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Mathematics 21Teacher and Student Support Resource

December 2013DRAFT

Mathematics 21

Table of Contents

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Teaching and Learning Guidelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Websites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Planning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Sample Lesson: Reaction Time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Sample Lesson: Making a Paper Airplane. . . . . . . . . . . . . . . . . . . . . . . . . 15

Theme Overviews and Suggestions for Teaching and Learning . . . . . . . . . . . . . 16Concept Map of Themes and Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . 16 Outcome: Solving and Manipulating Equations. . . . . . . . . . . . . . . . . . . . . 17Theme Overview: Earning and Spending Money . . . . . . . . . . . . . . . . . . . 19Theme Overview: Home . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Theme Overview: Recreation and Wellness . . . . . . . . . . . . . . . . . . . . . . . 34Theme Overview: Travel and Transportation . . . . . . . . . . . . . . . . . . . . . . 37

AppendicesAppendix A: Earning and Spending Money . . . . . . . . . . . . . . . . . . . . . . . 39Appendix B: Home. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80Appendix C: Recreation and Wellness. . . . . . . . . . . . . . . . . . . . . . . . . . . . 134Appendix D: Travel and Transportation . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

Mathematics 21

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 21 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 DamentPrairie Spirit School DivisionDalmeny, Saskatchewan

Wanda PihowichSaskatoon Public School DivisionSaskatoon, Saskatchewan

Heather GrangerPrairie South School DivisionAvonlea, Saskatchewan

Kelly RussellLloydminster Catholic School DivisionLloydminster, Saskatchewan

Shelda Hanlan StrohGreater Saskatoon Catholic School DivisionSaskatoon, Saskatchewan

Mathematics 21

My Life

Earning and Spending

Money

Home

Recreation and Wellness

Travel and Transportation

Introduction

Recommended Prerequisite: Mathematics 11, Foundations and Pre-calculus 10, and/or Workplace and Apprenticeship 10

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.

In this course, emphasis is placed on making informed decisions about 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 knowledge about earning and spending money. They will 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.

Page 1 Mathematics 21

Teaching and Learning Guidelines

The teacher of a Mathematics 21 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.


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:

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 21 course to help students achieve the outcomes.

Strategy Description12 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.


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

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.


Frayer model

Write a term in the middle (e.g. rational number). Complete the other four boxes in regards to the term.

Give one/Get one

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


Definition Facts

Examples Non-Examples

Term:

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 Q-Matrix). 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.


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


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 effective2. 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?


http://www.sofweb.vic.edu.au/blueprint/fs1/assessment.asp

How did you go about it?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).

Student-generated 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”.


http://www.ncrel.org/sdrs/areas/issues/students/learning/lr2port.htm

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• 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 thisYellow: about the same as I could have done/no major omissions or mistakesRed: 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: and students choose which box to


put their work into.

(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).


http://www.sofweb.vic.edu.au/blueprint/fs1/assessment.asp

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.

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


http://www.fcac-acfc.gc.ca/ft-of/home-accueil-eng.html

http://www.virtualmaths.org/

http://www.hrsdc.gc.ca/eng/jobs/les/tools/support/trades_math_workbook.shtml

http://mathforum.org/

http://nlvm.usu.edu/en/nav/vlibrary.html

http://www.math.hmc.edu/funfacts/

http://www.math-aids.com/

http://www.mathtv.com/

http://www.mathisfun.com/

http://www.learner.org/interactives/dailymath/

http://mathcentral.uregina.ca/

http://intermath.coe.uga.edu/dictnary/homepg.asp

http://www.cut-the-knot.org/content.shtml

http://www.theapprenticeshipnetwork.com/earat/manuals/

http://math.rice.edu/~lanius/Lessons/

http://www.figurethis.org/index.html

http://www.coolmath4kids.com/

http://www.cimt.plymouth.ac.uk/

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.


Sample Lesson: Reaction Time

Outcome(s):M21.1 Extend and apply understanding of the preservation of equality by solving problems that involve the manipulation and application of formulae within home, money, recreation, and travel themes.

M21.3 Extend and apply understanding of measures of central tendency to analyze data.

M21.4 Demonstrate and extend understanding of similarity and proportional reasoning related to scale factors, scale drawing, scale models, surface area, and volume.

Suggested Theme(s): Introduction: An important skill drivers must have is the ability to react to obstacles that may suddenly appear in their path. You be the driver! What types of obstacles might you encounter? How quickly do you think you could react to an obstacle in the road? You are going to calculate your reaction time.

Investigate: Work with a partner. Your partner will hold a 30-cm ruler vertically in front of

you, with the zero mark at the bottom. Position your thumb and index finger on each side of

the ruler so that the zero mark can be seen just above your thumb. Neither your thumb nor your finger should touch the ruler.

Your partner will drop the ruler without warning. Catch the ruler as quickly as you can by closing your thumb and finger.

Read the measurement above your thumb to the nearest tenth of a centimetre. This is your reaction distance.

Perform this procedure five more times, recording each distance.

Switch roles to determine your partner’s five reaction distances.

Activity: Calculate your average reaction distance. The

formula d=12g t 2 can be used to calculate reaction time,

where d is the reaction distance, in metres; g is the acceleration due to gravity, which is 9.8 m/s2; t is time, in seconds.


Resource(s):

Reaction Time. MathLinks 9 (2009). pp. 86 – 87

Material(s):30-cm ruler


Problem:1. Imagine you are driving a car in a residential area and

a ball rolls onto the road in front of you. You move your foot toward the brake. Based on the reaction time you calculated, if you are driving at 40 km/h, how far will the car travel before you step down on the brake?

2. What distance would you have travelled before stepping down on the brake if your original speed was 100 km/h?

Discuss: What other factors might influence your reaction time and your stopping distance?


Sample Lesson: Making a Paper Airplane

Outcome(s):M21.3 Extend and apply understanding of measures of central tendency to analyze data.

M21.4 Demonstrate and extend understanding of similarity and proportional reasoning related to scale factors, scale drawing, scale models, surface area, and volume.

Suggested Theme(s): Activity:1. Make a paper airplane by following the folding

instructions (http://www.10paperairplanes.com/).

2. Use the airplane to find the total surface area of the top view of the two wings. Fly the airplane 5 times. Record the average distance and direction travelled in each flight.

3. Design and create a second airplane, which has a different surface area. Record the new surface area and the average distance and direction travelled in 5 trial flights.

Discuss: Which of the airplanes you constructed is the most functional? Consider surface area when you explain your thinking.

Home


Resource(s):

Making a Paper Airplane. MathLinks 9 (2009).pp. 40 – 41

Material(s):

Ruler

Scissors

Different sized colored paper


http://www.10paperairplanes.com/

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 21 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 21.


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 Skill Building GameMaterials Instruction Watch

Introduction Practice ResearchPre-Assessment Questions Terminology

Activities Interactive BrainstormInvestigate Project Discuss

Assessment Problem AdaptationsExtension Connections Conclusion

The Solving and Manipulating Equations (M21.1) outcome overlaps in all four themes and the intent is that this outcome 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.

Solving and Manipulating Equations OutcomeM21.1 Extend and apply understanding of the preservation of equality by solving problems that involve the manipulation and application of formulae within home, money, recreation, and travel themes.

At a GlanceSolving and manipulating formulas: Surface area and volume Primary trigonometric ratios Mean, median, mode and range Leasing, renting and buying Simple and compound interest Pythagorean theorem Slope

Guiding Questions How do you maintain equality in an equation? Do you know the difference between an equations and an expression? Can you read a problem and identify the given variables? Can you isolate the unknown variable? What are you looking for, what is the unknown value, and what are you asked to

find? Do you prefer isolating the variable and then substituting known values for the

variable or substituting known values and then isolating for the unknown? What are the units required?


Sample Formulas and Problems1. A formula that estimates the stopping distance for a car on an icy road is

d=0.75 s ( c1000 )

2

. The distance, d, is measured in metres. The speed of the car, s,

is in kilometres per hour. The mass of the car, c, is in kilograms. What is the stopping distance for 1000-kg car travelling at 50 km/h? (Answer: 37.5 m) What is the mass of the car if the stopping distance is 180 m when the car is travelling at 60 km/h? (Answer: 2000-kg) (MathLinks 9, p. 119)

2. A formula that approximates the distance an object falls through air in relation to time is d = 4.9t2. The distance, d, is measured in metres, and the time, t, in seconds. A pebble breaks loose from a cliff. What distance would it fall in 2 seconds? (Answer: 19.6 m). (MathLinks 9, p. 121)

3. A formula for estimating the volume of wood in a tree is V = 0.05hc2. The volume, V, is measured in cubic metres. The height, h, and the trunk circumference, c, are in metres. What is the volume of wood in a tree with a trunk circumference of 2.3 m and a height of 32 m? (MathLinks 9, p. 123)

4. The amount of food energy required by a canoeist can be modeled by the equation

a= C100

−17, where a represents the person’s age and C represents the number of

calories. (MathLinks 9, p. 247)

5. The average speed of a vehicle, s, is represented by the formula s=dt where d is

the distance driven and t is the time. If you drove at an average speed of 85 km/h for 3.75 h, what distance did you drive? (Answer: 318.75 km). If you drove 152 km at an average speed of 95 km/h, how much time did your trip take? (Answer: 1.6 h) (MathLinks 9, p. 302)

6. For a fit and healthy person, the maximum safe heart rate during exercise is

approximately related to their age by the formula r=45

(220−a ) . In this formula, r is

the maximum safe heart rate in beats per minute, and a is the age in years. At what age is the maximum safe heart rate 164 beats/min? (Answer: 15 years old) (MathLinks 9, p. 321)


Theme Overview: Earning and Spending Money

Theme IntroductionSome students may have already entered the workforce and will have some knowledge about earning and spending money. The intent of this theme is to develop an awareness of financial decision making. Students will explore budgeting, financial institution services, and leasing, renting, and buying on credit.

Outcome that overlaps in all four themesM21.1 Extend and apply understanding of the preservation of equality by solving problems that involve the manipulation and application of formulae within home, money, recreation, and travel themes.

OutcomesM21.8 Demonstrate understanding of budgets.

M21.9 Demonstrate understanding of financial institution services.

M21.10 Demonstrate understanding of financial decision making including analysis of renting, leasing, and buying on credit.

At a GlanceBudgetingFixed and variable expensesFinancial institution servicesBank accountsBank feesInvestments

Simple interestCompound interestBuying on creditRentingLeasing

Guiding Questions What is a budget? What are fixed and variable expenses? What are home, recreation, wellness, travel, and transportation expenses? What types of accounts are you familiar with at a financial institution? Do you have a banking account? What are some ways to save money? How can you save for a large expense? How old do you want to be when you retire? What is the difference between a chequing and savings account? What is a bank statement? What are some ways to borrow money? Can you be charged interest on interest?


Should I buy, lease or rent a vehicle?

Career ConnectionsRealtorMortgage brokerCar sales person

Rental Property ownerBankerFinancial advisor

TOPIC:BUDGETS

OUTCOME: SUGGESTED TEACHING AND LEARNING:

Exploring Terminology

M21.8 TerminologyBudgeting Key Terms

Appendix A.1.

ResourcePersonal Budgets

MathWorks 11 (2011). pp. 300 – 343

Introduction to Budgeting

M21.8 ActivityBudgeting Worksheet for Kids (Click on Excel link partway down the page)

http://www.myliferoi.com/2009/10/budgeting-worksheet-for-kids/

Fixed and Variable Expenses

M21.8 ActivityDocument Your Spending

http://www.financialliteracymonth.com/30steps/step21.aspx

Create a Personal Budget with Fixed and Variable Expenses

Appendix A.2.

Budgets M21.8 ProjectBudgeting to Live Away From Home

MathWorks 11 (2011). pp. 301, 325, 339

Budgeting to Live Away From Home Additional QuestionsAppendix A.3.

Alternate Project TopicsInvestigate, plan, design, and prepare a budget based on the estimated cost from one of the other themes:

HOME: plan a home renovation/improvement.






Include the cost of contractors, equipment, supplies . . . OR landscaping a property.Sample problem: Plan, design, and prepare a budget for the renovation of your bedroom for under $1500. The renovations could include repainting the walls, replacing the flooring, changing the fixtures, and refurnishing the room.

RECREATION and WELLNESS: choose a leisure activity or sport. Include the cost of equipment, fees, travel, . . . OR choose a meal plan. Include the cost of groceries, eating at restaurants, …

TRAVEL: plan a trip. Include the cost of gasoline, accommodation, food, entertainment, car rental…OR TRANSPORTATION: purchase and operate a vehicle

TOPIC: UNDERSTANDING

FINANCIAL INSTITUTIONS

SERVICES



M21.9 TerminologyFinancial Institutions Services Key Terms

Appendix A. 4.

ResourceFinancial Services

MathWorks 11 (2011). pp. 252 – 275

Banking Services and Fees

M21.9 ActivityResearching Types of Banking Services and Fees

Appendix A.5.

Career ConnectionHave students research the various banking officer positions, including the banking service each provides.

ActivityAdvantages and Disadvantages of Banking Services

Appendix A.6.

Writing Cheques M21.9 Instruction and Practice


Writing ChequesAppendix A.7.

ResourcesWriting Cheques and Record Keeping

Mathematics 11 Workplace and Everyday Life (2007) pp. 111 – 119

How to Write a Check – Check Writing 101http://uninvitedwriter.hubpages.com/hub/How-to-write-a-check

Banking Security

M21.9 ActivityProtecting Your Personal And Financial Information

MathWorks 11 (2011). pp. 262

ResourceBMO How We Protect You

http://www.bmo.com/home/about/banking/privacy-security/how-we-protect-you

Investments M21.9 LessonInvestment Options

Appendix A.8.

GameFree Stock Market Simulation Exchange Game

http://www.smartstocks.com/

ResourceModule 9 – Investing

http://www.themoneybelt.gc.ca/theCity-laZone/eng/ta/docs/html/Module_9.html

Simple and Compound Interest

M21.9 PracticeComparison of Simple and Compound Interest

Appendix A.9.

Simple Interest Worksheethttp://public.clinton.k12.mi.us/CCS/CHS/brown/Senior%20Math/Consumer%20Math/4-4_Simple_Interest.pdf

Simple and Compound Interesthttp://www.kutasoftware.com/FreeWorksheets/PreAlgWorksheets/Simple%20and%20Compound%20Interest.pdf


http://www.kutasoftware.com/FreeWorksheets/PreAlgWorksheets/Simple%20and%20Compound%20Interest.pdf



http://public.clinton.k12.mi.us/CCS/CHS/brown/Senior%20Math/Consumer%20Math/4-4_Simple_Interest.pdf

http://public.clinton.k12.mi.us/CCS/CHS/brown/Senior%20Math/Consumer%20Math/4-4_Simple_Interest.pdf



http://www.smartstocks.com/



http://uninvitedwriter.hubpages.com/hub/How-to-write-a-check

http://uninvitedwriter.hubpages.com/hub/How-to-write-a-check

Simple and Compound Interest and The Rule of 72http://www.teensguidetomoney.com/saving/simple--compound-interest--the-rule-of-72/compound-interest/

ResourceSimple and Compound Interest

MathWorks 11 (2011). pp. 264 – 275

TOPIC:FINANCIAL

DECISION MAKING



M21.10 TerminologyFinancial Decision Making Key Terms

Appendix A.10.

ResourceFinancial Services

MathWorks 11 (2011). pp. 276 – 299

Credit and Credit Rating

M21.10 Instruction and PracticeAn Introduction to Credit and Credit Rating

Appendix A.11.

InstructionRisks and Benefits of Types of Credit

Appendix A.12.

Instruction and PracticeCredit Cards and Exploring Credit Card Use

Appendix A.13.

ActivityCredit Card Comparison

Appendix A.14.

ActivityExploring Credit Card Use

Appendix A.15.

ResourcesHow Do I Find Information About Credit Cards?

http://www.creditcardflyers.com/credit-education/how-to-find-credit-card-information.php




http://www.teensguidetomoney.com/saving/simple--compound-interest--the-rule-of-72/compound-interest/

http://www.teensguidetomoney.com/saving/simple--compound-interest--the-rule-of-72/compound-interest/

Best Canadian Credit Cardshttp://canada.creditcards.com/best-canadian-credit-cards.php

Credit Card Selector Toolhttp://www.fcac-acfc.gc.ca/iTools-iOutils/creditcardselector/CreditCard-eng.aspx?lang=eng

Be Smart With Your Credit Card: Tips to Help You Use Your Credit Card Wisely

http://www.fcac-acfc.gc.ca/eng/resources/publications/paymentoptions/tscreditshop-eng.asp

Credit Card Payment Calculator Toolhttp://www.fcac-acfc.gc.ca/iTools-iOutils/CreditCardPaymentCalculator/CreditCardCalculatorCalculate-eng.aspx

Installment Accounts and 30 Day Accounts

M21.10 ResourcesYour Guide to Revolving Credit and Installment Credit

http://www.debthelp.com/kc/215-your-guide-revolving-credit-and-installment-credit.html

The Types of Accounts on a Credit Historyhttp://www.ehow.com/list_7339759_types-accounts-credit-history.html

Installment Accountshttp://www.articlesbase.com/credit-articles/installment-accounts-619406.html

What is an Accounts Payable Billing Cycle?http://www.ehow.com/info_8405037_accounts-payable-billing-cycle.html

Loans M21.9 M21.10

ActivityComparing the Cost of a Loan

Appendix A.16.

Rent, Lease or Buy a Vehicle

M21.9 M21.10

ActivityPurchasing a New Vehicle

Appendix A.17.

ResourcesRent, Lease, or Buy?

Foundations of Mathematics 12 (2012). pp. 120 - 133Buying a Vehicle

http://www.cmcweb.ca/eic/site/cmc-cmc.nsf/eng/fe00108.html#buy

Loans and Savings Rates Tables: Car Loanshttp://www.financialpost.com/personal-finance/rates/


http://www.financialpost.com/personal-finance/rates/loans-car.html



http://www.ehow.com/info_8405037_accounts-payable-billing-cycle.html

http://www.ehow.com/info_8405037_accounts-payable-billing-cycle.html

http://www.articlesbase.com/credit-articles/installment-accounts-619406.html

http://www.articlesbase.com/credit-articles/installment-accounts-619406.html

http://www.ehow.com/list_7339759_types-accounts-credit-history.html

http://www.ehow.com/list_7339759_types-accounts-credit-history.html



http://www.fcac-acfc.gc.ca/iTools-iOutils/CreditCardPaymentCalculator/CreditCardCalculatorCalculate-eng.aspx





http://www.fcac-acfc.gc.ca/iTools-iOutils/creditcardselector/CreditCard-eng.aspx?lang=eng

http://www.fcac-acfc.gc.ca/iTools-iOutils/creditcardselector/CreditCard-eng.aspx?lang=eng

http://canada.creditcards.com/best-canadian-credit-cards.php

http://canada.creditcards.com/best-canadian-credit-cards.php

loans-car.htmlCanadian Personal Loan Rates for Secured and Unsecured Lines of Credit

http://www.redflagdeals.com/features/canadian-mortgage-gic-rrsp-savings-rate-comparison/canadian-personal-loan-rates-for-secured-and-unsecured-lines-of-credit/

Insuring Vehicles and Insurance Rates

M21.10 ActivityUse automobile insurance websites to investigate the degree to which the type of car and the age and gender of the driver affect insurance rates.

ResourcesRegistration and Insurance Rates

http://www.sgi.sk.ca/individuals/registration/rates/index.html

Vehicle Insurance Coveragehttp://www.sgi.sk.ca/individuals/registration/coverage/index.html

Basic Plate Calculatorhttp://www.sgi.sk.ca/online_services/rate/index.html


http://www.sgi.sk.ca/online_services/rate/index.html

http://www.sgi.sk.ca/individuals/registration/coverage/index.html

http://www.sgi.sk.ca/individuals/registration/coverage/index.html






http://www.financialpost.com/personal-finance/rates/loans-car.html

Theme Overview: Home

Theme IntroductionThe intent of this theme is to develop a deeper understanding of the applications of similarity, proportional reasoning, measurement, geometry, and trigonometry for the purpose of designing, building, and maintaining a home and yard.


OutcomesM21.4 Demonstrate and extend understanding of similarity and proportional reasoning related to scale factors, scale drawing, scale models, surface area, and volume.

M21.5 Demonstrate understanding of angles created by parallel, perpendicular, and transversal lines and solve problems within the home theme.M21.6 Demonstrate understanding of primary trigonometric ratios (sine, cosine, and tangent) and slope.

At a GlanceSimilarityProportional reasoningScale factorScale drawingsScale modelsSurface area

VolumeAnglesTransversal, parallel, and perpendicular linesPrimary trigonometric ratiosSlope

Guiding Questions How do you determine the scale factor from scale drawings? What scale models have you seen? How are scale models useful? How can you ensure that the constructed object is proportional to the scale drawing? What do you know about surface area and volume? What is the difference between area and surface area? What do you need to know to measure surface area? How can you calculate surface area? How many surfaces does an object (e.g. cereal box) have? How many surfaces does a cylinder have? How can you calculate volume? Why are the units for volume cubed? What is the difference between volume and capacity?


What are the units of measurement of volume? capacity? Where have you seen units of mL? m3? cm3? What is a parallel line? Where have you seen a parallel line? How do you know that lines are parallel? What is a perpendicular line? Where have you seen a perpendicular line? How do you know a line is perpendicular? What are the units of measurement in a triangle? What do you know about the sum of the three angles in a triangle? How can you find the measure of an angle in a right triangle if you have two side

lengths? If you were given the length of one side is it possible to find the lengths of the other

two sides? If given one angle, that is not the right angle measure; can you determine all three

angles in a right triangle? If given an angle measure and one side length can you determine the other side

lengths? What is slope? What kinds of things have a slope or slant? What would you need to change in the triangle to change the slope? How can you measure slope? What are common sense safety requirements where slope is used? What would be a reasonable incline to push a wheelchair up if a door step is n

meters from the ground? How long would the ramp be? How could you determine the length?

How could you apply trigonometry to solve for a real-life situation?

Career ConnectionsCarpenterConcrete MixersSurveyorsRoad constructionArchitectMasonryFurniture designerWeb designer

PlumbersTruckersDrafts personBuilding InspectorHome InspectorUrban plannerFashion designerAutomotive designer


TOPIC: SCALE

FACTORS, SCALE

DRAWINGS, SCALE MODELS, SURFACE AREA,

AND VOLUME

OUTCOME: SUGGESTIONS FOR TEACHING AND LEARNING:

Measurement M21.4 Brainstorm, Discuss and PracticeWhat Do You Already Know About Measurement?

Appendix B.1.

Proportional Reasoning and Scale Factor

M21.4 ActivityEnlargements, Reductions, and Scale Factor

Appendix B.2

ActivityScale Factor, Scale Drawings, and Scale Models

Appendix B.3.

ActivityCars, Critters, and Barbie

Appendix B.4.

Teacher Resource Cars, Critters, and BarbieAppendix B.5.

ActivityGingerbread House

Appendix B.6.

ActivityGlowing Rectangles

Appendix B.7.

ResourceScale Factors and Similarity

MathLinks 9 (2009). pp. 126 – 145

Surface Area M21.4 Pre-AssessmentGeometric Shapes

Appendix B.8.

Pre-Assessment


What is Surface Area?Appendix B.9.

ApplicationHow Many Sheets of Dry Wall Are Needed?

Appendix B.10.

InvestigateHeat and Frost Insulators

Appendix B.11.

ActivityYou are employed by the city and responsible for determining how much to sell new development lots for. Find information on available lot dimensions in your area and investigate. Determine the criteria you are going to use to set the price.

ActivityBody Surface Area Calculator

http://www.ultradrive.com/bsac.htm

ResourcesHuman Resources and Skills Development Canada: Trades Math Workbook.

http://www.hrsdc.gc.ca/eng/jobs/les/tools/support/trades_math_workbook.shtml#intro

Surface AreaMathLinks 9 (2009). pp. 26 - 35

Surface AreaMathWorks 10 (2010). pp. 115 – 123

Volume M21.4 Pre-AssessmentWhat is Volume?

Appendix B.12.

ApplicationHow is Volume Used?

Appendix B.13.

Watch and InvestigateYou Pour, I Choose

http://threeacts.mrmeyer.com/youpourichoose/Volume Cylinder

http://www.learner.org/interactives/geometry/area_volume2.html




http://threeacts.mrmeyer.com/youpourichoose/



http://www.ultradrive.com/bsac.htm

GameMinecraft Volume: Rectangular Prism Game

http://www.xpmath.com/forums/arcade.php?do=play&gameid=118

ProjectLandscape Design

Appendix B.14.

ResourceInteractives Geometry 3D Shapes

http://www.learner.org/interactives/geometry/index.html

TOPIC:ANGLES

CREATED BY PARALLEL,

PERPENDICULAR AND

TRANSVERSAL LINES


Angles Created by Lines

M21.5 InvestigateAngles Formed by Transversals

Appendix B.15.

Diagram 1 and Beige Cards: Parallel LinesAppendix B.16.

Diagram 2 and Pink Cards: Non-Parallel LinesAppendix B.17.

Diagram 3Appendix B.18.

ApplicationAngles in Construction

Appendix B.19.


http://www.learner.org/interactives/geometry/index.html



TOPIC: PRIMARY

TRIGONOMETRIC RATIOS AND

SLOPE


Triangles M21.6 Pre-AssessmentTriangle Properties

Appendix B.20.

InvestigateBuilding Bridges Teacher Resource

Appendix B.21.

Building Bridges Student TaskAppendix B.22.

ResourceMr. Quenneville’s Website: Unit 2 Trigonometry: 2.0 Intro to Trigonometry

https://sites.google.com/a/hdsb.ca/mr-quenneville/home/grade-10-applied-math/unit-2-trigonometry

Trigonometry M21.6 InvestigateWhat is the Problem? Teacher Resource

Appendix B.23.

What is the Problem? Student TaskAppendix B.24.

WatchHow to Measure a Tree

http://www.youtube.com/watch?v=F6fltSqImFM

Trigonometric Ratios

M21.6 InvestigateSame Shape Triangles Teacher Resource

Appendix B.25.

PracticeMr. Quenneville’s Website: Unit 2 Trigonometry2.4.1 What’s My Triangle2.4 Solving for a Missing Side2.5.2 Tangent or Something Else





http://www.youtube.com/watch?v=F6fltSqImFM



ActivityGoing the Wrong Way

Appendix B.26.

ActivitySolving Trigonometric Problems

Appendix B.27.

Constructing a ClinometerAppendix B.28.

ProjectWho Uses Trigonometry? Teacher Resource

Appendix B.29.

Who Uses Trigonometry? Student TaskAppendix B.30.

ResourcesTrigonometry of Right Triangles.

MathWorks 10 (2010). pp. 270 - 319Trigonometry Activities

http://www.cimt.plymouth.ac.uk/projects/mepres/book9/y9s15act1.pdf

Mr. Quenneville’s Website: Unit 2 Trigonometryhttps://sites.google.com/a/hdsb.ca/mr-quenneville/home/grade-10-applied-math/unit-2-trigonometry

Slope M21.6 InvestigateStaircases, Steepness, and Slope

Appendix B.31.

Staircases HandoutAppendix B.32.

Slope Applications

M21.6 ProjectRamp It Up

Foundations and Pre-Calculus 10 (2010). p. 128

ApplicationsPitch of a Roof

Appendix B.33.

ResourceWhat Does the Road Sign Mean?






http://www.angelfire.com/ultra/mathproject/


http://www.angelfire.com/ultra/mathproject/

Theme Overview: Recreation and Wellness

Theme IntroductionRecreational 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, reasoning, and budgeting skills. Students will apply an understanding of measures of central tendency to make predictions or inform decisions in order to effect changes in their own lives in terms of recreation and personal wellness.


OutcomesM21.2 Demonstrate understanding of numerical reasoning and problem solving strategies by analyzing puzzles and games.

M21.3 Extend and apply understanding of measures of central tendency to analyze data.

M21.8 Demonstrate understanding of budgets.

At a GlanceStrategizingSolving puzzlesNumerical reasoningInductive and deductive reasoning

MeanMedianModeBudgeting

Guiding Questions When you think of your favorite game, what comes to mind? What is your strategy used 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 difference between inductive and deductive reasoning? How is statistics used to support an argument or a claim? How can statistics be used to lead to different conclusions? When is it appropriate to use the mean, median and mode? How can the measures of central tendency be used to make informed decisions? Are they used correctly to present information? Should all data be included when finding measures of central tendency?


Career ConnectionsChess masterPuzzle makerPsychologist

Sports analystStatisticianPublic health nurse

TOPIC:PUZZLES AND

GAMES


Inductive and Deductive Reasoning

M21.2 Instruction and PracticeInductive and Deductive Reasoning

Appendix C.1.

Analyze and Strategize

M21.2 Activity (similar to Activity Puzzles and Games in Mathematics 11)

Puzzles and GamesAppendix C.2.

GameGolf Card Game

http://www.pagat.com/draw/golf.html#six

TOPIC:MEASURES OF

CENTRAL TENDENCY


Measures of Central Tendency

M21.3 ActivityMeasures of Central Tendency

Appendix C.3.

ActivityUse measures of central tendency to compare goals scored by professional hockey players 10 years ago compared to present day.

ActivityWeb Quest 1 – Baseball Stats

http://www.mathgoodies.com/Webquests/sports/

Activity


http://www.mathgoodies.com/Webquests/sports/

http://www.pagat.com/draw/golf.html#six

Personal WellnessAppendix C.4.

TOPIC:BUDGET


Budget M21.8 ActivityRecreation and Personal Wellness Budget

Appendix C.5.


Theme Overview: Travel and Transportation

Theme IntroductionThe Travel and Transportation theme will be used as the context of the mathematical skills it takes to plan a trip. Students will explore map reading, budgeting, and the mathematics involved in an area of interest. When planning a trip, students will consider transportation, lodging, entertainment, and meals.


OutcomesM21.4 Demonstrate and extend understanding of similarity and proportional reasoning related to scale factors, scale drawing, scale models, surface area, and volume.

M21.7 Demonstrate understanding of the mathematics involved in an area of interest.

M21.8 Demonstrate understanding of budgets.

At a GlanceSimilarityProportional reasoningDirectionLocationDistance

Scale factorScale drawingsMap readingMathematics in an area of interestPlanning and budgeting a trip

Guiding Questions What is the difference between direction and location? How are direction, location, and distance related? How do direction, location and distance relate to math? Is there more than one way to get to a location? What are the key components to giving directions? What are the key components to giving locations? What are the key components to determining distances? What units are used for distance? How do you read a map? How do you use a map? How do you scale diagram to create a map? How does direction, location, and distance factor into travel plans? What is an area of interest?


What makes an area of interest significant? How is math related to an area of interest? What fixed and variable expenses do you consider when creating a travel budget?

Career ConnectionsBus driverTaxi driver

PilotTraveller

TOPIC:SCALE FACTOR

AND SCALE DRAWINGS


Direction, Location, and Distance

M21.4 Pre-AssessmentDirection, Location, and Distance

Appendix D.1.

Scale Factor, Scale Drawings, and Map Reading

M21.4 ActivityMap Reading

Appendix D.2.

TOPIC:AREA OF INTEREST


Area of Interest

M21.7 ActivityArea of Interest

Appendix D.3.

TOPIC:BUDGETS


Budgeting for a Trip

M21.8 ActivityBudgeting for a Trip

Appendix D.4.


Appendices

Appendix A: Earning and Spending Money

Appendix A.1 Budgeting Key Terms

Use a learning strategy to help students familiarize and understand these terms.

Terminology:

Balanced budget Fixed expense Unexpected expense

Budget Recurring expense Utilities

Deficit Surplus Variable expense


Appendix A.2 Create a Personal Budget with Fixed and Variable Expenses

Home Daily Living Transportation EntertainmentMortgage Groceries Driver’s licence Cable/SatelliteProperty tax Laundry Car payments MoviesRent Dining out Fuel ConcertsUtilities Clothing Car plates Books/MagazinesCell/Home phone Gifts Package policy MusicInternet Hair salon Repairs Video gamesHome decorating Credit card payments Oil changesHome repairs Makeup Tires

Manicure/Pedicure Car washPersonal care (shampoo, deodorant, etc.)

Parking

TicketsBus pass

Health and Recreation

Vacations Savings/Investments Other

Club/Team fees Travel: bus, car, plane, train

Savings accounts Pet expenses

Sports equipment Accommodations RESP CharitiesLessons Food Piggy bank Petty cashGym membership Souvenirs Bank chargesPrescriptions Activities Post-Secondary

tuitionOver-the-counter Medications (Tylenol, etc.)

Post-Secondary books

Dental costsATV/SnowmobileLeisure activities (hunting, fishing, etc.)

1. Identify the items that apply to you now. List them on the budget template.2. What items might apply to you 3 – 5 years from now?3. Identify five items in your template that you think are fixed expenses.4. Identify five items in your template that you think are variable expenses.5. Identify five items in your template that you think are essential expenses (not

optional when it comes to day-to-day living).6. Identify five items in your template that you think are non-essential expenses.7. After finishing the activity, explain what you learned about budgeting. Include

advantages and challenges.


BUDGET TEMPLATEThis budget template can be modified by the teacher/student for other projects.

Category Monthly Budget Actual Amount DifferenceINCOME: Estimate Your Income Your Actual IncomeWagesAllowanceBabysittingOther:Other:INCOME SUBTOTAL

EXPENSES Estimate Your Expenses Your Actual ExpensesHome

Daily Living

Transportation

Entertainment

Health/Recreation

Vacation

Saving/Investing

Other

EXPENSES SUBTOTAL

NET INCOME(Income – Expenses)


Appendix A.3 Budgeting to Live Away From Home Additional Questions

Questions:1. How would you adjust your budget if you were only able to work part-time?2. How would you adjust your budget if you had an $800 electrical problem with your

vehicle?3. Research the cost of a major purchase (boat, motorcycle, vehicle, laptop, etc.).

Adjust your budget on a new template to demonstrate how you could keep a balanced budget.

4. How would you adjust your budget if you wanted to save 10% each month as a down-payment for a home?

5. What were the challenges in the creation of your budget?6. List some advantages of working with a budget.7. What categories would you expect to increase in 10 years?8. What categories might you need to add to/delete from your budget in 10 years?9. What were the top three concepts you learned in this project?


Appendix A.4 Financial Institutions Services Key Terms


Terminology:

Account Encryption Quarterly

Annum Financial advisor RESP

ATM Full-service RRSP

Balance GIC Rule of 72

Bank card Interest Savings account

Canada Savings Bond Investment Self-service

Cheque Mobile banking Semi-annual

Chequing account Monthly Simple interest

Compound interest Monthly fee Telephone banking

Compounding period NSF cheque Term

Daily Overdraft protection Term investment

Debit Post-dated cheque Transaction

Debit card PIN Transfer

Deposit Principal Withdrawal


Appendix A.5 Researching Types of Banking Services and Fees

Use this chart to compare the banking services provided by at least two financial institutions. Either research on the Internet or obtain brochures from various financial institutions.

Financial Institutionsa) b) c)

1. What service charges are there on the account?

2. What are the fees for transactions?

3. Are there incentives or rewards with the account?

4. Is online banking service available? Is there a fee for this service?

5. Is telephone banking service available? Is there a fee for this service?

6. Is mobile banking service available? Is there a fee for this service?


7. What is the interest rate for the savings account(s)?

8. Are cheques available for the accounts? What is the cost to order cheques? Is there a cost for writing cheques?


Appendix A.6 Advantages and Disadvantages of Banking Services

Read: Advantages and Disadvantages of Savings and Checking Accountshttp://www.ehow.com/info_8093699_advantages-disadvantages-savings-checking-accounts.html

Type of Banking Service Advantages DisadvantagesOnline Banking

Mobile Banking

Debit Card

Chequing Account

Savings Account


http://www.ehow.com/info_8093699_advantages-disadvantages-savings-checking-accounts.html

http://www.ehow.com/info_8093699_advantages-disadvantages-savings-checking-accounts.html

Appendix A.7 Writing Cheques

Resource: Saskatchewan Learning Mathematics 21 (2007-2013).

Instruction: One way of paying for things or taking money out of your chequing account is by writing a cheque. A cheque is a written order to the bank to pay a certain amount of money from your account as ordered. A cheque is not money but it is used like money. It may be cashed only by the person to whom it is written unless the person signs it over to a second party (another person). To take money out by cheque, you must fill in a cheque. It may be a personalized cheque or a non-personalized cheque. It is usually better to use a personalized cheque if you have one.

Before we go over how to fill in a cheque blank, you are going to practice writing dollar amounts in words.

1. It is important to write amounts in words correctly on checks. The words for numbers between 20 and 100 are hyphenated when the number has two words.

Example: 45 is written as “Forty-five”99 is written as “Ninety-nine”

2. The word “and” is reserved for the decimal point. The cents are written as a fraction of a dollar, since the word “dollars” appears at the end of the line.

Example: $706.10 is written: Seven hundred six and 10/100$17.36 is written: Seventeen and 36/100

3. When there are no cents, the fraction is usually written in zeros.

Example: $82.00 is written: Eighty-two and 00/100

When you write a cheque, you must fill in five items. Notice the placement of each item on the blank cheque shown on the next page.

1. The date2. The name of the person or company who is to receive payment (payee)3. The amount written in digits4. The amount written in words5. Your signature

An optional line “For_______________” should be filled in to remind you what the cheque was written for.


Additional points to keep in mind:

Be sure not to leave any blank areas on your cheque. Start at the beginning of the line when you are writing the cheque amount. Write clearly and only use ink when writing your cheque to help prevent anything

from being changed on your cheque. Your cheque is not legal until you sign it. Keep your cheques in a safe place until

you are ready to use them. Also, never sign a blank cheque. Make sure the amount box (in numbers) and the amount line (in words), match. If you make a mistake when writing a cheque, write “VOID” in big letters on the

cheque and then rip it up. Make sure you record the cheque in the register and mark that it was VOID.

Practice: Write out each dollar amount in words:1. $235.002. $200.393. $60.984. $1819.215. $607.776. $910.007. $25.868. $1327.569. $705.1510. $384.4811. $37.1612. $56.00


Fill in the four cheque blanks with the information given for each.

13.Date Payee Amt. of cheque Payer For

(optional)12/20 Reader’s

Choice$18.99 Betty L. Rain subscription


(optional)12/20 M& L Meats $62.75 Betty L.

Rainfrozen steaks


15. Date Payee Amt. of cheque

(words and numbers)

Payer For(optional)

6/13 Fishing Spot $23.00 Joe Fox reel


(optional)7/25 Mrs. Smith $101.03 Carol Fox candles

Answers: 1. two hundred thirty-five and 00/1002. two hundred and 39/1003. sixty and 98/100


4. one thousand eight hundred nineteen and 21/1005. six hundred seven and 77/1006. nine hundred ten and 00/1007. twenty-five and 86/1008. one thousand three hundred twenty-seven and 56/1009. seven hundred five and 12/10010. three hundred eighty-four and 48/10011. thirty-seven and 16/10012. fifty-six and 00/10013.

14.


15.

16.


Appendix A.8 Investment Options

Resource: The CITY A Financial Life Skills Resource

Prior Knowledge:1. List some of your short-term goals and long-term goals.2. How much money will you need for each of the goals?3. What is your plan for making these goals a reality?4. How could you save for a large purchase?5. What are savings? What do you know about investments?

Activity: Have students work through the following information using a strategy (e.g. think-pair-share, jigsaw, concept circle, etc.)

Instruction: People can choose from a wide variety of investments. This chart shows you some things to consider about some of the main types of investments.

Type Expected Return Risk LiquiditySavings accounts, Guaranteed Investment Certificates (GICs), term deposits:

Money deposited with banks, trust companies and credit unions

• usually a fixed annual rate

• GICs sometimes tied to performance of an index or other standard

• low to moderate

• principal amount is usually insured, but interest rates can be fixed or variable

• savings may be withdrawn at any time

• some GICs and term deposits must be held to maturity, but many allow for early redemption or cashing out at a cost

Treasury bills:

Short-term (less than 1 year) debt securities issued by government

• determined by difference between purchase price and value at maturity

• very low • not redeemable, but can usually be sold quickly through investment dealers

Equities:

Shares in ownership of a company (also called stocks)

• may pay regular dividends to share holders

• potential return may depend entirely on changes in share price

• moderate to high

• depends on size and stability of company, management, competition, etc.

• shares traded on stock exchanges are usually quite easy to sell

• shares that aren't listed on an exchange may be difficult or impossible to sell


Type Expected Return Risk LiquidityFixed income investments:

Government and corporate bonds and debentures

• interest rate is usually fixed

• bonds with longer terms will usually pay higher interest rates

• high risk "junk" bonds offer even higher rates

• risk of borrower defaulting is very low for government bonds but can be low to high for corporate bonds

• bond values go up and down with changing market interest rates

• most bonds can be bought and sold quickly through investment dealers

• some bonds are traded on stock exchanges

Mutual funds:

Units in a pool of money that's managed for a large number of investors by a professional money manager

• may include interest, dividends and capital gains (or losses)

• return will depend on manager's investment decisions and on the management fees charged

• low to very high, depending on what the fund invests in and on the skill of the fund manager

• most mutual funds allow investors to cash in (redeem) their holdings on short notice

Real estate:

Property such as land or houses

• depends on price, location, real estate market, etc.

• may include rent or increase in value

• low to high • depends on price, location, real estate market, etc.

• takes more time to sell than many other investments

• hard to sell small portions

• depends on market

Direct investment:

Investing your money to finance a private business

• low to very high

• success depends on the business concept, the manager and on economic conditions

• medium to very high • depends on type of business, competition, skill of the business manager, and the economy

• low

• may be very hard to sell


Investors can choose from thousands of different investments. The investments that offer the highest expected returns are those with the highest risk. Wise investors diversify their investments to help manage the risk.

Some investments are very complex. Factors like commissions, sales fees and tax levels can have a major impact on the final return. Investors usually seek expert advice from professional advisers to be sure they fully understand their investment and that the investment is a good choice for their investment goals. Companies that offer investment advice must be registered (licensed) and must comply with detailed standards of conduct.

Find out more about investment by visiting your provincial or territorial regulator's website (see the Financial Consumer Agency of Canada for links at www.themoneybelt.gc.ca).


http://www.themoneybelt.gc.ca/

Appendix A.9 Comparison of Simple and Compound Interest

Resource: Exploring Compound Interest. Foundations of Mathematics 12 (2012). p. 19

Example: Sebastian invests $2000 at 3.5% interest, compounded annually for 4 years. Determine the interest earned.

I = P r t Simple InterestA = P + P r t Year End Investment Value

***Because we are calculating compound interest, we need to calculate the interest every year separately.**

Determine the difference in the future value of simple interest compared to compound interest.

Compound Interest Simple InterestYear Principle

at Beginning

of the Year

InterestI = P r t

Year End Investment Value A = P

+ P r t

Principle at Beginning of the Year

I = P r t

1 2000 I = (2000)(0.035)(1)

A = 2000 + 70

2000 I = (2000)(0.035)(1) = 70


= 70 = 2070

2 2070I = (2070)(0.035)(1) = 72.45

A = 2070 + 72.45 = 2142.45

2000 70

3

4

Total: Total:

Determine how much more interest was earned using compound interest.

Example: Levi invests $13 000 for 6 years at 2.8% interest, compounded annually.

a) Complete the following chart:

Compound InterestYear Principle at

Beginning of the Year

InterestI = P r t

Year End Investment Value A = P + P r t

1 13000

2

3

4

5

6

b) Determine the interest earned to the nearest cent.

c) What is the maximum amount you can withdraw from the account at the end of the investment?


Appendix A.10 Financial Decision Making Key Terms


Terminology:

Amortization period Default Mortgage

Cash advance Down payment Outstanding balance

Charge account Financial institution Overdraft protection

Consolidate Fixed term Premium

Co-signer Installment plan Promotion

Credit Lease Rent

Credit card Line of credit Return

Credit rating Loan Thirty-day account


Appendix A.11 An Introduction to Credit and Credit Rating


Instruction:

The Use of Credit: Credit is defined as the advance of goods/services in exchange for a promise to pay at some future date. If you take advantage of a “buy now, pay later” opportunity you will pay more than the cash price. The longer you take to repay, the greater the cost of credit will be.

Types of Credit:

1. Sales Credit: Credit extended for a purchase of an item at the time of purchase.

a) Installment PlanFor bigger items (appliances, furniture) it usually involves a down-payment followed by regular payments of principal and interest over a period of months. Failure to make payments could result in the item being repossessed.

b) Charge AccountsSales credit with a specific limit. If the entire amount billed is paid, there is no interest charged. If the full amount is not paid, a minimum amount must be paid with interest due in the next month on the amount not paid. For example, Sears, Target, Petro, and Shell cards.

c) Credit CardsA credit card is a plastic card that allows you to pay for something by charging it and paying for it later. Each card has a credit limit. If the bill paid by the statement date no interest is charged. Interest is charged in the next month for the amount not paid. A minimum payment of principal and interest must be made each month if the entire balance is not paid by the statement date. For example MasterCard, Visa, and American Express. Interest rate is substantially higher than a loan from a bank, because interest is compounded daily.

2. Cash Credit: Credit received by borrowing money from a bank and paying it back later.

a) Personal LoanThe loan may be paid back in equal payments of principal and interest or in a single payment. The quicker it is paid off, the less interest that is paid. b) Mortgage A long term personal loan (usually for a house) in which the house purchased is used as security for repayment. Payments are usually PIT (principal, interest, tax). Interest is charged on the outstanding balance at each payment date


therefore the amount of interest paid in the early payment is a very high percentage of the payment. As the principal is paid down, the interest portion of the payment becomes smaller. The loan is usually paid down over a period of 15-25 years.

c) Personal Line of CreditA one-time approved loan allowing you to borrow up to a prearranged limit by simply writing a cheque. It can be used to purchase anything. The interest rates are usually lower than credit cards.

d) Pay Day LoanA small, short-term unsecured loan, not necessarily linked to the borrower’s payday. The loans are also sometimes referred to as “cash advances” but are different from credit card cash advances. Pay day loans rely on the consumer having previous payroll and employment records.

3. Service Credit:

Credit extended for services provided on a daily basis but paid for only once a month. For example, telephone, power, gas.

Interest: The amount of money paid or earned for the use of money.

Credit Rating: Credit rating is an evaluation of your past use of credit, your character, your ability to repay and the security or collateral you have for the loan.

When being rated on character and past use of credit (will you repay what you borrow) you will be judged on the following:

Have you used credit before?Do bills get paid on time?How long have you lived at your current address?How long have you been at your current job?Can you supply a character reference?

When being rated on your ability/capacity to repay, you will be judged on the following:Do you have a steady job?Do you have other loans you are paying off?What are your living expenses?Do you have dependents (someone depending on you for support)?

When being rated on the security or collateral you have for the loan you will be judged on the following:

Do you have a savings account?Do you have any investments to use as collateral?


Do you own any property?

Building a Good Credit Rating: If you are starting out, financially speaking, the first thing to do is build a good credit rating.

1. Open a savings account and make regular deposits. The idea is to save money and show that you are responsible and reliable about money.2. Pay bills promptly.3. When borrowing, borrow only what you need and can repay back.4. Arrange a loan repayment schedule and try to repay the loan as soon as

possible.

Good Credit Risk: You can be considered a good credit risk if you pay back loans on time, pay back loans regularly and on time, and have a regular salary to use to pay back loans.

One who pays back all loans One who pays loans back regularly and on time One who has a regular salary to use to pay back loans

Practice: Indicate if the statement presents credit as an advantage or a disadvantage. 1. Credit eliminates the need to carry large quantities of cash.2. Credit available through a store’s credit card cannot be used in other stores

therefore discouraging comparative shopping.3. Credit allows the immediate possession of goods to be paid over a period of time.4. Credit allows the consumer to take advantage of sales opportunity.5. In the event of non-payment, credit may lead to the loss of property.6. Credit helps in dealing with financial emergencies.7. Credit encourages impulse buying.8. Credit may increase your debt load so that you cannot save for the future.9. Credit increases the overall price of goods. (Most credit card companies charge

retailers a 3% fee. This fee is added to the cost of all items in the store).10.Easily available credit may encourage poor buying decisions.11.Do you or your classmates have credit cards? How does one get a credit card?

What is meant by the limit of a credit card? 12.Do you think a person should have several credit cards? Why or why not?13.What causes people to get into financial difficulty? Is it always the fault of the

individual?14.At what age do you see yourself taking out a mortgage for a house? Explain.15.The qualities you look for in a friend are the same qualities a lending institution

hopes to find in you. Do you agree or disagree with this statement? Explain.16.Suppose you are a loans officer in a bank. List three questions you would want to

ask a customer who has come in to borrow $15 000 to buy a new boat?


17.What is a debit card? List several tips that you should follow in order to protect your debit card while using it?

18.Decide which of the items below you would use to credit to purchase. When making your decisions consider:

- Do you need the item?- Could you wait until you have saved up enough money?- Could you better use the money for some other purchase?- Does the purchase over-extend your regular budget?- Will you be able to repay the borrowed money?

Would you purchase the following items on credit? Why or why not?

a) A ticket to a concert?b) A compact disc on sale for $16.99?c) A $500.00 leather jacket on sale for $350.00?d) Groceries for the family?e) Taking your friend out for lunch?f) A vacation to Disneyland at $500.00 each for a family of 4?g) A second computer for the family?h) A second television for the family?

Use the chart to put the following into one of two categories: i) good credit risk ii) high credit risk. Be prepared to discuss your answers.

19.SaskTel employee, full time, employed for 5 years20.Secretary, part time, employed for 10 years21.Gas jockey, works part time on weekends, employed for 2 months22.Student, no job23.Lawyer, full time, employed for 20 years24.Teacher, full time, employed for 7 years25.Grain farmer, full time, employed for 32 years26.Management trainee, part time, employed for 2 weeks27.Taxi driver, full time, employed for 17 years28.Delivery person, works part time on weekends, employed for 10 months29.Waiter, part time, employed for 1 year30.Waitress, full time, employed for 12 years31.Dentist, full time, opened own practice 2 months ago32.Seasonal worker with the city, full time, employed only for summer months33.Unemployed person34.Business owner, part time, employed for 5 years


Good Credit Risk High Credit Risk

Answers:1. Advantage2. Disadvantage3. Advantage4. Advantage5. Disadvantage6. Advantage7. Disadvantage8. Disadvantage9. Disadvantage10. Disadvantage11. to 34. Answers will vary.


Appendix A.12 Risks and Benefits of Types of Credit

Instruction:Student LoansStudent loans can be granted by governments or by financial institutions.

Possible benefits of a student loan: Allows you to continue post-secondary studies. The government pays the interest on your loan while you are studying full-time.

You repay the loan upon completion of your studies. The interest on your loan starts when you cease to be a full-time student.

Potential risks of a student loan: At the end of your studies, you may have to deal with substantial study debts.

This may delay other plans, such as travelling or buying a house.

Credit CardsGenerally, credit cards allow you to make purchases, up to a specific credit limit, for which you will be billed at a later date. They allow you to transfer your balance from one billing cycle to another. Nevertheless, you must pay a minimum amount every month, and unpaid balances are subject to interest charges, based on an annual percentage rate or APR.

Possible benefits of a credit card: Helps you create a credit history and earn a credit rating. Can be more practical than carrying cash. Allows you to borrow free of charge if you always pay the balance in full by the

due date. Can offer incentives, such as reward points that you can use towards purchasing

certain products. Allows you to pay conveniently for purchases made over the telephone or on the

Internet.

Potential risks of a credit card: Can lead you to spend more and drive you into more debt than you can handle. Can affect your credit rating if your monthly payments are late. Can carry conditions that are hard to understand. Is generally more expensive than other forms of credit like personal lines of credit

or personal loans. Chance of fraud.

Personal Line of CreditProvided by financial institutions, this type of loan allows you to withdraw money, as needed, up to a maximum credit limit. You are charged interest from the day you withdraw money from your line of credit until you pay back the loan in full.


Possible benefits of a personal line of credit: Gives you the convenience of borrowing money whenever you need it: you do

not have to reapply for loans. Offers flexible reimbursement methods. Offers lower interest rates than credit cards.

Potential risks of a personal line of credit: Some people use this loan as a source of revenue. Can force someone into more debt than he/she can afford.

Personal LoansYou can get a personal loan to buy a car, to buy furniture, to go on a trip, etc. You then use the borrowed amount as you wish. The amount, the rate and the conditions of reimbursement are fixed at the time of the contract. A personal loan is reimbursable in a predetermined time frame through monthly payments.

Possible benefits of a personal loan: There are various options that allow you to obtain a loan to meet your needs. The loan is negotiable. You use the borrowed amounts as you wish.

Potential risks of a personal loan: Since this loan is not linked to a specific purchase, if the goods are defective or if

there is any other problem (e.g. the goods are not delivered), the loan must still be reimbursed.

Can drive you into more debt than you are able to pay back if the loaned amount does not take into account your ability to repay.

Increases your monthly obligations.

Instalment PlansInstalment plans normally apply when you make a significant purchase at a business. For example, you may purchase a television or a refrigerator but pay for it through monthly instalments, usually accompanied by a certain interest rate.

For this type of contract, the seller has ownership of the goods until they are paid in full, even though you are in possession of them. Therefore, if you miss a payment, the seller can demand that the goods be returned. Remember that in this type of contract, the merchant is responsible for accidental loss of the goods as long as you are not yet the owner.

Possible benefits of instalment plans: The merchant is responsible for accidental loss of the goods as long as he/she is

still the owner.


Potential risks of instalment plans: They increase the total price due to the interest charges. The seller remains the owner of the goods until they are fully paid. If you miss a

payment the store can repossess. They increase your monthly obligations.

Beware of “buy now, pay later” promotions; several stores offer this type of promotion. You buy goods today, but pay nothing for one year, for example. This kind of advertisement usually does not indicate the consequences of not making payments on time. In fact, according to some store policies, interest starts to accrue on the date of purchase. This interest is cancelled if the person pays within the time limit. However, if someone pays after the time limit, he or she must pay interest for the whole period and interest rates are usually quite high! These plans often mention there are no additional fees and no interest; however the selling price has been increased so the retailer makes a higher profit for the time they have to wait until it has been paid in full.

For example: You buy electronic equipment worth $1000. You do not pay within the one-year limit. The interest rate is 28.8%.

You will have to pay $1000 plus the year's accrued interest (from the date of purchase). In addition, people who resort to this sort of agreement often do not have the means to pay off the goods at the time of purchase, nor do they have the means to do so in one year. Many possible events can change your financial status over such a long period of time, so be careful.

MortgageA mortgage is a long-term loan granted to an individual in order to buy a home. The home itself is given as a guarantee for the loan. There are different types of mortgage loans, such as open or closed, that offer variable of fixed rates and various options concerning the term, the payment frequency and the amortization period.

Possible benefits of a mortgage: Allows you to purchase a home, which would be impossible without a loan. Offers favorable rates.

Potential risks of a mortgage: Monthly payments are sometimes high. Because it is a long-term purchase, a change in household revenue could have a

negative effect on your ability to pay it back. The home is given as a guarantee of the loan, meaning that in case of

nonpayment the home could be taken.

The purchased property can easily cost double because of the length of the loan.


Payday loans – EZ cash etc. If consumers can’t get a loan from a bank because they are of high risk or they need money quickly before payday they can borrow money from one of these institutions on site or online.

Benefits – NONE

Risks – Tremendously high interest rates the most frequently posted APE was 652% followed by 780%

How does the cost of a payday loan compare with other credit products?Payday loans are much more expensive than other types of loans, including credit cards. But how much are you really paying? How does the cost of a payday loan compare with taking a cash advance on a credit card, using overdraft protection on your bank account or borrowing on a line of credit?

Let's compare the cost of using different types of loans. We'll assume that you borrow $300, for 14 days. Note the considerable difference in the cost of each type of loan.

Comparing the cost of a $300 loan, taken for 14 days1

Payday loan

Cash advance on a credit

card

Overdraft protection on a bank account

Borrowing from a line of credit

Interest — $2.13 $2.42 $1.15

+ + + +

Applicable fees $50.00 $2.00 —2 —

= = = =

Total cost of loan $50.00 $4.13 $2.42 $1.15

Cost of the loan expressed as a percentage of the amount borrowed3

435%per year

36%per year

21%per year

10%per year


http://www.fcac-acfc.gc.ca/eng/publications/PaydayLoans/PaydayLoans-6_e.asp#note1%23note1


Appendix A.13 Credit and Exploring Credit Card Use


Instruction:Credit Cards: Allow you to buy an item from a retailer or business, which accepts

the card as a method of payment. The customer can then pay the full amount or a portion per month, but interest is charged on the outstanding balance.

Credit Limit: The highest amount of money one can charge to the credit card.

Promise to Pay: You must pay for all purchases you charge, and for all purchases charged by anyone you allow to use your card.

Past Due Accounts: If you do not make a minimum payment each month, you may be required to make immediate payment of your entire balance.

Example:

Card Name Annual Fee Rate of interest %

Credit LimitBenefits (Air miles, discounts, etc.)

1. Royal Bank Student Classic Visa

$0.00 17.9% $500.00 None

2. TD Canada Trust GM CardVisa

$0.00 18.5% $2000.00 Collect up to $500 off a new GM vehicle

3. CIBC Aerogold

$120.00 19.5% $3000.00 Collect points that can be used for travel

4. Bank of Montreal Air miles MasterCard

$35.00 18.9% $2500.00 For every $20 spent, collect 1 Air mile

For you, which would be the best card and why?

Which would be the worst card and why?

How Is Interest Calculated? An individual has until payment day to pay back the amount owing. If the amount

can’t be repaid, then interest is charged.


Interest is paid on the full amount of the purchase until the purchase has been entirely paid (e.g. $1000.00 stereo with $800.00 paid off and only owes $200.00. Must still pay interest on $1000.00)

Formula: I = P r t Principle daily interest rate # of days

Note: If you are given the annual percentage rate (APR), divide it by 365 to get the daily interest rate. Now convert this to a decimal by dividing by 100.

Example 1: APR = 18.5% 365 = 0.0506849% 100 = 0.0005068 (use this in the formula)

Example 2:Suppose that Jill had made purchases as shown in the statement below. If the payment due date was June 6, but her payment was not received until June 21, find out the total amount of interest that would be charged. Daily interest rate is 0.05067% (0.0005067). (Include purchase date and payment date when counting number of days).

Transaction DateM/D

Description Amount $ Numberof Days of Interest

Interest Charged

05/12 Esso $32.45 41 $0.6705/17 Bike Doctor $416.72 36 $7.6005/23 Hair Affair $55.90 30 $0.85

Total Interest = $9.12

Determining the Minimum Payment RequiredIf the new balance is:

1. Less than $10.00, then pay out that amount.2. Less than the credit limit, then pay the greater of $10.00 or 3% of the balance rounded up to the next highest dollar.3. Higher than the credit limit, then pay 3% and the amount the new balance is over the credit limit.

Using the above information, determine the minimum payment required if the credit limit is $2000.00 on a new balance of:

Example 1 : $8.00Solution: $8.00 (#1 - new balance was less than $10.00)


Example 2 : $1415.00Solution: 0.03 x 1415 = $42.45 $43.00 (#2 – don’t forget to round)

Example 3 : $288.00Solution: 0.03 x 288 = $8.64 $10.00 (#2 – 3% of balance is less than $10)

Example 4: $2345.00 (#3 – balance is higher than credit limit)Solution: 0.03 x 2345 = $70.35 $71.00

$2345 - $2000 = $345 (over limit amount)$71.00 + 345.00 = $416.00

Example 5: $3005.00 (#3 – balance is higher than credit limit)Solution: 0.03 x 3005 = $90.15 $91.00

$3005.00 - $2000 = $1005.00$91.00 + $1005 = $1096.00

Practice: The credit limit is $9000.00 on a new balance of:1. $8.502. $40.003. $550.004. $920.005. $762.95

The credit limit is $500.00 on a new balance of:6. $450.217. $562.008. $895.009. $9.9510. $49.72




If the daily interest is 0.05067% (0.0005067), calculate the amount Jill will be charged if she has the given amount overdue for the given number of days.21. $306.52 for 27 days22. $54.97 for 101 days23. $2 952.00 for 11 days24. $1 875.26 for 127 days25. $972.00 for 6 days

26. Suppose that Dan had made purchases as shown in the statement below. If the payment due date was June 2, but his payment was not received until June 24, find out the total amount of interest that would be charged. Daily interest rate is 0.05067% (0.0005067). (Include purchase date and payment date when counting number of days).

Transaction DateM/D

Description Amount $ Numberof Days of

Interest

Interest Charged

05/03 Broadway Café

$17.45

05/11 Safeway $31.2605/11 Blockbuster $9.7205/13 Boston Pizza $12.7605/17 Canadian Tire $45.8605/17 Future Shop $432.7505/21 Boom Town $236.7105/22 Extra Foods $27.4505/24 Shell $34.96

Total = Answers:1. $8.502. $10.003. $17.004. $28.005. $23.006. $14.007. $79.008. $422.009. $9.9510. $10.0011. $10.0012. $23.0013. $10.0014. $174.00


15. $39.0016. $10.0017. $10.0018. $74.0019. $14.0020. $6.0021. $4.1922. $2.8123. $16.4524. $120.6725. $2.96

26. Transaction

DateM/D

Description Amount $ Numberof Days of

Interest

Interest Charged

05/03 Broadway Café

$17.45 53 $0.47

05/11 Safeway $31.26 45 $0.7105/11 Blockbuster $9.72 45 $0.2205/13 Boston Pizza $12.76 43 $0.2805/17 Canadian Tire $45.86 39 $0.9105/17 Future Shop $432.75 39 $8.5505/21 Boom Town $236.71 35 $4.2005/22 Extra Foods $27.45 34 $0.4705/24 Shell $34.96 32 $0.57

Total = $16.38


Appendix A.14 Credit Card Comparison


Find information about five different credit cards by asking parents, family members, friends, etc. You can use the same card more than once if it is available from more than one institution (e.g. GM Visa, Scotia Bank Visa). You can also include retail cards (e.g. Sears, Target, Shell, etc.). You may get assistance on-line.

Card Name Annual Fee Rate of interest

%

Credit Limit Benefits (Air miles, discounts, etc.)

1.

2.

3.

4.

5.

Questions: In your opinion, which would be the best card to use? Why? In your opinion, which would be the worst card to use? Why?


Appendix A.15 Exploring Credit Card Use

Debit CardsUsing a debit card is like using cash, you may pay a transaction fee, but as long as you have money in your account you won’t have to pay interest. Things to consider when you have a debit card:

Read the information you received at the time your debit card is issued, so you know the service charges related to the use, the importance of your PIN number and the potential liability for losses due to unauthorized transactions, what to do if it is lost or stolen, and how to resolve complaints

In many cases your financial institution may not send you a detailed report of your purchases. This can make record keeping confusing and difficult. The result: it's harder to keep on top of things. Your record keeping needs to be very accurate.

Ask your financial institution to send you a detailed monthly report of your purchases. See if you can receive it at a student rate or at the lowest possible cost. Your debit card might be attached to a line of credit, which makes it very easy to overspend — and costly too.

If something goes wrong — say, someone gets your card and personal identification number (PIN), and makes a fraudulent purchase or withdrawal — you'll probably lose the money, with no recourse. If your debit card is attached to a line of credit, the thief could clean out your line of credit too. If you have divulged your PIN number your insurance is devoid and you are responsible for the losses.

If you have a debit card, keep your PIN and card in separate places To complete an ATM transaction form a screen with your hand or body to prevent

anyone from seeing you enter your PIN. *when you use a private automatic teller machine – you will pay the ATM fee (e.g. $1.75) and your bank‘s service charge.

Credit Cards Generally, credit cards allow you to make purchases, up to a specific credit limit, for which you will be billed at a later date. (Exception is cash advances they are charged interest from the date of the transaction.)They allow you to transfer your balance from one billing cycle to another. Nevertheless, you must pay a minimum amount every month, and unpaid balances are subject to interest charges, based on an annual percentage rate or APR.

Your responsibilities of owning a credit card:Borrow only what you can _________.Read and understand the credit contract.Pay debts _____________.Notify creditors if you cannot meet __________.Report lost or _________ card immediately.Never give your card number over the phone or over the internet unless you are certain of the identity or security of the site.


Never leave you cards unattended work, car,….Protect your __________________________.Always check your card when returned after a purchase.Sign the back as soon as you get it. Make a list of your cards and their ____________.Always ______________ your monthly statement.

When shopping for a credit card, compare items such as: annual interest rates, grace period, annual fees, method of finance charge, transaction fees, credit limit, how widely accepted, and services/features.

A credit card statement provides the following information: 1. Statement and due date2. APR and daily interest rate3. New and previous balance4. Total amount of the credit line and available credit line5. Minimum payment6. The amount of time to repay if you only make minimum payments

Resource: Foundations of Mathematics 12 Teacher Resource (2012). p. 88


Comparing Different Credit Cards Jayden saw the new sound system he wanted on sale for $2623.95, including taxes. He had to buy it on credit and had two options:

Use his new bank credit card, which has an interest rate of 14.5%, compounded daily. Because his credit card is new, he has no outstanding balance from the previous month. It has an annual fee of $50, which is added to the balance at the beginning of the year.


Apply for the store credit, which offers an immediate cash rebate of $100 on the price but has an interest rate of 19.3%, compounded daily.

As with most credit cards, Jayden would not pay any interest if he paid off the balance before the due date on his first statement. However, Jayden cannot afford to do this. Both cards require a minimum monthly payment of 2.1% on the outstanding balance, but Jayden is confident that he can make regular payments of $110.

Will a regular monthly payment of $110 enough to cover the minimum amount required?

Present Value Present Value Present Value

Future Value Future Value Future Value

Payment Payment Payment

Interest/Yr in %

Interest/Yr in %

Interest/Yr in %

Periods Periods Periods

Periods/Yr Periods/Yr Periods/Yr

Compounds/Yr Compounds/Yr Compounds/Yr

Interest Paid Interest Paid Interest Paid

Total Cost Total Cost Total Cost

Cost of Borrowing on credit card __________ Cost of Borrowing paying minimum on credit card _____________

Cost of Borrowing on store card ___________


Appendix A.16 Comparing the Cost of a Loan

Resource: Saskatchewan Learning Mathematics 21. (2007-2013)

Choose two banks to complete the following activity:

Bank 1: ______________________________________Bank 2: ______________________________________

1. Amount: Your teacher will assign the amount to use as your borrowing amount. _________________

2. Purpose: Loan payments are scheduled at various rates depending on the purpose of the loan. Your teacher will assign one of the following loan types:

Car loan Mortgage loan Student loan RRSP loan Personal loan

3. Interest Rate: The bank will have different rates throughout the year. The interest rate can change daily. Contact the two banks and find the current interest rate for your loan types. You may wish to find this information on the internet, by a personal contact with the bank or advertised rates.

Bank 1 Interest Rate: _________________________Bank 2 Interest Rate: _________________________

4. Time: The amount of your loan can vary depending on how quickly you are able to pay your loan off. Use both the maximum amount of time you can borrow the money and the minimum amount of time you can borrow the money. You will need to contact the bank regarding this.

a) Maximum Time Calculate the monthly payment: ________________________ Calculate the total payment: ___________________________

b) Minimum Time Calculate the monthly payment: ________________________ Calculate the total payment: ___________________________

5. What bank and loan payment was the best for you? Explain in detail.


Appendix A.17 Purchasing a New Vehicle

Instruction: Remember that a car is not an investment. Quite the contrary — it loses value over time. The instant you leave the dealership with your new car, it loses 10% of its value. During the first year, it will depreciate by approximately 30%!

Here are some justifications for used cars. Thanks to regulations and standards concerning safety and environment, among others, used cars are now more trustworthy than they once were. Some are still protected by the guarantee of the manufacturer.

With technology, you can easily retrace a car's history to make sure that you are the lawful owner. Many dealerships offer lower financing rates for used cars. Negotiations are often done in a more friendly and less stressful manner when you buy from an individual. You must, however take extra precautions when dealing with an individual.

1. Verify that you are dealing with the true owner.2. Have the vehicle thoroughly inspected by a certified and independent garage.

No matter whom you buy a vehicle from, always conduct a road test and make sure that you are very comfortable with your choice. It is your money and it will be your responsibility. Get an opinion from someone who knows about cars. Don't let yourself be pressured and don't make forced decisions.


Appendix B: Home

Appendix B.1 What Do You Already Know About Measurement?

Brainstorm: To review units of measurement from Math 11, pose the question “What do you already know about measurement?” and brainstorm with students the things they know or recall about measuring.

Discuss: You may want to use the following probing questions to generate discussion: What’s bigger: a metre or a yard? What’s bigger: a centimetre or an inch? What’s bigger: a kilometre or a mile? How far is Regina from Saskatoon? (People often answer in units of time not

distance. Why do we do this? Is this done in other places, countries?) What measuring tool do you use to measure area? What item is about 1 foot long? (Leading students to referents) How tall is a flagpole or a tall structure? How can you get the measurement? How many cm in a foot?

Practice: Measurement Worksheets http://www.math-aids.com/Measurement/


http://www.math-aids.com/Measurement/

Appendix B.2 Enlargements, Reductions, and Scale Factor

Resource: MathLinks 9 (2009). pp. 129 – 131, 138

Materials: centimetre grid paper, tracing paper, ruler

Introduction: Many occupations require people to design projects using drawings or models. For example, architects create plans for homes. These plans are called blueprints. Architects work with ratios and proportions to produce floor plans that represent accurate dimensions of the various areas of a home. The floor plan helps people judge if the proposed design is suitable for their lifestyle.

Practice and Questions: Designers. MathLinks 9 (2009). pp. 129

Discuss: Use the following probing questions to generate discussion. Why do you think accuracy is important in developing a floor plan? Why is it important to maintain the same proportions for the dimensions of an

actual object and its image? What are other examples in which ratios are used to compare objects in daily life?

Investigate: 1. Find an illustration (e.g. cartoon character). Brainstorm with a classmate how you

might enlarge the illustration. What different strategies can you develop?2. Try out two of your strategies and draw an image that is twice as large as the

illustration. What will be the ratio of the lengths of the sides of the enlargement to the original?

Discuss: Use the following probing questions to generate discussion. Which strategy for making an enlargement do you prefer? What method might you use to check that the enlarged image is twice as large as

the original? How are the enlargement and the original the same? How are the enlargement and the original different?

Activity: Create a scale drawing of your classroom. Measure the dimensions of the classroom and items that can be seen in a top view, including desks, tables, cupboards, and shelves. Choose a scale factor and draw the scale drawing on grid paper. What changes would you make to the layout of your classroom? Where would you place desks or tables? Draw a scale drawing of your new classroom layout.

Practice: Enlargements and Reductions. MathLinks 9 (2009). pp. 136 – 138.


Appendix B.3 Scale Factor, Scale Drawings, and Scale Models

Resource: MathLinks 9 (2009). pp. 141

Materials: Canadian quarter, caliper

Investigate: What measurements would help you compare the illustration of the quarter to an

actual quarter? Take the measurements. (Diameter of actual Canadian quarter: 23.88 mm).

What is the scale factor?

Discuss: Use the following questions to generate discussion: How do you determine the actual length of an object using a scale drawing? How do you use scale factor to determine the actual length?

Practice: Scale Diagrams. MathLinks 9 (2009). pp. 142 – 145.

Activity: Shadow, Shadow. MathLinks 9 (2009). p. 164

Problem: Your family is moving to a new house with a living room that is 17 ft. by 15 ft. Cut out and label simple geometric shapes, drawn to scale, to represent every piece of furniture in your present living room. Place all of your cut-outs on a scale drawing of the new living room to find out if the furniture will fit appropriately (e.g., allowing adequate space to move around).


Appendix B.4 Cars, Critters, and Barbie

Resource: Authentic Activities for Connecting Mathematics to the Real World: Project 4 Cars, Critters, and Barbie http://www.wfu.edu/~mccoy/mprojects.pdf

Watch: The Future Channel: Designing Toy Cars http://thefutureschannel.com/videogallery/designing-toy-cars/

Investigate Part 1: Known Scale ToysMeasure four known-scale toys and record scale and toy measurements. Calculate the actual measurements using a proportion.

toy scaleactual scale

= toy measureactual measure

Investigate Part 2: UnKnown Scale ToysMeasure four unknown-scale toys and record toy measurements. Find actual measures in reference book. Calculate the scale using a proportion.

1actual scale

= toy measureactual measure

Investigate Part 3: BarbieMeasure the Barbie doll and determine her real life measures (select a height).

Barbie heightreal-life height

= Barbie measurereal-life measure


http://thefutureschannel.com/videogallery/designing-toy-cars/

http://www.wfu.edu/~mccoy/mprojects.pdf

Doll Measurements Real-life MeasurementsHeightWidth at ShouldersInseamLength of HeadLength of ArmWidth of ThighWidth of StomachLength of FootOtherOtherOther

Draw your life-sized Barbie on large paper and colour to complete her picture.

Discuss: Generate a discussion about the life-sized Barbie and her proportions. Discuss her influence on young girls.

Extension: Following the discussion about Barbie have students write about their mathematical and social findings.


Appendix B.5 Teacher Resource for Cars, Critters, and Barbie

Resource: Authentic Activities for Connecting Mathematics to the Real World: Project 4 Cars, Critters, and Barbie http://www.wfu.edu/~mccoy/mprojects.pdf

Materials:

Known-Scale Toys that work well for this activity are model cars of various sizes. The scale is usually given on the box (for example, 1:24). A variety of different sizes provide an interesting context. Students may also bring their own models from home, provided that they still have the box or information giving the scale. Students measure the cars and use the given scale to estimate the size of the real car. Once this part of the project is completed, students may go to websites of car manufacturers to find actual sizes and check their work.

Unknown-Scale Toys may be any type of animal models. Small zoo or farm animals are inexpensive and appropriate for this activity. These typically do not include the scale. So this time students work in reverse. They look up the animal in a reference book and obtain its average length, width, or height. Then they measure the toy, and calculate the scale.

Barbie: The model Barbie is sketched on large butcher-paper, and students may use colored markers to complete her picture. This is a valuable lesson for many reasons, including the fact that the life-size Barbie is somewhat grotesque. The proportions of the doll do not translate well to real life size, and this is apparent to students.


http://www.wfu.edu/~mccoy/mprojects.pdf

Appendix B.6 Gingerbread House

Resource: Stories from the Classroom. Gingerbread math: A sticky investigation http://www.tc2.ca/pdf/T3_pdfs/GingerbreadMath.pdf

Materials: Gingerbread house, rulers

Key Questions: Could we live in our gingerbread houses and ride in the sleigh that came in our

kit? How big would the reindeer be if we could build life size replicas in their image? What is their scale and how would we have to change their measurements in

order to make our Christmas wish a reality?

Investigate: Give students a gingerbread house kit to assemble. Have them determine the measurements of height, length and width and any other relevant dimensions that will assist them in answering the key questions.

Have them redraw their floor plans so that they can use them as blueprints for an actual house. They should complete a net (a 2D pattern of a 3D figure) of their original house and a net of their modified house including the four walls, roof, door, windows, and one other feature of their choice such as a chimney, sleigh, reindeer or Santa.

Additional Questions:Other examples of questions that arose from students: Stories from the

How big Santa be based on the gummy figure in the kit? How big would the doorknob be based on the size of the house?


http://www.tc2.ca/pdf/T3_pdfs/GingerbreadMath.pdf

Appendix B.7 Glowing Rectangles

Resources: Yummy Math: Glowing Rectangles. http://www.yummymath.com/wp-content/uploads/glowing-rectangles.pdfChoosing a Television to Suit Your Room. MathLinks 9 (2009). p. 287

Materials: measuring tape, grid paper

Introduction: We spend a lot of time sitting in front of televisions, computers, and other electronic devices with screens. Have you ever noticed that not all screens are the same rectangular shape? That is to say, they are not proportional or similar. The height to width ratio is not the same when you start comparing analog tube televisions, HD televisions, and movie theatre screens. If you have been to an electronics store recently, you may have noticed many HD televisions showcased along a wall. HD screens are all similar to teach other, because the height to width ratio is always the same. The same can be said for analog tube televisions and for most movie theatre screens and movie formats.

Instructions: The typical HD screen has a width to height ratio of 16 to 9.

1. Find the missing dimension for each of the HD screens. Assume that all dimensions are in inches.

24

48


126

http://www.yummymath.com/wp-content/uploads/glowing-rectangles.pdf

2. Give a length/width dimension that is not similar to this screen type.

3. An HDTV screen is 40 inches long. What is the height of the screen?

4. Sketch your own HD screen below. Make sure to label the side lengths. The screen should be similar to the other HD screens.

5. Here is one type of dimension for a movie theatre screen: Movies and movie theatre screens are often made in the format 2.35 to 1 (widescreen format, width to height). Find the missing dimensions. Assume that the dimensions are in feet.

37.6

6. Is the screen below similar to a movie theatre screen? Show mathematical evidence to support your answer.

7. In the past, there were many drive-in theatres. The giant screen was about 150 feet wide. How tall was the screen?


12

3

7

8. Regular, old, analog tube television is a 4 to 3 ratio (width to height). Find the missing dimensions. Assume all dimensions are in inches.

9. Give different lengths and widths for screens that are similar to the tube screen. You might use a ratio table to organize your thinking:

Length

Width

10. At home, measure your own glowing rectangles (e.g. computers, phones, portable video game systems, digital cameras, I Pod, I Pad, I Phone or anything else with a screen). Find the dimensions of the screens in millimeters. Use the table below to record your data:

Product Length Width Simplified Ratio of L:W

Are any of your screens similar to the widescreen, HD, or analog tube screen? Explain.

11. Sort the following glowing rectangles. Label each as either HD, tube, wide screen, or none of the above.


32

15

A B

C

D

E F

G H


Project: Choose a television that best suits your needs and considers your room size and the location for the television. Does a standard or high-definition television (HDTV) make the most sense for your room? How large of a screen should you get?

The following table gives you the best viewing distance for the screen size for two types of TVs.

Screen Size (cm) Viewing Distance (cm)Standard TV HDTV

68.8 205.7 172.781.3 243.8 203.294.0 281.9 233.7

1. Given this information, what size of television would be best? Make a sketch of your room, including where you plan to place the TV and the best place for a person to view it from.

2. If the television is 320 cm away from your chair/couch, how large of a standard TV would be best?

3. How will your answer change if you have a HDTV?

What type and size of TV would be best for your room? Justify your answer.


Appendix B.8 Geometric Shapes

Materials: Volumetric shapes or Geomodel folding shapes

Brainstorm: Pose the question “What is a geometric shape?” and brainstorm with students the things they know or recall.

Discuss: You may want to use the following probing questions to generate discussion. What is the name of each geometric shape shown?

Activity: Have students group the geometric shapes into categories. Discuss the categories the students chose and have them justify why they chose those categories.


Appendix B.9 What is Surface Area?

Brainstorm: Pose the question “What do you know about surface area?” and brainstorm with students the things they know or recall.

Activity: Provide students with a variety of different sized boxes and wrapping paper. Ask them how wrapping a gift relates to surface area.

Discuss: You may want to use the following probing questions to generate discussion. What is the difference between area and surface area? What do you need to know to measure surface area? How can you calculate surface area? How many surfaces does an object (e.g. cereal box) have? How many surfaces are there in a cylinder?

Investigate: Provide students with net diagrams and ask them to find the surface area of the 3D shape. Have students cut them out and build them or leave them as 2D.

Suggestions: For those students who need more guidance, ask them to recall from Math 11 how they found the area of an object. Ask them to consider how many surfaces them now have on the 3D object and how they could find the area of each object separately and then the 3D object as a whole. They may discover the “shortcut” by multiplying congruent surfaces.

Additional Questions: What is the surface area? Do you still have the same number of shapes? What are the units? Is there a more efficient way to find the surface area?

Practice: MathLinks 9 (2009). pp. 29 – 30. MathWorks 10 (2010). pp. 121-122.


Appendix B.10 How Many Sheets of Drywall Are Needed?

Resource: Human Resources and Skills Development Canada. Trades Math Workbook. http://www.hrsdc.gc.ca/eng/jobs/les/tools/support/trades_math_workbook.shtml#form

Journeypersons working on a construction site follow specifications from a set of drawings or prints that show different views of the finished building project. Journeypersons in all trades scan the drawings for the detailed information they need.

Investigate: Look at the drawings for a residence to estimate the number of drywall sheets needed for the walls of the ensuite bathroom.Drywall sheets: 4 ft. × 8 ft.Width of pocket door: 3 ft.


http://www.hrsdc.gc.ca/eng/jobs/les/tools/support/trades_math_workbook.shtml#form

Appendix B.11 Heat and Frost Insulators

Resource: Human Resources and Skills Development Canada. Trades Math Workbook. http://www.hrsdc.gc.ca/eng/jobs/les/tools/support/trades_math_workbook.shtml#form

Materials: paper towel rolls, toilet paper rolls or Pringles can, paper to imitate insulation.

Investigate: Heat and frost insulators cover pipes to keep substances hot or cold. How many square meters of material are needed to insulate a pipe that is 6 m long and has a diameter of 2 m?

Suggestions: Have students think of the cylinder as being laid out flat so that the circumference becomes the width measurement.

Use the formula:


http://www.hrsdc.gc.ca/eng/jobs/les/tools/support/trades_math_workbook.shtml#form

Appendix B.12 What is Volume?

Materials: 3D objects

Terminology: faces, edges, vertices

Brainstorm: Pose the question “What do you know about volume?” and brainstorm with students the things they know or recall.

Discuss: You may want to use the following probing questions to generate discussion. What is the difference between surface area and volume? What do you need to know to measure volume? How can you calculate volume? If two boxes have the same volume, must they also have the same surface area? What is the difference between volume and capacity? (e.g. The capacity of a fuel

tank on a vehicle refers to the volume the tank will hold inside. The volume of the fuel in the tank refers to the space the fuel takes up).

Investigate: Provide students with 3D objects and ask them the following questions: What is the base shape of the 3D object? How do you find the area? Are there are any unit conversions needed? What are the units of area? What is the height (or length) of the 3D object?

Suggestions: To bridge surface area to volume relate surface area by height to volume. Explain that volume is surface area with a height. Use stacks of paper, poker chips or pennies to show that a nearly flat object can have volume when stacked.

Volume = Surface area of the base × height

Watch: Surface Area and Volume Video http://www.learnalberta.ca/content/mejhm/index.html?l=0&ID1=AB.MATH.JR.SHAP&ID2=AB.MATH.JR.SHAP.SURF&lesson=html/video_interactives/areavolume/areaVolumeSmall.html

Interactive: Surface Area and Volume Interactive http://www.learnalberta.ca/content/mejhm/index.html?l=0&ID1=AB.MATH.JR.SHAP&ID2=AB.MATH.JR.SHAP.SURF&lesson=html/video_interactives/areavolume/areaVolumeInteractive.html

Activities: Create a cube and calculate the surface area and the volume of the entire

geometric solid.


http://www.learnalberta.ca/content/mejhm/index.html?l=0&ID1=AB.MATH.JR.SHAP&ID2=AB.MATH.JR.SHAP.SURF&lesson=html/video_interactives/areavolume/areaVolumeInteractive.html



http://www.learnalberta.ca/content/mejhm/index.html?l=0&ID1=AB.MATH.JR.SHAP&ID2=AB.MATH.JR.SHAP.SURF&lesson=html/video_interactives/areavolume/areaVolumeSmall.html



List all the possible ways that 24 one-inch squares of candy might be packed in a box. Be sure to include the surface area and volume of the box needed for packing.

Draw a diagram that explains how to calculate surface area and volume. Use a Venn diagram to compare surface area and volume. Write 2 word problems that involve surface area and two that involve volume. Be

creative! Use manipulatives to explain surface area and volume to your teacher. Create a song or rap to explain how to find surface area or volume. Write a fairy tale about Queen Area and King Volume. Create a game and game board that involves surface area and/or volume. Write a poem that illustrates the differences in surface area and volume. It must

have at least eight lines.(Math Contract – Area and Volume. http://view.officeapps.live.com/op/view.aspx?src=http%3A%2F%2Fdaretodifferentiate.wikispaces.com%2Ffile%2Fview%2FHandout%2B08.doc)


http://view.officeapps.live.com/op/view.aspx?src=http%3A%2F%2Fdaretodifferentiate.wikispaces.com%2Ffile%2Fview%2FHandout%2B08.doc

http://view.officeapps.live.com/op/view.aspx?src=http%3A%2F%2Fdaretodifferentiate.wikispaces.com%2Ffile%2Fview%2FHandout%2B08.doc

Appendix B.13 How is Volume Used?

Resource: Human Resources and Skills Development Canada. Trades Math Workbook. http://www.hrsdc.gc.ca/eng/jobs/les/tools/support/trades_math_workbook.shtml#cn-tphp

Problems:1. A construction craft worker needs to know how much material is in the cone-

shaped pile shown below. Calculate the approximate volume of the pile in cubic yards. Use this formula to calculate the radius of a pile of material:

r = ¾ × height 27 ft.3 = 1 yd.3

2. A landscape horticulturalist needs to order enough sand to create a border 152 mm deep around a square surface, as shown below. How many cubic meters of sand are needed?

3. Compare the volumes of concrete needed to build three steps that are 4 ft. wide and that have the cross-sections shown below. Explain your assumptions and reasoning.


http://www.hrsdc.gc.ca/eng/jobs/les/tools/support/trades_math_workbook.shtml#cn-tphp

4. Dave has a very small yard but needs a rain barrel against his house. What shape of a rain barrel would maximize volume and minimize the area of the base? Discuss the different three dimensional shapes and the design of the rain barrels. For example a cylinder is the area of a circle through a height, a rectangular prism is the area of a rectangle through a height, triangular prism is the area of a triangle through a height, a half-cylinder (flat side can go along the wall) is the area of half a circle through a height.

Extension: Research how to choose a furnace or air conditioner based on the volume of the house (ABE Level Three: Mathematics Curriculum Guide (2006). p. 106).


Appendix B.14 Landscape Design

Resource: Landscape Design. MathLinks 9 (2009). p. 253, 281

Introduction: Gardeners and landscapers are often required to calculate areas when designing a landscape for a backyard, commercial property, or park. When determining how much soil, gravel, mulch, and seed they need for a project, landscape designers also calculate volumes. Here is a landscape design created for a property.

Practice and Questions: Landscape Design. MathLinks 9 (2009). p. 253

Project: You have been hired to create a landscape design for a park. The park is rectangular and covers an area of 500 000 m2. The park includes the following features:

A play area covered with bark mulch A sand area for playing beach volleyball A wading pool

The features in your design include the following shapes: A circular area A rectangular area A parallelogram-shaped area with the base three times the height

Include the following in your design: A scale drawing showing the layout of each of the required features A list showing the area of each feature and the volume of each material (mulch,

sand, and water) required to complete the park.

Extension: Research the cost of the items in your home community and determine a budget for your new park.


Appendix B.15 Angles Formed by Transversals

Resource: Grade 6-9 Math Workshop: Symmetry, Lines, and Angles, pp.13 – 14.

Materials: Diagram #1 and #2 handouts Angle pairs and counter example cards Enlarged alternate diagram MIRA Compass Straight edge

Introduction: When a transversal crosses lines that are not parallel, corresponding angles are formed. When a transversal crosses lines that are parallel, the corresponding angles are congruent.

Terminology: transversal, parallel, perpendicular, corresponding angles

Instructions: Have students work in small groups or pairs. 1. Provide each group with a copy of the diagram with parallel lines and one

transversal with numbered angles as well as a beige card with one angle set on it and a non-example on the back of the card.

2. Have students identify the characteristics defining the pairs of angles that are on their card. Next, the students are to consider the pair of angles that is given as a counter-example on the back of the card and to see what characteristic(s) this particular pair of angles does not have. If they cannot see the contradiction, they must go back and reconsider their defined characteristics so that there is a contradiction.

3. Once all of the groups feel they understand the type of angle they have been given examples of, put up the second diagram that has two non-parallel transversals. Repeat the process above with the pink cards. Have the class discuss what lines, if any are parallel, and why; and which lines are transversals and why. Next, ask the students to identify all pairs of angles in this new diagram that are the same type as what they have been looking at.

4. Put up the third diagram that is labeled using letters. Have the class discuss what lines, if any are parallel, and why; and which lines are transversals and why. How many transversals and how many sets of parallel lines are there? Next, ask the students to identify all pairs of angles in the new diagram that have the same characteristics as those they had in the first two diagrams.

5. Following the completion of each group creating their list, select a pair of angles and ask the students which groups had that type of angle. Have those groups explain how they know (give the characteristics). It may be beneficial to also post the original diagram for the students to refer to. As a class, write out the characteristics of the pairs of angles and give a few minutes for the groups who had worked with other types of angles to identify all pairs of angles on the new


diagram that have the same characteristics. Finally, give the students the name for the type of angles (vertically opposite, adjacent, etc.). Allow the students some time to discuss how they would remember the name and/or recognize the angles in other situations, such as non- parallel lines. Repeat the process with the other types of angles.

Extensions: Students could be asked to focus on vertically opposite angles. Can they draw

them in different contexts of the home? How are they related to each other? The students could be asked to measure, cut out, paper fold, and use the MIRA to explore this relationship.

Students could be asked to create a set of parallel lines using paper folding, the MIRA, or compass and straightedge and then to identify the different pairs of angles. Using the compass, paper folding, and/or the MIRA, the students could then be asked to look for relationships. These relationships would then be discussed within small groups, and each small group could be assigned one type of angle to report about their findings. An example would be to have the students create paper dolls/paper chains and describe/highlight different lines that they can see in their resulting creations – parallel lines, perpendicular lines, transversals. The paper chain/doll designs are made by repetitively folding paper in half, then cutting along the edge(s) that have the open side(s) on them. Legal paper works well.

Students could be asked to construct non-parallel lines with a transversal. Have them write a journal entry about what they are able to determine about the different types of angles in this situation. What is the relationship between the angles if the lines are not parallel? What is the relationship between the lines if the angles are not congruent?

Students could be asked to identify examples of each type of angle from within their environment. Using a map or pictures, have the students highlight with different coloured markers, lines which are parallel, perpendicular, or neither. Also ask the students to highlight lines that are transversals. This activity could include physical objects, pictures in the media, photos they have taken, or drawings they have created. Students could use markers to highlight pairs of angles and to write a description about the type of angles, the relationship between the different lines, etc.


Appendix B.16 Diagram 1 and Beige Cards: Parallel Lines


1413

109

65

ℓ1

21

ℓ2

Angle Pair Set #1

<1 and <6<2 and <5<9 and <14

<10 and <13

Angle Pair Set #2

<1 and <2<1 and <5<2 and <6<5 and <6<9 and <10

<10 and <14<9 and <13

<13 and <14

Angle Pair Set #3

<5 and <10<6 and <9

Angle Pair Set #4

<1 and <9<2 and <10<5 and <13<6 and <14

Angle Pair Set #5

<1 and <14<2 and <13

Angle Pair #6

<5 and <9<6 and <10


Non-example #1

<1 and <14

Non-example #2

<1 and <6

Non-example #3

<5 and <14

Non-example #4

<1 and <10

Non-example #5

<2 and >14

Non-example #6

<2 and <13


Appendix B.17 Diagram 2 and Pink Cards: Non-Parallel Lines


16151413

1211109

8765

ℓ1

4321

ℓ2

ℓ4

ℓ3

Angle Pair Set #1

<1 and <6<2 and <5<3 and <8<4 and <7<9 and <14

<10 and <13<11 and <16<12 and <15

Angle Pair Set #2

<1 and <2 <9 and <10<1 and <5 <9 and <13<2 and <6 <10 and <14<5 and <6 <13 and <14<3 and <4 <11 and <12<3 and <7 <11 and <15<4 and <8 <12 and <16<7 and <8 <15 and <16

Angle Pair Set #3

<5 and <10<6 and <9<7 and <12<8 and < 11

Angle Pair Set #4

<1 and <9<2 and <10<3 and <11<4 and <12<5 and <13<6 and <14<7 and <15<8 and <16

Angle Pair Set #5

<1 and <14<2 and <13<3 and <16<4 and <15

Angle Pair #6

< 5 and <9<6 and <10<7 and <11<8 and <12


Non-example #1

<1 and <14

Non-example #2

<3 and <8

Non-example #3

< 6 and <11

Non-example #4

<1 and <10

Non-example #5

<2 and <14

Non-example #6

<5 and <11


Appendix B.18 Diagram 3 (l1 // l2 )


Appendix B.19 Angles in Construction

Application: In construction of homes and buildings, angles are created when two lines meet. Pick two of the following items from within your environment:

Porch Veranda Railings on stairs Trusses Fence

Take a photo of the item and highlight with different coloured markers, lines which are parallel, perpendicular, or neither. Also ask the students to highlight lines that are transversals.

Additional Questions: How do you know if the lines are parallel? Justify your answer. How do you know if the lines are perpendicular? Justify your answer. What objects represent transversals?


Appendix B.20 Triangle Properties

Materials: Protractor, straight edge

Brainstorm: To review what students know about triangles, pose the question “What do you know about the triangle below?”

and brainstorm with students the things they know or recall about triangles. Students’ knowledge could include: number of sides and angles, the names of the sides of a right triangle, triangle type (isosceles, scalene, right, and equilateral), measures of angles inside a triangle, etc.

Investigate:1. Have students draw triangles using a straight edge and measure and label each

angle in the triangle. What conclusion can they make about the sum of the measures of the angles in a triangle?

2. Have students draw a right triangle and label the right angle at 90°. Have students label the hypotenuse.

3. Have students use a protractor and straight edge to draw scalene, isosceles and equilateral triangles. Show students how to indicate which angles and sides are congruent.

4. Ask students to draw an equiangular triangle. What conclusion can you make about this triangle in comparison to the triangles previously drawn?


Appendix B.21 Building Bridges Teacher Resource

Resource: NSW Department of Education and Training Teaching Trigonometry: Building Bridges Lesson http://www.curriculumsupport.education.nsw.gov.au/secondary/mathematics/years7_10/teaching/trig.htm

Introduction: This activity encourages students to discover the importance of triangles in real-life constructions. Students build bridges, using a limited supply of resources, and test the bridges ability to hold weight.

Materials: 6 drinking straws (preferably the straight plastic variety, not the bendy type) 2 sticky labels 2 math textbooks a ruler per group a pair of scissors per group one set of small graduated masses (1g – 200g)

Visualize and Discuss: Using photographs of appropriate bridges in your area or the PowerPoint Building Bridges (http://www.curriculumsupport.education.nsw.gov.au/secondary/mathematics/years7_10/teaching/trig.htm), ask students to think of bridges they have crossed. Perhaps they have walked across a suspension bridge or have been fortunate enough to cross some of the great bridges of the world. Ask students to view the bridge photographs then visualize the bridges they know. Discuss the various features of these bridges and the following questions.

Questions: What do the bridges look like? What features do the bridges have in common? What two dimensional shapes have occurred repeatedly in these bridge

constructions?

Task: In groups, have students complete the Building Bridges Task (Appendix B.22). Pose the question: As you have limited resources to build the bridge, what strategies might you use to ensure you do not waste materials? Bridges are load tested and results recorded. The group with the best load bearing bridge is presented with merit certificates.

Discussion: What have you learnt while building this bridge? Where else do you see triangles?


http://www.curriculumsupport.education.nsw.gov.au/secondary/mathematics/years7_10/teaching/trig.htm




Extension: Ask students to bring in as many pictures of triangles as they can over the next few lessons and make a collage on the classroom wall.


Appendix B.22 Building Bridges Student Task

Materials: 6 drinking straws (preferably the straight plastic variety, not the bendy type), 2 sticky address labels, 2 maths textbooks, a ruler and a pair of scissors

Task:Place the two textbooks (supports for the bridge) so that the distance between them is further than the length of one straw. These books represent the banks of a fast-flowing river, infested with leeches and people-eating crocodiles.

Your group must build a bridge to carry people from one side to the other. You have 30 minutes to construct this bridge, using any of the given materials except the scissors and the ruler which may not be part of the bridge.

At the end of this time your bridge will be tested for strength and the results recorded. The winning group will receive merit certificate.


Appendix B.23 What is the Problem? Teacher Resource

Resource: NSW Department of Education and Training Teaching Trigonometry: What is the Problem? http://www.curriculumsupport.education.nsw.gov.au/secondary/mathematics/years7_10/teaching/trig.htm

Introduction: This activity assesses a starting point for learning trigonometry. It encourages divergent thinking and attempts to address the reasons why trigonometry was developed. Students contribute their own solutions to problems before the introduction of scale drawings or trigonometric ratios.

Watch: A video or show images of abseiling down a rock face. An example is Abseiling with Melbourne Adventure Hub http://www.youtube.com/watch?v=29u1ER5Z0Z8.

Discuss and Share: Pose the problem to the class (see What is the problem? Student Task (Appendix B.24). In groups of 3 or 4, students have 10 minutes to discuss the problem. Each group shares their ideas with the class. All ideas are recorded.

Questions: What information is available? How could you measure the height? What units of measure could you use? How accurate would this method be? What problems may arise using the method you have described? What is another way of measuring the height?

Task: Each group selects three or four ideas, from the board, to test outside in the school grounds e.g. on the tallest building, a flag pole, tree or appropriate structure. Allow 15 minutes maximum and students are not allowed to use a measuring instrument or tool.

Discuss: Whole class discussion on the accuracy and limitations of the different ways of calculating the height. You may want to use the following probing questions to generate discussion.

What is the accuracy and limitations of the different methods? How do you know?


http://www.youtube.com/watch?v=29u1ER5Z0Z8



Appendix B.24 What is the Problem? Student Task

You are in a group which is to abseil down a rock face tomorrow. Your task is to estimate the height of the face. You have no measuring instruments. You need to determine the height to know how much rope to take. You cannot take excess rope as you are at the start of a four day exercise and you must not have extra weight with you. Tomorrow morning you will walk the track which will take you to the top of the rock face. Brainstorm as many ways as possible to estimate the height of the rock face. Record all ideas, even if they appear absurd. Each group will share their ideas with the class.


Appendix B.25 Same Shape Triangles Teacher Resource

Resource: NSW Department of Education and Training Teaching Trigonometry: Same Shape Triangles http://www.curriculumsupport.education.nsw.gov.au/secondary/mathematics/years7_10/teaching/trig.htm

Introduction: In this activity, students use practical measurement skills and ratio calculations to find a pattern linking the ratio of sides of a triangle with the angles. This lesson is designed to develop the concepts of sine, cosine and tangent ratios of angles.

Materials: Rulers three large charts (enlarge to A3) – one for each ratio (opp/hyp, adj/hyp and

opp/adj) - for a class graph one set of triangles per group. Triangle sheets A-G should be photocopied onto

coloured cardboard. Carefully cut out the triangles and place each set (8 triangles in a set) into plastic bags.

one calculating ratios for similar triangles worksheet per group (Triangle Sheets website: http://www.curriculumsupport.education.nsw.gov.au/secondary/mathematics/years7_10/teaching/trig.htm )

Discuss and Practice: Show the students a large right-angled triangle with one angle marked.

Remind the students about the hypotenuse (from Pythagoras’ theorem) and show them the opposite and adjacent sides in relation to the marked angle. Discuss the meaning of the words opposite and adjacent in this context. Practice labelling right-angled triangles from the board. Explain that the lesson involves investigations of the ratios of pairs of sides of right-angled triangles with angles of different sizes. Discuss the word ratio and what it means in this context. Compare opp/hyp for a very large and a very small angle, as shown in diagram, and have students estimate which one will have the larger ratio.






Questions: What is the hypotenuse of a right-angled triangle? Where do you find it? What is ratio? What happens to the opp/hyp ratio when the angle is large? What happens to the opp/hyp ratio when the angle is small?

Investigate: Divide class into groups of 3 or 4 students. Hand out one Calculating ratios for similar triangles worksheet (Appendix C.21) and a set of triangles (Appendix C.21) to each group. Each student takes two triangles. They measure each side to the nearest millimetre and complete the worksheet for their triangles writing the ratios as a fraction and using a calculator to estimate them to 3 decimal places. Each group completes the worksheet including the mean values for each ratio to 2 decimal places. Members of the group stack their triangles as neatly as possible on top of each other and discuss their findings.

Connect and Discuss: When every group worksheet is completed, one member of each group brings it forward with their group’s stack of triangles and briefly reports their findings. Each group now plots its mean values on the three class graphs. At this stage, do not join the plotted points as the next lesson will add more values to the graph. Class discusses graphs.

Note the fact that triangles which have the same ratios also have the same angles. This is the basis for scale drawings where although the triangles are different sizes, the angles are in the same proportion or ratio. Explain to students that these ratios have special names:

opp/hyp is sine of the angle (sin) adj/hyp is cosine of the angle (cos) opp/adj is tangent of the angle (tan)

These ratios are used in a branch of mathematics called trigonometry or trig for short.

You may want to use the following probing questions to generate discussion. What did your group find when you stacked the triangles on top of one another?

(They should discover that triangles with the same angles have approximately equal ratios).

What information can you observe from each graph? (They should be able to see that the ratio increases as the angle increases for the opp/hyp graph; the ratio


decreases as the angle increases for adj/hyp and the ratio increases as the angle increases for opp/adj).

What occupations use trigonometry in their jobs? (All kinds of engineers, navigator, surveyor, architect, air traffic controller, cartographer, landscape architect, meteorologist, electronics designer, oceanographer, roofing contractor, marine engineer, geologist and sheet metal, heating and air-conditioning engineers).

Where is the word trigonometry derived? (The word trigonometry is derived from two Greek words meaning ‘triangle’ and ‘measurement’).


Appendix B.26 Going the Wrong Way

Resource: Mr. Quenneville’s Website: Unit 2 Trigonometry https://sites.google.com/a/hdsb.ca/mr-quenneville/home/grade-10-applied-math/unit-2-trigonometry

Instructions: There are two problems shown below. For each problem, the answer provided is incorrect. Partner A will identify the errors in the given solutions. Partner B will write a correct solution to the problem.

Partner A Partner BSolve for the missing side labelled x.

Solve for the missing side labelled x.

Solve for the missing side x.

x = 37.74

Solve for the missing side x.




Appendix B.27 Solving Trigonometric Problems

Resources: Math Open Reference: Solving Problems Using Trigonometryhttp://www.mathopenref.com/trigprobslantangle.html

Mr. Quenneville’s Website: Unit 2 Trigonometry https://sites.google.com/a/hdsb.ca/mr-quenneville/home/grade-10-applied-math/unit-2-trigonometry

Skill Building: Provide students with an overview of how to use a calculator in trigonometry

Make sure the calculator is in degree mode To find the value of a trigonometric ratio given an angle, in degrees. e.g. sin 30°

= To find the angle given a trigonometric ratio. e.g. sin θ = 0.7071 Rounding to four decimal places. Why are trigonometric ratios rounded to four

decimal places? Why isn’t one decimal place used?

Problem: A ramp has been built to make a stage wheelchair accessible. The building inspector needs to find the angle of the ramp to see if it meets regulations. He has no instrument for measuring angles. With a tape measure, he sees the stage is 4ft high and the distance along the ramp is 28ft.

Solution:

1. Draw a diagram: Include all the information given and label the measure we are asked to find as x. Draw it as close to scale as you can.

2. Find right triangles: We can assume the side of the stage is vertical and makes a right angle at the floor (point C). So the ramp itself is a right triangle (ABC).

3. Choose a tool: Right Triangle Toolbox




http://www.mathopenref.com/trigprobslantangle.html

Reviewing what we are given and what we need: We are asked to find x, the angle at which the ramp goes up to the stage. We are given the hypotenuse (AB) and the side opposite the angle

Looking at our toolbox, we are looking for a function that involves an angle, it's opposite

side and the hypotenuse. We see that the sin function meets our needs: where O = the side Opposite the angle, H is the Hypotenuse.

4. Solve the equation:

Inserting the values given and the unknown(x): sin (x) = 4

28 Using a calculator, divide 4 by 28: sin (x) = 0.1429 What angle has 0.1429 as it's sine? For this we use the inverse function arcsine.

It tells us what angle has a given sine: x = sin-1 (0.1429) Using a calculator again, we find that sin-1 (0.1429) is 8.22°: x = 8.22°

5. Is it reasonable?: We see from our calculation that the ramp angle is somewhere around 9°. Looking at our diagram we see this looks about right. If you get a very different answer, the most common error is not setting the calculator to work in degrees.

Practice: Solve the application questions. Draw a diagram where necessary. Find angles to the nearest degree and distances to the nearest tenth of a unit.

1. A ladder is leaning against a building and makes an angle of 62 with level ground. If the distance from the foot of the ladder to the building is 4 feet, find, to the nearest foot, how far up the building the ladder will reach.

2. The Dodgers Communication Company must run a telephone line between two poles at opposite ends of a lake as shown below. The length and width of the lake is 75 feet and 30 feet respectively.


?

55

4 ft.

What is the distance between the two poles, to the nearest foot?

3. A ship on the ocean surface detects a sunken ship on the ocean floor at an angle of depression of 50 . The distance between the ship on the surface and the sunken ship on the ocean floor is 200 metres. If the ocean floor is level in this area, how far above the ocean floor, to the nearest metre, is the ship on the surface?

4. Draw and label a diagram of the path of an airplane climbing at an angle of 11 with the ground. Find, to the nearest foot, the ground distance the airplane has traveled when it has attained an altitude of 400 feet.

5. If an engineer wants to design a highway to connect New York City directly to Buffalo, at what angle, x, would she need to build the highway? Find the angle to the nearest degree.

To the nearest mile, how many miles would be saved by travelling directly from New York City to Buffalo rather than by travelling first to Albany and then to Buffalo?

6. In order to safely land, the angle that a plane approaches the runway should be no more than 10. A plane is approaching Pearson airport to land. It is at an altitude of 850 m. It is a horizontal distance of 5 km from the start of the runway. Is it safe for the plane to land?

7. An 8 m long ramp reaches up a vertical height of 1m. What angle does the ramp make with the ground?

8. A tree casts a shadow 42 m long when the sun’s rays are at an angle of 38° to the ground. How tall is the tree?


Application: We use trigonometry to determine inaccessible distances. Have students measure an inaccessible distance (e.g. flagpole, tree, height of a tall building) applying trigonometry and using a clinometer (Constructing a Clinometer Appendix C.24).


Appendix B.28 Constructing a Clinometer

Resource: Mr. Quenneville’s Website: Unit 2 Trigonometry https://sites.google.com/a/hdsb.ca/mr-quenneville/home/grade-10-applied-math/unit-2-trigonometryClinometer http://www.virtualmaths.org/activities/topic_shapes/theod2/resources/clinometer.pdf

Materials: protractor or protractor template, scissors, cardboard, string, paperclip, straw

Introduction: A clinometer is used to find the angle of elevation of an object.

Instructions: Read all directions carefully before you begin:

1. Cut along the dotted line above, and glue the protractor onto a piece of cardboard. Carefully cut around the edge of the protractor.

2. Take a 20 cm piece of string, and tie a washer or paperclip to one end. The other end should be taped to the flat edge of the protractor so that the end touches the vertical line in the center, and the string can swing freely. This can best be done by taping the string to the back of the protractor and wrapping it around the bottom.

3. Glue a straw to the flat edge of the clinometer. The finished product should look like figure 1 below:


http://www.virtualmaths.org/activities/topic_shapes/theod2/resources/clinometer.pdf

http://www.virtualmaths.org/activities/topic_shapes/theod2/resources/clinometer.pdf



You can now use your clinometer. To find an angle of elevation, look through the straw to line up the top of an object. The string hanging down will then be touching the angle of elevation.

Note: The angle you measure will always be less than 90º when you are reading the clinometer.


Appendix B.29 Who Uses Trigonometry? Teacher Resource

Resource: Mr. Quenneville’s Website: Unit 2 Trigonometry 2.3.1 Who Uses Trigonometry Project https://sites.google.com/a/hdsb.ca/mr-quenneville/home/grade-10-applied-math/unit-2-trigonometry

Instructions: Choose a career of interest that uses trigonometry.Suggestions:Aerospace Archaeology AstronomyBuilding Carpentry ChemistryEngineering Geography ManufacturingNavigation Architecture OpticsPhysics Sports Surveying

Process: Decide how you will learn more about the use of trigonometry in your chosen career.Suggestions:Internet research text research interviewjob shadow job fair

Product: Select the way you will share what you learn.Suggestions:Skit newspaper story Brochure posterelectronic presentation

photo essay verbal presentation report

Personal Selection ChartYour name:Due date:

ContentProcess

(you may choose more than one)

Product




Teacher’s comments and suggestions

Your final submission must include the following: the career/activity investigated a brief description of your process description of the career/activity, including how trigonometry plays a role list of sources used

Your final submission can include some of the following:i) for a career

type of education/training required potential average salary employability example of job posting (newspaper, Internet, etc.)

ii) for a topic or activity historical background related issues


Appendix B.30 Who Uses Trigonometry? Student Task

Resource: Mr. Quenneville’s Website: Unit 2 Trigonometry 2.5.3 Who Uses Trigonometry Research Assignment https://sites.google.com/a/hdsb.ca/mr-quenneville/home/grade-10-applied-math/unit-2-trigonometry

You are to investigate someone who uses trigonometry in their professional lives. You will be responsible for submitting:

a report a presentation

The Report: The report should describe what the profession is all about. Let us know what they do and what type of education is needed to enter that profession. The report should also include a description of how trigonometry is used by the professional in their work. What types of problems do they need trigonometry for? Include one example of a problem that could be solved using trigonometry from the field of work you are researching. A list of resources that you used must be included. These may be articles, books, websites, magazines, etc…

The Presentation: The presentation should provide a quick snapshot of your research. Include visuals (pictures, graphics, etc…) related to the profession. The presentation can be a poster, newspaper article created by you, a brochure that you have created, a skit, an electronic presentation, etc.

Your presentation should highlight: your chosen profession education needed (e.g. college / university / workplace) and courses in high

school what kind of problems the professional will need to use trigonometry to solve

Where do you get information?The internet is a great place to start. You can do a search using the title at the top of the page. This will give you an idea of different professions and then you can investigate the specific one you pick. If you know someone who actually is in one of those professions, ask them!! The library is a great place to start and to get help on research.

Types of presentationsIf you decide to present a skit it should be 5 minutes and could involve 3 people maximum. If you select to write a newspaper story it should 350-400 words, one graphic, proper newspaper format, and includes one interview quote. A presentation done as a brochure should be 4 or 6 sided and has 2 graphics. If you want to do an e-presentation, it should include 12-14 slides and make use of different transitions. A verbal presentation would be 2-3 minutes and have interaction with the audience. A visual poster would be bristle board size.




Appendix B.31 Staircases, Steepness, and Slope

Resource: Finding Ways to Nguyen Students Over: Staircases and Steepness. http://fawnnguyen.com/2012/05/03/20120503.aspx?ref=rss

Materials: ruler, protractor

Introduction: Pose the question “What do you see?” (Possible responses: going down, going up, all using their legs, exercise, at an angle).

Activity: Provide students with the Staircases Handout (Appendix C.28). (Answer: D, A, B, E, C, F or D, A, E, B, C, F because B and E have the same steepness).

Questions: What was your ranking? What tools did you use to measure? Who measured with a protractor? What if we didn’t have a protractor? What if we only had a ruler? What would you

measure instead?


http://fawnnguyen.com/2012/05/03/20120503.aspx?ref=rss

Which of these lengths would you measure? Do you need to measure more than one? And if you measured more than one, what would you do with the two/three numbers you have?

Watch: Tutorial – Measure Slope Steepness by Bruce Temper, Director of the Utah Avalanche Center. http://www.youtube.com/watch?v=hIlFqnvgVlY

Discuss: Use the following questions to generate discussion: What is slope? How can you measure slope? What would you need to change in the staircase to change the slope? What would be a reasonable incline to push a wheelchair up if a door step is n

meters from the ground? How long would the ramp be? How could you determine the length?

Watch: What is the slope of a staircase? http://www.youtube.com/watch?v=R5wKjst_sMM

Watch: How to calculate, layout and build stairsPart 1 of 3 http://www.youtube.com/watch?v=531UPCjZTm0Part 2 of 3 http://www.youtube.com/watch?v=8QrWlMC4qCYPart 3 of 3 http://www.youtube.com/watch?v=b9etXSmeW1w


http://www.youtube.com/watch?v=b9etXSmeW1w

http://www.youtube.com/watch?v=8QrWlMC4qCY

http://www.youtube.com/watch?v=531UPCjZTm0

http://www.youtube.com/watch?v=R5wKjst_sMM

http://www.youtube.com/watch?v=R5wKjst_sMM

http://www.youtube.com/watch?v=hIlFqnvgVlY

http://www.google.ca/url?sa=i&source=images&cd=&cad=rja&docid=hLa2inwQPQlyJM&tbnid=kbLHG001TUlX1M:&ved=0CAgQjRwwAA&url=http://www.calculator.net/stair-calculator.html&ei=xizfUdyzLq7EiwLf0IHwBw&psig=AFQjCNGB2xOPqjvsuRvStce99LjgCudqKg&ust=1373666886791275

Appendix B.32 Staircases Handout

1. Without measuring the staircases, put them in order of "steepness," starting with the shape with the least “steepness.”

2. Explain how you came up with your ranking of “steepness” in #1. Because you were asked NOT to measure, what “tools” or strategies did you use to make your decision?

3. Now discuss your ranking in #1 with another classmate. Are you going to change your ranking? If so, please indicate your new ranking.

No, I’m sticking with my original ranking. I’m changing my ranking to this…


4. Now discuss your ranking in #3 with a different classmate. Are you going to change your ranking? If so, please indicate your new ranking.

No, I’m sticking with my original ranking. I’m changing my ranking to this…

5. You may now measure the staircases with whatever tool(s) you need. Use the space below to keep track of your measurements, calculations, and notes.


Appendix B.33 Pitch of a Roof

Consider how the pitch of a roof relates to slope:

Questions: How do you convert roof pitch from a ratio to degrees? (Tangent ratio)


http://www.google.ca/url?sa=i&source=images&cd=&cad=rja&docid=VNY4ySkDxOqA9M&tbnid=ifJ7aKU-IMh2bM:&ved=0CAgQjRwwAA&url=http://www.sketch2plan.com/building-a-garage-tricks-and-tips-and-tribulations.aspx&ei=lTHfUf-KFcrAigLov4BY&psig=AFQjCNGXyI9JPBGWy4YrMTd8LJ0twFfmVg&ust=1373668117396256

http://www.google.ca/url?sa=i&source=images&cd=&cad=rja&docid=VNY4ySkDxOqA9M&tbnid=ifJ7aKU-IMh2bM:&ved=0CAUQjRw&url=http://www.dciproducts.com/html/roof_pitch.htm&ei=yTHfUcCcMon3iwL0n4CwBA&psig=AFQjCNGXyI9JPBGWy4YrMTd8LJ0twFfmVg&ust=1373668117396256

http://www.google.ca/url?sa=i&source=images&cd=&cad=rja&docid=1gRhXVc5Kx7KfM&tbnid=6G_SsiD85AL_IM:&ved=0CAgQjRwwAA&url=http://www.dciproducts.com/html/roof_pitch.htm&ei=HDLfUeIX5ZCKAoqhgdAD&psig=AFQjCNFSacuHCJk9L26y1F73CcalqobJvQ&ust=1373668252046410

Appendix C: Recreation and Wellness

Appendix C.1 Inductive and Deductive Reasoning

Instruction:Inductive Reasoning:

Inductive reasoning is a conclusion based on several past observations. Conclusion is probably true, but not necessarily true.

Inductive reasoning is used when we collect evidence, observe patterns and draw conclusions from these observed patterns. This evidence does not prove conclusions, but suggests the conclusion.

Examples: After eating mushrooms for the first time, you experienced stomach cramps. You

also developed stomach problems the next three times you ate mushrooms. You reason inductively that you are allergic to morels.

On your way to school on Monday, Casey’s dog races out and barks at you. The dog repeats his performance on Tuesday and again on Wednesday. You reason inductively that the Casey’s dog doesn’t like you.

Deductive Reasoning: Deductive reasoning is a conclusion based on accepted statements such as

definitions, postulates, theorems, given information, and known properties of mathematics.

Deductive reasoning uses logic that is based on accepted facts to draw conclusions.

Examples: If a student is on the E.D. Feehan basketball team, then he/she must have at

least a C average. Jody is on the basketball team. If you accept these two statements as true, you must also be willing to accept the logical conclusion that Jody must have at least a C average.

Practice: Inductive and Deductive Reasoning. Foundations of Mathematics 11 (2011). pp. 2 - 64


Appendix C.2 Puzzles and Games

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.

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.

Games: Create stations with different games such as Cribbage, Magic Square, Yahtzee, Sudokus, Kakuro, Kaponk, Guesstamations, and Qwirkle. 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.


Appendix C.3 Measures of Central Tendency

Materials: Linking cubes

Introduction: Each year, Canada’s Prairie Provinces produce tens of millions of tonnes of grains, such as wheat, barley, and canola. The growth of a grain crop partly depends on the quantity of heat it receives. One indicator of the quantity of heat that a crop receives in a day is the daily average temperature. This is defined as the average of the high and low temperatures in a day (MathLinks 9, p. 314).

Brainstorm and Discuss: What is an average? What are applications/examples of where you have used averages before? What are measures of central tendency?

Activity:1. Ask 5 students to come to the front of the room. Using a number of linking cubes

that is a multiple of the number of people at the front of the room, build trains of linking cubes of various sizes and give one train to each person. For example, if 5 people are selected, 25 linking cubes could be used and divided into five groups such as: 1, 2, 4, 6, 6, 6.

2. Ask the group to line up in a logical order. Questions could be raised regarding whether it matters which person with 6 goes first in the line and why.

3. Ask the group, or the audience, or both to identify the person with the train that is in the center of the trains (data). Compare this to the median of a roadway being in the center of the road, and that the number of cars on either side is irrelevant – it is just the center. Ask the group and/or audience to define what median of a data set means to them based on this experience.

4. Ask the group what the most common length of train is represented in this set. Relate this to something being “in the mode” or common or preferred (as in fashions, etc.). Again, have the group and/or audience create a definition for mode.

5. Ask the group to determine how they could equally share the linking cubes amongst themselves – what would the length of the train be? Ask the group for alternative methods of determining this number – do they use the formula approach – lump them all together and then divide by 7, do they lump them together and then deal them out, or do they gradually adjust by people with greater numbers of cubes giving some to ones with smaller numbers of cubes.

6. Have the group members take back their original number of cubes. Try a number of different changes to the number of cubes and/or who is holding them. Some examples are: add two more people and give each 4 cubes – does this change any of the measures of central tendency; add another person to the group and


give them a train of 25 – does this change any of the measures of central tendency; give one more cube to one of the original people – does this change any of the measures of central tendency; remove two cubes from any train, or from two different trains – does this change any of the measures of central tendency; and so on. What is important here is that they get an understanding of the impact that different changes in the data set can result in.(Grade 6-9 Math Workshop: Subtraction of Fractions, Data Management, and Probability, pp. 5 – 6)


Appendix C.4 Personal Wellness

Note: Use the information gathered in Activity Personal Wellness in Mathematics 11 or have students complete the task again.

Activity: For each statement, e.g. number of hours of sleep, compile individual data over a two week period and calculate the mean, median, and mode.

Research: Using web-based resources, research what a typical number of hours should be for each of the categories. Take into consideration gender, age, weight, etc. What measures of central tendency did the research use? Make an analysis of your overall individual personal wellness by comparing and contrasting your gathered information with what you researched.


Appendix C.5 Recreation and Personal Wellness Budget

Task: Pick an activity, hobby, sport, etc. that you are currently involved in or would like to be involved in. Gather as many details as possible, for example:

What is the activity, hobby, or sport? (e.g. gym membership, club volleyball, guitar lessons, horseback riding, hockey camp, etc.)

What is the time frame? (e.g. days, weeks, months, years) Where is the activity, hobby, or sport? How do you get there? (e.g. drive, bike, bus, etc.) Is it a group or individual activity? Who are the participants? (e.g. coach, friends, family, etc.) Is there any out of town travel? Is there any special equipment required? Is there any special clothing or uniforms required? Is there a registration fee? Are there any other details that are important?

After gathering as many details as possible, list all of the costs (e.g. registration fees, uniform, out of town travel, tournament fees, etc.) and create a budget using these costs.

Questions: Was the total cost of the activity lower or higher than you expected? How will you finance this activity? If you are financing this activity, can you afford it or do you need to reduce some

of your expenses?


Appendix D: Travel and Transportation

Appendix D.1 Direction, Location, and Distance

Pre-Assessment: 1. Pose the problem:An exchange student is a new arrival in your math class today. When he is called to the main office, you give him instructions on how to get there. Write your detailed instructions considering direction, location, and distance and be thorough. 2. The exchange student only understands a minimal amount of English, so you decide to illustrate the instructions instead.

Extension: Have students exchange written instructions then maps. In pairs, one partner will be blindfolded and the other will give read exactly the written instructions (only divert from the written instructions if the partner is unsafe). The teacher can follow students as they proceed to the main office to see which students had the best written instructions and best illustration.

Practice: Chippy’s Journey http://nrich.maths.org/2813

Prior Knowledge: Latitude and longitude is the most common grid system used for navigation. Each degree of latitude is approximately 111 km apart. Each degree of longitude varies from 0 to 111 km. A degree of longitude is widest at the equator and gradually decreases at the poles.

Practice: In partners, pick locations on the map. Practice stating the location, giving directions and determining the distance.


http://nrich.maths.org/2813

Appendix D.2 Map Reading

Materials: Road maps, GPS

Introduction: You are going on a trip with a group of fellow students. Determine the context:

What is the purpose of the trip (e.g. class trip, sports team, extracurricular club, band, drama club, etc.)?

Who is going? Chaperones? How many people in total? Where are you going? (e.g. Edmonton for band trip) What is a location of interest or tourist attraction that your group will visit? For

example:Royal Canadian Mounted Police Academy and Depot Division, Regina, SKWestern Development Museums, Moose Jaw, North Battleford, Saskatoon, and Yorkton, SKFort Walsh National Historic Site, Maple Creek, SKHeritage Historical Park Village, Calgary, ABCalgary Tower, Calgary, ABWest Edmonton Mall Water Park, Edmonton, ABRoyal Tyrell Museum of Palaeontology, Drumhellar, ABFairmont Hot Springs, Fairmont, BCVancouver Aquarium, Vancouver, BCButchart Gardens, Victoria, BC

Task: Determine the distance from your home community to your destination. Pick the most direct route and determine the distance in both kilometres and miles. Then pick a stretch of highway that is “under construction”. Determine an alternate detour route and recalculate the distance in both kilometres and miles.

Brainstorm and Discuss: Twice on previous trips, your GPS did not pick up a satellite signal and wouldn’t work. How could you find your way without the use of technology?

Task: Write detailed directions from your home community departure location to the city limits of the destination location and illustrate. Follow the same format as a GPS in detailing the directions.

Extension: Use scale factor and proportional reasoning to estimate and then calculate fuel economy.


Appendix D.3 Area of Interest

Activity: Compare and contrast two areas of interest at your destination (determined previously in the Map Reading Activity or pick a new destination). Use the following table:

Area of InterestHours of operation

Entry costs

Transportation options to get there

Travel reviews

Safety concerns

Time needed at attraction

Description

Historical significance

Why it is an area of interest

How the area of interest relates to math

Would you go? Justify.

Other


Task: Organize the information gathered about your first choice in the form of a presentation, such as a travel brochure, video or guidebook. If you or someone you know has been there, use those photos. If not, find photos on the internet. Be prepared to present to the class and justify why you choose the area of internet.

Research and Journal Entry: Have student research online and create a math journal entry in regards to the following points based on the chosen area of interest:

Identify and describe situations, experiences, or locations around the area of interest that are relevant to self, family, or community.

Compare social justice issues that are present in the location of choice to those present in your community or another community.

Identify and explain cultural activities and/or views of mathematics related to the location of interest.

Identify and analyze cultural items related to the mathematics at the location of interest.

Identify controversial issues or historical events that are or have occurred at the location of interest.

Analyze the influences that historically significant events have had on the current field of mathematics.

Discuss: Have a class discussion on the findings and the following key questions: What is an area of interest? What makes an area of interest significant? How is math related to an area of interest?


Appendix D.4 Budgeting for a Trip

Introduction: In the Map Reading and Area of Interest activities, plans have already been set for going on a trip. The context that was created in these activities can be expanded on or a new scenario can be created.

Task: Create an itinerary of what you will be doing each day. Indicate what you will be doing, how you will be getting there, where and when you will be eating, etc.

Activity: To create a budget for your trip, consider the following areas of expense:1. Determine the cost of accommodations (how many people/room; cost per person/night; cost per person for the entire trip)2. Estimate a food allowance (cost per day; cost per trip)3. Estimate an entertainment allowance (include area of interest; cost per day; cost per trip)4. Estimate spending money (consider shopping, gifts, souvenirs)5. Estimate the cost of transportation (how are you getting there (e.g. chartered bus, vehicle) and how are you traveling around the location when there (e.g. chartered bus, vehicle, city bus, taxi cab).Compile the information in a budget format (***money***), indicate which of the above are fixed and variable expenses, complete the calculations and indicate the total cost of the trip.

Task: You have fundraised $______ for your trip, however it is not enough. Analyze and modify your budget to be able to go and not return from your trip in debt.

Discuss: Have a class discussion on the following key questions: What fixed and variable expenses do you consider when creating a travel budget? Was the total cost of the trip lower or higher than you expected? What expenses were higher than you expected? What expenses were lower than you expected? If you were planning a trip again, what changes would you make to lower your

expenses?

Resource: Travel Math. http://www.travelmath.com/


http://www.travelmath.com/

Documents

Course Overview - GSSD Blogsblogs.gssd.ca/.../06/Math-21-Draft-Teacher...2013.docx · Web viewAccurately “time” the 60-seconds to allow quiet ... trying to recall the key concepts