Course Profile Mathematics of Data Management (MDM4U), Grade 12, University Preparation, Combined

Unit 1: Posing Questions With Data

Time: 21 hours

Activity 1.1 | Activity 1.2 | Activity 1.3 | Activity 1.4 | Activity 1.5 | Activity 1.6 | Activity 1.7

Unit Description

Students learn to find, retrieve, and organize credible data. They learn to pose significant questions through the use of journals and critique the work of others. Some activities are grouped to teach the expectations in an instructional activity followed by an assessment activity.

Using Fathom, students locate and retrieve large data sets from a variety of Internet sites, including Statistics Canada (E-STAT). Students answer questions using the data sets and consider and explore other factors that could influence the collection of data. Students use the features of Fathom to analyse one- and two-variable data; analyses include cause-and-effect and regression. Students present their findings in small-group settings and critique the data analyses of others clearly, honestly, and with sensitivity. Students complete the unit by posing a problem, finding and analysing data, presenting their work on a poster, and critiquing the work of others.

Throughout the unit, students keep a journal in which they reflect on their responses to questions, posed in a way that demonstrates their respect for the rights, responsibilities, and contributions of self and others. Through class discussions, students in Catholic schools develop attitudes and values founded on Catholic social teaching.

The activities require the use of computers with Internet access. It is recommended that this course be scheduled in a computer lab. If this is not possible, computers should be reserved for a minimum of 20 hours. The 20 hours can be reserved as a solid block with Unit 1 taught as outlined. It is also possible to block smaller amounts of time and teach the data analysis tools of Unit 2 between the lab days. Following this plan, students would be expected to complete their data analysis using the additional tools.

Note: An independent assignment in Activity1.6, requiring that students design a checklist to identify the strengths, shortcomings, validity, etc. websites, should be assigned at the beginning of the course. The assignment can be completed individually or in pairs.

Journal Organization

A journal, in the form of a binder or folder, is used as an organizer for the course and gives teachers an opportunity to provide formative feedback. The following suggested sections are referenced:

· Ethical Implications of Data – reflections about social issues and considerations of possible motives (and bias) for collecting data;

· Data Sites – record of all data sites and a summary of the credibility of the data; some type of classification should be used to organize data sites;

· Posing Questions/Problems – used to consider what makes a good problem/question; teachers should use this section to provide formative assessment on posing a problem;

· Critiquing – reactions to critiques;

· Deadlines – record of deadlines for assignments and checkpoints for final project;

· Final Project Brainstorm – any sites, data articles that interest students. Students may want to use the articles for their final projects.

Resources

Data

Statistics Canada – www.statcan.ca or http://estat.statcan.ca

Environment Canada – www.ec.gc.ca

Transport Canada – www.tc.gc.ca

Key Curriculum Press – www.keypress.com/Fathom

Data and Story Library – http://lib.stat.cmu/DASL

Exploring Data – Introductory Statistics – http://exploringdata.cqu.edu.au

Quantitative Environmental Learning Project – www.seattlecentral.org/qelp/

Internet Site Credibility – http://cybrary.uwinnipeg.ca/

Activity 1.1: Posing Questions and Reading Graphs

Time: 1 hour

Description

This activity is a launching pad for the focus of Unit 1 – posing questions and finding data. In groups, students create questions concerning a given set of graphs and then answer questions designed by another group. Students also begin an assignment from Activity 1.6 that will be used at a later date. Students have an opportunity to discuss democracy and solidarity for a just, peaceful, and compassionate society and students in Catholic schools will relate them to Catholic teachings.

Strand(s) & Learning Expectations

Ontario Catholic School Graduate Expectations

CGE5a - works effectively as an interdependent team member;

CGE7e - witness Catholic social teaching by promoting equality, democracy, and solidarity for a just, peaceful, and compassionate society.

Strand(s): Integration of the Techniques of Data Management

Overall Expectations

DMV.02 - present a project to an audience and critique the projects of others.

Specific Expectations

DM2.02 - answer questions about a project, fully justifying mathematical reasoning.

Prior Knowledge & Skills

· Read and interpret a variety of different graphs (bar and broken-line graphs/dot and scatter plots).

Planning Notes

· Photocopy the Student Activity handout.

· Assign Activity 1.6 assignment – How to Determine if a Website is Credible.

Teaching/Learning Strategies

For the first 10 minutes of class, the teacher and students brainstorm and review graphs, including independent variable, dependent variable, trends in data, the different types of trends or models students have previously seen, and reading points from graph. Place students in groups of three and distribute the handout. Students create questions that can be answered from the graphs. Groups then switch papers and answer the questions; students should critically look at the questions to see if they truly can be answered from the graph. For the remaining class time, groups present their questions and solutions. As students present their work in groups, the class gives constructive feedback as to whether they agree or disagree with the groups’ findings. The depth and richness of the questions is discussed (using waste graph and population graph to determine and compare waste per capita in Canada for 1996).

Journal Reflection: Students write a reflection of their thoughts and values for each graph, which become important when students evaluate websites in later activities. The ethical implication of the data can provide insight into the motive of posting the website and determining any bias in the data or its findings.

Student Activity

On a separate sheet of paper, create questions that could be answered by the given series of graphs. Your questions should be both factual and theoretical. Design questions that may be answered using one graph and questions that can be answered using two related graphs. Switch your completed question sheet with another group and answer the questions they have designed.

Chicago Murders in January and July (www.icpsr.umich.edu/nacjd/SDA/chd95.htm)

This graph depicts the relationship between the victim and the offender (who killed them). Points that appear darker than the rest represent two points.

This graph depicts the sex of the victim and the sex of the offender.

Amount of Waste Disposed by Province (http://estat.statcan.ca/cgi-win/CNSMCGI.EXE)

Population of the Provinces in 1996

(http://estat.statcan.ca/cgi-win/CNSMCGI.EXE?Lang=E&DBSelect=SD1ALL)

Canadian Youth Property Crimes (theft, break-and-enter, fraud)

http://estat.statcan.ca/cgi-win/CNSMCGI.EXE

Youths Charged with Property Crimes

(theft, break and enter, fraud)

Note:

Top line: Property crimes 4th line: Theft, motor vehicle

2nd line: Theft, over and under 5th line: Have stolen goods

3rd line: Breaking and entering 6th line: Frauds

Air Pollution (http://lib.stat.cmu.edu/DASL/Datafiles/AirPollution.html)

SO₂: Sulphur dioxide content of air in micrograms per cubic metre.

Temp: Average annual temperature in degrees Fahrenheit.

Journal Reflection: In Ethical Implications of Data, reflect on the usefulness and ethical implications of this data. Could this data be used to improve society or the environment and by whom (the Church? schools?) How could it be used constructively and could it also be misused? In Posing Problems, select two questions from the class discussion and discuss the strengths and weaknesses of each question.

Assessment & Evaluation of Student Achievement

· Focus on formative assessment of student ideas/work during activity.

· Collect journals – or discuss journal entries about strengths and weaknesses of questions.

Resources

Background information on the Young Offenders Act and violent crimes can be found at:

– http://estat.statcan.ca/content/English/articles/cyb/cyb-just.htm

– http://www.statcan.ca/Daily/English/980127/d980127.htm#ART1

Activity 1.2: Exploring and Retrieving Data Using E-STAT

Time: 3 hours

Description

This activity is an introduction to E-STAT. Students navigate through E-STAT and learn the tools of E-STAT by investigating data concerning the number of Canadians who went to a casino; the number of trees harvested and replenished by each province; and the production of beer and impaired driving charges. Students copy data and graphs created by E-STAT into a word-processing document.

Strand(s) & Learning Expectations

Ontario Catholic School Graduate Expectations

CGE2b - reads, understands, and uses written material effectively;

CGE3c - thinks reflectively and creatively to evaluate situations and solve problems;

CGE3d - decisions in light of gospel values with an informed moral conscience;

CGE7i - respects the environment and uses resources wisely.

Strand(s): Organization of Data for Analysis

Overall Expectations

ODV.01 - organize data to facilitate manipulation and retrieval.

Specific Expectations

OD1.01 - locate data to answer questions of significance or personal interest, by searching well-organized databases;

OD1.02 - use the Internet effectively as a source for databases.

Prior Knowledge & Skills

· Read and interpret information from line, bar, and scatter graphs.

· Calculate slope.

Planning Notes

· Ensure that your school has E-STAT by going to www.statcan.ca >> English >> Learning Resources >> ESTAT >> MEMBERS. If your school name is not on the list, contact board personnel; all school boards in Ontario have access to ESTAT. For future information, data in E-STAT is free. If you are asked to pay for data, you are no longer in E-STAT.

· Try E-STAT lesson in Part B Method 1 of Student Activity, (comparing trees harvested and replenished in Canada) and photocopy it for students.

· Part A will take one hour; Part B, Method 1 will take one hour; Part B, Method 2 will take a half hour. Method 1 can be shortened or lengthened depending on the number of years investigated.

· If computers are limited students could work in pairs and switch for each part.

· Use a multimedia projector to introduce Statistics Canada to the class and to solve common problems or questions during the activity.

· In both oral and written discussions, students can discuss the moral and ethical implications of gambling, respect for all human life and the earth, the ability to make free decisions, and the consequences of those decisions in light of the gospel values

Teaching/Learning Strategies

Students keep a glossary of terms. As a possible assignment, italicized words should be defined in a glossary for later reference when students are searching for their own data. After students finish writing their summary for Part A, the class discusses the findings. The graphs do not necessarily support the statement that casinos are successful in Canada; to answer that question, look at their revenues. Part B demonstrates the different types of data in E-STAT. Method 1 is a ready-made lesson demonstrating the creation of scatter plots with census and other types of data. The lesson can be printed and photocopied for students to follow. Method 2 demonstrates creating scatter plots using CANSIM time series data. There is not a strong relationship between beer production and impaired driving. It is important that students understand that not all data leads to a relationship.

Journal Reflection: Students summarize their learning of the Statistics Canada website. They include data they found interesting and reflect on the moral and ethical implications of the data (gambling, forestry issues, drinking and driving). They create questions concerning the data that they feel are good questions, which can done as a homework assignment. Provide feedback for questions.

Student Activity

Part A: Are Casinos Successful in Canada?

This activity is an introduction to the Statistics Canada website. You learn methods of data retrieval and create line and bar graphs using E-STAT. Graphs are copied into a word-processing document and summaries are written. You describe the set-up of Statistics Canada and how to access data in the Data Sites section of your journal. You will be assessed at a later date on your ability to navigate through E-STAT to find, analyse, and display data.

Using E-STAT

1. Go to website www.statcan.ca >> English >> Learning Resources >> E-STAT.

2. Read the Welcome Page and the Licence Agreement, then Accept.

3. If the page looks jumbled, Refresh (on toolbar).

4. You are looking at the Table of Contents of Statistics Canada’s E-STAT data. Across the top of the Table of Contents are Overview, Articles, and Data. For each topic, look at the Overview of the topic, or Articles about the topic, or Data related to the topic.

Selecting a Topic of Interest in ESTAT

5. Select Service Industries for an Overview of a particular Service Industry topic. Below the graph, statcan tells you where you can access the data. Also below the graph are Articles and Data.

6. Select Articles. This provides a list of articles that relate to different Service Industry topics. Note: this list is updated regularly as new articles become available.

7. Select Data (at bottom of page).

Getting Data for a Topic of Interest

8. Here is a list of topics that are related to the Service Industry. We will look at how many Canadians have gone to a casino over the years.

9. Select Accommodation service industry for a list of data tables related to the Accommodation Service Industry. There are active tables and terminated tables. While terminated tables may still be used, they are not updated. The data on active tables are updated on a regular basis (monthly, annually).

10. Select the code 426-0006. From the Subset Selection:

· Select Canada from 1st list.

· Select Went to a casino from the 2nd list (use the scroll bar).

· From the years, select the earliest year and the most recent year (click on arrows).

· Continue

11. Generally, we use the Time series (Option 2) rather than Table (Option 1) option.

12. Select Time Series >> Continue. Note: We will add more series later.

Graphing the Data of Interest

13. Output Format Selection lets you choose how to view the data. Select Graphic: line chart, which is best for a relationship over along period of time (but it is sometimes useful to display the data as a bar chart, table of values, etc.). Select Go to generate the graph.

14. Select Change Titles and change the title to “The Number of Canadians who have gone to a Casino”.

Importing the Graph into a Word-Processing Document

15. Right click on the graph. Select copy. Open a word-processing document and paste. You may have to adjust the graph (e.g., in Microsoft Word double click and in Layout select square). Write a summary about how this graph could help you answer the question, “Are casinos successful in Canada”. Save the document, but do not close it.

Graphing More Than One Data Set

16. Return to your Internet Browser. To compare the number of people who went to a casino who live in Ontario to those who live in Quebec and British Columbia, use the back button until you are at Subset selection again.

· While holding down the Control key (or the Command key on a Macintosh computer), select Quebec, Ontario, and British Columbia.

· Select Went to a casino.

· Select earliest year and most recent year.

· Continue >> Time series >> Continue.

17. For Output Format Selection, select Graphic: vertical bar chart. Select Go. Change the title to a more appropriate one. Copy the graph into the word-processing document.

18. Go back to E-STAT and Output Format Selection (use Back Button). Select Line chart. Copy the resulting graph into your document. In your document, discuss which graph tells you more about the casinos in Canada.

Viewing the Data as a Table of Values

19. You may notice that there are some data missing from the graphs. Go back to the Output Format Selection. Select HTML Table, time as rows. At the bottom of the table is an explanation of why some data are missing; they are labelled secure or confidential. Copy it into your document by holding control and selecting the cells in the table. Then right click and paste into your word processing document.

20. Write a final summary about the success of casinos in Canada using and referring to the data and graphs. Print the document.

Journal Reflection: In Ethical Implications of Data, reflect on the moral and ethical implications of gambling. In Posing Questions/Problems, create a question related to gambling that could be investigated by analysing data.

Part B: Analysing Relationships Using Scatter Plots

Before importing data into a statistical program, it is important to see if there is a relationship between two variables – is it worthwhile data? E-STAT has two methods for creating scatter graphs, depending on the data you are using.

For CANSIM time series data (which shows trends over time), the numeric values of two characteristics for each period of time become the x and y coordinates respectively for a single point on the scatter plot (i.e., the two characteristics being graphed are matched for each time period and plotted as a single point on the graph). The number of points on the scatter plot is exactly the number of time periods observed.

For Census and other geographic oriented data, the numeric values of two different characteristics for each geographic area become the x and y coordinates respectively for one point on the scatter plot (i.e., the two characteristics being graphed are matched for each area and plotted as a single point). The number of points on the scatter plot is exactly the number of geographic areas for which we have data.

Method 1: Census and Other Data

In E-STAT, there is a ready-made lesson to demonstrate the creation of scatter graphs for examining the relationship between the volume of tree harvesting and tree planting for provinces in Canada.

To access this lesson:

· E-STAT >> For Teachers >> Lesson Plans >> Mathematics: Analysing Relationships Using Scatter Graphs

In a word-processing document, students answer the questions in the activity.

Journal Reflection: In Ethical Implications of Data, reflect on the moral and ethical implications of forestry. How does this data relate to your reflections? In Posing Questions/Problems, create a question related to forestry that could be investigated by analysing data.

Method 2: CANSIM Data

Investigate if there is a relationship between beer production and impaired driving in Canada.

Getting the Data for Beer Production

· E-STAT >> Data >> Manufacturing >> Food Industries >> Production, bottling or stocks of beverages, monthly (303-0019)

· Select: Canada for Geography, Beer Production (Litres) for Type of beverage.

· Select earliest to latest year (notice data are monthly).

· Continue >> Time series.

Adding Other Variables from Different Topics: Getting the Data for Impaired Driving

· Select Add more series; E-STAT has several methods to find other data sets of interest. If you choose Subject, the initial E-STAT list of topics is displayed. The Keyword search is useful for looking for a specific topic.

· Select Keyword.

· Under 3- Search for: type “impaired driving.” Press Enter.

· Select Table 255-0002 Actual traffic offences reported, by type of offence, Canada, provinces and territories, annual (notice data are annual).

· Select Canada for Geography.

· There are many options for Type of traffic offence. To see the options better select View checklist and footnotes. The format is easy to view and to select options click on box. Select Impaired operation of motor vehicle or over 80 milligrams (section 237 Criminal Code). You must then select Return to pick list at the bottom for your option to be selected. Do not press Back.

· Select Number of reported offences (actual) for Unit of measure.

· Select earliest and latest date >> Continue >> Time Series.

· You can see both of your selections. You could add more series. Notice the WARNING: Series do not have the same Frequency (beer is monthly, impaired is annually). Select Continue.

Viewing Data Graphically: The Line Chart and the Scatter Graph.

· View data as a Graphic: line chart. Select Go. An Error message is displayed - the frequency of the data is a problem since it is not the same. Press Back. This time under The frequency of the output data will be converted to annual (sum). Now select Go. The graph is displayed. Press Back.

· View data as a Graphic: scatter graph (min. 2 series). Press Go. A scatter plot is produced comparing the number of impaired drivers and the production of beer for the period that E-STAT contains data. Notice E-STAT automatically puts a line of best fit through the data. When you analyse the data, a line may not always be the best model to use. The scatter plot is more useful as a check to see if there seems to be a clear relationship between the data variables and if this relationship can be modelled by a line.

· Copy this graph into a word-processing document and discuss: What might this data imply? What information may also be helpful to investigate? Is there a relationship? Would you investigate this data further?

· What factors might explain the overall trend in impaired driving charges?

· What factors might explain the overall trend in beer production?

Journal Reflection: In Ethical Implications of Data, reflect on moral and ethical implications of drinking and driving. How does this data relate to your reflections? In Posing Questions/Problem, create a question related to beer production and drinking and driving that can be investigated by analysing data.

Assessment & Evaluation of Student Achievement

This is an instructional activity. Focus on formative assessment of knowledge and skills. Activity 1.3 is the assessment activity that complements this activity. The questions created in the journals can be formatively assessed by the teacher or peers could critique each others’ questions and decide if the questions are too open or too narrow. Critiques should be written in the journal alongside questions. Teachers can provide feedback for the critiques – are the critiques constructive and thorough? The learning strategies of working independently and teamwork could be assessed.

Accommodations

This activity has a high density of words and instructions. Students who have difficulty with reading instructions should check off the instructions they have accomplished so they are not lost when they return to the instructions. The use of a highlighter would help students to see the commands most frequently used in E-STAT. All commands in bold type and selections in bold italic type should be highlighted.

Resources

Statistics Canada is currently developing an online student activity called Statistics: Power from Data, which could be an additional resource for the exploration of statistical data. Links for it are Learning Resources >> List of Learning resources >> Statistics: Power from Data.

Appendix 1.2.1

Sample Responses

Casino Activity (Part A)

From the first graph, it seems that the number of people going to Casinos is on the rise. In 1996, about 1400 people went to a casino; in 1999, about 2750 people went to a casino. The more people casinos attract, the more money they will make. The bar graph shows the data more clearly. It is easier to compare the provinces.

The number of Canadians who went to a casino

Statistics Canada – www.statcan.ca or http://estat.statcan.ca

The number of Canadians from Ontario, Quebec, and British Columbia who went to a casino

Statistics Canada – www.statcan.ca or http://estat.statcan.ca

Annual	Canada	Quebec	Ontario	BC
1996	1333	406	454	X
1997	1786	X	1026	X
1998	2289	433	1162	X
1999	2739	487	1439	253

The X’s indicates that there is data missing which are confidential.

Statistics Canada – www.statcan.ca or http://estat.statcan.ca

In Ontario, there is definitely an increase over the years of people attending casinos. This however does not necessarily mean that casinos are successful in Canada. In Quebec, attendance has not increased. It looks like in BC casinos are just starting to attract people (this may not be the case since previous data is confidential).

We need to look at the revenues and costs of casinos to determine if they are successful in Canada. This data set is not enough to answer the question.

Appendix 1.2.1 (Continued)

Part B, Method 1– Tree Replenishing and Harvesting

Statistics Canada – www.statcan.ca or http://estat.statcan.ca

Highest to Lowest Harvesters: Quebec, Ontario, BC, NB, and NS

Quebec, Ontario, and British Columbia are large provinces that have many forests. The prairie provinces are large but do not have forests – flat farm land.

Part of the Northwest Territories lies above the tree line – so it is not useful for tree harvesting.

PEI is small and so is the Yukon (which also lies above the tree line).

1997 Data (km²)

Area	Total Area of Trees Harvested	Tree Replenishment by Seeding	Tree Replenishment by Planting with Seedlings
Alberta	507	7	453
BC	1758	5	1885
Manitoba	155		62
New Brunswick	1124		200
Newfoundland	200		34
NW Territories	4	0	2
Nova Scotia	695		81
Ontario	1979	219	728
PEI			0
Quebec	3627	17	728
Saskatchewan	175		157
Yukon Territory			0

Statistics Canada – www.statcan.ca or http://estat.statcan.ca

It is clear that the main method of replenishment is by planting seedlings, not seeding.

BC, Saskatchewan, and Alberta roughly replenish the same amount of trees as harvested.

Activity 1.3: Posing Questions, Finding Data, and Critiquing Conclusions

Time: 2 hours

Description

This activity is designed to promote thought and discussion more than simply answering a question. Students use E-STAT to find data to respond to a statement. Students are assessed on their skills of navigating through E-STAT to find data, producing graphs, and hypothesizing a possible answer. In small groups, students present their findings and group members critique the written and oral presentation using a rubric. The feedback is used to improve the written response. Groups also discuss other factors that could influence the data or other questions that could be asked.

Strand(s) & Learning Expectations

Ontario Catholic School Graduate Expectations

CGE5a - works effectively as an interdependent team member;

CGE5b - thinks critically about the meaning and purpose of work;

CGE5e - respects the rights, responsibilities, and contributions of self and others.

Strand(s): Organization of Data for Analysis, Integration of the Techniques of Data Management

Overall Expectations

ODV.01 - organize data to facilitate manipulation and retrieval;

DMV.02 - present a project to an audience and critique the projects of others.

Specific Expectations

OD1.01 - locate data to answer questions of significance or personal interest, by searching well-organized databases;

OD1.02 - use the Internet effectively as a source for databases;

DM2.01 - create a summary of a project to present within a restricted length of time, using communications technology effectively;

DM2.02 - answer questions about a project, fully justifying mathematical reasoning;

DM2.03 - critique the mathematical work of others in a constructive fashion.

Prior Knowledge & Skills

· Finding data on E-STAT; creating graphs and tables.

· Analysing and describing trends shown in graphs.

Planning Notes

· Students have seen E-STAT and/or have completed the previous activity.

· Students require individual computer access. If individual access to computers is not possible, students can work in pairs and the assessment can involve more direct questioning about how to access the files rather than teacher observation.

· Four questions are provided that have data available on E-STAT; other questions can be developed to address the particular interests of your class.

· Students become skilled at navigating the Internet to find data; the teacher should observe individual students’ abilities to follow the instructions from the previous activity.

· Students submit their original and revised presentation and the peer-assessment rubrics.

· In small groups, students have the opportunity to work effectively as a team member and to think critically about the feedback that the individual provides to the presenter.

· Students write a reflective journal following the presentations to provide constructive criticism of their work by peers. In their journal, students reflect on their ability to offer constructive criticism to a peer and on their acceptance of criticism.

Teaching/Learning Strategies

Day 1: Assign four students to a group and provide each group with the four questions to be researched, providing four different presentations later in groups. Each student works individually at a computer, using the instructions from the previous activity, to answer their question using data on E-STAT. They copy their graphs into a word-processing document and respond to the statement. The teacher observes students’ ability to find the data and provides help as needed. Provide a copy of the rubrics that are used for observation, peer assessment, and final assessment.

Day 2: In their groups, students take turns presenting their question and their answer. Peer assessment provides individual students with information on how to improve their presentations. Students generate other questions that could be asked using the data or other factors that could be investigated that may have an impact on the data (e.g., population changes, international crises, etc.).

At the end of the group activity, students hand in their original and revised presentations, as well as their peer assessment rubrics. Presentations could be posted on a bulletin board to help students determine their ‘significant problem’ for the final assessment.

Student Activity

Part A: Find Data to Respond to the Statement

1. Using E-STAT data and graphs, respond to one of the following statements:

· The ice storm of January 1998 caused extensive damage to the maple trees in Quebec and Ontario; this damage caused a significant decrease in the production of maple syrup in both provinces.

· Telephone companies stated that the cost of local service is subsidized by the revenues from long-distance (toll) calls. With the introduction of long-distance options, prices for local service increased significantly and now forms a significant proportion of total revenues.

· Employees with a university degree continue to increase their use of the Internet at work and at home and differ significantly from employees with less education.

· With the change in the Young Offenders Law, there are more kids committing more violent crimes since they can get off easier.

2. Using available data, select the pertinent series that will help you respond to the statement.

3. Produce line and vertical bar graphs with appropriate titles and copy into a word-processing document.

4. In your document, respond to the initial statement using the data you found in E-STAT.

Part B: Critiquing Work and Posing New Questions

1. Present your response and graphs to your group.

2. Allow your peers to critique your presentation (Appendix 1.3.2).

3. Discuss the assessment with your peers and record feedback to improve your presentation.

4. As a group, discuss factors that could influence the data (e.g., population, income levels, disease, etc.). These factors would require more research to be completed before fully responding to the statement.

5. Generate other questions/statements that could possibly be answered using the same data. Record in Posing Questions/Problems of your journal.

6. Amend your document to include any improvements and add additional factors that could be influencing the data.

7. Hand in your initial report and the amended document to your teacher for assessment.

Journal Reflection: In Critiquing, discuss: Did I provide both positive and negative components in my analysis? Did I accept and use the suggested improvements for my presentation?

Assessment & Evaluation of Student Achievement

This activity is initially assessed by peers, using the Critique Sheet (Appendix 1.3.2). Students make improvements to their report and submit the original report and the amended report along with questions or factors that could be investigated. The final report is assessed by the teacher to provide feedback on use of the Internet, mathematical communication, and critiquing others’ work (Appendix 1.3.1). Initiative and teamwork can be assessed using a rubric.

Accommodations

· Pair students for appropriate support.

· Provide oral discussion prior to and after the activity to increase the student’s level of comprehension.

Resources

Statistics Canada, E-STAT – http://estat.statcan.ca

Background information on the Young Offenders act and Violent crimes can be found at:

– http://estat.statcan.ca/content/English/articles/cyb/cyb-just.htm

– http://www.statcan.ca/Daily/English/980127/d980127.htm#ART1

Appendix 1.3.1 – Rubric

Criteria	Level 1 (50-59%)	Level 2 (60-69%)	Level 3 (70-79%)	Level 4 (80-100%)
Knowledge Use the Internet effectively as a source for databases (OD1.02) · accesses E-STAT Table of Contents, selects topic, and navigates through process · produces graphs and tables with relevant titles	- demonstrates limited understanding of how to use the Internet effectively	- demonstrates some understanding of how to use the Internet effectively	- demonstrates considerable understanding of how to use the Internet effectively	- demonstrates thorough understanding of how to use the Internet effectively
Problem Solving Answer questions about a project, fully justifying mathematical reasoning (DM2.02)	- rarely justifies answers with mathematical reasoning	- sometimes justifies answers with mathematical reasoning	- justifies answers with mathematical reasoning	- fully justifies answers with complex mathematical reasoning
Communication Create a summary of a project to present within a restricted length of time, using communications technology effectively (DM2.01)	- uses technology with limited effectiveness	- uses technology with moderate effectiveness	- uses technology with considerable effectiveness	- uses technology with a high degree of effectiveness

Note: A student whose achievement is below Level 1 (50%) has not met the expectations for this assignment or activity.

Appendix 1.3.2

Critique Sheet

Author of Report:

1. The report is: ( ) excellent ( ) very good ( ) good ( ) fair

2. Information on the visuals (graphs, charts, etc.) is: ( ) thorough ( ) considerable ( ) some ( ) limited

What do you recommend the author do to improve the visuals?

3. Use of analytical methods (consider all the methods studied to date and methods appropriate for this data) is: ( ) thorough ( ) considerable ( ) some ( ) limited

Give your reasons. (Support for correctly chosen methods and suggestions for omitted methods.)

4. Justification and clarity of conclusions is: ( ) thorough ( ) considerable ( ) some ( ) limited

Justification of reasoning is: ( ) thorough ( ) considerable ( ) some ( ) limited

Give your reasons. (Support what has been done well and provide suggestions for improvement.)

Excerpted from “Problem Posing and Critiquing”, NCTM Journal Mathematics Teaching in the Middle School,
Vol. 4, No. 2, October 1998, pp. 128.

Knowledge	Level 1	Level 2	Level 3	Level 4
Critique the mathematical work of others in a constructive fashion (DM2.03)	- demonstrates limited understanding of critiquing math work	- demonstrates some understanding of critiquing math work	- demonstrates considerable understanding of critiquing math work	- demonstrates thorough understanding of critiquing math work

Note: A student whose achievement is below Level 1 (50%) has not met the expectations for this assignment or activity.

Activity 1.4: Using Fathom to Organize Data

Time: 4 hours

Description

Students organize and summarize data from secondary sources by creating a spreadsheet template using the statistical program, Fathom. This activity can be used as a lead in for several expectations from
Unit 2. In Part A, students learn how to use the analysis features of Fathom, such as least squares regression line and correlation coefficient. Students review an Internet site addressing cause-and-effect. The teacher can further develop these Unit 2 expectations using other resources. In Part B, students merge two different sets of data into one Case Table. In Part C, students make a curve of best fit for normal data and calculate the mean and median. The teacher can further develop the Unit 2 expectation of analysing data involving one variable and solving problems involving normal distribution.

Strand(s) & Learning Expectations

Ontario Catholic School Graduate Expectations

CGE2b - reads, understands, and uses written material effectively;

CGE2c - presents information and ideas clearly and honestly and with sensitivity to others.

Strand(s): Organization of Data for Analysis, Statistics

Overall Expectations

ODV.01 - organize data to facilitate manipulation and retrieval;

STV.01 - demonstrate an understanding of standard techniques for collecting data;

STV.02 - analyse data involving on variable, using a variety of techniques;

STV.03 - solve problems involving the normal distribution;

STV.04 - describe the relationship between two variables by interpreting the correlation coefficient;

DMV.01 - carry out a culminating project on a topic or issue of significance that requires the integration and application of the expectations of the course.

Specific Expectations

OD1.03 - create database or spreadsheet templates that facilitate the manipulation and retrieval of data from large bodies of information that have a variety of characteristics;

ST1.04 - organize and summarize data from secondary sources;

ST2.01 - compute, using technology, measures of one-variable statistics, and demonstrate an understanding of the appropriate use of each measure;

ST2.02 - interpret one-variable statistics to describe characteristics of a data set;

ST3.02 - demonstrate an understanding of the properties of the normal distribution and use these properties to solve problems;

ST4.01 - define the correlation coefficient as a measure of the fit of a scatter graph to a linear model;

ST4.02 - calculate the correlation coefficient for a set of data, using graphing calculators or statistical software;

ST4.03 - demonstrate an understanding of the distinction between cause-effect relationships and the mathematical correlation between variables;

DM1.02 - select an apply the tools of the course to design and carry out a study of the problem.

Prior Knowledge & Skills

· Understanding of mean, median, mode, linear models, and trends in data

· Transformations of functions

· Cause-and-effect when describing relationships

Planning Notes

· Book computers for the entire activity (four hours) and photocopy the activity for students.

· The teacher can teach many expectations from Unit 2.

· In Part A (1 hour), students visit a website dealing with criteria for determining causation (www.agius.com/hew/resource/assoc.htm). Visit the site ahead of time. Teach cause-and-effect (Unit 2 expectation) when describing relationships between two variables. Discuss how the correlation coefficient is not an indicator of cause-and-effect. After Part A is completed, the class can more thoroughly explore the relationship between two variables (Unit 2 expectation). Part B (1 hour) reinforces relationships between two variables.

· Briefly introduce normal distribution; students can research normal distribution for homework from textbook the night before. Part C (2 hours) involves data that can be modelled by a normal curve using sliders in Fathom. The power of this activity is that students have a visual, created using technology, of normal distribution. Solving problems involving normal distribution (Unit 2 expectation) can be taught after this activity.

· Use a multimedia projector to introduce Fathom to the class and address common questions (or use an AVERY key, which is a device that connects a computer to a TV and VCR).

· In their journals students summarize the Data and Story Library (DASL) website, reflect on the moral and ethical importance of analysing data without bias, and present their ideas clearly and honestly with sensitivity to others.

· Do this activity beforehand to be able to anticipate students’ questions.

· Impress upon students that this is real data and will not fit the models exactly.

Teaching/Learning Strategies

For the wealth activity, the approximate values for the sliders a, b, k, and d are a = 11, b = - 63.6, k = -0.097, d = 0.93 (these transformation are the same from Grade 11).

Fathom can calculate range, variance, and standard deviation. These Unit 2 expectations could be taught within this activity. However, student instruction is not given for these measures of one-variable statistics. It would be helpful to students to do the calculations on the wealth investigation step 4 so that they have a visual when learning about it in the classroom. To access the tools, right click on graph, select Plot Value, Functions, Statistical, One Attribute (see Fathom manual).

Journal Reflection: Students briefly describe and reflect on the websites used and pose questions concerning the data.

Student Activity

Part A: Smoking and Cancer

Finding the Data

1. Use data from Data and Story Library (DASL) http://lib.stat.cmu.edu/DASL/. Follow Links: Data Subjects >> Health >> Smoking and Cancer (not Smoking and Cancer Datafile). Read what the file and the variables are about.

2. Using your mouse, start at Number of Cases: 44 and highlight to the end of the explanation of the fifth variable (Leuk). Copy this by clicking right mouse key or selecting copy from the edit menu. Do not close the Internet window.

Using Fathom

3. Open Fathom. From the tool bar, select the A tool (text tool). Click on your screen and a text box appears. Right click and paste text. The box can be made larger by dragging the sides of the box.

4. Return to the Smoking and Cancer site and highlight the data, starting at the beginning of state to the end of the data table. Right click and copy (Method 1 for retrieving data).

5. Return to Fathom and select the box beside the arrow from the toolbar. Click on your screen and the box appears. Right click on box and Paste Cases. Objects that look like gold balls should appear in the box. To name the collection, double click on Collection 1.

6. Double click on the Collection Box. Under comments, record the URL and any links you used to access the Internet site.

7. Make sure the box is selected (grey outline). From the toolbar, select the table icon (beside box). Click on screen and the table appears. The data should be in the table of values.

8. Make the table of values box wider so you can see all the headings. Notice that the last two headings are not properly imported into Fathom. Always verify that Fathom has properly imported your data.

Cleaning Up the Data

9. Double click on KIDLEUK and rename it Kidney. Double click on Attr6 and rename it Leukemia.

10. Verify that the rest of the data is imported correctly. Make both Fathom and the Internet window smaller so that you can view both at the same time. In Fathom, use the scroll bar to see all the data in the table of values.

Graphing the Data

11. Maximize space on the Fathom desktop. Make your table of values smaller so that you can only see the attribute names and the first three cases.

12. Select the graph icon (beside table of values icon) and place on Fathom desktop. Grab the attribute CIG by holding down on the left mouse button and dragging it over to the graph. Drop it on the x-axis (only the x-axis should have a bolded box around it). Grab the attribute BLAD and drop it onto the y-axis. The graph should say scatter plot in the top right corner.

13. Select the graph icon again. Place another graph on your Fathom desktop. Compare CIG with LUNG. Do this for the remaining attributes.

14. Select the A tool and create another textbox. Explain the conclusions you can make from the graphs.

Linear Regressions using Fathom

15. If there is a trend, it is useful to do a linear regression. In Fathom, right click on the graph and select the Least Squares line. An r^2 value will appear at the bottom of the graph. To determine the correlation coefficient, take the square root of this value.

Changing Axis Scales

16. The basic way to work with axes in Fathom is to drag on the numbers of the axis. Dragging in the middle translates the axis, moving the range without changing the scale. Dragging closer to the ends expands or contracts the range, keeping the opposite end of the axis constant. Think of this action as zooming in or zooming out (Fathom Reference Manual, p. 20).

17. You can double click on the graph and manually adjust the xmin, xmax, ymin, and ymax. To return to original scale, select Rescale Graph Axes from the Graph menu.

Tips for Maximizing your Fathom Desktop

· Hide items you are not using (e.g., the box with the gold balls). Select the item and from Display select Hide Collection. If you need to see it again, select from Display Show Hidden Objects (this will show all hidden objects).

· When finished with a table of values and only the graphs are important, delete the table of values and the graphs remain. To retrieve the table of values, select the collection box (with gold balls), select the table of values from the toolbar, and bring it onto the Fathom desktop.

In Your Notebooks: Go to www.agius.com/hew/resource/assoc.htm. List the 11 criteria for determining causation. Discuss each criterion in reference to the smoking and cancer data from DASL. Discuss the research that is needed to be sure that there is a cause-and-effect relationship between smoking and cancer. Return to the website where the data is from to get additional information. Also discuss the role of the correlation coefficient and cause-and-effect relationships. Write your report within the Fathom document.

Journal Reflection: In Ethical Implications of Data, reflect on the moral and ethical implications of smoking and how they relates to this data. In Posing Questions/Problems, create a question related to cancer and/or smoking that could be investigated by analysing data.

Part B: Sport Injuries in Football

1. Access www.unc.edu/depts/nccsi/ >> Data Tables >> Annual Survey of Football Injury Research.

2. Copy the table Fatalities Directly Due to Football.

3. Open Fathom. Paste cases into a Collection Box (Method 1).

4. Create a Case Table and observe the data. We need to do a little clean up. Create a scatter plot.

5. The first two cases cause problems when graphing. Holding shift, select Case 1 and Case 2; right click and select Delete Cases.

6. Delete the last three attributes since there is no data in the columns. Holding shift, select the last three columns; right click and select Delete Attributes.

7. Relabel the attributes to the appropriate headings. Minimize the Fathom screen so that you can see both Fathom and the Internet page.

8. Relabel the collection Football Fatalities by double clicking on the name Collection 1.

9. Double click on the Collection Box and record the URL in the comments section and the name of the site. Do this for all data that you use.

10. Create a scatter plot for Year and High School Fatalities.

11. Notice it does not produce a scatter plot because the last case has the word TOTAL. Delete the last case and create a new scatter plot. Create the least squares line.

In Your Notebook: Discuss the possible reasons for this trend and discuss the correlation coefficient.

Importing a Second Table of Data from a Different URL

12. Return to the website and press Back. Select Annual Survey of Catastrophic Injuries.

13. Copy the table Cervical Cord Injuries.

14. On the same desktop as Football Fatalities, select a new Collection Box and paste cases.

15. Create a Case Table and clean the table up. Relabel this collection Cervical Cord Injuries in Football. Create a scatter graph of Year and High School.

In Your Notebook: Discuss the possible reasons for this trend and compare it to the football fatalities. Notice the scale of each graph.

Merging Case Tables

16. Create a new Case Table. Create the attribute labelled x.

17. Notice a new Collection Box is automatically created.

18. Compare football fatalities with cervical cord injuries for each year.

19. Relabel the Collection Football Fatalities compared to Cervical Cord Injuries.

20. Click on Year from the Football Fatalities Case Table. The column should be highlighted. From the Edit Menu, select Copy Attribute. Click on x. From the Edit Menu, select Paste Attribute. Copy the high school Attribute and paste it in y. Relabel this attribute Secondary School Fatalities (use an underscore for a space).

21. Since Cervical Cord Injuries only begin in 1977, delete all cases prior to 1977 in the Football Fatalities compared to Cervical Cord Injuries Case Table.

22. Copy and paste high school attribute from Cervical Cord Injuries Case Table. Relabel it.

23. Create a scatter plot comparing Football Fatalities and Football Cervical Cord Injuries.

In Your Notebook: Discuss the criteria for determining causation with reference to this data for sports injuries. What additional information is needed for determining if this is a cause-and-effect relationship? What does the correlation coefficient tell us about this data?

Journal Reflection: What are the moral and ethical implications of this relationship? In Posing Questions/Problems, create a question related to Sport Injuries that could be investigated by analysing data.

Part C: Investigating Wealth

1. Use data from DASL: Data Subjects >> Economics >> Billionaires 92 Datafile.

2. Import Data into Fathom (Method 2). Right click on URL and copy. In Fathom, from File Menu, select Import from URL. Right click on address box and select paste. Select OK. A case box should appear with Gold Balls in it. Select table of values and check to see if data was imported. If not, use Method 1 from the cancer activity.

3. Create a table of values on the desktop. Graph age versus wealth. Notice that the graph says Dot Plot at the top right corner and does not have a scale for the x-axis. To make a scatter plot, there must only be numbers in the table of values. If you scroll down to case 105, there is an asterisk in the cell. This is another type of data clean up that you will have to check for. Delete all asterisks and delete the graph.

Analysing One-Variable Data

4. Select graph and place on desktop. Drag age and put it on the x-axis. Notice the shape of the dot plot. This looks to be a normal distribution. To verify, calculate the mean and median of the data. If they are equal, then it is a normal distribution.

5. Right mouse click on graph. Select Plot Value. Type on the screen mean(age). Press OK. Repeat this process to calculate the median. Notice they are approximately the same and they are in the middle of the dot plot.

6. Change this graph to a histogram by clicking on Dot Plot and selecting Histogram. It is easy to see the mode if you double click on the x-scale and change bin width to 1. The mode is 68; this data is not exactly normal. To return to the original graph, select Rescale Graph from Graph Menu.

Using Sliders to Analyse Data

7. Create another graph on the desktop and put age on the x-axis and wealth on the y-axis.

8. Bring down 4 sliders from the toolbar (the icon beside the A). Label a, b, k, and d.

9. Right click on the graph. Select Plot Function. Click on + sign beside Function. Click on + sign beside distribution. Click on + sign beside Normal. Double click on normalDensity (the description of this tool is at the bottom of the Expression for function screen).

10. Type in the letters a, k, b, and d. Select OK.

11. Using the sliders, try to fit a curve of best. Drag the slider on the scale to change the value of a, b, k, and d.

Changing a Slider’s Scale: Use the same rules as Changing Axis Scale

Journal Reflection: In Ethical Implications of Data, reflect on how this data could be useful: What is this data telling us? In Data Sites, write a summary concerning the DASL website. In Posing Questions/Problems, create a question related to wealth that could be investigated by analysing data.

Assessment & Evaluation of Student Achievement

· Focus on formative assessment (i.e., giving informal feedback to students). Activity 1.5 is the assessment activity that complements this activity.

· Use peer assessment to provide feedback for cause-and-effect entry in notebook.

· Collect journals to provide feedback on the questions posed. Are they too narrow or too open?

· Learning skills could be assessed in this activity.

Resources

Fathom (information and teacher resources) – www.lat-olm.com.au/Fathom.htm.

Exploring Data (introductory statistics) – http://exploringdata.cqu.edu.au/ .

Information Literacy Skills – http://score.rims.k12.ca.us/infolit.html .

Activity 1.5: Finding Data to Answer Questions Using Fathom

Time: 4 hours

Description

This activity is an assessment activity of the skills and techniques learned in Activity 1.4. Students are given a question or statement and the URL for the data site. Students extract information from the sites and import the data into Fathom; manipulation of data may be required. Students analyse the data and produce a report responding to the initial question and suggesting other factors that could influence the observed data.

Strand(s) & Learning Expectations

Ontario Catholic School Graduate Expectations

CGE2b - reads, understands, and uses written materials effectively;

CGE2c - present information and ideas clearly and honestly and with sensitivity to others;

CGE3d - makes decisions in light of gospel values with an informed moral conscience;

CGE4e - applies effective communication, decision-making, problem-solving, time, and resource management skills.

Strand(s): Organization of Data for Analysis, Statistics, Integration of the Techniques
of Data Management

Overall Expectations

ODV.01 - organize data to facilitate manipulation and retrieval;

STV.01 - demonstrate an understanding of standard techniques for collecting data;

DMV.01 - carry out a culminating project on a topic or issue of significance that requires the integration and application of the expectations of the course;

DMV.02 - present a project to an audience and critique the projects of others.

Specific Expectations

OD1.03 - create databases or spreadsheet templates that facilitate the manipulation and retrieval of data from large bodies of information that have a variety of characteristics;

ST1.04 - organize and summarize data from secondary sources using technology;

DM1.02 - select and apply the tools of the course to design and carry out a study of the problem;

DM2.03 - critique the mathematical work of others in a constructive fashion.

Prior Knowledge & Skills

· Finding data on the Internet; creating graphs and tables using Fathom

Planning Notes

Data sites have been provided to allow quick access to the data; students need time to import, clean up and merge data and then produce their report. This activity is an assessment of the student’s ability to complete these actions. Students are not expected to thoroughly investigate the question. Students may discover that they have more questions than answers; students become more aware of relevant factors that could affect the data or of alternate ways in which they must analyse the data.

Suggestions

Question 1: Only three time periods are included; students should realize that it is a weak data site. Be sure that students look at daily smokers.

Question 2: For Air – choose PASSENGER TRAFFIC, by Sector; Rail – choose PASSENGER SERVICE, Total Passengers; Bus – choose INTERNATIONAL COMPARISONS, Intercity Passengers; Cars – choose VEHICLES, Registrations by Region. To make comparisons, all data should be expressed as 000’s. In Fathom, create a <new> attribute and insert formulas that multiply/divide the required attribute by the appropriate value. Delete extra attributes and cases (1988-1999 are common to all tables). Students should address the validity of a linear relation between air travel and car registrations, which requires the merging of four tables from the one site.

Question 3: Requires the merging of two tables that are produced from different sites; students need to recognize the inverse nature of income level of Canadians vs. year and poverty percentage versus year; other graphs are possible.

Question 4: Looks at a simple normal distribution.

Teaching/Learning Strategies

Students complete individual work on the computers to produce a written assignment. If individual access is possible, students should complete their assignment on the computers. If time is restricted, students can complete the data retrieval and analyses on the computer but complete the assignment by hand. If individual access to computers is not possible, students can work in pairs to retrieve data and complete analyses and then finish the assignment by hand, individually.

The teacher observes students’ ability to retrieve data from the Internet and to use Fathom software for analysing data. If students worked in pairs, they should exchange their papers with a different student for the peer critique. Students critique the work of a classmate using the rubric in Activity 1.3. Students then submit their work for a summative assessment and the critique of a student’s work for formative assessment. In their critique, students present their ideas clearly and honestly and with sensitivity to others. In their journals, students reflect on their reaction to the quality of the other student’s work and on their ability to offer constructive criticism to a peer.

Student Activity

Part 1: Start with a Question and Search for the Data

There are four questions to answer. Find each of the data sites through the identified link. Choose the appropriate descriptors to extract the required data and import the data into Fathom. Create case tables, merge attributes from two tables into one new table, and add formulas to allow for comparisons of data (e.g., 1’s to 000’s). Create one or more graphs that support or refute the question. Prepare a report that includes the data, the graph(s), and a short summary that outlines the techniques used to prepare the report. Analyse the data using skills learned in previous lessons and write a conclusion. Discuss other factors that could have an influence on the data and explain your reasons.

· Have the education and advertising campaigns addressing the harmful effects of smoking caused a decrease in the total number of adolescent daily smokers across Canada? Has the change been more significant in males or females? E-STAT >>Search CANSIM for Table 104-0027.

· How do Canadians travel within their own country? As more people buy more cars, has the rail system (passengers) and bus companies (intercity travel) noticed a decrease in the number of travellers? Can the number of car registrations (highways) be used to predict the air passengers (http://www.tc.gc.ca/en/menu.htm – passenger traffic by sector, Transport Canada). Using the menu across the top of the page, drop down menu on Road and select More, then look on the left and select “Statistics and forecasts,” scroll down to Statistical Data. Use the terminology indicated to find the relevant data.

· Canada is a wealthy nation but many children continue to live in poverty. Is the income level of Canadians a factor that affects the percentage of child poverty in Canada? (Search, data child poverty in Canada) www.ccsd.ca/cpovhist.htm (Child Poverty Rates, Canada) and http://estat.statcan.ca/, Personal finance and household data, Table for income based on selected family type in Canada

· Flies are all the same, aren’t they? Is there any variation in the lengths of housefly wings? www.seattlecentral.org/qelp/index.html

Part 2: Peer Critiques

Exchange your assignment with another student. Use the Critique Sheet to critique your classmate’s work.

Hand in the critiqued assignment, along with the critique, to the teacher for separate assessments.

Journal Entry: In Ethical Implications of Data, discuss your reaction to the data and articles on child poverty. How can we change this situation in Canada? In Critiquing, reflect on your reaction to the quality of work that you saw and on your ability to offer constructive criticism to a peer.

Assessment & Evaluation of Student Achievement

· Summative assessment of written report using rubric

· Formative assessment of the critique

Resources

Statistics Canada – http://estat.statcan.ca

Transport Canada – www.tc.gc.ca/en/menu.htm

Child Poverty – www.ccsd.ca/cpovhist.htm

Data and Story Library – http://lib.stat.cmu.edu/DASL/

Child Poverty 2000 – www.campaign2000.ca/NATrc00.pdf

Quantitative Environment Learning Project – www.seattlecentral.org/qelp/index.html

Appendix 1.5.1

Rubric

Knowledge	Level 1 (50-59%)	Level 2 (60-69%)	Level 3 (70-79%)	Level 4 (80-100%)
Use the Internet effectively as a source for databases (OD1.02)	- demonstrates limited understanding of how to use the Internet effectively	- demonstrates some understanding of how to use the Internet effectively	- demonstrates considerable understanding of how to use the Internet effectively	- demonstrates thorough understanding of how to use the Internet effectively
Organize and summarize data from secondary sources using technology (ST1.04)	- demonstrates limited understanding of organizing and summarizing data	- demonstrates some understanding of organizing and summarizing data	- demonstrates considerable understanding or organizing and summarizing data	- demonstrates thorough understanding of organizing and summarizing data

Activity 1.6: Looking Critically at Websites

Time: 2 hours

Description

Students evaluate the credibility of websites. In Activity 1.1, students were given the assignment How to Determine if a Website is Credible; students designed a checklist to identify the strengths, shortcomings, biases, validity, etc. of different websites. Students use their checklists to examine different websites that may be useful as data sources for their final project.

Strand(s) & Learning Expectations

Ontario Catholic School Graduate Expectations

CGE1d - develops attitudes and values founded on Catholic social teaching and acts to promote social responsibility, human solidarity, and the common good;

CGE3e - adopts a holistic approach to life by integrating learning from various subject areas and experience;

CGE5a - works effectively as an interdependent team member;

CGE5e - respects the rights, responsibilities, and contributions of self and others.

Strand(s): Organization of Data for Analysis; Statistics

Overall Expectations

ODV.01 - organize data to facilitate manipulation and retrieval;

STV.01 - demonstrate an understanding of standard techniques for collecting data.

Specific Expectations

OD1.02 - use the Internet effectively as a source for databases;

ST1.04 - organize and summarize data from secondary sources using technology.

Prior Knowledge & Skills

· Knowledge of the dynamic statistics software Fathom.

Planning Notes

· Book computers with Internet access for the activity.

· Reserve multimedia projector for display of checklists.

· Read and do the assignment on Internet Site Credibility.

· Require that students have their checklists on a disk for the discussion.

· Students use the attitudes and values developed by Catholic social teaching when discussing the motivation of Internet websites.

Teaching/Learning Strategies

Students display their checklists from the completed assignment. The teacher leads a discussion of the completed assignment and the checklists during which the class develops the final checklist for this activity. Students record the checklist in their journals.

This activity follows a jigsaw strategy. The teacher organizes students into Home groups of five students. In the Home groups, students select an Internet site from the list. Students form their Expert groups according to the site they have chosen to review. Students return to their Home groups and share interesting observations and information the Expert group found important.

Assignment: How to Determine if a Website is Credible

Use a tutorial created by the University of Winnipeg to create a checklist for critiquing the credibility of Internet sites. Follow the links to access the tutorial: http://cybrary.uwinnipeg.ca/ >> EMANUEL or learning about information >> 8: Evaluation the Weakest Link >> Evaluation Criteria.

Answer the following questions.

1. Why is print material considered more credible than Internet material? (Robert Harris “Evaluating Internet Research Sources”).

2. According to Robert Harris what kind of Information Exists on the Internet?

3. What tip does Robert Harris offer to determine if a source is reliable/credible?

4. What test is a single perfect indicator of reliability, truthfulness, or value? For the Credibility, Accuracy, Reasonableness, Support (CARS) checklist?

5. Summarize the CARS checklist. Include important questions you must ask yourself and indicators of poor information when evaluating an Internet site for each of the topics.

6. How can you tell the motivation and source of a document from the Internet address? Is this a strong indicator of motivation?

7. Using Robert Harris’s article and The University of Winnipeg’s Evaluation – The Weakest Link Page, create a checklist for evaluating an Internet site.

Student Activity: Evaluating Websites

1. The teacher assigns you to a Home group. In your Home group, each person chooses an Internet site to review using the checklist developed in class as a guide.

2. Evaluate your chosen site using your checklist, recording any interesting observations and sharing this information with the other students in your Expert group.

3. Return to your Home Group; report on your reviewed site and listen to the reports of the other sites.

4. Following this sharing of information, search for an Internet data site and complete a review.

5. Return to your Home group and report on the site and listen to the reports of other sites.

6. Choose one site to share with the class.

7. Hand in your review to be posted for class use.

8. Complete the journal entry.

Journal Reflection: In Ethical Implications of Data, write a brief description and address the credibility of each of the websites presented. List the strengths and weaknesses of each site. Use the websites as examples to reflect on the moral and ethical importance of analysing data without bias. In Final Project Brainstorm, record any data sites that you may want to use for your project.

Sites to Review in Expert Groups

· Environment Canada – www.ec.gc.ca/Ind/ >> English.

· Transport Canada – www.tc.gc.ca/ English >> place your arrow on Rail and wait for drop down menu, select [More …] >> Statistic’s and forecasts >> Scroll Down to Statistical Data.

· Economagic.com: Economic Time Series Page – www.economagic.com. Data cannot be copied and pasted directly. Select Display series in COPY/PASTE format. Not all data is shown. You must be a subscriber to access the full dataset. Fathom Tip: Data is shown by years and then by months and cannot produce a graph in Fathom (try to!!). To graph this over the years, create a new attribute and label it Time. Right click on Time and select Edit Formula. Enter the formula Attr1 + (Attr2 – 1) *1/12. This combines months and year.

· US Naval Observatory – http://aa.usno.navy.mil/data/

· The World Bank – www.worldbank.org/data/

To find a data website to review on your own:

1. Search for Data on a search engine.

2. Try the Fathom site: http://www.keypress.com/Fathom >> Links to Data >>.

Assessment & Evaluation of Student Achievement

· Collect student website critiques journals and provide formative assessment feedback.

· Learning strategies could be assessed in this activity.

Accommodations

This activity has a moderate density of words and instructions. To ensure all students understand the instructions, the teacher should read them to the class as a whole.

Resources

Explanations of jigsaw teaching strategy can be found at the following sites:

– www.discover.tased.edu.au/english/strategy.htm

– www.broward.k12.fl.us/ci/whatsnew/strategies_and_such/strategies/jigsaw.html

Activity 1.7: Culminating Activity for Unit 1

Time: 5 hours

Description

This culminating activity is a scaled-down version of the culminating project. Students select a topic; find secondary data and supporting data to investigate their topic; evaluate the sites; import the data into Fathom; do analysis; and form conclusions. They use a poster to display their analysis and conclusions. Students then critique the posters of their peers, applying effective communication and responsible decision-making.

Strand(s) & Learning Expectations

Ontario Catholic School Graduate Expectations

CGE3b - creates, adapts, and evaluates new ideas in light of the common good;

CGE3e - adopts a holistic approach to life by integrating learning from various subject areas and experience;

CGE4e - sets appropriate goals and priorities in school, work, and personal life;

CGE4f - applies affective communication, decision-making, problem-solving, time, and resource management skills.

Strand(s): Organization of Data for Analysis, Integration of the Techniques of Data Management

Overall Expectations

ODV.01 - organize data to facilitate manipulation and retrieval;

DMV.01 - carry out a culminating project on a topic or issue of significance that requires the integration and application of the expectations of the course;

DMV.02 - present a project to an audience and critique the projects of others.

Specific Expectations

OD1.01 - locate data to answer questions of significance or personal interest, by searching well-organized databases;

OD1.02 - use the Internet effectively as a source for databases;

OD1.03 - create database or spreadsheet templates that facilitate the manipulation and retrieval of data from large bodies of information that have a variety of characteristics;

DM1.01 - pose a significant problem whose solution would require the organization and analysis of a large amount of data;

DM1.02 - select and apply the tools of the course to design and carry out a study of the problem;

DM1.03 - compile a clear, well-organized, and fully justified report of the investigation and its findings;

DM2.03 - critique the mathematical work of others in a constructive fashion.

Prior Knowledge & Skills

· Knowledge of Fathom or statistical software.

Planning Notes

· Book computers with Internet access for the entire activity.

Teaching/Learning Strategies

Student Activity

Investigate a topic of your choice and produce a poster displaying your report.

· Pose a Significant Problem whose solution would require the organization and analysis of a large amount of data. Your problem should be broad in scope and consider a variety of factors that might influence the outcome of your conclusions. You may use data found in a previous activity.

· Use the Internet to find a large amount of data to analyse your problem. You must evaluate the credibility of your site and include this evaluation in the bibliography.

· Organize the Data by importing into Fathom. Look at the trends in the data and state conclusions concerning the data.

· Find Supporting or Influencing Data or Information concerning your problem (you could import data into Fathom, use E-STAT graphs, include an article, etc.).

· Compile a clear, well-organized, and fully justified report of the investigation and your findings to be summarized and displayed on a poster. Include a complete bibliography and a reflection piece on the moral and ethical implications of the data and your conclusions.

· Critique the mathematical reports of your peers in a constructive fashion.

Assessment & Evaluation of Student Achievement

Provide formative feedback for the course project. The assessment rubric consists of both formative and summative assessment. Feedback should be provided so that students understand what type of question is significant for their Culminating Project (Unit 5). The other part of the rubric is summative since students have already been assessed for using the tools of the course, their reasoning, and their critiquing skills.

Accommodations

Students could use alternative strategies to present their projects (e.g., oral, PowerPoint).

Appendix 1.7.1

Formative Assessment

Criteria	Level 1 (50-59%)	Level 2 (60-69%)	Level 3 (70-79%)	Level 4 (80-100%)
Thinking/ Inquiry and Problem Solving DM1.01	- poses a problem of limited scope - allows for limited connections to other influencing factors	- poses a problem of some scope - allows for few connections to other influencing factors	- poses a problem of considerable scope - allows for some connections to other influencing factors	- poses a problem of broad scope - allows for many connections to other influencing factors

Summative Assessment

Expectation	Level 1 (50-59%)	Level 2 (60-69%)	Level 3 (70-79%)	Level 4 (80-100%)
Application – selection and sequencing of tools DM1.02 ODV.01	- rarely selects and sequences appropriate tools (Internet site critique, data organization tool, data finding technique)	- sometimes selects and sequences appropriate tools (Internet site critique, data organization tool, data finding technique)	- most often selects and sequences appropriate tools (Internet site critique, data organization tool, data finding technique)	- always or almost always selects and sequences appropriate tools (Internet site critique, data organization tool, data finding technique)
Communication DM1.03	- communication is limited and rarely clear and complete	- communication is generally understandable and complete	- communication is generally clear and complete	- communication is consistently clear and complete
	- limited use of correct mathematical forms	- some correct use of mathematical forms	- generally correct use of mathematical forms	- consistent correct use of mathematical forms
Thinking/ Inquiry and Problem Solving DM2.03	- judges the validity of conclusions with limited effectiveness	- judges the validity of conclusions with moderate effectiveness	- judges the validity of conclusions with considerable effectiveness	- judges the validity of conclusions with a high degree of effectiveness

Note: A student whose achievement is below Level 1 (50%) has not met the expectations for this assignment or activity.

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