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Course Profile (for a locally developed course)

Essential Mathematics, Grade 9

Unit 1

Course Profiles are professional development materials designed to help teachers implement the new Grade 9 secondary school curriculum. These materials were created by writing partnerships of school boards and subject associations. The development of these resources was funded by the Ontario Ministry of Education and Training. This document reflects the views of the developers and not necessarily those of the Ministry. 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 writers of this sample Course Profile, and do not reflect any official endorsement by the Ministry of Education and Training or by the Partnership of School Boards that supported the production of the document.

ã Queen’s Printer for Ontario

Acknowledgments

Public and Catholic School Board Writing Team – Essential Mathematics

John Dallan, Lead Writer, Upper Grand District School Board

Bernie McGarry, Halton District School Board

Tina Noel, Renfrew County Catholic District School Board

Rob Samson, Simcoe Muskoka Catholic District School Board

Shirley Scott, District School Board of Niagara

Emilia Veltri, Lakehead Public District School Board

Jim Vincent, Peel District School Board

Lead Board

Halton District Secondary School Board

Kit Rankin

Susan Orchard

Larry Zavitz

Kelly Terry

With assistance from:

The writing team for the Applied and Academic Grade 9 Public Course Profile

Unit 1: Making Sense of Data

Time: 28 hours

Unit Description

Students develop an understanding of data analysis as a powerful tool for decision making. Students are involved in activities that allow them to collect, organize, and display data from primary and secondary sources. Many contextual problems are studied in which students construct, read, and interpret tables, charts, and graphs and select an appropriate method for displaying data from real-world situations. Emphasis is placed on identifying patterns and relationships, summarizing trends, making predictions, and communicating observations. Students conduct investigations with and without technology to verify or refute their own conjectures using tables, charts, mean line of best fit, and pattern descriptions.

Strand(s) and Expectations

Relationships Strand Specific Expectations: All those in the Relationships Strand

Number Sense Strand Specific Expectations: NS1.02

Activity Titles

What follows is a suggested sequence, with timing, for teaching Unit 1. These activities are designed to make sense of mathematics by working through concrete experiences to develop students' understanding of various mathematical concepts. Many skills are developed within the activities themselves. However, the need for remediation and further development of skills will arise from the activities. Time has been allotted within the activities and an additional *260 minutes outside of the activities has been designated for work, as needed, on developing skills.

Activity 1	What’s My Style? Gather, Organize, and Display Learning Styles Data	110 minutes
Activity 2	Data Collection	150 minutes
Activity 3	Graphing Data	75 minutes
*Time for activity completion and follow-up work on graphing: 35 minutes
Activity 4	Collecting and Displaying Data using Tables, Bar and Circle Graphs	150 minutes
Activity 5	Take Your Chances	75 minutes
*Time for activity completion and follow-up work on per cent: 75 minutes
Activity 6	Illustrating Data	150 minutes
Activity 7	Walk This Way	75 minutes
Activity 8	Population Explosion	75 minutes
Activity 9	Is There a Pattern?	75 minutes
Activity 10	Misuse of Data	75 minutes
*Time for activity completion and consolidation of skills: 75 minutes
Activity 11	Mean Line of Best Fit	75 minutes
Activity 12	Is it Strong Enough?	75 minutes
Activity 13	"Bounce-ability"	110 minutes
*Time for activity completion and consolidation of unit expectations: 75 minutes

Activity 14	Summative Activity: Selecting and Constructing Appropriate Graphs	75 minutes
Activity 15	Summative Activity: What's the Connection?	75 minutes

Prior Knowledge Required

Students will arrive in the classroom from varied backgrounds with a wide range of experiences and, for many, limited success in mathematics. This unit takes this issue into account and does not assume students have achieved the expectations of the previous year's course.

Unit Planning Notes

· The first activity is intended to help gain some insight into the range of learning styles in the class and to help students better understand themselves as learners. Teachers use this information to balance and adjust the types of learning and assessment activities that they use.

· Students should be encouraged to work in pairs or small groups, but growing independence is a goal. This does not imply that a co-operative learning structure is necessarily in place. At this level, students often find comfort and gain confidence when allowed to sit near a friend and work on the same task. Students need reinforcement or extra direction from the teacher or their peers.

· There are several occasions for teachers to use spreadsheets and data collecting probes in this unit. Provide opportunities to become familiar with technology early in the course to allow greater flexibility in future units.

Teaching/Learning Strategies

This unit requires flexibility of timing while at the same time it requires structure so that students are engaged in meaningful tasks. Teachers will be working diagnostically with students to determine what type of support each student requires. Time has been built into the activities to allow for these opportunities.

Students will often be working in pairs or small groups, but growing independence is also a goal.

Activities that are suggested as teaching tools could be used as assessment tools, and vice versa, since assessment activities should be learning activities.

Assessment/Evaluation Techniques

When students do open-ended, multi-dimensional work that requires them to perform in a situation which calls for mathematics, it is not useful to only score their work on the basis of right or wrong. Teachers need to look at the strengths and weaknesses of the whole piece of work or entire performance as it pertains to the specific expectations conveyed in the purpose of the task. Work can be scored holistically, with consistent standards, using a rubric. Rubrics are required when there is a range of student responses possible and when there is a need for teachers to be much more precise about criteria for assessment. Examples of assessment activities and their scoring rubrics are included in this profile. Rubrics provide an effective means of measuring student performance on the Thinking/Inquiry/Problems Solving and Communication and Applications in unfamiliar settings categories of the Achievement Chart.

Most traditional pencil and paper tests do not offer students opportunities to demonstrate Level 4 performances. This profile includes sample questions for pencil and paper tests that do allow students to demonstrate Level 4 work.

Resources

Burrill, G. and P. Hopfensperger., Exploring Linear Relations: Data- Driven Mathematics. Dale Seymour Publications, 1998.

Landwehr, J. and A. Watkins. Exploring Data. Dale Seymour Publications, 1995.

Murphy, E. Tables and Graphs. Dale Seymour Publications, 1995.

Specht, Jim. More Than Graphs: Activities for TI Graphics Calculators. Key Curriculum Press, 1996.

Statistics Canada. Canadian Social Trends (journal). Marketing Division, Publication Sales, Statistics Canada, Ottawa K1A 0T6 (1-800-267-6677).

Swan, M. The Language of Functions and Graphs. Nottingham, England: Shell Centre for Mathematics Education, 1987.

Texas Instruments. Math and Science in Motion: Activities for Middle School. 1997.

Texas Instruments. Explorations: Modelling Motions: High School Math Activities with the CBR. 1997.

MARS ( Mathematics Assessment Service )

http://www.educ.msu.edu/mars

Statistics Canada

http://www.statcan.ca

Activity 1: What’s My Style? Gather, Organize, and Display Learning Styles Data

Time: 110 minutes

Description

In this introductory activity students gather information about their own learning styles and strengths using a Learning Styles Inventory (a website reference is provided). They use the following instruments included in this activity:

· Assessing Your Learning Style (see Resource 1.1 at the end of this activity);

· Determining Intelligences: Howard Gardner’s Multiple Intelligences (see Resource 1.2).

In this activity, the data collected using these instruments is organized into charts at the direction of the teacher and displayed in graphs in a future activity. In addition, information on students’ learning styles gives the teachers useful information about the class and promotes the idea that each student is unique and special. It should be noted that these activities are not meant to rigidly categorize students, but to help them better understand that they all have different strengths that they can use to be successful in learning mathematics.

Strand(s) and Expectations

Strand(s): Relationships

Specific Expectations: RE1.03, 04.

Planning Notes

· Copies of the following materials are required for each student:

Assessing Your Learning Style (Resource 1.1);

Gardner’s Multiple Intelligences Cards (Resource 1.2).

· To aid in the collection of class data from the Learning Styles Inventory, a sheet of chart paper or a piece of acetate for the overhead projector is required.

· The student’s scores are compiled and computed by the student as follows:

Sample Chart
Students	Tally of List A Scores	Tally of List B Scores	Strengths: Stronger A, Stronger B, or Similar Strengths
Student 1	14	9	Stronger A
Student 2	13	12	Similar Strengths
Student 3	6	15	Stronger B
Student 4	7	13	Stronger B

· The teacher should become familiar with the learning styles inventory ahead of time in preparation for any questions which may arise.

· This data should be kept for use in later activities

Teaching/Learning Strategies

Student Activity:

· Students complete Resource 1.1 - Assessing Your Learning Style and calculate their dominant learning style. These results are copied for the entire class onto a tally chart of learning styles.

· Students rank the Multiple Intelligence Cards from the one that best describes them to the one that is least like them.

· Students discuss the results with the teacher, looking for trends or patterns after the teacher records the class results.

· Students provide a written answer to the following questions:

1) Is there a relationship between the results of the two activities? (The Learning Styles Inventory and the Multiple Intelligences Cards)

2) Do you agree/disagree with the results you obtained? Why or why not?

Teacher Facilitation:

· Prior to the activity, teachers should review the Resource 1.1 - Assessing Your Learning Style, making sure that the items are understood.

· The teacher should also review the information provided about Gardner’s Multiple Intelligences and the cards that the students use to find their strongest intelligences.

· Introduce the topic with a discussion of the uniqueness of every student - different strengths, talents, and ambitions.

· Introduce the learning styles inventory vocabulary (auditory, visual, tactile/kinesthetic) and Howard Gardner’s Multiple Intelligences (see Resource 1.2, Part B).

· Discuss how information about learning styles can help students and teachers.

· Read the learning styles inventory aloud and have students complete it with you.

· Record the students’ results on the prepared class chart and discuss the results with the class.

· Collect the students’ lists for future reference.

· Lead the students through the Multiple Intelligences cards activity and then record the class results on the grid chart paper. The three strongest intelligences could be tallied for each student in the following manner.

		X
		X
		X
X		X
X	X	X
X	X	X
linguistic	logical/mathematical	visual/spatial	-------	------

Assessment/Evaluation Techniques

The teacher can assign a short, journal writing activity to summarize what students have learned about themselves (this provides the teacher an opportunity to assess students’ abilities to communicate in writing).

Resources

Terence, Parry and Gregory Gayle. Designing Brain Compatible Learning. Skylight Publishing, 1998.

Chapman, Carolyn. If the Shoe Fits. Skylight Publishing, 1993.

Resource 1.1

Assessing Your Learning Style

Instructions: If you agree with the statement mark that item with a 4, if not leave it blank.

List A

o People say you have terrible handwriting.

o You don’t like silent films, pantomimes, or charades.

o You would rather perform (or listen to) music than do (or view) art, and you would rather listen to a tape than look at a filmstrip.

o You sometimes leave out words when writing, or sometimes you get words or letters backwards.

o You can spell out loud better than when you have to write it down.

o You remember things that you talked about in class much better than things you had read.

o You dislike copying materials from the blackboard or bulletin board.

o You like jokes or riddles better than cartoons or crossword puzzles.

o You like games with lots of action or noises better than checkers or most other board games.

o You understand better when you read aloud.

o Sometimes you make math mistakes because you don’t notice the sign or because you read the numbers or directions wrong.

o It seems like you are the last one to notice something new—e.g., that the classroom was painted or that there is a new bulletin board display.

o Map activities are just not your thing.

o You must struggle to keep neat notes and records.

o You must use your finger as a pointer when you read.

o You hum frequently or whistle to yourself when you are working.

o Sometimes your eyes just bother you, but your eye test was normal, or, you have glasses that your eye doctor says are right for you.

o You hate to read from the computer, especially when the backgrounds are busy.

o Matching test questions are a problem to sort out (over and above not knowing some of the answers).

o Sometimes when you read you mix up words that look similar (pill-pull, bale-hale).

Resource 1.1 (Continued)

List B

o It seems like you always have to ask somebody to repeat what s/he said.

o Sometimes you may find yourself day dreaming, maybe staring out the window when you were really trying to pay attention to something.

o Often you know what you want to say, but you just can’t think of the words.

o Sometimes you may be accused of talking with your hands or calling something a thing- a-ma-jig or a what-cha-ma-call-it.

o You have been in speech therapy some time previously (or currently).

o You may have trouble understanding a person who is talking to you when you are unable to watch the person’s face while s/he is speaking.

o You would rather receive directions in a demonstration format than in spoken form.

o When you watch TV or listen to the radio, someone is always asking you to turn it down.

o People who know you say that you say “Huh?” too much.

o You would rather demonstrate how to do something than make a speech.

o Spoken words that sound similar (bell-bill, pin-pen, Mary-marry) give you trouble. Sometimes you can’t tell them apart.

o You have trouble remembering things unless you write them down.

o You like board games such as checkers better than listening games.

o Sometimes you make mistakes when speaking (like saying “He got expended from school.”).

o You like art work better than music.

o You have to go over most of the alphabet in order to remember which letter comes first (e.g., whether M comes before R).

o You like it better when someone shows you what to do rather than just telling you.

o You usually answer questions with yes or no rather than with complete sentences.

o You can do a lot of things that are hard to explain with words (like fixing machines or doing macrame).

o Often you forget to give verbally received messages (such as telephone messages) to people unless you write them down.

o You are always drawing little pictures on the edges of your papers, or doodling on scratch paper.

TOTAL 4’s FROM:

List A _________________ List B _________________

My Personality Type: _____________________________

This Learning Style Assessment tool is found at <http://snow.utoronto.ca/Learn2/lstyle.htm

Resource 1.2, Part A

Gardner’s Multiple Intelligences

Cut the information below into their separate boxes.

Instructions

· Place a 4 beside all the words that describe what you like, what you are good at, and how you best learn.

· You will need to add up all the 4’s that were placed in each box and put this number on the bottom line where it says total.

A

· I LIKE:

Building

Drawing things

Designing

Making pictures

· I’M GOOD AT:

Imagining

Charting/Mapping

Creating models

· I LEARN BEST THROUGH:

Using My Mind’s Eye

Using Colours/Pictures

Memorizing Layout

TOTAL 4’s: ___________

B

· I LIKE:

Interacting

Talking

Working with People

· I’M GOOD AT:

Understanding Others

Leading/Organizing

Communicating

Negotiating

· I LEARN BEST THROUGH:

Sharing

Collaborating

Observing Others

TOTAL 4’s: ___________

C

· I LIKE:

Sounds

Rhythm

Playing Instruments

Singing

· I’M GOOD AT:

Recognizing Sounds

Musical Memory

Manipulating Sound

Creating Music

· I LEARN BEST THROUGH:

Associating Patterns

Listening To Sounds

Putting Works To Beats

TOTAL 4’s: ___________

D

· I LIKE:

Working Alone

Pursuing Own Interest

Quiet Reflection Time

· I’M GOOD AT:

Understanding Myself

Thinking

Planning

Imagining

Dreaming

· I LEARN BEST THROUGH:

Working Alone

Individualized Projects

Self-Paced Materials

TOTAL 4’s: ___________

E

· I LIKE:

Words

Reading

Writing

Storytelling

· I’M GOOD AT:

Prose/Poetry

Composition/Plays

Using Words

Expressing Myself

Understanding

Language

· I LEARN BEST THROUGH:

Saying Words

Hearing

Following Written Directions

TOTAL 4’s: ___________

F

· I LIKE:

Numbers

Patterns

Relationships

Formulae

· I’M GOOD AT:

Mathematics

Reasoning

Logic

Problem Solving

· I LEARN BEST THROUGH:

Categorizing

Classifying

Making Relationships

TOTAL 4’s: ___________

G

· I LIKE:

Moving

Touching

Handling Materials

· I’M GOOD AT:

Body Control

Manipulating Objects

Refining Movements

Moving in Different Ways

· I LEARN BEST THROUGH:

Interacting

Body/Space

Using Objects

Physically Moving Things

TOTAL 4’s: ___________

Resource 1.2, Part B

Gardner’s Multiple Intelligences: a brief overview

Howard Gardner developed the theory of multiple intelligences based on the idea that every individual possesses several different capacities for solving problems and creating products. Although Gardner has since expanded his list of intelligences, listed below are the first seven that he identified along with a brief description and some career information about each intelligence that the students may find interesting.

A/ VERBAL/LINGUISTIC INTELLIGENCE

· People with this intelligence have a strong sensitivity to the meanings of words and a skilled aptitude for the use of language. They are able to communicate effectively by listening, speaking, reading, writing, and making connections.

· The following are people who have exhibited verbal/linguistic intelligence: John F. Kennedy, Jerry Seinfeld, Bill Clinton, Margaret Atwood, and Robin Williams.

· Some career choices: author, speaker, teacher, lawyer, talk-show host, politician, actor, salesperson.

B/ MUSICAL/RHYTHMIC INTELLIGENCE

· People with a heightened musical/rhythmic intelligence are able to understand, appreciate and use the musical elements of pitch, rhythm and timbre. They are keenly aware of sound in their environment. Though each of us has musical capabilities to some degree, some have more skill than others. No matter what range of talent, we can all enjoy a musical experience.

· The following are people who have exhibited musical/linguistic intelligence: Mozart, The Beatles, Alanis Morissette, Celine Dion, and Pavarotti.

· Some career choices: composer, conductor, disc jockey, singer, instrumentalist, dancer, sound engineer.

C/ LOGICAL/MATHEMATICAL INTELLIGENCE

· The logical/mathematical intelligence is the capacity to use inductive and deductive reasoning to think abstractly, to understand complex relationships and to solve problems involving mathematical reasoning and the scientific process. Mathematicians enjoy working with abstraction and exploring new ideas. Scientists enjoy building models and creating theories to describe the way the world operates.

· The following are people who have exhibited logical/mathematical intelligence: Albert Einstein, Carl Sagan, Stephan Hawkins, Bill Gates, Roberta Bondar, and David Suzuki.

· Some career choices: engineer, physicist, computer programmer, mathematician, inventor, astronomer, retail buyer, banker.

D/ VISUAL/SPATIAL INTELLIGENCE

· The visual/spatial intelligence is the ability to understand the visual world accurately and to be able to see form, colour, shape and texture mentally. People with a strong visual/spatial intelligence can transfer what they see in their mind’s eye to concrete representations such as drawings and models.

· The following are people who have exhibited visual/spatial intelligence: Leonardo da Vinci, Frank Lloyd Wright, and Tom Thomson.

· Some career choices: sculptor, engineer, painter, designer, architect, artist, landscaper, graphic designer, layout editor.

Resource 1.2, Part B (Continued)

E/ BODILY/KINESTHETIC INTELLIGENCE

· The bodily/kinesthetic intelligence is based on the ability to control one’s body motions, to manipulate objects deftly, and to establish harmony between the mind and the body. People with a strong bodily/kinaesthetic intelligence often enjoy sports and physical movement, and often have a keen sense of direction and are well coordinated.

· The following are people who have exhibited bodily/kinaesthetic intelligence: Wayne Gretzky, Michael Jordan, Karen Caine, Marcel Marceau, and Chevy Chase.

· Some career choices: actor, coach, athlete, physical therapist, martial artist, juggler, dancer, acrobat.

F/ INTRAPERSONAL INTELLIGENCE

· The intrapersonal intelligence is about understanding one’s own feelings. People who have a strong intrapersonal intelligence have an accurate picture of themselves and are able to use their strengths to relate effectively with others. They like to reflect on what is happening around them.

· The following are people who have exhibited intrapersonal intelligence: Budha, Robert Frost, and Margaret Lawrence.

· Some career choices: explorer, psychologist, philosopher, computer analyst, theologian, author, elite athlete.

G/ INTERPERSONAL INTELLIGENCE

· Interpersonal intelligence lies in the ability to understand others, to be sensitive to the feelings of others, and to be very aware of the people in one’s environment. Those who have a strong interpersonal intelligence get along with other people and enjoy working with others.

· The following are people who have exhibited interpersonal intelligence: Oprah Winfrey, Princess Diana, and Jean Chretien.

· Some career choices: psychologist, social worker, nurse, counsellor, doctor, teacher, political leader, salesperson, religious leader.

Resource 1.2 has been adapted from an exercise in: Hewitt, J. Teaching Teachers. Thornhill, On.: Willsdowne Press, 1994.

Activity 2: Data Collection

Time: 150 minutes

Description

Students are provided with questionnaires to discuss and explore the language and concepts of data management. The questionnaire(s) engage students in the process of data investigation: posing questions, collecting, analysing, and interpreting data. One questionnaire allows students to collect general information about people in their community. A second questionnaire deals with the different types of characters seen on television.

Strand(s) and Expectations

Strand(s): Relationships

Specific Expectations: RE1.02, 03, 04

Planning Notes

· This activity requires the development of a suitable, general questionnaire(s)/ survey(s) modelled after the example(s) provided (see Resource 1.3 and 1.4).

· Students are required to generate a chart to tally their totals. This may be provided by the teacher (see an example in Resource 1.3, Part B).

· Data should be kept for later activities.

Teaching/Learning Strategies

Student Activity:

· The students examine, discuss, and possibly adapt:

· a general information survey to be used to collect information about the people in their community (fellow students and adults in their lives);

· a data collection chart for collecting information dealing with the characters on programs that students watch.

· They participate in teacher-led discussion about bias in data collection methods (the use of statistics in advertising, opinion-poll trends, estimates of health risks, etc.) and about how predictions can be based on data and provide a powerful means of decision making.

· Prior to collecting data students should make predictions about survey results.

· They conduct the surveys and collect data; (it may be possible to distribute the surveys to school staff and other classes in order to get a significant number of participants).

· They evaluate the data collected and make conclusions from the analysis of the data.

· Students communicate their conclusions, making inferences and convincing arguments that are based on data analysis.

· Finally, they evaluate the arguments of other students.

Teacher facilitation:

· Provide the appropriate survey and accompanying data collection instruments.

· Discuss the process of data collection; with the general information survey students may want to ask the questions and record responses or they may choose to allow respondents to fill out the prepared questionnaire.

· When using the TV characters survey (Resource 1.4) students commit to watching one-half hour of television on a specified evening.

· Group students into working teams of three or four students. With the general information survey (Resource 1.3 Part A) provide at least five questionnaires per student ensuring that at least 15 to 20 surveys can be tabulated per group.

· The questionnaire (which can be modified) is used to collect data. Each team member collects data for the group. The more people that complete the questionnaire, the better. Students may have people fill out the questionnaire themselves or may survey people directly by asking them the questions out loud and recording their responses. (Discuss the problems with each approach.) Students are to try to get the information from a variety of people, including other students, friends, family members, and staff.

· Provide time before the surveys are conducted for students to make some predictions about results, to formulate some hypothesis related to the data to be collected (e.g., (1) adults spend less time on computers than students, (2) students prefer listening to music over reading books as a recreational activity).

· After the data has been collected, select one or more areas where student teams can organize the data and represent it visually, (e.g., frequency table, charts, bar graphs).

· Provide opportunities for students to present their data displays and communicate their findings.

· Keep the responses to your survey as you may use the data collected in other activities, later on in this unit.

Assessment/Evaluation Techniques

Observations of student's individual work habits could be recorded at this time (see Appendix 1 - Learning Skills Rubric). Collect and assess each student's work for accuracy of calculations, quality of communication, and completeness.

Resource 1.3, Part A

Questionnaire/Survey

Sex M o F o Age______ Are you married? YES o NO o

Do you have a pet? YES o NO o

If YES, dog o cat o bird o other o _______________

Do you recycle any products? YES o NO o

If YES, paper o aluminum o glass o plastic o

Which are you more concerned about, the economy o or the environment o ?

Do you consider yourself more of a “day person” o or a “night owl” o ?

How many hours of television do you watch per week?		How much time do you spend using a computer each week?
0-4 o	13-16 o	0-1 o	6-7 o	9-10 o
5-8 o	17-20 o	2-3 o	8-9 o	>10 o
9-12 o	>20 o	4-5 o

Are you satisfied with the current prime minister? YES o NO o

Do you belong to a sports team? YES o NO o

Which of the following is your favourite sport to play?

o baseball o hockey

o basketball o other: ________________________

o volleyball

What is your favourite type of movie (e.g., drama, western, horror)? __________________________

Should the Canadian Military be involved in conflicts in other parts of the world?

YES o NO o No opinion o

If you could only keep one of the following in your life for the rest of time, what would it be?

Books o Music o Movies o TV o Car o Video Games o

Who has had the most influence on your life (e.g., parent, spouse, friend)? ______________________

Do you believe the availability of jobs will be better o , worse o , or about the same o for Canadians in the next 10 years?

Part B

Record Sheet

Count up the responses to your survey using the space below. Use tally marks and then write the totals in the blank spaces provided.

Sex	Age	Married	Pets	Yes ___	Recycling	Yes ___
				No ___		No ___
Male ___	15-24 ___	Yes ___	Dog	___	Paper	___
Female ___	25-34 ___	No ___	Cat	___	Aluminum	___
	35-44 ___		Bird	___	Glass	___
	45-54 ___		Other	___	Plastic	___
	55-64 ___
	65-74 ___
	>74 ___

Biggest Concern		"Day person" or "Night owl"
Economy	_____	Day	_____
Environment	_____	Night	_____

Hours of TV per Week		Computer (hours)
0-4	_____	0-1	_____
5-8	_____	2-3	_____
9-12	_____	4-5	_____
13-16	_____	6-7	_____
17-20	_____	8-9	_____
>20	_____	9-10	_____
	_____	>10	_____

Satisfied with P.M. Play Sports Favourite Sport

Yes _____ Yes _____ _______________________

No _____ No _____

Favourite type of movie

________________________

Canadian Military	Most Important		Influential Person	Next 10 Years
Yes _____	Books	_____
No _____	Music	_____	_______________________	Better _____
	Movies	_____		Worse _____
	TV	_____		Same _____
	Car	_____
	Video Games	_____

Resource 1.4

Collecting Data About Television Characters

Purpose of the Activity:

To gain a better understanding of the processes involved in gathering data and how data can be used to make predictions and draw conclusions about the world around us.

Instructions to Students:

Watch television for one-half hour and observe at least three characters that you see during a regular program and/or commercials.

To record the data, when you see a person put a tally mark ( / ) in the appropriate column. Sometimes it may be more interesting to take specific information (e.g., types of car driven, whether a person wears glasses).

Hint: When you have recorded four tally marks in a row your fifth mark should be a slash through the four marks.

Provide the students with a chart like the one presented below. It may be worthwhile to begin with a blank chart and lead the students through some discussion in order to generate the headings for the columns. The discussion can continue the following day when all the data is collated for the entire class.

WHO ARE THE CHARACTERS THAT WE SEE ON T.V.?
Male	Female	Young Child	Teen-agers	Young Adult (20-30)	Other Adults	Occupation	Rich	Poor
/			/			Surgeon	/

Activity 3: Graphing Data

Time: 75 minutes

Description

Students are provided with different types of graphs to interpret and analyse. They examine the differences involved in the construction of each type of graph (e.g., appropriate choice of scale and labelling). The information from Activity 1 and 2 are used here to construct bar graphs. Discuss the appropriate use of each type of graph given a particular set of data. This activity provides an opportunity for students to develop, along with the teacher, a rubric/checklist for assessing the components and quality of a graph.

Strand(s) and Expectations

Strand(s): Relationships

Specific Expectations: RE1.04, 05.

Planning Notes

· Graphs are provided with this activity. However, it would be desirable to gather and copy graphs and charts from a variety of sources such as newspapers, magazines, and the Internet. Students can also perform this task.

· Other graphs can be obtained from teachers of other disciplines (e.g., science, geography).

· The information from Activities 1 and 2 are required to construct bar graphs.

· When constructing graphs, materials such as large grid graph paper, rulers, and coloured pencils are required.

· A blank copy of a rubric template could be prepared on an acetate for use with an overhead projector, or in the form of a wall chart to be posted in the class.

Teaching/Learning Strategies

Student Activity:

· Students examine a variety of graphs and determine information from each to answer the questions provided.

· They examine the key elements and necessary construction techniques required to draw different graphs.

· Bar graphs are drawn to display data from Activities 1 and 2. The learning styles can be graphed on the horizontal axis and the number of students in the class who learn in those particular manners on the vertical axis.

· With the help of the teacher students develop a rubric for assessing the quality of a graph. A sample copy of the "rubric" is provided at the end of this activity (Resource 1.6).

Teacher facilitation:

· Provide worksheets for students to complete (see Resource 1.5).

· Circulate around the room giving necessary assistance.

· When working to develop the key elements of a graph, students should be helped to identify features (e.g., title, labels, appropriate scales and symbols, a legend if required, appropriate spacing of bars or symbols, connected or non-connected points).

· Guide the discussion to elicit the responses for the choice of graph type. For example:

Pictograph: makes it easy to compare distinct facts and make comparisons quickly; it is a variation of the bar graph and can be used to display data in a more appealing manner.

Bar graph: makes it easy to compare distinct facts; easily organizes and displays data.

Circle graph: shows how parts of something are related to the whole thing.

Line graph: often shows a change over time.

Scatter plot: uses points to show pairs of values; may help to show trends.

· Guide the discussion for construction of the rubric for assessing a graph. Provide a template for students and use clear, concise language that the students understand.

· Select information from Activity 2 for students to graph.

Assessment/Evaluation Techniques

Collect and assess work for completion and quality of response. Evaluate the bar graph using the rubric that was created during the lesson or the rubric at the end of this activity (Resource 1.6).

Resources

Obtain graphs from a variety of publications such as newspapers and magazines.

Internet sites such as www.statcan.ca contain a great deal of interesting data.

Resource 1.5

Interpreting Graphs Worksheet

Bar Graph

A bar graph can be used to make comparisons between similar data. Each bar shows the number of items of data in that category.

1. How many students are 15 years old?

2. Which age group has the fewest students?

3. Which age groups have the same number of students?

4. How many students are older than 16 years old?

5. How many students are the same age as you are?

6. How many students are younger than you are?

7. What are the important features of a bar graph?

8. When is it best to use a bar graph to plot data?

Pictograph

Similar to a bar graph, a pictograph can be used to make comparisons between similar data. Each row (symbol) shows the number of items of data in that category.

1. What does each symbol represent?

2. How many students are in each grade?

3. How many students are enrolled at Westside Secondary school?

4. What are the important features of a pictograph?

5. When is it best to use a pictograph to plot data?

Circle Graph

Circle graphs show how parts of something are related to the whole.

1. What per cent of students take the bus to school?

2. What fraction of students take the bus to school?

3. What fraction of students walk to school?

4. If there are 300 students at the school. How many walk to school?

5. In which category do you fit?

6. What are the important features of a circle graph?

Line Graph

Line graphs use dots connected by lines to show trends. The shape of the line makes it easy to see how some thing changes.

1. Use the graph to complete the chart.

Speed (km/h)	0	10	30			40	80	90
Stopping distance (km)				25	40				90	120

2. What happens to the stopping distance as the speed increases?

3. Approximately how much greater is the stopping distance at 80 km/h than at 50 km/h?

4. What are the important features of a line graph?

Scatter Plot

Scatter plots use points to show pairs of values. They may help show whether or not there is a trend or relationship between the values. Scatter plots are different from line graphs because the points are not connected and because there may be several points for given values.

1. On the graph there are three clusters of data. Describe what people in the school each cluster of points represents.

2. When is it best to use a scatter plot to plot data?

This is an opportunity for students to develop their ability to interpret different graphs from a variety of sources.

Resource 1.6

Rubric for Assessing Graphs

	Level 1	Level 2	Level 3	Level 4
Choice of graph	- needs assistance to make an appropriate choice.	- usually chooses the most appropriate type but cannot clearly explain reasoning	- usually chooses the most appropriate type and can usually explain reasoning	- chooses the most appropriate type and provides clear explanation for choice
Construction of graph	- rarely selects the appropriate scales, labels the title and scales, uses appropriate tools for construction	- sometimes selects the appropriate scales, labels the title and scales, uses appropriate tools for construction	- usually selects the appropriate scales, labels the title and scales, uses appropriate tools for construction	- selects the appropriate scales, labels the title and scales, uses appropriate tools for construction
Describes trends and relationships observed in data	- makes correct inferences from data, with teacher support - has difficulty discussing any relationship that exists in the data	- makes correct inferences from data, with some prompting - discusses only one relationship that exists in the data with minor errors	- makes correct inferences from data with minor errors - discusses only one relationship that exists in the data	- makes correct inferences from data - discusses other relationships that might exist in the data
Communication	- has difficulty describing the events illustrated in the graph	- some events illustrated in the graph are correctly described	- correctly describes most of the events in the graph clearly	- describes correctly all events illustrated in the graph with a high degree of clarity and provides insight and additional observations
Solve and pose Problems	- needs coaching for each step	- solves the problem but requires regular reassurance from the teacher	- can solve the problem after some teaching or discussion; occasionally checks with the teacher for reassurance.	- is able to decide on the necessary procedure to solve the problem independently and solves it correctly.
Students' initial attempts to develop a rubric will most likely look like a checklist. Through exposure to rubrics throughout the course students gain greater insights into the elements of a rubric. At this stage, students should be encouraged to develop a model that is concrete for them. Categories may appear as follows:
Scales
Labels
Neatness
Problem Solving

Activity 4: Collecting and Displaying Data using Tables, Bar, and Circle Graphs

Time: 150 minutes

Description

Students collect and display data using tables, bar graphs, and circle graphs. Circle graphs are initially introduced without the formal development of per cent and constructed without a compass or protractor. From these graphs students identify trends and draw conclusions.

Strand(s) and Expectations

Strand(s): Relationships, Number Sense

Specific Expectations: RE1.02, 03, 04, 06, 07; NS1.03, 04.

Planning Notes

· Students require the following materials: strips of graph paper (approximately 30 units long), coloured pencils, tape, and a box of Smarties for each pair of students.

· Provide a circle template with 100 increments on the circumference.

· A sheet of chart paper or a piece of acetate for the overhead projector is required to collect information from the entire class.

Teaching/Learning Strategies

Student Activity:

· Students work through the worksheets provided.

· Pairs of students count the number of different colours of Smarties in their given box. They organize the data onto a table and draw the corresponding bar graph.

· Students display their results on an overall class bar graph provided by the teacher.

· Once this has been completed students engage in discussions revolving around the concepts of sampling.

· Students then produce another circle graph using the given data.

· Once the Smarties Experiment worksheet (Resource 1.7) is completed the students complete the Fast Foods worksheet (Resource 1.8).

Teacher Facilitation:

· Teachers should discuss the work of the previous day, focusing on the variety of ways of displaying data and the key elements of a graph.

· Encourage students to place their results on the main chart periodically as they work through their tasks.

· Circulate around the classroom, assisting students in the construction of the graphs.

· Once students have completed the first circle graph, the class comes together to discuss what they have accomplished and how each sector represents the fraction of one colour of Smartie. Connections should be made to other circle graphs students would have seen that utilize per cent in construction.

· Once the Smarties Experiment worksheet (Resource 1.7) is completed the students complete the Fast Foods worksheet (Resource 1.8) which is used to illustrate the construction of a circle graph using parts broken into hundredths.

· Once students have completed the second circle graphs, discussion should focus on the concept of using per cent to construct a circle graph.

· To bring closure to the activity, discussion revolves around the differences between graphing using a bar graph and circle graphs, focusing on when one would be more appropriate than the other.

· Additional work may be required on fractions, per cent, and on calculating averages.

Assessment/Evaluation Techniques

Observations of the students' group work and organizational skills are recorded at this time. The rubric located in Appendix A can be used to facilitate assessment of individual student's learning skills. The worksheet can be assessed for accuracy of calculations, quality of communication, and completeness. The graphs can be assessed with the rubric from Activity 3.

Resource 1.7, PART A

The Smarties Experiment

With your partner, count the number of Smarties and complete the chart.

Sample Chart
	Colour of Smarties
Group	red	blue	--
A
B
--
Class totals
Average

1. Record your information on the class bar graph.

2. Take your class total for each colour of Smartie.

Divide it by the number of boxes (groups).

Average for Red = total number of red Smarties

number of groups

3. Draw one bar graph to display your own data and a second bar graph to display the averages from your entire class.

4. Are the two graphs the same? Are there any similarities?

5. Do you think that all Smartie Boxes have the same number of each colour in them?

6. How might the company that makes Smarties distribute the different colours into the boxes?

PART B

Teacher-led Instruction

1. On a strip of graph paper students record the colour frequency by colouring the appropriate number of squares matching colour and frequency. The two ends of the strip are connected to form a circle, which can be used to create a circle graph

2. Students construct a circle graph using the strip of paper.

b represents brown, g-green, r -red, y-yellow, o-orange

3. Students place their "Smartie ring" on a sheet of paper, mark the centre of the circle and carefully trace around the outside of the circle. Connect each point where the smartie colour changes to the centre of the circle and label each sector with that Smartie colour e.g.,

Resource 1.8

Fast Foods Worksheet

1. Complete the table below.

In a high school, students were surveyed about their favourite foods. Their responses are tallied below.
Fast Foods	Students	Per cent
(P) Pizza	7	= 28 = 28% 100
(T) Tacos	3
(H) Hamburgers	11
(F) Fried Chicken	4

2. Why was the number of students divided by 25?

3. Explain how the per cent was calculated for each category.

4. Use your circle template to create a circle graph.

5. Explain why each sector represents a specific per cent.

Activity 5: Take Your Chances

Time: 75 minutes

Description

This activity builds on the students’ ability to collect, organize, and display data in an appropriate fashion. It also allows an opportunity for students to examine how the results of an experiment can change when different sample sizes are used.

Strand(s) and Expectations

Strand(s): Relationships

Specific Expectations: RE1.01, 02, 03, 04, 05, 06, 07.

Planning Notes

· This activity can be done in pairs, with each set of students sharing a single die.

· Provide worksheets for each student to record the data and graph paper to draw the graphs (see Resource 1.9).

· A chart on the chalkboard or chart paper is required to allow students to record the results of their experiment so that the entire class' data can be graphed and compared to individual results.

Teaching/Learning Strategies

Student Activity:

· Pairs of students roll a die 25 times and record their results in chart form.

· They display their results on a bar graph.

· Data from the whole class are totalled and a second bar graph produced. The two graphs are compared.

· A discussion about the effect of sample size takes place.

· Students may perform other similar experiments provided by the teacher (e.g., coin toss, spinners, drawing cards).

Teacher facilitation

· Prior to beginning the activity, discuss the factors that influence an experiment. Explore the concepts of sample size, representivity, and randomness as they relate to conducting a survey.

· One way to manage the rolling of the die is to put it into a paper cup. Place a piece of plastic wrap over the top of the cup and secure it with tape or an elastic. Students shake the cup and set it down on the desk. By looking into the cup, they are able to see the results of the roll of the die.

· Circulate around the classroom to assist students when necessary in completion of the tasks.

· Encourage students to place their results on the main chart periodically as they work through the experiment.

· Connections should be made to the prior day’s activity where students collected and graphed individual and group data.

· Further connections should be made at the end of the activity to the value of selecting a large number of people when conducting a survey.

Assessment/Evaluation Techniques

Collect and assess each student's work for accuracy of calculations, quality of communication, and completeness. Ask students to answer, in their journals or notebooks, questions such as “Why is it important to select a larger number of people when taking a survey?” and “How can people be randomly selected for a survey?”

Resource 1.9

Take Your Chances Worksheet

1. If you rolled a die 25 times, how many times do you think the number 1 would come up? Explain.

2. Roll one die 25 times and record the outcomes in the chart.

Number of

1's

Number of

2's

Number of

3's

Number of

4's

Number of

5's

Number of

6's

Tally

Total

3. Did each number appear at least once?

4. Display your results using a bar graph.

5. Record your results on the large chart on the chalkboard or wall. Transfer the class totals to the chart below.

Number of

1's

Number of

2's

Number of

3's

Number of

4's

Number of

5's

Number of

6's

Class

Totals

6. Display the class results on another chart using a bar graph.

7. Compare the bar graphs. Does it seem to make a difference if you use a larger sample size for the data? Why do you think this happens?

Activity 6: Illustrating Data

Time: 150 minutes

Description

In this activity students are given tables containing different sets of data. With the teacher's assistance, students display the data using the appropriate type of graph (pictograph, bar, double bar, histogram, and circle graphs). Students are asked to summarize the information in the graphs and answer related questions.

Strand(s) and Expectations

Strand(s): Relationships

Specific Expectations: RE1.04, 05

Planning notes

· A variety of tables containing different types of information are provided (see Resource 1.10). However, teachers may wish to simplify or supplement the selection.

· Students require the following materials: circle templates (circles marked with increments on the circumference), rulers, and coloured pencils.

· If access to a computer lab is possible, this section can be completed by students with the aid of a spreadsheet program with graphing capabilities. Students can input the information from the tables and select what type of graph they wish the data to be plotted on. The ability to easily switch between the different types of graphs available to them through the spreadsheet may not only facilitate students' understanding of the different ways a set data can be graphed but also help to highlight inappropriate methods. Students can be asked to print out an appropriate and an inappropriate way to graph each selection and then write a brief explanation of why they chose each option.

· Depending upon the comfort level students have with graphs the teacher may wish to provide students with magazine and newspaper to first collect and later sort different types of graphs. These could be used for analysis and in future activities.

Teaching/Learning Strategies

Student Activity:

· Students provided with sets of data (Resource 1:10) that they display in the most appropriate manner.

· Students, with the assistance of their teacher, begin by determining which type of graph to use for the given set of data.

· They construct their graph and use the questions provided to analyze the trends in their data.

· Students are given a set of graphs. They write a short summary of what the data implies and create their own questions.

Teacher Facilitation:

· A class discussion of the different types of graphs should occur at the beginning of the activity.

· To further help students make decisions on what types of graphs they believe are most appropriate for a set of data, students may be asked to collect different types of graphs from sources such as magazines, newspapers, and the internet. As a class or in small groups, students can try to identify common types of information that are being displayed and why certain types of graphs may be inappropriate. Students should also be made aware that certain types of graphs are selected because of visual impact such as in advertising. Mathematical links may be pursued in this career area.

· Prior to students beginning to construct their graphs, teachers may need to provide helpful hints as to what type of graph students should select to display their information. For example:

Healthy Living

This could be displayed as a circle graph to emphasize parts out of a whole or as a bar graph.

Animal Life Spans and Oldest Recorded Ages

This could be displayed as a double or single bar graph depending upon whether both columns are used.

Population by Age

This could be displayed as a histogram. The relationships to a bar graph should be discussed.

Computer Access

This could be displayed as a pictograph using "computers" as a symbol. The difficulties with decimal values should be discussed. A bar graph is another alternative here.

Fat

This could be displayed as a pictograph using "french fries" or "hamburgers" as a symbol. A bar graph is another alternative here.

· Teachers may also wish to discuss, prior to students actually graphing, how to use the scale on a graph to accommodate large numbers. For example students may wish to approximate large numbers on their graph and choose a scale that represents millions.

· Students should be encouraged to use their graphing rubric to help them construct their graphs.

· During this activity the teacher circulates and observes students as they work to ensure they are making the correct choices in the selection of their graph types.

· The teacher should connect the circle template to the activity that students performed previously with the Smarties.

Assessment/Evaluation Techniques

Graphs can be assessed with the rubric from Activity 3 (Resource 1.6). Peer evaluation of graphs could also be performed using the rubric. Students’ written work should also be assessed. This could be accomplished using a rubric similar to Resource 1.15 - Assessing Student Presentations Rubric from Activity 9.

Resource 1.10

Making the Best Choice

In a survey, 300 adults were asked the following question: What is the single most important thing you can do to improve your health? Responses are summarized in the table.

Healthy Living

Response	Per Cent
Exercise	40%
Quit smoking	25%
Eat healthy	18%
Weight reduction	9%
Reduce drug/alcohol abuse	5%
Other	3%

1. What advantage would there be in using an all-inclusive category like “other”?

2. How could a graph be used to educate people regarding their health?

Animal Life Spans And Oldest Recorded Ages

Animals	Average Life Span	Oldest Recorded Age
African elephant	45	70
Arctic clam	110	220
Alligator	30	56
Parrot	60	80
Chimpanzee	30	44
House cat	16	32
Bald eagle	15	22
Dog	12	20
Tortoise	95	150

1. Which animal outlived its average live span by

a) the largest amount? b) the least amount?

2. How long did the oldest recorded house cat live?

3. Describe the image that you have of this cat?

4. Suggest reasons why a tortoise has such a long average life span.

Similar questions to above can be student- or teacher-generated for the following graphs.

Population by Age in Canada, 1991

Age	Population
0-14	5 846 600
15-24	4 032 100
25-44	9 646 800
45-64	5 534 400
65+	3 257 600

Estimates based on 1991 Canadian Census (Information obtained from Statistics Canada, http://www.statcan.ca)

Resource 1.10 (Continued)

Computer Access

Canadian Regions	Number of computers per 100 students
Yukon	22.2
B.C.	12.7
Manitoba	12.5
Ontario	11.8
New Brunswick (francophone)	10
Nova Scotia	10
Alberta	9.4
P.E.I	7.9
New Brunswick (anglophone)	7.1
Quebec	4.8

Maclean's August 1996 issue

Fat from Diet

Country or Region	Percentage of Calories from fat
Finland	39
Britain	38
Untied States	36
Canada	36
Japan	24
Korea	16
China	15
Central Africa	7

Maclean's January 1995 issue

Activity 7: Walk This Way

Time: 75 minutes

Description

In this activity, students match different patterns of motion and their graphs with and without the use of technology. They also sketch the graphs of different situations, as well as create stories that describe given graphs.

Strand(s) and Expectations

Strand(s): Relationships

Specific Expectations: RE1.01, 02, 03, 04, 05, 06, 07.

Planning Notes

· Data collection devices are required for this activity. These tools may be found in the math or science department.

· This experiment requires a motion detector, Calculator Based Laboratory unit (CBL), unit-to-unit link cable, graphing calculator, and the MATCH-IT program OR

· This experiment can be done using a Calculator Based Ranger (CBR), unit-to-unit link cable, graphing calculator, and the DIST MATCH application.

· A graphing calculator overhead viewscreen, in conjunction with either group of materials listed above, is also required.

· Student worksheets should be provided at the end of the activity to consolidate the activity. Sample questions are provided (see Resource 1.11).

Teaching/Learning Strategies

Student Activity:

· Students are asked, on an individual basis, to walk in front of the motion detector and copy the graph that is being displayed on the screen.

· Students not working at the motion detector are asked to provide helpful information to the "walker".

· All students complete a worksheet based on the activity.

Teacher Facilitation:

· To ensure the experiment works properly:

1) Check that the cables are firmly pushed into the units.

2) When walking, students must remain directly in front of the detector.

3) The detector will only record a person's motion that is beyond one-half metre.

· Prior to beginning the activity, students are asked to make conjectures such as:

1) If someone walks in front of the motion detector, their distance away from the unit is plotted.

How do you think this will look?

2) Will the speed the people walk in front of the detector change the graph? How?

· Before any student is asked to match the given graph a simple demonstration should occur. Choose a volunteer to move straight back from the detector, wait a few seconds and then move towards the detector, once the program has been activated. Students can analyse this simple function before they have to match one themselves.

· Ask the following questions:

1) What do the scales on the axis represent?

2) Was the student walking up or down a hill?

3) What do the sloped lines represent?

4) How can you tell by the graph that the student had stopped?

5) Was the student moving at a constant rate? How do you know?

6) What parts of the graph describe your motion forward, backward, and when you were stationary?

· Encourage each student to participate in a "walk".

· Students who have difficulty should be encouraged to perform the "walk" more than once and ask help from their peers if required.

· Encourage students to read aloud the stories related to the graphs provided by the teacher to others in the class.

Assessment/Evaluation Techniques

Collect and assess each student's work for accuracy of calculations, quality of communication, and completeness. Ask students to write short stories that describe similar graphs to those found in the activity. The Language of Functions and Graphs (see Unit Resources) is a good source for graphs of this nature. Similarly, students may be given short vignettes and be asked to construct their graphs.

Resource 1.11

Walk This Way Worksheet

1. Write a story that describes Pat's trip to the video store.

2. Jordan woke up late this morning and had to race off to school. On the way she had to stop to tie her shoe laces. When she arrived at school she realized it was Saturday morning and there was no school. She turned around and went back home to bed. Which one of the following graphs describes what happened to Jordan? Explain what is wrong with the other two graphs.

3. From the graph you have chosen:

a) How long did it take Jordan to tie her shoe laces?

b) Did Jordan walk/run on the way to school or on the way home? How can you tell by the graph?

c) How far is Jordan's school from home?

4. Toshi rode his bike to a friend's house for dinner. After dinner he realized that his bike had a flat and he had to walk home. Draw a graph that represents this situation.

Activity 8: Population Explosion

Time: 75 minutes

Description

In this activity, students are given data tables that they transform into broken line graphs. An analysis of the trends indicated by the graphs is a major focus of this activity.

Strand(s) and Expectations

Strand(s): Relationships

Specific Expectations: RE1.04, 05.

Planning Notes

· Tables with accompanying questions (see Resource 1.12) have been provided that will form the basis for this activity. Teachers are required to supplement the selection. Other choices of graphs could include the population growth of zebra mussels and purple loosestrife in Canada.

· Students may use a computer spreadsheet (or graphing calculator) to graph the tables. Students can print out their graphs for their own records.

Teaching /Learning Strategies

Student Activity:

· Students are provided with data tables to construct broken line graphs.

· They answer questions associated with each graph.

Teacher facilitation:

· Circulate and provide feedback while the students are working on the Canadian Population graph.

· As students complete each graph and answer the accompanying questions, the teacher periodically stops them and discusses their solutions, other trends, and their implications.

Assessment/Evaluation

Collect and assess each student's work for accuracy of calculations, quality of communication and completeness. The graphs can be assessed with the rubric from Activity 3 (Resource 1.6).

Resource 1.12

Population Explosion Worksheet

Average Life Span of Canadian Males

Year	Life Span (years)
1936	61
1946	65
1956	67
1966	68
1976	70
1986	72

1. What do you think the life expectancy of a man was in 1906? Why do you think was true?

2. Why do you think the life expectancy in 1936 was so low?

3. Predict what the average life expectancy of a person will be in the year 2006?

4. What do you predict will be the average life expectancy of a person will be in the year 2106? Why?

5. Who do you think has a higher average life expectancy, men or women? Why?

How Many of Us Are There? (Canadian Population)

In order to analyze these trends you will use the following information to construct a line graph. You will also answer the questions that appear at the end of the table.

Year	Population (to closest million)
1871	4
1881	4
1891	5
1901	5
1911	7
1921	9
1931	10
1941	12
1951	14
1961	18
1971	22
1981	24
1991	28

1. During what ten year period did Canada experience

a) the fastest growth? What was happening in the World at this time?

b) the least growth? What was happening in the World at this time?

2. Estimate the population in the following years:

a) 1896 d) 1996

b) 1926 e) 2010

c) 1976

3. In your opinion, how many people could live in Canada without being overcrowded?

Resource 1.12 (Continued)

Is There a Population Explosion Taking Place?

Imagine you work for Statistics Canada and your job is to plot the Global Population growth over the past thousand years and predict future trends. You use the data in the chart below to accomplish this task. You also use your graph to answer the questions located below the table

Year	Global Population
1000	270
1100	280
1200	300
1300	325
1400	360
1500	410
1600	490
1700	620
1800	980
1900	1 620

1. Which hundred year period experienced

a) the slowest growth? Explain why.

b) the most rapid growth?

2. Describe the trend that is shown in the graph. Is the population growing at a steady rate? Why do you think this is so?

3. Use you graph to estimate the Global Population in the years:

a) 1450

b) 2000

c) What is the current population of the world? Does this fit with your graph? Give reasons for this.

4. At the current rate of growth predict the population for the year 2100.

5. Will the Earth be able to support a population of this size? Explain.

Activity 9: Misuse of Data

Time: 75 minutes

Description

In this activity, students determine how data can be displayed so as to be misleading and construct their own graphs. They become aware of biases that may be present in the use of statistics. Students are encouraged to question the manner in which numerical data is collected and displayed graphically. Through brief classroom presentations students also have the opportunity to share misleading graphs they have constructed.

Strand(s) and Expectations

Strand(s): Relationships

Specific Expectations: RE1.04.

Planning Notes

· Copy the examples of misleading graphs that have been included at the end of this activity onto acetates. (See Resource 1.14.)

· Copy examples of misleading data from authentic sources (e.g., newspapers and magazines).

· Prepare statistical information that students can use to create both accurate and misleading graphs. (See Resource 1.13.)

· Provide chart paper (with one inch squares) for presentations.

Teaching/Learning Strategies

Student Activity:

· Students discuss the role and persuasiveness of advertising in our society and investigate how information displayed in graphs can be misleading.

· Students work in groups of two to display data both accurately and in a misleading manner.

· Students display their information on construction paper or grid chart paper and present it to the rest of the class.

· Classmates are encouraged to identify how the graphs are misleading.

Teacher facilitation:

· Introduce the topic by asking the class a number of leading questions that demonstrate the powerfully persuasive nature of advertising, e.g., What do people typically use to:

a) blow their nose (Kleenex/facial tissues);

b) clean their ears (Q-tips/cotton swabs);

c) listen to tapes when jogging (Walkman/portable cassette recorder)?

Students typically answer these questions by providing brand names instead of actual product names.

· Allow time for students to present their graphs and encourage other students to ask questions and identify what is misleading about each graph.

· Students may be asked to search through newspapers and magazines for other misleading graphs.

Assessment/Evaluation Techniques

Teachers may use Resource 1.15 - Assessing Student Presentations Rubric at the end of this activity. Teachers are encouraged to collaborate with teachers of other disciplines who use presentation rubrics in their programs. Alternatively, teachers may choose to have the misleading graphs posted at the front of the class and allow students to select one graph and describe in writing why the graph is misleading and how it benefits the “advertisers”. As a further extension students can be required for homework to find other misleading graphs in sources such as newspapers and magazines.

Resource 1.13

Misuse of Data Worksheet

Select one of the following scenarios and create a graph that:

1) displays the data accurately;

2) displays the data in a way that advances your cause.

A) You are the advertising executive for the ABC Toy Company. Their signature toy is the Furball. What you want to do is to highlight how the Furball is a more popular toy compared to the competitor's Spaceball and Smooshball. At one store, Furball sales for last week were 570, Spaceball 350, and 420 Smooshballs were sold.

B) You are the owner of a sports equipment store and are trying to promote the sport of scuba diving. A survey was taken and the following data was collected:

Water Sport

Wind Surfing

Water

Skiing

Snorkling

Surfing

Scuba Diving

Number of participants

C) You are the president of your school's Cycle Club. You wish to persuade your principal to allocate more school resources to the School Cycle Club which has not received an increase in funds for many years despite the fact that the number of students participating has grown each year.

Year	1995	1997	1998	1999
Number of participants	46	52	63	71

Resource 1.14

Visuals to Facilitate Class Discussions

Explain why the graphs are the same and how one could be misleading. Give an example of when one graph would be used over the other.

Explain why the graphs are the same and how one could be misleading. Give an example of when someone chooses one graph over the other.

Imagine that there are two groups that have opposing views on the cutting of trees. Explain what type of groups might use each of the graphs below. Do they represent the same information? Why?

Resource 1.15

Assessing Student Presentations Rubric

	Level 1	Level 2	Level 3	Level 4
Describes effects on graph	- has difficulty describing misleading components of graph	- describes some misleading components of the graph correctly	- clearly describes the misleading components of their graph	- correctly describes the misleading components of the graph with a high degree of clarity and insight; provides additional observations
Communication	- communicates with limited clarity	- communicates results with moderate clarity with some inappropriate forms	- communicates clearly using appropriate forms	- communicates and justifies clearly and concisely with a high degree of effectiveness
	- uses little or no justification	- uses faulty logic to justify conclusion	- justifies relationships with respect to the class	- generalizes relationship beyond the content of the classroom

Activity 10: Is There a Pattern?

Time: 75 minutes

Description

This activity introduces students to the investigation of two variable relationships and the possibility that some sets of data will not yield a specific relationship. Students are provided with data tables that they graph using a scatter plot and determine whether a pattern (linear relationship) exists. If so, they make predictions and draw conclusions.

Strand(s) and Expectations

Strand(s): Relationships

Specific Expectations: RE1.04, 05.

Planning Notes

· The teacher provides data tables for each student. (See Resource 1.16, Parts A and B.) Tables have been provided with this exercise however, more graphs may be required or the lengths of the existing tables may require modification.

· If students use a software program they can print a hard copy for their notes.

· For demonstration purposes, a computer with projection device or a graphing calculator with a viewscreen could be used.

Teaching/Learning Strategies

Student Activity:

· Students may work alone or in pairs.

· Provide students with tables of data which they will plot on a graph.

· They will analyse the general trends and determine if a relationship exists between the variables and describe the relationship.

Teacher facilitation:

· A general discussion about possible relationships that may occur in a real-life context should occur before the activity begins (e.g., people with pets or who floss their teeth, live longer).

· Students should be shown graphs that show general trends. These could be specific or general, e.g.,

pattern no pattern pattern

· Prior to the students beginning to graph, students should be engaged in a discussion about what types of information each table contains. The teacher may wish to point out which values should be graphed on the horizontal and vertical axes.

· Circulate and provide feedback during the Oil Change graphing activity (Resource 1.16, Part A). When students complete their graph have them check their work against other students work.

· There should be a class discussion after students have completed the first graph to ensure that students are looking at the key features of the graph that helps them to identify trends.

Assessment/Evaluation

Collect one or more of each student's graphs and assess their work for accuracy and their ability to identify and articulate patterns within the graphs. Resource 1.17 - Is There a Pattern? Rubric can be used to facilitate assessment.

Resource 1.16 Part A

Are Oil Changes Necessary?

Imagine you work for a company that is trying to determine different ways to improve the life of a car. One thing you have been asked to study is how effective oil changes are in keeping a car running. Below is a comparison of the number of oil changes in a year and the cost of auto repairs. Using the data provided, plot the points on a graph. The graph should have an appropriate scale, labelled axes, and a title. Use the graph to answer the questions listed below the table.

Do Oil Changes Payoff?
Driver	Oil Changes (Per Year)	Annual Repair Cost($)
Lloyd	0	850
Samantha	5	310
Tom	5	270
Laura	3	240
Jeff	7	125
Glenda	5	400
Gord	8	110
Marlene	4	165
Jim	6	150
Sharon	1	925
Terry	8	95
Bill	5	300
Helen	0	1290
Gary	4	190
Darren	1	560
Pat	10	0
Michelle	3	400
Jean	2	650
Gavin	1	750
Shirley	3	450

1. Analyse the pattern of points on your graph. What does this indicate about the relationship between the number of oil changes and repair bills?

2. Do frequent oil changes guarantee lower repair bills? Explain.

3. If you were a car owner how often would you change your oil? Explain.

Resource 1.16, Part B

Who Runs Faster?

Imagine you just got a new job as the coach of a track team. You have collected the data contained in the following table and wish to see if there is a relationship between the height and speed of your athletes. Plot this information on a graph and answer the questions below.

Name	Height (cm)	Time to run 50 m (sec)
Doug	166	7.0
Angela	173	8.9
Steve	171	7.5
Barb	175	8.0
Nicole	155	7.1
Randy	183	7.9
Rachel	175	8.2
Ron	170	7.8
Nick	170	8.2
Jane	168	8.4
Ross	155	8.5
Mary	163	9.2
Gene	168	9.1
Sheila	158	9.3
Karen	180	7.3

1. Analyse the pattern of points on your graph. Is there a relationship between height and speed?

2. Another coach you know recruits only tall people over 170 cm tall for his team. Would that be a wise thing to do based on the information on your graph? Explain.

3. If you were coaching a track team how would you go about recruiting the fastest runners on your team? Explain.

Resource 1.17

Is There a Pattern? Rubric

	Level 1	Level 2	Level 3	Level 4
Display data using appropriate techniques (RE1.04)	- displays data with many errors or needs teacher support to display data	- displays data with some accuracy (scale on graph, intervals)	- displays data accurately on table and graph	- displays data accurately on table and graph with considerable creativity
Describes trends and relationships observed in data (RE1.05)	- makes correct inferences from data, with teacher support	- makes correct inferences from data, with some prompting	- makes correct inferences from data with minor errors	- makes correct inferences from data
	- has difficulty discussing any relationship that exists in the data	- some errors in analysis and requires assistance in recognizing linear relationship	- consistently recognizes approximate linear relationship	- consistently recognizes linear relationship and identifies other relationships that might exist in the data
Communication	- has difficulty describing the events illustrated in the graph	- some events illustrated in the graph are correctly described	- correctly describes most of the events in the graph clearly	- describes correctly all events illustrated in the graph with a high degree of clarity and provides insight; provides additional observations

Activity 11: Mean Line of Best Fit

Time: 75 minutes

Description

Students draw scatter plots and estimate the location of the line of best fit for the data. They also learn how to calculate and draw the mean line of best fit and use it to make predictions.

Strand(s) and Expectations

Strand(s): Relationships

Specific Expectations: RE1.04, 05.

Planning Notes

· Student worksheets have been provided that contain samples of different types of information that may be used to construct a scatter plot (Resource 1.18). Additional examples are required for students to practise and reinforce their skills. Examples from Activity 10 can be used to supplement this activity.

· Provide grids for graphing and questions for interpretation and prediction.

· To help students graph the mean line of best fit it would be helpful for students to have a clear plastic ruler.

Teaching/Learning Strategies

Student Activity:

· Students examine some scatter plots to look for trends and correlations.

· Students first draw in a line of best fit by eye, i.e., they draw a line that generally follows the direction/trend that the points imply.

· Secondly, students learn how to determine the placement of the mean line of best fit. To do this students calculate the mean co-ordinate by taking the average of the first and second variable and plotting it as a point. They then draw a line passing through this point with half the number of remaining points on either side.

· They interpret the graphs and make predictions using the mean line of best fit.

Teacher facilitation:

· Provide clear, well-organized data charts, scatter plots, and worksheets.

· Circulate around the room giving necessary assistance where required.

· Depending upon the types of data plotted the teacher may wish to discuss the idea that the mean line of best fit may or may not be required to pass through the origin and the implications of this.

Assessment/Evaluation Techniques

Collect and assess each student's work for accuracy of calculations, quality of communication, and completeness.

Resource 1.18

Line of Best Fit Worksheet

Which graphs seem to have a pattern? Explain.

When the points on a scatter plot seem to follow a pattern we can sometimes draw a line that helps us to make predictions. The line might even go through some of the points. Look at this example.

How many points are on each side of the line?

Do any points lie on the line? How many?

Plot the given data and try to draw the line of best fit using your ruler and estimating where it should lie.

Minutes spent studying	Mark on exam
120	53
340	62
170	49
250	70
275	64
200	51
325	77
90	35
470	80
320	55
100	25

2. There is a way to draw the line of best fit more accurately. It is called the mean line of best fit. Use the data and scatter plot from question 1 that we completed earlier.

Minutes spent studying	Mark on exam
120	53
340	62
520	86
170	49
250	70
275	64
200	51
325	77
90	35
140	43
600	90
470	80
320	55
100	25
Total = 3220	Total = 840
Mean A= 3220 14 = 280	Mean B= 840 14 = 60

Plot (mean A, mean B) = ( , )

Draw the line of best fit through the points above so that there are the same number of points on either side of the line.

Answer these questions from the graph.

a) How many minutes should a person study to earn 75% on an exam?

b) What mark might you expect to receive if you spend 400 minutes studying?

c) What mark might you expect to get if you spend 3 hours studying?

d) Complete the following sentence. The trend seems to be that the more time you spend studying...

3. Determine the mean line of best fit and answer the questions for the table below

Hours of TV watched per week	Hours spent reading per week
6	12
20	6
30	2
12	9.5
15	8.5
18	4.5
21	5.5
26	3
25	3
10	8
9	8.5
15	5
13	7
24	4
23	4
21	5.5