 21
Page 42
Mathematics 11
Theme Overview: Recreation and Wellness
Theme Introduction
Recreational activities such as playing games, solving puzzles, and participating in
sporting events as well as activities connected to personal wellness will be used to
teach problem solving strategies and reasoning skills. Students will use data collection
and analysis to make predictions and inform decisions in order to effect changes in their
own lives in terms of recreation and personal wellness.
Outcomes that overlap in all four themes
M11.1 Extend understanding of arithmetic operations to rational numbers to solve
problems within the home, money, recreation, and travel themes.
M11.7 Demonstrate understanding of proportional reasoning within the home,
recreation, and travel themes.
Outcomes
M11.2 Demonstrate understanding of reasoning by analyzing puzzles and games.
M11.3 Demonstrate understanding of data collection and analysis within the home,
money, recreation, and travel themes.
At a Glance
Number sense
Estimation
Proportional reasoning
Strategizing
Solving puzzles
Reasoning
Data collection
Data analysis
Guiding Questions
Page 43

When you think of your favorite game, what comes to mind?

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What strategies do you use to win a game?
What is an effective strategy?
Can games/puzzles be solved more than one way?
What is your favorite approach to solving a game/puzzle?
What is the purpose of collecting and analyzing data?
Why display data?
Can the data be presented in such a way to give a different message?
Which is the best way to display the data?
Can you make predictions from data?
Can you make decisions from data?
Mathematics 11

Can you identify trends?
Career Connections
Weather forecaster
Lifestyle analyst
Gamer
Nutritionist
Athlete
Data Analyst
Education policy analysis and researchers
Business owners
TOPIC:
PUZZLES AND
GAMES
OUTCOME:
Dietician
Personal trainer
Sports analyst
Statistician
Health Care Analyst
Manager
Scientific researcher
Financial Analyst
SUGGESTED TEACHING AND LEARNING:
Analyze and
Strategize
M11.2
Activity
Puzzles and Games
Appendix E.1.
Create a Game
M11.2
Task
What’s the Name of the Game?
Appendix E.2.
TOPIC:
OUTCOME:
SUGGESTED TEACHING AND LEARNING:
DATA
COLLECTION AND
ANALYSIS
Read and
Interpret
Graphs
M11.3
Pre-Assessment (replicate in Home and Travel and
Transportation)
Reading and Interpreting Graphs
Appendix D.1.
Collect and
Analyze Data
M11.3
Pre-Assessment (replicate in Home and Travel and
Transportation)
Collect, Organize, and Analyze Data
Appendix D.2.
Activity
Personal Wellness
Appendix E.3.
Page 44
Mathematics 11
Practice:
Data Analysis
MathLinks 9 (2009). pp. 410 – 429.
TOPIC:
PROPORTIONAL
REASONING
OUTCOME:
SUGGESTED TEACHING AND LEARNING:
Unit Rates and
Unit Pricing
M11.7
Skill Building
You are training for an upcoming cross-country meet. You
run13 km, three times a week. Your goal is to increase you
average speed by 1.5 km/h, so that you can complete each
run in 1 ¼ h. How long does it take you to complete each
run now, to the nearest tenth of a minute? (Answer: 1 h 27.6
min) (MathLinks 9, p. 321).
Activity
Which is Your Cookie of Choice?
Appendix E.4.
Activity (replicate in Travel and Transportation)
What Are We Going To Do For Entertainment?
Appendix E.5.
Activity
Exercise and Fitness
Appendix E.6.
Activity
Measuring Heartbeat
http://www.glencoe.com/sec/math/t_resources/lab_manu
al/pdfs/mac1_04/scimath_lab02.pdf
Target Heart Rate: Calculating the Math
http://www.kcautv.com/Global/story.asp?s=275590
The Beat Goes On Activity – Heartbeat Math Worksheet
http://www.teachengineering.org/collection/cub_/activities/
cub_human/cub_human_lesson05_activity2_mathworksh
eet.pdf
Resources
Proportional Reasoning
MathWorks 10 (2010). pp. 12 - 22
Unit Price
Page 45
Mathematics 11
MathWorks 10 (2010). pp. 23 – 27
Page 46
Mathematics 11
Theme Overview: Travel and Transportation
Theme Introduction
In the Travel and Transportation theme, students will use data collection and analysis to
inform decisions in regards to planning a trip. Students will explore the parts of travel
such as time, time zones, temperature, measurement conversions, price comparison,
and currency exchange.
Outcomes that overlap in all four themes
M11.1 Extend understanding of arithmetic operations to rational numbers to solve
problems within the home, money, recreation, and travel themes.
M11.7 Demonstrate understanding of proportional reasoning within the home, money,
recreation, and travel themes.
Outcomes
M11.3 Demonstrate understanding of data collection and analysis within the home,
recreation, and travel themes.
M11.4 Demonstrate understanding of measurement in the Système International
(metric) and Imperial System within the home and travel themes.
At Glance
Number sense
Estimation
Proportional reasoning
Data collection
Data analysis
Time
Time zones
Temperature
Measurement
Conversions
Unit pricing
Price comparisons
Currency
Guiding Questions
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Page 47
What is the purpose of collecting and analyzing data?
Why display data?
Can the data be presented in such a way to give a different message?
Which is the best way to display the data?
Can you make predictions from data?
Can you make decisions from data?
Can you identify trends?
How does the concept of time factor into travel plans?
How is time a measurement?
What words are used to refer to time?
What units are used for time?
How does the concept of temperature factor into travel plans?
Mathematics 11
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
How is temperature a measurement?
What words are used to refer to temperature?
What units are used for temperature?
How does the concept of measurement conversions factor into travel plans?
How do Canadian prices compare to foreign prices for the same item?
Career Connections
Travel agent
Bank teller
TOPIC:
Travel show host
Flight attendant
OUTCOME:
SUGGESTED TEACHING AND LEARNING:
DATA
COLLECTION AND
ANALYSIS
Read and
Interpret
Graphs
M11.3
Pre-Assessment (replicate in Home and Recreation and
Wellness)
Reading and Interpreting Graphs
Appendix D.1.
Collect and
Analyze Data
M11.3
Pre-Assessment (replicate in Home and Recreation and
Wellness)
Collect, Organize, and Analyze Data
Appendix D.2.
Activity
Survey the class on the mode of transportation they take to
school each day. Represent the data graphically.
Activity
Where Should We Stay?
Appendix F.1.
Practice:
Data Analysis
MathLinks 9 (2009). pp. 410 – 429.
Page 48
Mathematics 11
TOPIC:
MEASUREMENT
CONVERSIONS
OUTCOME:
Time
M11.4
SUGGESTED TEACHING AND LEARNING:
Activity
How Old Am I?
Appendix F.2.
Activity
Happy New Year!
Appendix F.3.
Temperature
M11.3
M11.4
Activity
What’s The Temperature?
Appendix F.4.
Linear and
Weight
Measurements
M11.4
Activity
Carry-On Safety Requirements
Appendix F.5.
M11.3
M11.4
Activity
Come Fly With Me
Appendix F.6.
TOPIC:
PROPORTIONAL
REASONING
OUTCOME:
Unit Rates and
Unit Pricing
M11.7
SUGGESTED TEACHING AND LEARNING:
Activity (replicate in Recreation and Wellness)
What Are We Going To Do For Entertainment?
Appendix E.5.
Resources
Proportional Reasoning
MathWorks 10 (2010). pp. 12 - 22
Unit Price
MathWorks 10 (2010). pp. 23 – 27
Currency
Page 49
M11.4
M11.7
Activity
Discuss items that students have recently bought. Have
students recall the exact price. Research the item in
another country, find the price and convert to Canadian
dollars. How do the prices compare? Students can use
online exchange rate charts and calculators to compare
costs of items.
Mathematics 11
Resources
Currency Exchange Rates
MathWorks 10 (2010). pp. 41 - 48
Converting Canadian and U.S. Dollars
Math Essentials 10 (2005). p. 238
Currency Converter
http://www.canadianforex.ca/currency-converter
M11.3
M11.4
M11.7
Page 50
Project
Let’s Travel!
Appendix F.7.
Mathematics 11
Appendices
Appendix A: Arithmetic Operations
Appendix A.1 Understanding Arithmetic Operations
Whole Numbers and Integers
Jillian was on page 56 of her book. She
read 15 more pages. On what page did
she end up?
How far is it from 109 to 143?
How many strategies can you use to
multiply 34 and 78?
Chris can put 8 pictures on one page of his
photo album. If he has 123 pictures, how
many pages will he need?
Why might it be easier to calculate 297 ÷ 3 mentally by thinking of 297 as 300 - 3?
Fractions
1
Jack and Jill ordered two medium pizzas,
Gemma had 4 4 of licorice twists. After her
5
one cheese and one pepperoni. Jack ate 6 brother asked her for some, Gemma broke
1
1
of 2 of one licorice twist and gave it to him.
of a pizza and Jill ate 2 of a pizza. How
How much licorice does Gemma have left?
much pizza did they eat together?
Elementary and Middle School Mathematics Teaching
Developmentally 2nd Ed. Van de Walle and Folk (p. 332)
1
First Steps in Mathematics Operation Sense (p. 38)
12
Lori bought 6 4 kilograms of potatoes. She
Why might it be easier to calculate 15 ÷
used 1 8 of a kilogram for mashed
potatoes. How much did she have left
over?
3 instead of 5 ÷ 3 using mental math?
7
4
Big Ideas from Dr. Small Creating a Comfort Zone for Teaching
Mathematics Grades 4-8 Small (p. 59)
Decimals
Mark jumps 2.38 m. If he jumps another
0.87 m, he will have jumped the same
distance as Sonya. How far did Sonya
jump?
First Steps in Mathematics Operation Sense (p. 39)
Yesterday the minimum temperature was
15.2°C in the morning. By the afternoon,
the temperature rose to a maximum of
38.8°C. How much did the temperature
rise?
First Steps in Mathematics Operation Sense (p. 39)
A painter needs to calculate the area of a
How many students will get 0.75 litres of
wall to know how much paint to order. The juice from a 21-litre container?
First Steps in Mathematics Operation Sense (p. 66)
wall is 7.1 m long and 3.5 m high. What is
the area?
First Steps in Mathematics Operation Sense (p. 55)
Page 51
Mathematics 11
Appendix A.2 Arithmetic Operations Choice Board
Complete three activities in a row (vertical, horizontal, or diagonal).
On a $10 purchase, Tom
was offered 3 successive
discounts of 20%, 10%, and
5% in any order he wished.
He selected the discounts
in the order 5%, 10% and
20%. Which of the following
order of discounts would
have been better for him?
A) 20, 10, 5
B) 20, 5, 10
C) 5, 20, 10
D) 10, 20, 5
Find a sale item and decide
whether or not it is a good
sale. Provide justification
for your response.
How does adding one to
the digits of any fraction
affect its size?
What is 30% of 40% of 50?
Precisely one of the
numbers:
234
2345
23 456
234 567
Represent your answer with 2 345 678
a picture.
23 456 789
is a prime number. Which
one must it be?
Write a justification for your
answer.
In January, fares went up
by 20%. In August, they
went down by 20%.
Sue claims that "The fares
are now back to what they
were before the January
increase."
Show a number between
0.6 and 0.7.
Is the effect always the
same?
Explain your answer using
a whole number fare of
$100.
Use a number line to
support your answers.
Write a justification for your
answer.
What if you double the
numerator of a fraction and
halve the denominator,
what happens to the value
of the fraction?
Go to the provided website
and solve the indicated
problem.
http://figurethis.org/challeng
es/c30/challenge.htm
If an item is reduced by
10% and then 10% again,
then what single percent
reduction is equivalent?
3
4
Compare 10 with 10.
3
4
Compare 10 with 11.
Experiment with some
numbers and draw a
conclusion based on your
results.
Page 52
Create your own question
that is similar to the one on
the website.
Now between 0.6 and 0.61.
How many numbers are
between 1 and 2?
Represent your answer
concretely, pictorially, or
symbolically.
Mathematics 11
Appendix A.3 Basic Skills Choice Board
Complete three activities in a row (vertical, horizontal, or diagonal).
Do stores order a
percentage of each size?
Why is my size always gone
when things go on sale?
What do you see in a photo?
 take a photo
 describe fractions
found within the
picture
What does your stride
length say about you?
Figure out the puzzle.
http://www.youtube.com/wat
ch?v=Dkvu4TE9cLg
Enlarge a photo on a
photocopier to 200%. Which
one is “more square”; the
original photo or the
enlargement? Do the
fractions, ratios, and percents
become 200% larger?
How have sizes changed
over the years?
 plate sizes and
silverware
 drink cups
 clothing sizes
Perfect 10.
http://www.yummymath.co
m/2012/perfect-10/
What proportions have gotten
smaller over the years? How
much smaller?
Which location is the
sunniest?
What does your stride length say about you?
Can the length of your leg and foot size predict the length of your stride? Take
measurements and investigate the relationship between the length of your leg and the
length of your stride.
How have sizes changed over the years?
Read Vanity sizing http://en.wikipedia.org/wiki/Vanity_sizing
Which location is the sunniest?
Explain how you know that one location will be the sunniest using fractions.
Page 53
Mathematics 11
Page 54
Mathematics 11
Appendix A.4 Cut It
Interactive: Try the Slice It application on Google or Android.
Practice:
Task: Develop your own Cut It game on paper.
Activity: Print or trace the Cut It pieces on graph paper. Count the square units of each
piece and calculate the percentage that you cut the original shape into.
Page 55
Mathematics 11
Appendix B: Proportional Reasoning
Appendix B.1 How Many Students in the Class?
Introduction: This activity can be used to get an understanding of the prior knowledge
of proportional reasoning that your students have.
Problem:
1. Suppose there are two groups in an after school program, one with 20 students
and one with 25. If the first class has 10 boys, and the second class has 12, which
class has more boys? (Possible student response: the program with 12 girls has
more).
2. If class C has 42 students, how many boys would there be if it is in proportion to
the class with 25 students?
3. If there are 5 boys in class D, how many boys would there be if it is in proportion
to the class with 20 students?
Questions:
 How did you find your answers? What strategies did you use?
 Did you compare ratios?
 What is a ratio?
 What is a proportion?
 How are ratios and proportions similar?
Appendix B.2 What`s The Cost Of Those Bananas?
Activity: Have students go to the local supermarket and select one item from the
produce department that is paid for by weight. Have them calculate the cost of the
object using the hanging pan scale present in the department. Record their data. At the
checkout counter, have the students record the weight given on the electronic balance
used by the cashier. Have students record the cost of the item. How do the two
measurements and costs compare? Have students explain the significance of the
number of digits (precision) of the scales.
This application can be done in the classroom if there is access to a pan scale and an
electronic balance. If done in the classroom, provide items for students to measure—
bunch of bananas, two or three potatoes.
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Mathematics 11
Appendix B.3 Proportional Reasoning Choice Board
Complete a row, column or diagonal line of activities.
How much smaller is Mini What’ s your favorite percent
Me in Austin Powers?
of chocolate milk?
http://robertkaplinsky.co
m/work/mini-me/
http://www.yummymath.com/
2010/chocolate-milk-andmixture-problems/
Would Usain Bolt still be the
fastest if they organized the
race according to body
proportions?
http://www.mathalicious.co
m/lesson/on-your-mark/
Write out 8
proportionality
statements you believe
are true and 2 you
believe are false.
How far apart are the freeway
exits?
How fast are you going?
http://robertkaplinsky.com/wo
rk/freeway-exits/
http://mrpiccmath.weebly.co
m/1/post/2011/08/roadlines.html
What would Barbie’s
proportions be if she was
human sized?
How much money is that?
How many Pepsi points
would it take to earn a
harrier?
http://180days201213.fawnnguyen.com/201
3/06/03/day-166---barbieproportions.aspx
Page 57
http://robertkaplinsky.com/wo
rk/drug-money/
http://mrpiccmath.weebly.co
m/1/post/2012/07/3-actspepsi-points.html
Mathematics 11
Appendix C: Earning and Spending Money
Appendix C.1 Does Money Grow on Trees?
Brainstorm: Pose the question “If you have a job, how do you get paid?” and
brainstorm with students the things they know.
Discuss: Use the following questions to generate discussion:
 Are there other ways of getting paid?
 What are the different ways that employees can be paid?
 How often are you paid?
Research: Have students search job ads in the newspaper or online to find examples of
other ways of getting paid.
Instruction:
Gross pay is the amount earned before deductions of income tax, employment
insurance, Canada pension plan, and other secondary deductions. Net pay is the
amount of money an employee earns after deductions.
The following is a list of ways employees can be paid depending on where they work.
The calculations in each of these examples will be gross pay.
1. A wage is the amount an employee earns for each regular hour of work. A
regular work week usually consists of 40 hours. According to Stats Canada, part
time work consists of less than 30 hours of work per week. Minimum wage in
Saskatchewan is _______. Any hours over 40, employers must pay overtime or
give equivalent time off to the employee. Overtime rates vary but usually are time
and a half (1.5 × wage). If you work on a statutory holiday you will be paid double
time. There are additional earning possibilities (e.g. tips) for people who receive a
wage.
Example: Alice works for minimum wage at a restaurant. She works 43 hours this
week and earns $250 in tips. Twenty-five percent of her tips must be shared with
the other employees. Calculate the wage she earns this week.
2. A salary is a fixed payment made by an employer at regular intervals, usually
monthly, bimonthly or occasionally weekly.
Example: An advertisement seeking people to teach English in Japan states the
applicant will receive $42 000/yr. Calculate the weekly gross salary and monthly
gross salary.
3. Straight commission is when an employee receives a percentage of the total
sales made, regardless of how much he/she sold.
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Mathematics 11
Example: The Falcon Real Estate agency pays a commission rate of 2%. If you
sold $425 000 worth of property in a month, what would you receive?
4. Graduated commission is a commission which offers incentive to employees to
sell more, because they receive a higher rate of commission as the volume of
sales increases.
Example: Russell is a computer retailer. He receives 4% commission on sales up
to $8000, for sales between $8000 and $15 000 the rate is 6%, for sales over $15
000 he receives 8% on the amount over the $15 000. If Dec Russ sold $33 500
worth of goods, calculate his earnings:
a) On the first $8000 – 4%
b) On the next $7000 ($8000 – $15 0000) – 6%
c) On anything over $15 000 - 8%
5. Salary or wage plus commission is a fixed amount of money plus commission on
top of your regular income.
6. Piece work is when you are paid for the amount of work you have done and not
the hours it has taken you. Examples include tree planters and servers (tips can
be considered piece work because it depends on the number of tables you have
served).
Practice:
1. Jane works at the recreation center for 8 hours Saturday and 6 hours on Sunday.
She is paid at a rate of $10.70/hr. During the week she referees 4 games of
basketball and is paid $25 per game. What is her total gross wage in a week?
2. Mark is a word processor operator. He makes $11.50 /hr. Determine his gross
earnings for a week if he worked 52 hours.
3. Mary earns a gross salary of $28 000 a year. She also gets a commission of 7%.
She sold $2673.19 in merchandise in her first two weeks of work. Determine her
gross wage for these two weeks.
4. As a travel agent, Sheila who has built a large clientele who travel frequently. Her
company pays her minimum wage plus 5% commission on total sales. February
is a great month for sales to warm vacations. She works 40 hours per week for
each week in February, and her total sales are $40 000. Determine her gross
wage.
5. Duke is a server at an upscale restaurant. He earns minimum wage and has
worked 30 hours this week. The customers have been very generous with tips
and he collected $643, however he must give 35% of this to the dishwashers.
Determine this week’s gross wage.
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Mathematics 11
6. Robin sells houses for a major real estate company in Saskatoon and works on
graduated commission. For total sales up to $300 000, she receives a
commission of 1.3% and anything over $300 000 the commission rises to 2.5%.
Last month Robin sold 3 houses at the following prices: $153 000, $165 000,
$292 000 which totals to ____________. Determine the gross wage this month
on her total sales.
7. Sam has been offered a job that pays $497.35 for a 35 hour work week. A
second company offers Sam a job earning $16.75/hour, but will only guarantee 30
hours /week. Which job would you take if you were Sam?
8. Two sales positions are available in retail stores. One pays an hourly rate of
$11.45 for 40 hours/week. The other pays a weekly salary of $405 for the same
number of hours, plus a commission of 5% of sales. If average sales for the
position are $750/week, then in which position would you earn the most?
Activity: Have students consider two careers that they are interested in and research
how they would get paid in those careers.
Have students identify advantages and disadvantages of the method of each payment.
Career: __________________
Starting wage/salary: _________
Method of Payment: ________________
Advantages
Disadvantages
Extension: Have students research the history of minimum wages in Saskatchewan.
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Mathematics 11
Appendix C.2 Reading Timesheets
Activity: Display timesheets that have been acquired from a local business, the internet
or a textbook (MathWorks 10 (2010). pp. 61, 73).
Questions:
 Do you use timesheets at your job?
 Have you ever completed a timesheet?
 What is the purpose of a timesheet?
 How many hours and minutes did each of the employees work each day?
 What are the similarities between the timesheets?
 What are the differences between the timesheets?
Appendix C.3 Reading Pay Stubs
Activity: Collect a variety of pay stubs and have students bring in their own examples
of pay stubs. Use the pay stubs as a starting point for discussion. A discussion should
lead into deductions and net pay.
Read: Reading a Pay Stub http://www.tv411.org/finance/earning-spending/reading-paystub
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Mathematics 11
Appendix C.4 Gross and Net Income
Discuss: Use the following questions to generate discussion:
 What is your understanding of gross pay?
 What is your understanding of net pay?
 What deductions would you expect on your earnings?
 How old do you have to be for the employer to begin to make deductions?
 If you work part time, do you have the same deductions as someone who works
full time?
 What are union dues?
 What occupations have to pay union dues?
Practice: Calculating Gross Monthly Income Appendix C.5
Activity: Using the two careers that your researched earlier, find the wage.
Calculate the yearly, monthly and weekly gross wages available for each job.
Instruction: (Note: Values will change annually, so blanks have been inserted for the
most current numbers. As well, information on Employment Insurance may need to be
updated with the most current practices).
Gross pay is subject to two types of deductions: Basic and Secondary
Basic Deductions include Income Tax, Canada Pension Plan and Employment
Insurance Premiums.
1. Income Tax is known as a progressive tax because the tax rate increases as
your gross wage increases. Income taxes are used to finance government
services.
Federal tax rates 20___
15% on the first $___________
22% for more than $________________ (on the next ___________)
26.0% for more than _________________ (on the next ____________)
29.0% on any remainder (over $_______________)
There are also Provincial taxes which are approximately 50% of the Federal tax.
2. Canada Pension Plan (CPP) contributions provide you and your dependents with
some financial protection throughout your life (retirement pension as early as age
60, disability benefits, or survivor benefits). Employees, employers and the self employed contribute to the CPP. You pay CPP if you are 18 years of age or older
and make more than $______________.
CPP pensionable earnings ceiling $______________.
Contributors who earn more than the $______________ ceiling on pensionable
earnings in the year 20____ are not required or allowed to contribute more to the
CPP.
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Mathematics 11
Employee and employer contribution rates for the year 20_____ are
_________%. The maximum employee and employer contribution to the plan will
be $______________.
3. Employment insurance (EI) has no age restriction. Every dollar is insurable. You
can receive regular EI benefits if you lose your job through no fault of your own
(for example, due to shortage of work, seasonal or mass lay-offs) and can't find
work, providing you meet these requirements:
 you must apply;
 you have paid into the EI account;
 you have been without work and without pay for at least seven consecutive
days;
 you have worked for the required number of insurable hours based on where
you live and the unemployment rate in your economic region at the time of
filing your claim for benefits.
In some instances, you may need more hours of insurable work to qualify. For
example :
 if you are in the work force for the first time you will need a minimum of 910
hours of insurable work in the last 52 weeks to qualify;
 if you are re-entering the work force after an absence of two years, you are a
re-entrant and will, in most instances, need a minimum of 910 hours of
insurable work in the last 52 weeks to qualify;
Employment Insurance premium rate for the year 20_____ is $_______ or
______%. As provided in legislation, employers will pay 1.4 times the employee
rate, or $_______ per $100 of employee earnings.
Maximum Insurable Earnings will remain at $____________ for 20_____.
($________/year)
Secondary Deductions vary greatly depending on your work and your contract with
your employer. Deductions may include group life insurance, union dues, disability
insurance, etc.
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Mathematics 11
Net Pay (take home pay) = Gross Pay – Deductions
Example: If you made a salary of $2800 a month, and had secondary deductions of
$70/month in union dues, determine your annual and monthly net wage.
Solution: It is easier to calculate deductions on a yearly basis.
Yearly Gross = _________________
a) Federal Income Tax
b) CPP
c) EI
Total Fed ______________________
Provincial (Total Fed x 0.5) ____________________
Total Income Tax
____________________
Yearly Gross = _________________
Yearly Net wage:
Federal Income Tax
Provincial Income Tax
CPP
EI
Secondary Deductions
__________
__________
__________
__________
__________
Total Deductions ______________
Gross - Total Deductions
_________ - _________
Monthly Net_____________
Determine the percent of total earnings deducted to the gross income:
Total deductions × 100% =
Gross Wage
Practice:
1. Shannon earns a monthly salary of $3625.00. Determine her net yearly and
monthly pay, and the percentage of deductions.
2. Terry earns an annual salary of $75 500. She pays into two secondary
deductions: union dues of $652/year and union pension of $6264/year.
Determine her net yearly and monthly pay and the percentage of deductions.
3. Curtis earns $54 300/year. He belongs to a union and pays yearly dues of
$369.72. Calculate his net yearly and monthly pay and the percentage of
deductions.
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Mathematics 11
Appendix C.5 Calculating Gross Monthly Income
If you are paid hourly
$ _________ × _________ × 52 weeks
(pay before (# of hours you
deductions) work in 1 week)
12 months = $ ____________
(gross monthly
income)
If you are paid weekly
$ _________ × 52 weeks
(pay before
deductions)
12 months = $ ____________
(gross monthly
income)
If you are paid bi-weekly
$ _________ x 26
(pay before
deductions)
12 months = $ ____________
(gross monthly
income)
If you are paid twice a month
$ _________ x 24
(pay before
deductions)
12 months = $ ____________
(gross monthly
income)
If you are paid monthly
Page 65
$ ____________
(gross monthly
income)
Mathematics 11
Appendix C.6 Spending Log
Activity: Log your spending over a two week period. Keep your receipts in an envelope
(for a later activity).
Date
Item
Purchased
Category and Cost
Category Total
Total Spent: ____________________
Questions:
 What are two of your main recurring expenses?
 Were you surprised by the total amount spent in any category? Where you
surprised by the total amount?
 Did you have any unexpected expenses? Did you have to add another
category?
 How much did you spend in a week?
 How much did you save in a week?
 Have you saved any money in case you have an opportunity to do something
unexpected? For example, go to a concert?
 What are the advantages of tracking your spending?
 Did you need to borrow money to make a purchase?
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Mathematics 11
Appendix C.7 Needs Versus Wants
Activity: Refer to the Spending Log Appendix C.6 created in the previous activity. Fill
in the following table, determining if each item purchased was a need or a want. Be
prepared to justify your choices.
Needs
Item
Total
Wants
Cost
Item
Cost
Total
Extension: Cut pictures of desired purchases from magazines or print off the Internet
and arrange them under the appropriate category. Discuss how one person’s want
could be another person’s need. A variation is to use the SMART board and display
pictures of potential purchases.
Questions:
 Are there any items in both columns?
 Was it challenging to classify each item?
 In which category did you spend more money?
 Are there items in the “Want” category that could be eliminated?
 What would you eliminate in order to save for a special event?
 Did you need to borrow money in order to make a purchase?
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Mathematics 11
Appendix C.8 PST and GST
Use the receipts you collected. Identify items that had GST and/or PST added. Make a
list below.
PST and GST on my purchases
Item
Cost
Before
Taxes
No Tax
PST
GST
Cost After
Taxes
Total
Questions:
 Which items had NO tax added?
 Which items had GST only?
 Did any items have only PST?
 What percent of the original cost of an item is the PST? The GST?
 What is the purpose of each tax?
 What are tax exemptions and when do they apply?
Activity: You have $35 to spend in a store. You know you can’t buy anything that costs
$35 because tax will be added. From the following list, identify 5 items you think you
could afford.
DVD............................. $31.20
Hoodie ........................ $32.80
Video Game ................ $27.00
Jeans .......................... $33.99
Phone Card ................. $30.00
Jacket ......................... $29.99
Headphones ................ $31.99
Shoes .......................... $31.82
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Mathematics 11
Record each item you circled. Estimate the amount of PST, GST, and total cost for
each item.
Item
Price
Estimated PST
Estimated GST
Estimated
Total Cost
Record each item you circled. Calculate the exact PST, GST and total cost for each
item.
Item
Page 69
Price
PST
GST
Total Cost
Under/Over $35
Under
Over
Under
Over
Under
Over
Under
Over
Under
Over
Mathematics 11
Appendix C.9 What are You Buying?
Brainstorm and Discuss: Pose the question “What do teenagers buy?” and brainstorm
with students what they buy. Extend the conversation to discuss where they shop
(online, in stores, malls, etc.) and determine if incentives increase their likelihood of
buying an item. Have a class discussion of past purchases that had incentives (e.g.,
SPC cards, Group on, Best Buy price zone points, Shoppers Optimum, Safeway Club
Card, BOGO, percent discounts, pre-sale gift with purchase).
Research: Search online to find out what teenagers are purchasing.
Activity: If you had $500 to spend on any items you would like, what would they be?
Find/take photos of the item(s), find the exact price and where you would purchase it
from. Why did you purchase this?
Instead of spending the $500 on yourself, spend the money on friends or family. What
would you buy, who would you buy it for, and what is the exact cost?
Activity: You are putting together a travel kit for a trip. Estimate the cost of each
individual toiletry, estimate the taxes and determine the total cost. Research on-line or
use flyers to determine the actual cost.
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Mathematics 11
Appendix D: Home
Appendix D.1 Reading and Interpreting Graphs
Activity: Search online for information that is related to the theme (home renovations,
sports or recreational activities, travel) that are displayed graphically.
Questions:
 What information can I interpret from the graph?
 Could a different message be interpreted?
 Can I identify any trends?
 Can I make any predictions from the data?
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Mathematics 11
Appendix D.2 Collect, Organize, and Analyze Data
Introduction: Research involves asking questions, collecting data, organizing the
information, and analyzing the data to draw conclusions.
Pre-Assessment: To review what students know about data collection and analysis,
give the class a survey with a question such as:
How many extracurricular activities (in and out of school) are you involved in?
List all of the activities and indicate the number of hours for each activity per week.
Collect the surveys and use to introduce the topic of collecting and analyzing data.
Discussion: Discuss that data can be numerical and non-numerical. Brainstorm ideas
of numeric and non-numeric and record.
Numeric
Age
# of siblings
Non-numeric
mode of transportation
favorite food or color
Activity: Use the data from the surveys to:
 Explain the differences between population and sample.
 Determine how the information gathered from the surveys can be organized and
displayed on the board.
 Represent graphically. Show visuals of graphs (bar graph, broken-line graph,
histogram) and discuss when best to use.
 Make conclusions about the data.
Example: The following are the marks from a previous assessment:
74 82 65 51 88
76 68 84 59 73 81
92
73
Organize Data in a Stem and Leaf Plot:
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Mathematics 11
Graphically Display Data:
Circle Graph
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Mathematics 11
Activity:
1. As a class, develop a question to determine the opinions of students at your
school about a topic of choice. For a topic, you might choose favourite foods,
sports, actors, or musicians.
2. As a class, write and edit the survey question.
3. Survey everyone in the class.
4. Organize the results. Based on the results of the class survey, predict the entire
school’s response to the question.
Questions:
 Does your prediction accurately reflect the opinions of all students in the school?
Explain.
 Is the class a population or a sample? Explain.
 What are other examples within your school that explain the terms sample and
population?
 How else might you choose people for your survey to reflect the opinions of all
students in your school?
Discuss: Use the following questions to generate discussion about data collection and
analysis:
 What is the purpose of collecting data?
 What is the purpose of analyzing data?
 Why display data?
 What are the different ways you have seen data displayed?
 Can the data be presented in such a way to give a different message?
 How do you compile and interpret data?
 Which is the best way to display the data?
 Can you make predictions from data?
 Can you make decisions from data?
 Can you identify trends?
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Mathematics 11
Appendix D.3 Exploring the Relationship Between Metric and Imperial Measures
for Length
Instructions: Measure how many centimetres make up an inch. This can be done
using a paper ruler or sewing tape measure. Create a table of values and graph the
values. Use paper and pencil or the following website for graphing: Meta Calculator
http://www.meta-calculator.com/online/
Sample of student work using http://www.meta-calculator.com/online/
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Mathematics 11
Appendix D.4 What is Perimeter?
Brainstorm: Pose the question “What do you know about perimeter?” and brainstorm
with students the things they know or recall.
Discuss: Use the following questions to generate discussion:
 What is perimeter?
 What do you need to know to measure perimeter?
 How is perimeter measured?
 Does every shape have a perimeter?
 How can you estimate the perimeter?
 How can you calculate perimeter?
Investigate: Provide students with diagrams and ask them to find the perimeter of the
shapes. Find the perimeter of different shapes in the classroom.
Appendix D.5 Perimeter Measurement and Conversions
Prior Knowledge: Review adding and subtracting like terms. For example, a movie is
2 hours and 30 minutes. How long is the movie? If you have 3 dimes and 2 nickels, then
how much money do you have? These responses lead to the idea that conversion may
be necessary before you can add or subtract lengths.
Introduction: Measurements cannot be added if they have different units of measure.
Conversion is required. Decisions need to be made about which unit is being converted.
There is choice depending on preference or context of the question.
Activity: Which room in your house requires the most, and which requires the least,
amount of baseboard? What is the difference in the two amounts?
Activity: Find the perimeter of baseboards, fencing, border around flower bed, or
retaining wall. Dimensions that are not in the same units and must first be converted
prior to adding.
 How many linear feet of fencing is required to go around your yard?
 How many linear feet of garden edging are required to build a garden?
 How many linear feet of baseboard/siding/window trim are needed to complete a
renovation at your home/living room?
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Mathematics 11
Appendix D.6 Exponents and the Product and Quotient Laws
How are these expressions the same? How are they different?
2+2+2
2×2×2
How are these expressions the same? How are they different?
feet + feet
feet × feet
How are exponents used when finding the units for perimeter and area?
Perimeter  cm + cm = cm (more centimetres directly measured and then counted)
Area cm × cm = cm2 (derived measure in units squared)
How does changing the dimensions change the perimeter and the area?
1’
3 feet
1’
1’
1’
3 feet
1’
1’
6 inches
2 feet
1’
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Mathematics 11
1’
Appendix D.7 What is Area?
Brainstorm: Pose the question “What do you know about area?” and brainstorm with
students the things they know or recall.
Discuss: Use the following questions to generate discussion:
 What is area?
 What is the difference between perimeter and area?
 What do you need to know to measure area?
 How is area measured?
 Does every shape have an area?
 How can you estimate the area?
 How can you calculate area?
 Why are the units for area always square units or units squared?
Investigate: Provide students with diagrams and ask them to find the area of the 2D
shapes. Find objects of different shapes in the classroom to find the area of.
Watch: Area of a Circle, How to Get the Formula
http://www.youtube.com/watch?v=YokKp3pwVFc
Proof Without Words: The Circle http://www.youtube.com/watch?v=whYqhpc6S6g
Activity: Develop the formulas for the area of a square, triangle, and circle.
Activity: Which room in your house requires the most, and which requires the least,
amount of carpet? What is the difference in the two amounts?
Activity: Calculate the area to paint or wall paper a wall, to tile a floor, to lay sod or
patio slabs.
Activity: You are asked to plant a garden with an area of 30 ft2. Using the seed packs
provided, decide how you will plant your crops to allow enough growing space.
Applications:
 How much paint is needed to paint the walls of the classroom?
 How many 2” × 4” boards are needed to build a fence in your backyard and stain
it?
 How much sod would be required to redo your front lawn?
Additional Questions:
 The environmental club has permission to use a rectangular plot of land in the
school yard for composting and recycling storage. If they know the dimensions of
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Mathematics 11


the plot of land, how can you they determine the area? If they know the area and
the length of the land, how can they determine the width? (MathLinks 9, p. 99)
How can we determine the area of irregular shapes by dividing it into regular
shapes?
How can we determine the area of composite figures?
Project: Draw plans for a landscape design. Include one of the following design
elements, which will be in the shape of a rectangle: swimming pool, concrete patio,
hockey rink, or beach volleyball pit. Also include a design element that is in the shape of
a triangle and one that is in the shape of a circle. (MathLinks 9, p. 271)
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Mathematics 11
Appendix D.8 What is an Angle?
Materials: protractor
Brainstorm: Pose the question “What is an angle?” and brainstorm with students the
things they know or recall.
Discuss: Use the following questions to generate discussion.
 If an angle is a measure of rotation, how many degrees is one rotation?
 How can you estimate the measure of an angle?
 How are angles measured?
 Can you measure a reflex angle?
Skill Building: Create referent angles of 30°, 45°, 60°, 90°, 180° using a clock face,
folding paper, etc. Sketch an angle of given measure (e.g. 38°) using the referents.
Activity: Use a circle to create and label acute, obtuse, right, straight and reflex angles.
Activity: Using objects in the classroom, identify and name types of angles (e.g. acute,
obtuse, right, straight and reflex).
Practice: Angle Worksheets www.math-aids.com/Geometry/Angles/
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Mathematics 11
Appendix D.9 Using Pattern and Fraction Blocks to Understand Angles
Resource: Grade 6-9 Math Workshop: Symmetry, Lines, and Angles, pp. 10 - 11
Materials: Pattern and fraction blocks, protractor
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Mathematics 11
(Understanding Fractions
http://mathcentral.uregina.ca/RR/database/RR.09.95/hanson4.html)
Activity: Have students:
1. Identify all of the different angles in the pattern block shapes as acute, right, or
obtuse.
2. Using the square as the benchmark, determine the size of the different angles
(without a protractor). For each angle, trace the pattern block, identify on the
diagram the angle being referred to and give a written explanation of how they
determined the angle.
3. Share the different ways that they have determined the size of the angle.
4. Find the reflex angle on a pattern block. What is its measure?
5. By combining two or more pattern blocks, create a new angle. Have a classmate
find the measure of the angle using benchmarks. What type of angle is this?
6. Using pattern blocks, create a straight angle. How many different ways can you
do this?
7. Use the blocks to measure other angles in the environment.
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Mathematics 11
Appendix D.10 Construct and Bisect Angles
Resource: Grade 6-9 Math Workshop: Symmetry, Lines, and Angles, pp. 17 - 18
Materials: Mira, compass, protractor, straight edge
Instruction:
Constructions
Angle Bisectors
Paper Folding
(Informal Construction)
Fold paper at the vertex, making sure that one
ray is directly matched over the other.
MIRA
(Informal Construction)
Place MIRA on the vertex, through the middle of
the angle. Reflect one ray onto the other. Draw
in the dotted line.
Compass and Straight Edge
(Formal Construction)
Note: It is easier to draw the intersecting
arcs when the radius of the compass is
greater than half of the length of the line
segment shown.
No quantitative measuring is involved in
constructions!
Place compass on vertex. Draw an arc of the
same length on each ray. Place compass on
points where arcs intersect the rays and draw a
new arc from each. Draw a line connecting
vertex and the new intersection point.
Skill Building: Practice constructing and bisecting angles of different measures using
the angle construction and bisection methods.
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Appendix D.11 Complementary, Supplementary and Vertically Opposite Angles
Resource: Grade 6-9 Math Workshop: Symmetry, Lines, and Angles, p. 11
Materials:
 Brads
 Straight angle (2) and right angle templates (made of cardstock)
 Paper strip
 Protractor
Introduction: Complementary and supplementary angles come in pairs and as the
measure of one angle of the pair increases, the other decreases. The purpose of this
activity is to have students physically manipulate angles to develop a better
understanding of complementary and supplementary angles. Students will also develop
a better understanding of vertically opposite angles.
Investigate: Have the students:
1. Using the right angle template, attach the ray template to the vertex of the angle
using a brad, and then move the ray up and down, measuring the resulting
angles with a protractor. Record the measures of angles 1 and 2 in the table
below and determine the relationship.
∠1
∠2
2. Using the straight angle template, attach the ray template to the center of the line
using a brad, and then move the ray up and down, measuring the resulting
angles with a protractor. Record the measures of angles 1 and 2 in the table
below and determine the relationship.
∠1
∠2
3. Using two straight angle templates, attach them in the center of each line using a
brad, creating an X. Measure the angles with a protractor. Record the measures
of angles 1 and 2 in the table below and determine the relationship.
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∠1
∠2
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Appendix D.12 Go Fish or Memory Card Games
Resource: Grade 6-9 Math Workshop: Symmetry, Lines, and Angles, pp.11 - 12
Materials: Cards numbered 0° to 180° plus any extras.
Instructions: Each group is provided with a set of cards that are to be shuffled. The
game can be played in a variety of ways:
1. Each player is dealt 6 cards. Taking turns, each player asks someone else if he/she
has a particular card. The card that is requested must be one that is a supplement
to a card in the player’s hand. If the card is a supplement, he/she must give it to the
requester. If not, the player requesting draws one card. If the card is a supplement
to a card in the player’s hand, he/she may lay the two cards down. If not, the player
keeps the card in his/her hand and play moves to the next player. The game is
completed when one player has laid down all of his/her cards as supplementary
angles.
2. Each player is dealt 6 cards. The goal of this version is also to collect pairs of angle
cards that are supplements, but in this version a player does not request cards from
other players. Rather he/she draws a single card at the start of each turn or takes
the last previously discarded card. The player ends his/her turn by discarding one
card. When a player has all of the angle cards in his/her hand matched as
supplements, the game is completed.
3. Spread the cards out face down. Players take turns flipping over two cards. If the
cards are supplementary angles, the player removes the two cards and draws again.
If they are not supplementary, the cards are flipped back over and the next player
starts his/her turn. The game ends after a set period of time or once there are no
remaining pairs. The player who has collected the most pairs is the winner.
Adaptations:
 Have students write the rules for their favorite version of the game.
 Play these games using complementary angles. Remove all cards which have
obtuse and straight angle measures.
 The “go fish” version may also be played where rather than asking for a particular
value (40) the person asks for the complement to 50 degrees.
 Increase the difficulty level by playing both supplementary and complementary at
the same time.
 Once students are familiar with integers, negative angles could be introduced.
 Cards including angles with decimals may also be added to the game (e.g., 37.5,
78.6).
Extension: In any of the versions of the game, students with remaining angle cards
could be asked to either construct the angle and its complement and/or supplement or
to sketch them.
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Appendix D.13 Right Triangles and Pythagorean Theorem
Materials: shoes, measuring tape
Interactive: To learn about right triangles, try this site and select right triangles:
Triangles http://www.mathsisfun.com/geometry/triangles-interactive.html
Interactive: To learn about Pythagoras` Theorem, try this site:
Pythagoras http://www.mathsisfun.com/pythagoras.html
Instruction: In a right-angled triangle, we use certain words to describe its parts.
Pythagoras, a Greek, noticed a very special relationship among the sides of a rightangled triangle.
He noticed that for any right-angled triangle:
a2 + b2
=
c2
(leg)2 + (leg)2 = (hypotenuse)2
Any letters can be used to represent the angles and sides of the right-angled triangle. If
you will see the letters A, B, C used for angles and a, b, c used for the sides:
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a is opposite angle A (A)
b is opposite  B
c is opposite C
Activity: Got a Lot of Shoes? http://www.mathsisfun.com/activity/pythagoras-theoremshoes.html
Activity: A Walk in the Desert http://www.mathsisfun.com/activity/walk-in-desert.html
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Appendix D.14 Pythagorean Theorem Choice Board
Complete a row, column or diagonal line of activities.
Draw a right triangle and
label the right angle, legs,
and hypotenuse. State the
relationship of the sides of
a triangle.
Write a song that contains
one page of lyrics that
explain or describe
Pythagoras’ Theorem or a
parody of an existing song
or an original work.
Determine a set of 8
Pythagorean triples. Prove
them with equations.
Name a career in which
one would have to use the
Pythagorean Theorem.
Give an example of when,
where, and how it would be
used.
Draw a comic strip that
demonstrates Pythagoras’
Theorem. The comic strip
must contain at least eight
panels, clearly drawn
characters, an explanation
of a mathematical
technique, concept, or
rule, and element(s) of
humor, irony, drama.
Write a descriptive essay
about Pythagoras: his life,
accomplishments, and
failures.
Design a teaching tool with
a diagram of a proof of the
Pythagorean Theorem.
Create four contextual
problems that use the
Pythagorean Theorem.
Show all the solutions.
Find another mathematical
theorem. State it, diagram
its proof, and write a
paragraph about why, how,
and where it works.
(Choice Menus.
http://curry.virginia.edu/uploads/resourceLibrary/nagc_choice_menus.pdf)
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Appendix D.15 Square Roots and Irrational Numbers
Investigate: To determine your students’ understanding of square roots, perfect
squares, non-perfect squares and irrational numbers, have students try the Investigate
(Math Makes Sense 9, pp. 6 – 7). Use perfect squares as benchmark to explain how to
estimate non-perfect squares (p. 15).
Example: To estimate√12, 12 is almost halfway between 9 and 16, yet closer to 9. A
reasonable estimate may be: √12 ≈ 3.4
Check with a calculator.
Skill Building: Ask students for some of their favorite numbers (not too large!). For
example, hockey shirt, house address, birth date, birth year, number of Facebook
friends, etc. Use these numbers to create irrational numbers. Without the use of
calculators, have students order the irrational numbers on a number line.
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Appendix E: Recreation and Wellness
Appendix E.1 Puzzles and Games
Introduction: Many people have an interest in puzzles and games. Sometimes, it is
difficult to determine how puzzles work. However, with a few simple strategies, you can
usually figure them out.
Problem: On a shelf, there are 10 books with 100 pages each. If a bookworm starts at
the first page of the first book and eats through the last page of the last book, how many
pages does the bookworm eat through (excluding covers)? (Answer: 802)
Use a strategy such at Think, Pair, Share as students work on the solution. During
Think, individual students can work through the answer to the solution. During Pair,
they can share their solution with a partner as well as discuss the strategies they used
to solve the puzzle. During Share, the pairing can share the strategies they used to
solve the puzzle. The students or the teacher can record them on the board.
Discuss: the strategies that were used to solve the puzzle. Examples of strategies that
may have been used are:
 guess and check
 look for a pattern
 make a systematic list
 draw or model
 eliminate possibilities
 solve a simpler problem
 work backwards
 develop alternative approaches
The strategies that were not used by the students can be modelled by the teacher.
Problem Solving Strategies http://pred.boun.edu.tr/ps/ps3.html
Activity: Try the Handcuffs Puzzle http://britton.disted.camosun.bc.ca/jbhandcuff.htm
Task: In groups of 3 or 4, provide students with a variety of puzzles that require the
different strategies. Have each group work on one puzzle that is different from each of
the other groups and ask that they find their solution using two different strategies.
When each group member is confident with finding the solution and with the two
strategies used, have the students form a jigsaw. One member from each group joins a
new group. In the newly formed groups, each member will present their puzzle, provide
time for the other members of the group to solve the puzzle, assisting when necessary
and then providing the solution along with strategies as well.
Activity: Provide students with puzzles that have incorrect solutions, so they can
analyze them for errors.
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Games: Create stations with different games such as Tetris, Rubik’s cube, Blokus,
chess, checkers, Backgammon, Mastermind, Tic-Tac-Toe, Connect Four or Five,
Battleship, Cathedral World, and Mancala. Provide students with YouTube videos if they
are uncertain of how to play. Ask them to play and describe strategies of how they win
each game. Award prizes for the student(s) that win the most games.
Resources:
Problem Solving Strategy Guess and Check
http://library.thinkquest.org/25459/learning/problem/psguess.html
Math Playground http://www.mathplayground.com/games.html
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Appendix E.2 What’s The Name of the Game?
Introduction: When you think of your favorite game, what comes to mind? If may be a
computer game or video game. You may also enjoy playing games that have been
around a lot longer. These may include the use of a game board and may involve
cards, dice, or specially designed playing pieces. Examples of these games include
chess, checkers, dominoes, euchre, bridge, Monopoly, and Scrabble (MathLinks 9, p.
42).
Discuss: You may want to use the following probing questions to generate discussion.
 What kind of games do you play? (e.g. computer, video, board, card)
 What are your favorite games? Why?
 What makes a great game?
Activity: You are a game designer. You are developing an online computer game for
you and your friends to play. Describe the game and explain why it is going to be a
great game.
Task: Individually or in pairs, have students create their own game. They must provide
a materials list, provide the materials, and make the game. Have students describe the
rules of the game, including how the winner is decided, provide written instructions, and
provide a demonstration to their classmates.
Extension: Pair students with a younger grade. Have your students teach the younger
ones how to play. Your students will be required to observe the younger ones playing,
noting any strategies used in a math journal. Discuss as a class.
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Appendix E.3 Personal Wellness
Task: For a two week period, record the following information each day:
 Number of hours of sleep
 Number of hours of screen time (television, phone, computer, video games, etc.)
 Number of hours of vigorous activity
 Number of hours of leisurely activity
 Number of hours of sitting (at desk during school, homework, reading, traveling,
etc.)
 Number of hours of at work
 Number of well balanced meals
 Number of unhealthy snacks, meals, etc.
Assessment: Try one or more of the following:
 How Healthy is Your Lifestyle? http://definitionofwellness.com/wellnesshandouts/How_healthy_lifestyle.pdf
 Wellness Assessment http://definitionofwellness.com/wellness-assessment.html
 Personal Wellness Quiz http://www.definitionofwellness.com/wellnessassessments/personal-wellness-quiz.pdf
 Personal Health Assessment http://www.definitionofwellness.com/wellnessassessments/personal-wellness-quiz.pdf
 Fit Together: Personal Health Assessment http://www.fittogethernc.org/HRA.aspx
Activity: As a class, determine how each of the pieces of data will be displayed (e.g.
bar graph, line graph, broken-line graph, histogram, circle graph). Create eight different
graphs for each of the points to be displayed around the classroom so that students can
add their own information to the graphs.
Discuss:
 Can you make predictions from data?
 Can you make decisions from data?
 Can you identify trends?
 In comparison to the rest of the class, are you an outlier or average?
 After viewing the data, are there some changes you want to make to your
lifestyle?
Note: Ask students to keep this data for Mathematics 21. They will be asked to
complete the same data collection task again and they may want to compare and
contrast or use the same information they have already gathered.
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Appendix E.4 Which is Your Cookie of Choice?
Materials: boxes of cookies
Instructions: Display pictures of cookie boxes without explanation. Have students
come up with some possible questions that could go along with these pictures. Students
should try and figure out which is the best buy. This will lead into how to find the best
buy and unit pricing.
Appendix E.5 What Are We Going to Do for Entertainment?
Brainstorm and Discuss: Pose the question “What are we going to do for
entertainment on our trip?” As a class, brainstorm things to do (e.g. museum,
amusement park, sporting event, concert, zoo, sightseeing, drama production).
Activity: Individually, students pick three ideas and provide a short description for each
attraction. Research the cost per person and the group cost. Which one is a better
deal?
Problems:
1. You bought five concert tickets and paid $4.50 handling fee for each ticket. The
total cost, before tax, was $210.00. What was the cost of each ticket, excluding
the handling fee? (Answer: $37.50) (MathLinks 9, p. 320).
2. A local golf course offers two plans for paying for buckets of balls at the driving
range. The standard plan is $6 per bucket and the member’s plan is a $98
monthly fee plus $1.50 per bucket. If you use 25 buckets of balls per month, what
is the price per bucket with the member’s plan? What is the total cost with the
member’s plan? What is the total cost with the standard plan? Which is the better
deal? (MathLinks 9, p. 366).
3. You are going to rent a climbing wall for a school fun night. The rental charge for
the wall is $145/h. You have $800 to spend. For how many hours can you rent
the wall and stay within your spending limit? (Answer: 5.5 h) (MathLinks 9, p.
451).
Activity: Some amusement parks offer single-ride tickets, where you pay each time you
ride, and all-day passes, where you pay once for unlimited rides. The prices for both
types of tickets need to be high enough for the amusement park to earn a profit but low
enough that people decide to come. Search for information about ticket prices at
amusement parks. If you plan on going on seven rides at the amusement park, which is
the better option? (MathLinks 9, p. 359).
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Appendix E.6 Exercise and Fitness
Resource: Kids Health: Fitness.
http://classroom.kidshealth.org/classroom/9to12/personal/fitness/fitness.pdf
Introduction: To improve personal wellness, we need to make healthy eating choices
and increase our physical activity. Teens should be getting at least 60 minutes of
physical activity each day, but computers, TVs, and video games can make this more
difficult.
Discuss: Use the following questions to generate discussion:
 What is fitness?
 What does it mean to be physically f it?
 How can people get fit?
 Why is exercise important?
 How does it benefit both the body and mind?
 Why is it sometimes difficult for people to stay fit?
 Make a list of 10 simple things people can do to maintain fitness.
Activity: Exercise has many benefits — it can make you feel good, look good, and
even ward off some diseases. It’s recommended that teens exercise at least 60 minutes
a day — but if you don’t like sports (or you just aren’t very active) this can seem like a
daunting task.
1. Outline a 5-day program, Get off the Couch
http://classroom.kidshealth.org/classroom/9to12/personal/fitness/fitness_handout
1.pdf, which includes simple and fun exercises, to help you become more fit. The
ideal exercise program combines strength training, aerobic exercise, and
stretching. Consider different types of exercise and how you can break down the
60 minutes so it isn’t overwhelming. Be sure to incorporate warming up and
cooling down, too.
2. Keep track of your exercise each day. Take note of the type of exercise (strength
training, aerobic exercise, and stretching) you are doing and how many minutes.
3. At the end of the 5-day program, determine the proportion of strength training,
aerobic exercise, and stretching you did each day. Then determine the amount of
each you did on average over the 5 days. Are these the proportions of each type
of exercise that you want to be doing? If so, restart your 5-day program. If not,
reexamine and make changes to your 5-day program.
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Appendix F: Travel and Transportation
Appendix F.1 Where Should We Stay?
Resource: Math Essentials 10 (2005). pp. 228 – 231.
Introduction: When you travel out of town, one option for accommodations is a hotel.
Often, a hotel’s prices depend on its location and features. A location close to
restaurants, shopping, theatres, and other attractions is more desirable than a location
in the suburbs. Some hotels have features such as a pool, games room, fitness club,
free wireless, kitchenettes, and complimentary breakfast.
Practice: Math Essentials 10 (2005). pp. 228 – 231.
Activity: As a class, design a questionnaire about where you would like to go on a trip.
Narrow down the choices then use the top five locations to survey the class, grade,
family members, etc. (decide on the population and the sample). Based on the results
of the survey, use the top location as the destination and collect data for a select date
on hotel options and costs.
The following table is an example of how the data could be collected:
Hotel Name
Average Room
Rate per Night
Stars
Ratings
Amenities
In groups of 4, each group member takes one of the columns (e.g. average room rate
per night) and graphically displays the information.
Use the place mat activity for students to individually, based on their own information
and graph, to decide and justify the best hotel choice and then as a group to synthesize
the information and come to a consensus on which hotel is the best choice. Conclude
with a class discussion about which hotel is the best choice.
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Appendix F.2 How Old Am I?
Introduction: Introduce the concept of time by writing the question on the board “How
Old Are You?” Engage students in a discussion about age and how it relates to time.
Practice: There are:
_________ weeks in a year
_________ months in a year
_________ hours in a day
_________ days in a year
_________ days in a week
_________ weeks in a month (Explain why this is difficult to answer accurately)
Practice: Planning Trip Dates. Warm Up. Math Essentials 10 (2011). p. 194
Activity: To review what students know about time, pose the following questions:
 When is your birthday? (e.g. February 20, 1977)
 Can you write your birthday in numerical form? (e.g. 20/02/77) (For Explanation
and Practice, refer to Math Essentials 10 (2011). pp. 195-197)
 How old are you in years?
 How old are you in months (rounded to one decimal place)?
 How old are you in days?
 How old are you in minutes?
 How old are you in seconds?
 If your birthday were February 29, 2004, how old are you?
 If your birthday were February 29, 2004, how many times would you have
celebrated your birthday on your actual birth date?
Brainstorm and Discuss: Pose the following questions to be discussed in class:
 How does the concept of time factor into travel plans?
 How is time a measurement?
 What words are used to refer to time?
 What units are used for time?
Problem: A nurse wrote that I was born at 22:05. What time was I born at?
Instruction and Practice:
Time – AM/PM vs. 24 Hour Clock http://www.mathsisfun.com/time.html
Practice:
24 Hour Clock Sort http://www.collaborativelearning.org/12and24hourclocksort.pdf
Extension: Ask your parent(s)/guardian(s) or find the card given at the hospital that has
the time you were born. Write this time as both the 12 and 24 hour times. Find your
exact age in years, days, minutes and seconds.
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Appendix F.3 Happy New Year!
Problem: Pose the problem:
Your friend claims that when she graduates, she will spend New Year’s Eve in Times
Square, New York City (show an image or a video). Another friend claims he will
celebrate New Year’s with her in Times Square, and then fly home to Saskatchewan
to ring in the New Year with you. Is this possible?
Practice:
 Time Zones. Math Essentials 10 (2011). pp. 198 – 201.
 Crossing Time Zones. Math Essentials 10 (2011). pp. 202 – 203.
Problem: When a football game starts in Toronto at 3 p.m. ET, what time will the game
start in Saskatchewan in August? In November?
Resources:
World Clock Chart http://www.timeanddate.com/worldclock/
Daylight Savings Time? http://www.timeanddate.com/time/dst/
Practice:
 Getting There by Airplane. Math Essentials 10 (2011). pp. 204. – 207.
 Arrival Times. Math Essentials 10 (2011). pp. 208 – 209.
 Travel Times (12-h Clock). Math Essentials 10 (2011). pp. 210 – 211.
 Schedules and the 24-h Clock. Math Essentials 10 (2011). pp. 212 – 214.
 Travel Times (24-h Clock). Math Essentials 10 (2011). pp. 215.
Activity: Have students use the West Jet, Air Canada, Delta or United websites to look
up flights to a destination requiring an overlay (e.g., London, England). Have the student
look at the departure/arrival times versus the actual flying time (differences due to time
changes.
Brainstorm and Discuss: Revisit the Happy New Years! problem.
 Is it possible? If so, how? If not, could changes be made to make it possible?
 Where is the first place in the world to ring in the New Year? Where is the last
place?
 Where and how many places could you ring in the new year taking into
consideration flights, airport line ups/security, travel time during flights, to and
from airport, etc. Where should you start? Where should you end?
 If you had unlimited funds (e.g. private jet, private car), how would this change
your previous answer? Could you now visit more locations? Which ones?
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Appendix F.4 What’s the Temperature?
Problem: Pose the problem:
Can it be 32° in January?
Brainstorm: What should we consider before answering this question?
 What are the units of measure: °C and °F?
 What is the location?
 What is the time of day?
 If the location is Saskatchewan, can it be 32° in January?
Activity: Using your community as the location, pick a time frame (5 or 10 years) to
collect and organize the average monthly temperatures. Display each month’s average
temperature (in both Celsius and Fahrenheit) graphically.
Resources:
 What’s the Temperature? Math Essentials 10 (2011). pp. 216 – 219.
 Temperature Conversions MathWorks 10 (2010). pp. 138 - 145
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Appendix F.5 Carry-On Safety Requirements
Materials: rulers, tape measures, weigh scale, clear plastic bags in a variety of sizes, a
variety of toiletries (toothpaste, toothbrush, shampoo, conditioner, soap, deodorant,
contact solution, medicine, etc.), a variety of items to pack in carry-on (clothing, books,
electronics, shoes), carry-on suitcases, computer bags, bags, or purses in a variety of
sizes.
Introduction: Consider how the length + width + height and weight measurement is
used in air travel.
Research: Search online for carry-on safety requirements for airport security. Take
note of toiletry limitations and requirements. Search airline requirements for carry-on
luggage requirements and restrictions.
Discuss: Discuss how an understanding of linear and weight measurement is
necessary to pack toiletries and carry-on luggage.
Practice: Convert the following measurements:
1. 18 m to ft.
2. 36 mm to inches
3. 5 feet and 8 inches to cm
4. 120 km to miles
5. 42 inches to feet
6. Inches to feet
7. 96 inches to yards
8. 5 miles to yards
If more practice with measurement and conversions is needed, refer to Home or the
following:




Linear Measurement: Metric. Math Essentials 10 (2005). pp. 57 – 71.
Linear Measurement: Imperial. Math Essentials 10 (2005). pp. 79 – 95.
How Much Should I Bring? Math Essentials 10 (2005). Pp. 232 – 235.
Systems of Measurement. MathWorks 10 (2010). pp. 94 – 103
Activity: Using the researched information and the toiletry items available, decide
which system (imperial or metric) is more consistently used and change all
measurements to that system.
Task: Using the researched information, first have students pack their toiletry bag,
meeting the safety requirements. Second, have students pick a carry-on, pack it and
check the dimensions and weight to ensure that they could travel with it.
Extension: Create a mock security line up. Have students act as security guards and
others act as travellers. Travellers present their imitation passports, boarding pass to
security and are asked to remove items such as shoes, hats, jackets, belts, items from
pockets, etc. Security guards search carry-on and check toiletries for restricted items.
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Appendix F.6 Come Fly With Me
Materials: boarding pass
Introduction: The purpose of this project is for students to plan a trip taking into
consideration location, time, and temperature.
Brainstorm and Discuss: Where are we going on our trip? The location of the trip
and accommodations were previously determined in the activity Where Should We
Stay? Appendix F.1. If this activity was not completed, then have the class brainstorm,
discuss and choose a travel location (that requires air travel).
Research: Have students determine when the best time of year to travel to their
location would be. When the best month of the year has been agreed on, find the
monthly average low and high temperatures in both Celsius and Fahrenheit.
Research and Discuss: Use the internet to search for flights in that month. Determine
which dates are the best to travel based on price and flight times, the total number of
days on the trip, the number of travel days, the number of days that accommodations
will be needed, etc. When a flight has been decided, record the departure and return
information including location, times, and travel time. Have a discussion about the
number of hours of air travel, the number of hours of lay over, and total traveling time. If
a boarding pass is available, display and have students work individually or in pairs to
gather the important information to determine the number of hours of air travel, the
number of hours of lay over, and total traveling time.
Activity: Now that flights and airline(s) have been decided, have students go home and
measure their luggage to determine if the pieces they would choose as carry-on and
checked would meet the airline requirements for size and weight.
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Appendix F.7 Let’s Travel!
Introduction: Your task is to create a travel itinerary and trip journal to a destination of
your choice. You will need to plan your entire trip, including: accommodations,
transportation, entertainment, and meals. Make sure that you take into account currency
exchange if applicable.
Task:
1. Where and when are you going? Make a tentative plan of where you will be going,
possible dates and timeline for travel.
2. Accommodations: Where will you stay when you get there? Present three
options, advantages and disadvantages, about where you might stay while on
your vacation (e.g. hotel, resort, hostel, bed and breakfast, with family/friends).
The presentation must include prices and amenity considerations. In a summary,
identify your final lodging decisions and how you arrived at those decisions.
Include information about amenities as well as meals or other perks. Make sure
you also include your research and any other information you used to arrive at
your decision.
3. Transportation: Where are you going and how are you getting there? Present
three options, advantages and disadvantages, about how you might travel to and
from your destination. The presentation must include prices and time
considerations. Tell how you will get around while on the vacation (e.g. car, bus,
taxi, walking, rental car). You need to include prices. In a summary, identify your
final travel decisions and how you arrived at those decisions. Make sure you also
include your research and any other information you used to arrive at your
decisions.
4. Entertainment: What will you do when you get there? Present 15 options for
activities for you to do while on your vacation. The presentation must include
prices, travel and time considerations. Make sure all activities are school
appropriate. In a summary, identify your final activity decisions and how you
arrived at those decisions. Include the cost of the activities. The time frame for
each event should also be in your summary. Make sure you also include your
research and any other information you used to arrive at your decision.
5. Meals: What will you eat when you get there? Present 15 options for meals while
on your vacation. The presentation must include prices and transportation
considerations. You need to eat at least two really nice meals while on vacation. A
really nice meal is eaten at a restaurant where you must sit down and be waited
on. In a summary, identify your final meal decisions and how you arrived at those
decisions. Include the estimated cost of each meal as well as a description of the
type of cuisine. Give a brief description of the each restaurant and an approximate
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location. Make sure you also include your research and any other information you
used to arrive at your decision.
6. Packing: Prior to packing, you need to research the weather. What are the
average temperatures during the time of your travel (convert to the SI
measurement system where appropriate)? How will this affect the activities you
chose? How will this affect what you pack in your luggage? How will you pack?
What size/weight of luggage are you allotted? Include the size and weight of
luggage in both SI and Imperial systems where appropriate. How much spending
money will you take? Are you going to a different country? If so, convert your
spending money from Canadian currency to the local currency. How much
money do you have?
7. Present a day by day trip journal of transportation, lodging, entertainment and
meals. Add all of your expenses for a grand total cost of your trip. Organize the
information graphically and in a written format. Be prepared to present your travel
itinerary.
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