grd 5:6 dm & probability

Creating A Toy CompanyTic-Tac-Toe

Learning About GraphsMaking A Good Game Of It The Penny Flip Experiment

Spinner ExperimentGraphing the Data

Game SticksWhat Does the Data Tell Us?

River CrossingGames Expo

Including:

July 2001

Written by:

Janice Mackenzie, Jane Moore, Dave Wing, Kevin Woollacott

Making a Game of It!Gr. 5 / 6 Data Management and Probability

An Integrated Unit for Grade 5/6

Written using the Ontario Curriculum Unit Planner 2.51 PLNR_01 March, 2001* Open Printed on Jul 23, 2001 at 1:09:56 AM

Making a Game of It!Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6



Education Centre(705)742-9773

Kawartha Pine Ridge District School Board

Education Centre(705)742-9773

Kawartha Pine Ridge District School Board

[email protected]

[email protected]

Based on a unit by:

An Integrated Unit for Grade 5/6Written by:

This unit was written using the Curriculum Unit Planner, 1999-2001, which Planner was developed in the province ofOntario by the Ministry of Education. The Planner provides electronic templates and resources to develop and share unitsto help implement the new Ontario curriculum. This unit reflects the views of the developers of the unit and is notnecessarily those of the Ministry of Education. Permission is given to reproduce this unit for any non-profit educationalpurpose. Teachers are encouraged to copy, edit, and adapt this unit for educational purposes. Any reference in this unitto particular commercial resources, learning materials, equipment, or technology does not reflect any officialendorsements by the Ministry of Education, school boards, or associations that supported the production of this unit.

AcknowledgementsThe developers are appreciative of the suggestions and comments from colleagues involved through theinternal and external review process.

Participating Lead Public School Boards:Mathematics, Grades 1-8Grand Erie District School BoardKawartha Pine Ridge District School BoardRenfrew District School Board

Science and Technology, Grades 1-8Lakehead District School BoardThames Valley District School BoardYork Region District School Board

Social Studies, History and Geography, Grade 1-8Renfrew District School BoardThames Valley District School BoardYork Region District School Board

The following organizations have supported the elementary curriculum unit project through team building andleadership:

The Council of Ontario Directors of EducationThe Ontario Curriculum CentreThe Ministry of Education, Curriculum and Assessment Policy Branch


Making a Game of It! Page 1

Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6

Task ContextStudents have been invited to participate in a Games Expo. In order to take part in the Expo, they first need toinvestigate a variety of games of chance before creating their own unique game of chance andpresenting it at the Expo. "Purchasers" from various companies will evaluate the students' understanding ofdata management and probability concepts, skills, and knowledge based on their oral and writtenexplanations.

Task SummaryIn this unit, students will learn about data management and probability skills, concepts, and knowledgethrough the exploration of a variety of traditional and non-traditional games. Some expectations fromLanguage and the arts are addressed and assessed within the unit. Connections to Social Studies can alsobe made.

Each of the mathematics tasks is centred on the theme of "games," whether it be collecting, graphing, andanalysing data or investigating probability concepts. The subtasks are sequenced so that the students haveample opportunity to learn about and practise the identified skills, concepts, and knowledge before theirperformance is assessed in later subtasks. The investigations prepare students for the culminating task inwhich they design and present their own game of chance.

A variety of assessment tools are used throughout the unit. These include observation, rubrics, andchecklists.

Throughout the unit students explain their mathematical thinking through the use of a math journal. Studentscommunicate their understanding of relevant mathematics skills, knowledge, and concepts. Each journal entryis a response to one or more prompts outlined in the subtasks. Throughout the unit, the teacher will read thejournal entries to maintain an understanding of how well students are understanding concepts. At the end ofthe unit, the students revise and edit their final journal entry and two additional self-selected entries that werecompleted during the unit. These three entries are submitted for scoring by the teacher (using the JournalRubric).

Culminating Task AssessmentEach toy company (made up of two to four students) designs, field tests, and presents a game of chance ata Games Expo. From the data generated in the field test of their game, students predict the probability ofwinning and determine the average set-up and playing time. This information is presented by the toy companyalong with its game. The game and presentation are assessed for a number of data management andprobability skills, knowledge, and concepts using the Games Expo Rubric.

At this point, the students are asked to submit their math journal entry from River Crossing along with twoother entries (self-selected) that they believe demonstrate their understanding of data management andprobability concepts, skills, and knowledge. Students are encouraged to revise and edit their work (e.g.,clarifying or adding mathematical ideas). The Journal Rubric is used by the teacher for this assessment.

Links to Prior KnowledgeStudents are expected to have had opportunities to:- collect and record data- predict results- discuss probability concepts- communicate about mathematics concepts through talk and written language

Unit Overview

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Considerations

Notes to TeacherMath Journal:Students use a math journal throughout the unit in order write their ideas and reflect on what they arelearning. The Journal Rubric is provided to students at the beginning of the unit so that they can see whatthey need to do to be successful. Wherever a journal entry is required, students are given a journal promptand in some cases they can choose from a set of prompts.

Students are expected to concentrate on their mathematical thinking in their journals. The rubric provideddoes not assess students on conventions of language (e.g., spelling, grammar, and punctuation). They areassessed on their ability to revise and edit their entries. Assessment should be focused on their mathematicalthinking. Students should be encouraged to clarify and in some cases extend their original thinking. The finalentry should be attached to the original entry so that the teacher can assess the student's ability to reviseand edit their mathematical thinking.

The math journal does not have to be a separate book. Students can use their math notebook for theirresponses.

Using the Computer:Computer applications can be utilized for the collection, sorting, and presentation of data. Students should betaught how to use appropriate programs if they are not already familiar with them. Students can also useAppleworks slide show or Hyperstudio as part of the presentation of their game at the Games Expo.

Connections - Cross-Curricular and Cross-Cultural:There are natural curriculum connections in this unit. Language, Social Studies, and the Arts can be easilywoven into the subtasks. Some suggestions will be given in the subtasks themselves.

This unit provides many opportunities to tie in games from other cultures and countries. These can be boardgames or active games (for use in a Phys-Ed class, for example). Games that would make good extensionsto subtasks are attached directly to those subtasks. Additional games are provided in Unit Wide Resources.

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Subtask List Page 1List of Subtasks

Creating A Toy CompanyStudents are informed that they are the creative executives for a new toy company. Their job is toinvestigate a variety of games, find out what the market (their peer group) likes, and ultimately developand present a new game of chance based on their findings. In pairs or small groups (maximum four),the students create a company name and logo and register this information with the teacher.

At this time, students are introduced to their math journal, the Journal Rubric, and a choice of promptsfor their first entry. From this first entry the teacher is able to assess each student's level ofunderstanding of data management and probability skills, knowledge, and concepts.

1

Tic-Tac-Toe Students volunteer to play tic-tac-toe on the blackboard with the teacher while the rest of the classobserves. The teacher goes first each time. Students are encouraged to look for strategies forwinning and how the game is predictable. After discussing strategy and how probability does or doesnot relate to tic-tac-toe, the class develops a list of criteria that could be used to evaluate games (e.g.,enjoyment, difficulty level, time it takes to play). This criteria will be used in subtask 4 to help studentsdevelop a survey.

Students reflect in their journals about games that involve strategy and chance.

2

Learning About GraphsIn this subtask, students work in pairs to review, learn, about, and discuss five types of graphs: bar,double bar, circle, line, and pictograph. They are then given a set of data about games and asked tocreate their own graph with a specific audience in mind. This subtask is done over two periods.

Students use their math journals to reflect on graphing and on their data management task.

3

Making A Good Game Of It This subtask is a continuation of subtask 2, where students decided on the top three criteria for a"good" game. Students review their data and after a brief discussion on surveys, develop their toycompany's survey. A tracking sheet is provided for students to record information pertaining to theirsurvey (e.g., their survey question).

Students write a journal entry about surveys in the local community.

4

The Penny Flip ExperimentStudents flip a penny a given number of times in order to explore the probability of getting heads ortails. Each student creates a tally sheet and collects data which is later added to a class chart. Theteacher leads a discussion about the difference between experimental and theoretical results, andprobability and possibility. During this subtask, the teacher observes how the students go aboutcollecting and organizing their data.

Students are prompted to write about the results of their investigation in their math journals.

5

Spinner ExperimentIn this subtask, students construct a spinner and make predictions about what they think will happenwhen they spin a given number of times. Students record their spins in a self-constructed tally, andthen reflect on what happened in the experiment. The students will be assessed by the teacher ontheir understanding of probability and their ability to gather and record data.

In their math journals, students compare the spinner experiment with the penny flip experiment.

6

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Subtask List Page 2List of Subtasks

Graphing the DataIn this subtask, the students use the data generated in subtask 4 to construct a series of graphs.Students compare their graphs and analyse the data. This work is done independently and isself-assessed by the student using the Graph Rubric. (This subtask provides students with practicebefore they are assessed on their ability to create graphs in Subtask 9.)

7

Game SticksIn this game, each person (or team) uses 6 two-sided sticks (tongue depressors), which studentsmust first decorate. After the demonstration game, students record a few questions about probabilityas it relates to the game and then play the game, a few times to answer their questions and test theirtheories. In pairs, the students construct tree diagrams to determine the possible outcomes anddiscuss their findings.

In their journals, students then respond to prompts about the activity.

8

What Does the Data Tell Us?Students use data about a popular Canadian game in order to create graphs and calculate mean andmode. Grade 6 students also investigate median. For this subtask, point totals for Wayne Gretzky andMia Hamm are provided. The students must display one athlete's data in more than one way in order toshow bias. The student's graphs are assessed using a rubric.

9

River CrossingStudents take turns rolling two numbered cubes and using the sum to move their counters across thegame board. As students play River Crossing Game, they see which combinations of numbers are themost common and begin to strategically place their counters.

The probability of rolling sums is investigated and reflected upon by the students in their math journal.This entry is assessed by the teacher using the Journal Rubric (attached to the culminating task).

10

Games Expo Each toy company (made up of two to four students) designs, field tests, and presents a game ofchance at a Games Expo. From the data generated in the field test of their game, students predict theprobability of winning and determine the average set-up and playing time. This information is presentedby the toy company along with its game. The game and presentation are assessed for a number ofdata management and probability skills, knowledge, and concepts using the Games Expo Rubric.

At this point, the students are asked to submit their math journal entry from River Crossing along withtwo other entries (self-selected) that they believe demonstrate their understanding of datamanagement and probability concepts, skills, and knowledge. Students are encouraged to revise andedit their work (e.g., clarifying or adding mathematical ideas). The Journal Rubric is used by the teacherfor this assessment.

11

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Making a Game of It! Subtask 1Creating A Toy Company

Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6 mins40

Expectations5e3 • organize information to convey a central idea,

using well-developed paragraphs that focus on amain idea and give some relevant supportingdetails;

5e2 • use writing for various purposes and in a range ofcontexts, including school work (e.g., to summarizeinformation from materials they have read, to reflecton their thoughts, feelings, and imaginings);

5a26 • produce two- and three-dimensional works of artthat communicate a range of ideas (thoughts,feelings, experiences) for specific purposes and tospecific audiences;

6e2 • use writing for various purposes and in a range ofcontexts, including school work (e.g., to developand clarify ideas, to express thoughts and opinions);

6a25 • produce two- and three-dimensional works of artthat communicate a range of ideas (thoughts,feelings, experiences) for specific purposes and tospecific audiences, using a variety of familiar arttools, materials, and techniques;

DescriptionStudents are informed that they are the creative executives for a new toy company. Their job is to investigatea variety of games, find out what the market (their peer group) likes, and ultimately develop and present a newgame of chance based on their findings. In pairs or small groups (maximum four), the students create acompany name and logo and register this information with the teacher.

At this time, students are introduced to their math journal, the Journal Rubric, and a choice of prompts for theirfirst entry. From this first entry the teacher is able to assess each student's level of understanding of datamanagement and probability skills, knowledge, and concepts.

GroupingsStudents Working In Small GroupsStudents Working IndividuallyStudents Working As A Whole Class

Teaching / Learning StrategiesBrainstormingLearning Log/ JournalCollaborative/cooperative Learning

AssessmentThe teacher is able to read each journalentry and make notes about the students'understanding of data management andprobability concepts as they relate to games.Reading the journals will allow the teacher todecide which skills need to be emphasizedand which need to be attended to moreclosely.

Assessment StrategiesLearning Log

Assessment Recording DevicesAnecdotal Record

Teaching / LearningWhole Group

1. Information on the Context of the Unit:- Place the students into groups of two to four.- Explain to the groups of students that they are toy company executives who are researching games todiscover what makes them appealing. Once they complete a variety of investigations of games (backgroundresearch), they will incorporate all that they have learned into their own game of chance.

2. Brainstorming Session:- Ask the students to think of all of the names of companies that produce games. Make a list.

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Resources

3. Instructions to the Group:- Explain that each toy company will be inventing its own name and logo, and will be applying for copyrightprotection for both.- Introduce the concept of math journals. Explain that after many of the tasks, the students will be asked towrite in their math journals. Sometimes there will be specific prompts to follow, and sometimes the studentswill have their choice of what to write about.- Hand out the math journal scoring guide. Go over it with the class carefully, remarking on the expectationsthat are being assessed (math and language).

Small Group

Developing an Identity:- Have each group invent a name for its company and a logo to go with it.- Pass out the Copyright Application Form (BLM1.1 Copyright) before proceeding, in order to receive their"copyright."- Sign each group's application sheet, giving the students in that group exclusive rights to the name and logo.

Individual Work

Math Journal:- Explain that you will be reading the journal entries to find out what they know about data management andprobability. Ask students to respond to the following two prompts:1. How does probability relate to game playing? Give examples to help explain your thinking.2. Many people use math in their jobs. Explain why it would be important for a sports writer or TVbroadcaster to have a good understanding of data management skills. Give examples wherever possible.

AdaptationsThe journal prompts may be overwhelming for students with a learning disability. The teacher may wish togive the student the prompts orally and scribe the responses, or allow the student access to the computer.

Students who cannot cope with the complexity of the journal prompts may respond to a series of simplerprompts in a conversation with the teacher. For example:- What are three games that you have a good chance of winning? (The teacher writes down the informationin a T-chart)- What are three games that you have a poor chance of winning?- What is different about the games? Why do you win some and not the others?

Copyright Application Form BLM1.1 Copyright.cwk

Bristol board 1

Cardboard or a three-fold display board 1




Notes to TeacherGroupings:Since many games function ideally with two or four players.

Developing a Toy Company Name and Logo:The students may need to investigate the logos on a selection of games that are available in the school.

Copyright:The purpose of the copyright application is to ensure that students create a variety of names and logoideas. It also allows the teacher to prevent any inappropriate names or logos. The application also allowsthe simulation to be more realistic.

Math Journal:The math journal may be a separate document for this unit, or the students may use their math notebook. Inthe Notes to Teacher section at the front end of the unit, there is important information on the assessmentof math journal entries that are written throughout the unit.

Display Areas for Toy Companies:If space permits, the students can use three-fold display boards to create their own "desktop offices."These offices will allow the students to have a private workspace and, again, make the simulationsomewhat more real for the students. They can later be used for the presentation of the company's game inthe culminating task.

Teacher Reflections


Making a Game of It! Subtask 2Tic-Tac-Toe


Expectations5m109 • interpret displays of data and present the

information using mathematical terms;6m106 • systematically collect, organise, and analyse data;5e1 • communicate ideas and information for a variety of

purposes (e.g., to present and support a viewpoint)and to specific audiences (e.g., write a letter to anewspaper stating and justifying their position on anissue in the news);

5e48 • express and respond to ideas and opinionsconcisely, clearly, and appropriately;

5m121 – connect real-life statements with probabilityconcepts (e.g., if I am one of five people in a group,the probability of being chosen is 1 out of 5);

6e1 • communicate ideas and information for a variety ofpurposes (to inform, to persuade, to explain) and tospecific audiences (e.g., write the instructions forbuilding an electrical circuit for an audienceunfamiliar with the technical terminology);

6e50 • express and respond to a range of ideas andopinions concisely, clearly, and appropriately;

6m122 – connect the possible events and the probability ofa particular event (e.g., in flipping a coin, there aretwo possibilities; in rolling a die, there are sixpossibilities);

DescriptionStudents volunteer to play tic-tac-toe on the blackboard with the teacher while the rest of the class observes.The teacher goes first each time. Students are encouraged to look for strategies for winning and how thegame is predictable. After discussing strategy and how probability does or does not relate to tic-tac-toe, theclass develops a list of criteria that could be used to evaluate games (e.g., enjoyment, difficulty level, time ittakes to play). This criteria will be used in subtask 4 to help students develop a survey.

Students reflect in their journals about games that involve strategy and chance.

GroupingsStudents Working As A Whole ClassStudents Working In Small GroupsStudents Working Individually

Teaching / Learning StrategiesDemonstrationDiscussionCollaborative/cooperative LearningLearning Log/ Journal

AssessmentThrough observations the teacher will beable to determine how well Grade 5 and 6students are able to:- use terminology such as chance, likely,probability, fair, and possibility- communicate ideas and information in agroup discussion- respond to other students' opinions andideas concisely, clearly, and appropriately.

The teacher may wish to follow up on thejournal prompt responses. Consider creatinga class chart that lists games of chance,games of strategy, and games involvingboth chance and strategy.

Assessment StrategiesLearning LogObservation



1. Playing Tic-Tac-Toe:- Review the rules of tic-tac-toe (ask the students to explain).- Ask how the class could keep track of how many students can win against the teacher (make a T-chart on




Resources

the board or a piece of chart paper).- Invite a student to keep track of who wins.- Ask for one volunteer at a time to play tic-tac-toe with the teacher. The only stipulation is that the teacherwill always go first.- Ask students to look for patterns in winning and losing. - Is there a strategy to the game? - Is any chance involved in winning?

2. Discuss the Game:- Write the student observations on a piece of chart paper. Be sure to address the following ideas: - Is the game predictable? How? - Is the game fun once you know the strategy? - Is the game fair? - Can you determine the probability of winning? Why? Why not? - What is a game of chance? - Is this a game of chance?

Small Group (in Toy Companies)

What are the Criteria for "Good" Games:- Ask the students to brainstorm about what makes a "good" game (e.g., fun, challenging, not too long, oreasy to understand). The students should make their list on a large piece of paper with their company nameat the top.- After 3 or 4 minutes, have the groups circle the three criteria that they think are the most important.- Ask each group to post their list on the wall and present their top three criteria to the class.

Individual Work

Math Journal:Ask the students to respond to the following prompt:Some games involve strategy. Some games are pure chance. Can games be both chance and strategy?Explain your thinking.

AdaptationsThe journal prompts may be overwhelming for students with a learning disability. The teacher may wish togive the student the prompts orally and scribe the responses, or allow the LD student access to thecomputer.

Students who cannot cope with the complexity of the journal prompt may respond to a simpler prompt suchas:- Write about what happened when the teacher played tic-tac-toe with the students.

Game Connection: Go-Moku BLM2.1 Japanese Tic-Tac-Toe.cwk




Notes to TeacherExtension Idea:Extend this activity by discussing how the game can be "set up" to ensure a tie (what has to happen?) orby introducing Go-Moku, a Japanese version of tic-tac-toe (see BLM2.1 Japanese Tic-Tac-Toe).

Developing Criteria for a Good Game:These criteria will be needed again in subtask 4. Be sure to keep the results posted or handy in theclassroom.

Teacher Reflections


Making a Game of It! Subtask 3Learning About Graphs


Expectations5m110 • evaluate and use data from graphic organizers;5m114 – display data on graphs (e.g., line graphs, bar

graphs, pictographs, and circle graphs) by hand andby using computer applications;

5m116 – explain the choice of intervals used to construct abar graph or the choice of symbols on a pictograph;

5m119 – construct labelled graphs both by hand and byusing computer applications;

5m120 – evaluate data presented on tables, charts, andgraphs and use the information in discussion (e.g.,discuss patterns in the data presented in the cells ofa table that is part of a report on a scienceexperiment);

6m106 • systematically collect, organise, and analyse data;6m117 – explain how the choice of intervals affects the

appearance of data (e.g., in comparing two graphsdrawn with different intervals by hand or by usinggraphing calculators or computers);

6m119 – recognize that different types of graphs canpresent the same data differently (e.g., a circlegraph will show the relationship between the dataand a part of the data, a bar graph will show therelationship between separate parts of the data);

6m120 – construct line graphs, bar graphs, and scatterplots both by hand and by using computerapplications;

DescriptionIn this subtask, students work in pairs to review, learn, about, and discuss five types of graphs: bar, doublebar, circle, line, and pictograph. They are then given a set of data about games and asked to create their owngraph with a specific audience in mind. This subtask is done over two periods.

Students use their math journals to reflect on graphing and on their data management task.

GroupingsStudents Working As A Whole ClassStudents Working IndividuallyStudents Working In Pairs

Teaching / Learning StrategiesDirect TeachingGraphingDiscussionLearning Log/ JournalOpen-ended Questions

AssessmentTeachers should question students throughinformal conferences whenever possible andrecord their observations. This is invaluableformative assessment information that willassist teachers in determining whether or notstudents are learning new concepts.

Through questioning and observations theteacher will be able to determine how wellGrade 5 and 6 students are able to:- make comparisons between types ofgraphs- interpret data and make reasonablechoices about the type of graph to create- explain their choice of a graph (e.g., "Whydidn't you use a _____ graph?")- display data accurately on a graph- explain their choice of intervals- explain how their choice of intervals affectsthe appearance of data (Grade 6)- make comparisons between their graphsand those made by other students

Teachers can observe student performancethrough a variety of learning situationsincluding:- discussions- paired investigations of graphs- development of the graph to meet therequired audience/purpose- presentations of the graph and rationale- written reflections in the math journal




In this subtask, students are asked toassess their graph with their partner (BLM3.5Self-Assessment). This assessment shouldbe attached to their graph.

Assessment StrategiesExhibition/demonstrationLearning LogSelf AssessmentQuestions And Answers (oral)

Assessment Recording DevicesChecklistAnecdotal Record

Teaching / LearningDay 1: Investigating Five Types of Graphs

Paired Work

Looking at Different Types of Graphs:- Distribute to the students a copy of BLM3.1 Looking At Graphs and BLM3.2 Investigating Graphs.- Ask students to investigate the five kinds of graphs on the sheet, and respond to the prompts on BLM3.2Investigating Graphs with their partner.

Whole Class

Exploring the Purpose of Each Graph:- Ask the students to share their observations with the whole class. Record on chart paper.- Discuss the graphs in more detail, referring to the student responses. You may wish to use the followingprompts as discussion starters:1. The pictograph and circle graphs have a legend. What is the purpose of the legends? Why don't theother graphs have a legend? (Bar and line graphs have a scale on the y-axis that explains "how many.")2. Has anyone ever seen a bar graph that has no spaces in between them? Why is this? (Bars with nospaces between are called histograms. Each bar in a histogram represents an interval or range such asnumber of weeks.)3. Why use a line graph at all? Why not always use a bar graph? (A line graph is used to show change overtime. You can easily see whether something is increasing, decreasing, or staying the same over time.)4. When do we use a circle graph? What would make circle graphs hard to read? (Circle graphs show howa whole is broken into parts. Be careful of really small segments.)

Individual Work

Math Journal:Ask students to respond to one of the following prompts:a) Describe one type of graph in detail, as if the person you are describing it to has never seen one before(this person does not know any of the vocabulary associated with bar graphs).b) What kinds of graphs do you see most often in the media. Give specific examples. Why do you thinktthe media uses these graphs most often?




Resources

Day 2: Building Graphs!

Paired Work

1. Graphing Task:- Give each pair of students a copy of BLM3.3 Tally Sheet and one of the prompts from BLM3.4 What's It For?- Instruct students to use the tally sheet to develop their own graph. Students need to think about the purposeof the graph and the audience who will be viewing it. They should be prepared to explain why they chose tobuild the graph that they did.- Students can refer to the graphs that were investigated previously if they need reminders about thecomponents of the graphs.

2. Self-Assessment:- Go over the self-assessment sheet (BLM3.5 Self-Assessment)- Ask all pairs of students to complete a self-assessment form for their graphs and attach it.

3. Presenting the Graphs:- Ask the pairs who were making graphs for the same audience to come up to the front together.- Have all pairs quickly show their graphs and explain why they made them.

Individual Work

Math Journal:Ask students to respond to the following prompts:Write about the activity today. What did you learn? What did you notice about the graphs that the othergroups made? Were you satisfied with your graph?

AdaptationsStudents who need accommodations in order to get their ideas on paper should be paired up with a student whocan assist in the written portion of the task. During the whole group discussion about graphing, put large diagramson the wall or blackboard. Also, be cognizant of the speed of the discussion, as it often takes learning disabledstudents longer to formulate their ideas into verbal responses.

Looking at Graphs BLM3.1 Looking at Graphs.cwk

Investigating Graphs BLM3.2 InvestigatingGraphs.cwk

Tally Sheet BLM3.3 Tally Sheet.cwk

What's It For? BLM3.4 What's it For.cwk

Self-Assessment BLM3.5 SelfAssessment.cwk

grid paper 1

compass, large lids, masking tape 1




Notes to TeacherCreating the Graph:Students who choose to make a circle graph will need to have some method for making an appropriatesized circle. They should be able to brainstorm possible solutions to this problem (e.g., compass, large lid, ormasking tape roll).

Teacher Reflections


Making a Game of It! Subtask 4Making A Good Game Of It


Expectations5m113 – design surveys, collect data, and record the

results on given spreadsheets or tally charts;5m120 – evaluate data presented on tables, charts, and

graphs and use the information in discussion (e.g.,discuss patterns in the data presented in the cells ofa table that is part of a report on a scienceexperiment);

6m106 • systematically collect, organise, and analyse data;6m110 • evaluate data and make conclusions from the

analysis of data;6m114 – design surveys, organize the data into

self-selected categories and ranges, and record thedata on spreadsheets or tally charts;

DescriptionThis subtask is a continuation of subtask 2, where students decided on the top three criteria for a "good"game. Students review their data and after a brief discussion on surveys, develop their toy company's survey.A tracking sheet is provided for students to record information pertaining to their survey (e.g., their surveyquestion).

Students write a journal entry about surveys in the local community.

GroupingsStudents Working As A Whole ClassStudents Working In Small GroupsStudents Working Individually

Teaching / Learning StrategiesDiscussionDirect TeachingInquiryLearning Log/ Journal

AssessmentThrough questioning and observations theteacher will be able to determine how wellGrade 5 and 6 students are able to:- use data management vocabulary indiscussions (e.g,. sample, population,survey, and random sample)- generate and discuss a selection ofappropriate survey questions- design a survey with their small group- create an appropriate tally chart- tally their survey data

Students should also be asked to describetheir initial responses to the data. Forexample:Is the data as you predicted?What do you find surprising?Would you design the survey questionany differently if you had the chance todo it again?

Teachers should observe studentunderstanding of surveying through avariety of learning situations includingdiscussions, group decision making on thenature of their survey, and writtenreflections in the math journal.

Assessment StrategiesLearning Log




Observation



1. Reviewing the Criteria of a "Good" Game:- Facilitate a discussion about the criteria that was generated in subtask 2. Overall, what did the class thinkwere the most important criteria for a good game?- Suggest any criteria that may have been missed (e.g., use of skill, use of knowledge, appearance, subjectmatter, or rewards).- List the criteria again, or provide all of the charts with additions in plain view for the students.

2. Surveying Their Peer Group:- Explain that the students will be surveying students/siblings/neighbours who are in their approximate agegroup (since the game of chance they will be developing will be for their age group and must also bereflective of their survey results).- Ask students what they think the term "sample" means.- Have them apply their definition of sample to surveying. Is a sample supposed to include everyone?- Introduce the term "random sample" and ask what the students think it would mean ( i.e., If the target groupis 11- year-old students who live in X town, a random sample would be a selection of students from all overtown).- You may also wish to introduce the term "population" (the term given to the target group).- Discuss what the survey question might look like and make a list of all questions that are suggested.Discuss which ones will provide more information (e.g., if people are given a choice of factors to choosefrom, how many choices do they get?)

Small Groups (Toy Companies)

1. Creating a Survey:- Explain that the students will be creating a survey to find out what, according to game players, are the mostimportant factors or criteria of a good game. (keeping in mind the criteria they indicated as important insubtask 2).- Ask the students to use BLM4.1 Our Survey to: - indicate who their surveyed audience is - identify the number of people who will be surveyed - record their survey question - create their tally

2. Completing the Survey:** The survey does not have to be completed at school. Where and when the survey is completed will be upto the teacher and students.- Set a reasonable timeline for gathering the data. (The data is not required until Subtask 7, so the studentshave a bit of time to gather their information.)

Individual Work

Math Journal:Ask students to respond to the following prompt:




Resources

Who collects information in our local communities? Why do they collect it? Do you think this datacollection is important? Why?

AdaptationsStudents who cannot cope with the complexity of the journal prompt may respond to a simpler prompt suchas:What is a survey? What kind of worker might have to do a survey for their job?

Our Survey BLM4.1 Our Survey.cwk

Notes to TeacherDiscussion on Surveys:This discussion led by the teacher is very important for establishing mathematical terminology involved insurveying (population, sample, random sample). It is also very important for students to understand that asurvey question must be decided upon and used consistently in order to collect accurate information.

Teacher Reflections


Making a Game of It! Subtask 5The Penny Flip Experiment


Expectations5m111 • demonstrate an understanding of probability

concepts and use mathematical symbols;5m113 – design surveys, collect data, and record the



5m121 – connect real-life statements with probabilityconcepts (e.g., if I am one of five people in a group,the probability of being chosen is 1 out of 5);

5m122 – predict probability in simple experiments and usefractions to describe probability;

6m106 • systematically collect, organise, and analyse data;6m112 • examine the concepts of possibility and probability;6m113 • compare experimental probability results with

theoretical results.6m114 – design surveys, organize the data into



6m123 – examine experimental probability results in thelight of theoretical results;

DescriptionStudents flip a penny a given number of times in order to explore the probability of getting heads or tails. Eachstudent creates a tally sheet and collects data which is later added to a class chart. The teacher leads adiscussion about the difference between experimental and theoretical results, and probability and possibility.During this subtask, the teacher observes how the students go about collecting and organizing their data.

Students are prompted to write about the results of their investigation in their math journals.

GroupingsStudents Working As A Whole ClassStudents Working In PairsStudents Working Individually

Teaching / Learning StrategiesDemonstrationExperimentingCollaborative/cooperative LearningDiscussion

AssessmentThe teacher can read the student's mathjournal to gather formative assessment dataon the student's understanding ofprobability.

Through questioning and observations theteacher will be able to determine how wellGrade 5 and 6 students are able to:- use mathematical terminology appropriatelyin discussions and in their writing (e.g.,probability, chance, likely, possibility,theoretical probability, experimentalprobability)- keep a tally of their results- reflect on results in their tally and on theclass tally

Assessment StrategiesObservationQuestions And Answers (oral)Learning Log



Demonstration:- Explain to the students that they will will be gathering data on the results of a number of penny flips.




- Discuss the possible outcomes of one penny flip. Ask students to predict what will happen with one flip.- Choose a student to flip the penny and announce the results, heads or tails.- Record the results in a simple tally (on chart paper or an overhead).- Continue this process for 20 flips.

Paired Work

1. Penny Flip Experiment:- Ask students to decide who will be the recorder and who will flip the penny.- Distribute the Penny Flip Recording Sheet (BLM.5.1 Penny Flip) where students record their predictions.- Ask them to complete the experiment (30 flips) while keeping a tally.- Let students know that they can revisit their predictions during the experiment.- Ask partners to switch roles and repeat the experiment (total of 60 flips).

2. Collating the Data:- Pose the following question: Based on the results from your experiment (total of 60 tosses), predict theresults for the entire class. (Have the students calculate the total number of flips for the class first.Alternatively, they may wish to make their prediction in the form of a percentage (e.g., I think that 63% of theflips will be heads).- Ask the students to record their data on the class tally sheet.

Whole Group

1. Discussing the Results:- Initiate a discussion about the findings. The following prompts can be used to guide the discussion:- How did you come up with your predictions?- Did you change your predictions during the experiment? Why or why not?- Was anyone surprised by the results? Why?- Why do you think the class got the results it did?

2. Theoretical and Experimental Probability (Grade 6 students only; Grade 5 students can begin their mathjournal entry):** See Teacher's Notes for information on theoretical and experimental probability.- Explain to students that the theoretical probability of tossing heads in one toss is 1 / 2. Explain what eachnumber means and write it on the board.- Ask students what they think the theoretical probability of tossing heads is in a 20-toss experiment.- Explain the difference between experimental probability and theoretical probability.- Ask students the experimental probability of tossing heads in the whole group's initial experiment (20tosses). Discuss this calculation. Have students calculate the experimental probability of the combined resultsfor the class.- Discuss how the small sample differed from the large sample.** At this point, ask the Grade 6 students to go back to their recording sheet and indicate the experimentalprobability and theoretical probability of tossing heads and tails.

Individual Work

Math Journal:Ask students to respond to the following prompt:Write about the results of the penny flip experiment. Explain how the experimental results compare to thetheoretical results (what actually happened compared to what should have happened).




Resources

AdaptationsStudents with fine motor difficulties may have difficulty flipping the coin successfully. These students could tallytheir partner's tosses using two different coloured blocks or by making tick marks on the blackboard using widechalk.

Penny Flip Recording Sheet BLM5.1 Penny Flip.cwk

pennies 1




Notes to TeacherFlipping the CoinsIt can get pretty noisy flipping coins, and pennies have a tendency to roll off desks. These problems can besolved by lining shoeboxes or shoebox lids with felt and flipping the penny into the box or lid.

Theoretical and Experimental Probability - An OverviewIt is important that Grade 6 students begin to differentiate between these two types of probability.

1. Essentially, theoretical probability is what you would expect to occur in "theory". We would expect that in60 penny flips, 30 flips would be heads, and 30 flips would be tails. Experimental probability is what we findin an experiment. The students may notice that in 60 flips, 25 are heads and 35 are tails.

2. To show theoretical probability, we put the number of favourable outcomes as the numerator (for pennyflips there is only one favourable outcome if we are predicting heads) and the number of possible outcomesas the denominator (for penny flips there are two possible outcomes: heads and tails). The theoreticalprobability of flipping heads is 1/2. To figure out the theoretical probability of 60 flips, we would multiply 60by 1/2. Therefore, we know that the theoretical probability is that you will toss heads 30 times out of 60.

3. To show experimental probability, we use the actual number of times that heads were flipped as thenumerator (25), and use the number of trials as the denominator (60). The experimental probability istherefore 25/60 or .42. (The theoretical probability is 1/2 or .50.) The experimental probability is fairly closeto the theoretical probability.

Understanding ProbabilityThe probability of an event happening can be a number from 0 to 1. This number can be expressed as afraction, a percentage, or a decimal. (Note: Odds are given in a ratio. The odds of winning are expressedas the number of favourable outcomes compared to the number of unfavourable outcomes).

If the probability of an event happening is 0, then the event is impossible. If an event is sure to happen, theprobability is 1. The more unlikely an event is, the closer the number will be to 0. For example, a 25%chance of rain (.25) is closer to 0 than a 75% chance of rain (.75).

Important Definitions:theoretical probability - The number of favourable outcomes divided by the number of possible outcomes.experimental probability - The chance of an event occurring based on the results of an experiment.probability - A number that shows how likely it is that an event will happen.possibility - Any event or thing that is possible.

Teacher Reflections


Making a Game of It! Subtask 6Spinner Experiment


Expectations5m111 A • demonstrate an understanding of probability

concepts and use mathematical symbols;5m113 A – design surveys, collect data, and record the



5m122 A – predict probability in simple experiments and usefractions to describe probability;

5m114 A – display data on graphs (e.g., line graphs, bargraphs, pictographs, and circle graphs) by hand andby using computer applications;

6m112 A • examine the concepts of possibility and probability;6m113 A • compare experimental probability results with

theoretical results.6m114 A – design surveys, organize the data into


6m120 – construct line graphs, bar graphs, and scatterplots both by hand and by using computerapplications;

6m122 A – connect the possible events and the probability ofa particular event (e.g., in flipping a coin, there aretwo possibilities; in rolling a die, there are sixpossibilities);

6m123 A – examine experimental probability results in thelight of theoretical results;

DescriptionIn this subtask, students construct a spinner and make predictions about what they think will happen whenthey spin a given number of times. Students record their spins in a self-constructed tally, and then reflect onwhat happened in the experiment. The students will be assessed by the teacher on their understanding ofprobability and their ability to gather and record data.

In their math journals, students compare the spinner experiment with the penny flip experiment.

GroupingsStudents Working Individually

Teaching / Learning StrategiesGraphingLearning Log/ JournalDemonstration

AssessmentBLM6.5 Teacher Checklist is available forteachers to use to assess the students'understanding of selected datamanagement and probability concepts,skills, and knowledge. Two checklists areprovided within the blackline master, onefor each grade. It is very important thatanecdotal comments be used as often aspossible to expand on the ratings given onthe Observation Checklist.

In addition to assessing the students'written work, teachers should listen togroup or paired discussions (about thetwo spinners). Observe to assesswhether students:- realize that the spinners have the sameprobability of spinning each colour- understand why the results might bedifferent. (You need to spin many, manytimes before the experimental results beginto look more like the theoretical results.)

Ask questions of the Grade 6 studentsabout theoretical and experimentalprobability. Phrase your questions to get atthe mathematical language of probability.For example:- I notice that you are going to spin 40times and you predict that blue will belanded on 20 times. How did you comeup with this number? (Student explains.)Do you know what that is called?




(Theoretical probability.) What isexperimental probability then? (Studentexplains.)Note: This is formative assessment data.Students will need a lot of experience withusing the terms theoretical andexperimental before they are given asummative assessment.

Assessment StrategiesPerformance TaskLearning Log

Assessment Recording DevicesChecklistAnecdotal RecordRating Scale

Teaching / LearningIndividual Work

1. Spinner Experiment:- Explain to the students that they will be a) making spinners; b) conducting an experiment with their spinners;and c) graphing their individual results.- Demonstrate to the students how to make a spinner using one of the spinner templates provided in BLM6.2Spinner Template (instructions provided in BLM6.1 Making Spinners).- Explain that half of the students will make Spinner A and the other half will make Spinner B (students couldbe divided by grade).- Ask students to complete the worksheet My Predictions (BLM6.3 Predictions). Go over the worksheet withthe group.

2. Reflecting on the Results:- Ask the students to reflect on their findings on the worksheet Thinking About the Results of My SpinnerExperiment (BLM6.4 Results)

Group or Paired Work

Comparing the Results of the Two Different Spinners:- Group students together (e.g., one student who used Spinner A with a student who used Spinner B).- Ask students to discuss the following:- Compare your spinners. What is the same? What is different?- How did your predictions vary? How did your results vary? What are the reasons for these variations?- Have students submit their work (Predictions and Results pages) for scoring.

Individual Work

Math Journal:Ask students to respond to the following prompt:How was this experiment similar to and different from the penny flip experiment?




Resources

AdaptationsStudents with specific learning disabilities in the area of mathematics may be able to take part in the task if it isadapted to be appropriate for their level. For example:

Ask the students to make predictions for the spinner and explain orally why they made that prediction. Havethe students conduct their experiments and keep track of each spin. Once they are done, ask them to explainwhat they found. Have them repeat the experiment, asking them to make a new prediction. Observe to see ifthe students make the same prediction or adapts it to reflect the results of their first experiment. Does thestudent understand the idea of equal/unequal chance probability of landing on a certain colour?

Instructions for Making Spinners BLM6.1 Making Spinners.cwk

Spinner Templates BLM6.2 SpinnerTemplate.cwk

Making Predictions BLM6.3 Predictions.cwk

Results of the Spinner Experiment BLM6.4 Results.cwk

Observation Checklist BLM6.5 Teacher Checklist.cwk

10 cm x 10 cm squares of cardboard 1

paper clips 1

buttons 1

grid paper 1

Notes to TeacherPossible Extensions:

1 a) Present the students with two different spinners that contain the numbers 2, 3, 4, and 5. Pose thisproblem: if each participant gets five spins and the winner is determined by the highest sum of the fivenumbers, which spinner would you choose if you want to win. b) Have the students create pairs of spinners for this task.

2. Give the students some game data. Have them create the spinner that they think was used in the game.

Teacher Reflections


Making a Game of It! Subtask 7Graphing the Data


Expectations5m109 A • interpret displays of data and present the

information using mathematical terms;5m110 A • evaluate and use data from graphic organizers;5m114 A – display data on graphs (e.g., line graphs, bar


5m116 A – explain the choice of intervals used to construct abar graph or the choice of symbols on a pictograph;

5m119 A – construct labelled graphs both by hand and byusing computer applications;

5m120 A – evaluate data presented on tables, charts, andgraphs and use the information in discussion (e.g.,discuss patterns in the data presented in the cells ofa table that is part of a report on a scienceexperiment);

6m110 A • evaluate data and make conclusions from theanalysis of data;

6m117 A – explain how the choice of intervals affects theappearance of data (e.g., in comparing two graphsdrawn with different intervals by hand or by usinggraphing calculators or computers);

6m119 A – recognize that different types of graphs canpresent the same data differently (e.g., a circlegraph will show the relationship between the dataand a part of the data, a bar graph will show therelationship between separate parts of the data);

6m120 A – construct line graphs, bar graphs, and scatterplots both by hand and by using computerapplications;

6m121 A – make inferences and convincing arguments basedon the analysis of tables, charts, and graphs;

DescriptionIn this subtask, the students use the data generated in subtask 4 to construct a series of graphs. Studentscompare their graphs and analyse the data. This work is done independently and is self-assessed by thestudent using the Graph Rubric. (This subtask provides students with practice before they are assessed ontheir ability to create graphs in Subtask 9.)

GroupingsStudents Working In Small GroupsStudents Working Individually

Teaching / Learning StrategiesCollaborative/cooperative LearningGraphingDemonstration

AssessmentStudents will use the Graph Rubric to assesstheir two graphs as well as their discussions.It will have been very important for thestudents to have seen the rubric BEFOREthey begin the task. A review of theexpectations and rubric will help to focustheir work and their discussions.

The teacher should review the graphs andthe student self-assessment. Feedback willbe very important for the students since theyare assessed on many of these skills againin Subtask 9.

Assessment StrategiesPerformance TaskSelf AssessmentObservation

Assessment Recording DevicesRubricAnecdotal Record


Introducing the Task and Rubric:- Explain that the task is done independently (for the most part) in order to see how well students can creategraphs without the support of peers.- Review the task (compiling data, creating two graphs, reflecting on their graphs, discussing with a smallgroup, and assessing their work).- Go over the rubric with the students. Point out the slight differences in the Grade 5 and Grade 6 rubrics.




Resources

Small Groups (Toy Companies)

Compiling Survey Data:- Instruct each company to compile its collected data onto one master tally chart.

Individual Work

1. Creating a Graph:- Each student uses the compiled data to create two different types of graphs. Students must choose fromthe five that were investigated in subtask 3.

2. Reflecting on Their Graph:- Instruct each student to complete the My Choices worksheet (BLM7.1 My Choices).

Small Group / Paired Work

Defending the Graphs:- Ask students to discuss their graphs with each other. The following prompts can be used:- Think about your two graphs. Does the data look the same in both graphs? When would you need torepresent data in different ways?- Which of the two graphs do you think is the most effective? Explain why.- Look at all of the chosen graphs in the group. Which of these is the most effective? (Be prepared toexplain to the whole group.)- Allow the students to share their graphs with the whole group as appropriate.

** Students assess their graphs along with their rationale for choice of graph(s) and choice of interval(s)(written on the worksheet My Choices). They need to also consider their discussions with their peers.

AdaptationsThis graphing activity should be done independently. Students with IEPs will have specific accommodations listedfor assessment tasks. These students may need assistance creating their graph (e.g., using a computer) or inexplaining their choice of graph and intervals (e.g., scribe).

Some students will need support assessing their own work. Prompt the student through the rubric, referring to theirwork as you go. The student can circle the description that best matches their performance.

Graph Rubric - Self Assessment (5)


Rationale for Choice of Graph BLM7.1 My Choices.cwk

grid paper 1




Notes to TeacherGraphing the Data:Some students may need to review the five types of graphs that were investigated in subtask 3. A smallgroup of students who want a "refresher" could be invited to get together for a 5- to 10-minute review. UseBLM3.1 Looking at Graphs to help guide the discussion.

Choice of Graph:Students will likely use either the bar graph or pictograph to display their data. It will be important forstudents to have other opportunities to graph data using a line graph and circle graph.

Use of Computer Technology:The Ontario Curriculum Grades 1 - 8, Mathematics (1997) indicates that both Grade 5 and Grade 6 studentsshould be able to construct graphs using computer applications. If at all possible, students should be giventhe opportunity to learn how to make graphs on the computer.

Teacher Reflections


Making a Game of It! Subtask 8 Game Sticks


Expectations5m123 – use tree diagrams to record the results of simple

probability experiments;5m124 – use a knowledge of probability to pose and solve

simple problems (e.g., what is the probability ofsnowfall in Ottawa during the month of April?).

6m111 • use a knowledge of probability to pose and solveproblems;

6m124 – use tree diagrams to record the results ofsystematic counting;

DescriptionIn this game, each person (or team) uses 6 two-sided sticks (tongue depressors), which students must firstdecorate. After the demonstration game, students record a few questions about probability as it relates to thegame and then play the game, a few times to answer their questions and test their theories. In pairs, thestudents construct tree diagrams to determine the possible outcomes and discuss their findings.

In their journals, students then respond to prompts about the activity.

GroupingsStudents Working In PairsStudents Working In Small Groups

Teaching / Learning StrategiesDemonstrationLearning Log/ JournalCollaborative/cooperative LearningDiscussion

AssessmentThrough questioning and observations theteacher will be able to determine how wellGrade 5 and 6 students are able to:- use tree diagrams to record the possiblecombinations of plain and patterned sticks- use mathematical language in large andsmall group discussions as well as in theirjournal responses

Assessment StrategiesObservationLearning LogQuestions And Answers (oral)


Teaching / LearningDay 1

Whole Group

Introduction to the Activity:- Provide the class with some background information on the game (see subtask Notes).- Show the students a set of decorated sticks – one side is plain (no design), the other side is decorated –and explain that they will make their own sticks after they are introduced to the game.- Demonstrate the game with a volunteer, going over the rules detailed in BLM8.1 Game Sticks.- Distribute a copy of the instructions and a set of tongue depressors to each pair of students.




Individual Work

1. Math Journal:Ask each student to respond to the following prompts:Knowing the rules of the game, make some predictions about what you think will happen. Use the languageof probability to explain your thinking. Write any questions that you have.

2. Making "Sticks":- Distribute the tongue depressors and instruct the students to decorate them within a given period of time(e.g., 5 minutes maximum).

Paired or Group Work

1. Playing the Game:- Instruct the students to play the game a few times in order to answer their questions and test their theories.

Day Two

Paired or Group Work

1. Playing the Game:- Instruct the students to play the game one more time for review.

2. Reflecting on the Game:- Give each pair of students one of the prompts below (found in BLM8.2 Reflection). Let them know that theywill be sharing their ideas with the group. They should record their thinking.a) What number of counters are players most likely to collect on each turn? Why?b) Do you think you had more tosses that resulted in taking counters or not taking counters? Explain.c) What does the scoring for Game Sticks have to do with probability?d) How could you find out which combinations of sticks are most likely?e) Describe another game that you like to play that involves probability and explain how probability affectsthat game.

Whole Group

Analysing the Game:- Ask the students how the game could be broken down in order to figure out the probability of winning.- Suggest a simpler version of the game where one stick is tossed. Draw a tree diagram to show the possibleoutcomes.- Repeat with a two-stick version of the game. What are the possible outcomes now? Ask the students howthey would represent those outcomes with a tree diagram. Ask for volunteers to try it out.

Paired Groupings

Analysing the Game:Ask pairs of students to continue to play the game with three, four, and five sticks. Give them the followingprompts:- What did you discover about the way four sticks can land?- Do you see any patterns beginning to develop?- Describe the probability of getting different combinations.- How many ways can you get all four sticks to land design-side up?




Resources

Individual Work

Math Journal:Ask students to respond to the following prompt:Can you define the probability of winning the Stick Game? Explain your thinking.

AdaptationsBe cognizant of student participation in large and small group discussions. Less confident students who mayor may not have specific exceptionalities will need additional prompts and perhaps additional time to formulatetheir ideas and respond.

Students who cannot cope with the complexity of the journal prompt may respond to a simpler prompt suchas:Did you have a good chance of winning the Stick Game? Why?

Instructions for Playing BLM8.1 Game Sticks.cwk

Prompts for Pairs of Students BLM8.2 Reflection.cwk

tongue depressors 12

counters (e.g., toothpicks, cubes) 10

Notes to TeacherTree DiagramsTree diagrams are used to help show all combinations of items. For example, if an ice cream cone can havethree scoops of either strawberry (s), chocolate (c), or vanilla (v), a tree diagram can help show all of thepossible combinations. (Strawberry - sss, ssc, ssv, scc, svv, scv)

Rationale for this ActivityStick Games provides students with the opportunity to discuss a game of chance where the probability ofwinning is not immediately obvious. There is a considerable amount of investigative possibilities in thissubtask. The teacher is able to explore many levels (if desired) by looking at possible results when thegame uses five, four, or three sticks instead of six.

This activity also provides an authentic context for using tree diagrams. These diagrams help students tosort out the possible outcomes of each toss in a visual format.

Teacher Reflections


Making a Game of It! Subtask 9What Does the Data Tell Us?


Expectations5m19 – identify and investigate the use of number in

various careers;5m20 A – identify and interpret the use of numbers in the

media;5m114 A – display data on graphs (e.g., line graphs, bar


5m117 A – calculate the mean and the mode of a set of data;5m118 A – recognize that graphs, tables, and charts can

present data with accuracy or bias;5m119 A – construct labelled graphs both by hand and by

using computer applications;5m120 A – evaluate data presented on tables, charts, and


6m21 – identify the use of number in various careers;6m22 A – identify, interpret, and evaluate the use of

numbers in the media;6m110 • evaluate data and make conclusions from the

analysis of data;6m118 A – calculate the median of a set of data;6m119 A – recognize that different types of graphs can

present the same data differently (e.g., a circlegraph will show the relationship between the dataand a part of the data, a bar graph will show therelationship between separate parts of the data);

6m115 – experiment with a variety of displays of the samedata using computer applications, and select thetype of graph that best represents the data;

DescriptionStudents use data about a popular Canadian game in order to create graphs and calculate mean and mode.Grade 6 students also investigate median. For this subtask, point totals for Wayne Gretzky and Mia Hamm areprovided. The students must display one athlete's data in more than one way in order to show bias. Thestudent's graphs are assessed using a rubric.

GroupingsStudents Working In Small GroupsStudents Working IndividuallyStudents Working As A Whole Class

Teaching / Learning StrategiesCollaborative/cooperative LearningLearning Log/ JournalDirect Teaching

AssessmentThrough questioning and observations theteacher will be able to determine how wellGrade 5 and 6 students are able to:- create two graphs that give differentmessages (create bias)- understand the concept of mean andmode (and median - Grade 6)- calculate mean and mode (and median -Grade 6)- explain their choice of graph; and- use mathematical language in theirdiscussions and written work

The students' graphs are done individuallyand are assessed by the teacher using theGraph Rubric. Please note that only fiveexpectations will fit onto the rubric. Inaddition, the following expectations areassessed using the rubric: 5m20, 5m119,5m120, and 6m22.

Assessment StrategiesObservationPerformance TaskLearning Log

Assessment Recording DevicesRubricAnecdotal Record

Teaching / LearningDay One




Whole Group

Teacher Instruction on Mean, Median, and Mode:

Mean (average):- Display the following numbers on the board:12 15 7 17 18 10 12 14 12- Tell the students that these are a student's mathematics test scores (out of 20).- Ask students to quickly guess at what the student seemed to get each time?- Do a demonstration: Tell the students that each mark will be represented with a linking cube. Link 12 cubestogether to represent the results of the first test. Ask eight other students to represent the scores for theother tests using linking cubes. Stand the towers up side by side to show the differences in test results. Askstudents what the test mark would be if the total of all the test marks remained the same, but each student gotthe same mark. Redistribute the cubes to make equal towers (13 cubes high). Explain that this is the averagescore.- Discuss how to calculate the average, or the mean, score for the student without using cubes.(12+15+7+17+18+10+12+14+12 = 117. Divide this total by 9 to get the mean score of 13); Mean = 13- Ask the students what would happen to the mean if the next test score was 18 (the mean would go upslightly).

Mode:- Explain that the mode is the most frequent number in a set of data.- Ask the students what the most frequent score was in these test results (12).

Median (in the Grade 6 curriculum, but all students participate in the lesson):- Explain that the median is the score that is exactly in the middle of the data. There will be as many scoresunder the middle score as above it.- Ask a volunteer to line up the scores on the blackboard, in order from the lowest to the highest.- Ask the students to put up their hand when they have decided upon the median (12).7 10 12 12 12 14 15 17 18- Ask the students if scoring 18 on the next test would affect the median.- Discuss the fact that there is now an even number of test scores and therefore no middle number. Ask forpossible solutions. (Take the two middle numbers, 12 and 14. Add 12 and 14 together and divide by 2. Thenew median would be 13 and therefore the answer is yes, the median would be affected by an additionalmath score of 18.)

Paired Work

1. Mean/Median/Mode Investigation:a) Ask the students whether or not the mean, median, and mode could be the same number for a given set.Have them work in pairs. Give them a maximum of 5 minutes to figure it out, then discuss with the wholegroup.b) Ask the students if it would be accurate for a teacher to use the mean, median, or mode to predict whatthe next math test score for this student would be. Put three questions on the board for them to consider: - Would it make sense that the next score would be 18? Why or why not? - Which calculation would be the most useful to predict the outcome of the student's next test? - What factors, outside of these numbers, would you have to consider (e.g., difficulty of the next test andwhether or not the student studied)?- Discuss with the whole group.

2. Taking Notes:- Ask students to write down observations from this lesson in their math journals. They may also make note




Resources

of the definitions for mean, mode, and median. These observations can be made with support from a partner.

Day Two

Small Group

1. Wayne Gretzky or Mia Hamm's Career Statistics:- Provide each group of students with the statistics.- Explain that they will be investigating the goals, assists, and points data for: - mean - mode - median

2. Scoring Trends:- Introduce the two athletes: Wayne Gretzky and Mia Hamm (see Teacher Notes for details about Mia).- Explain that the students will be asked to choose which athlete's data they would like to analyse and thenrepresent on a pair of graphs. The graphs must contain the data provided for the athlete, but show the datadifferently or use certain portions of the data to convey two different messages; one to support signing theathlete for the team, and one to advise against signing the athlete.- Discuss what "signing" a player means. Why would you want to sign someone? Why not? (In this case,scoring trends as the career progresses are reasons for signing or not signing.)- Hand out the data sheet and accompanying instructions. (The instructions vary slightly between the twoathletes, but "get at" the same expectations.)- Reinforce that in both cases students must create two graphs that display the athlete's career. They mustbe the same type of graph. One of the two graphs must be able to support their recommendation (through themanipulation of intervals on the graph).- Each group must attach a brief written response which explains why they think their graphs conveydifferent messages to readers. The group must also explain its choice of graph (bar, line, pictograph, orcircle).

Individual Work

Math Journal:Ask each student to respond to the following prompt:How can you create a graph that shows bias? Give some examples.

AdaptationsStudents who have specific learning disabilities will need to have significant support to complete the tasksoutlined. A strong partner who can scribe the discussions will be of particular importance. Graphing may need tobe done using a computer that already contains the data. The student is then able to manipulate the data.

Graph Rubric

Mia Hamm's Statistics BLM9.2 Hamm.cwk

Wayne Gretzky's Statistics BLM9.1 Gretsky.cwk




Task for Mia Hamm's Statistics BLM9.4 HammInvestigation.cwk

Task for Wayne Gretzky's Statistics BLM9.3 GretzkyInvestigation.cwk

grid paper 2




Notes to TeacherImportant Definitions:bias - An emphasis on characteristics that are not typical of an entire population.mean - The average; the sum of a set of numbers divided by the number of numbers in the set.median - The middle number in a set of numbers, such that half the numbers in the set are less and half aregreater when the numbers are arranged in order. For example, 14 is the median for the set of numbers 7, 9,14, 21, and 39. If there is an even number of numbers, the median is the mean of the two middle numbers.mode - The number that occurs most often in a set of data. For example, in a set of data with the values 3,5, 6, 5, 6, 5, 4, 5, the mode is 5.Source: The Ontario Curriculum, Grades 1-8 (1997)

Who Is Mia Hamm:Mia is on the US National Soccer Team, which won the gold medal at the 1996 Olympics in Atlanta. Mia hasbeen on the team since she was 15. She plays forward. Mia is a role model for young athletes around theworld.

Using Other Data:Different data could be used to investigate mean, median, and mode and to discuss how bias is createdthrough the representation of data. For example, a student could research the data from a favourite athleteand then do the activity.

Possible Extensions:If time is available, the students could work on this task in pairs or small groups and present their findings tothe class along with their graphs. They could pretend they are making a convincing presentation to teamowners to convince them to sign or not to sign the athlete.

Wayne's Mean, Median, and Mode1. Mean: The total for Wayne’s scoring over 20 years was 2857 (Divide 2857 by 20). His mean scoring perseason was 142.85, or 143.2. Median: The middle two numbers are 142 and 149. (Total = 291, divide this number by 2.) The median =145.5, or 146.3. Mode: There are no two years with the same result!

Use of Computer Technology:The Ontario Curriculum Grades 1 - 8, Mathematics (1997) indicates that Grade 6 students should be able to :- experiment with a variety of displays of the same data using computer applications, and select the type ofgraph that best represents the data

In this subtask, the students use handmade graphs. It is certainly preferable for students to be inputtingtheir data and producing a variety of graphs electronically. Students would be able to create a wider varietyof graphs. These graphs would also be helpful in discussions about bias.

Teacher Reflections


Making a Game of It! Subtask 10River Crossing


Expectations5m111 A • demonstrate an understanding of probability

concepts and use mathematical symbols;5m112 A • pose and solve simple problems involving the

concept of probability.5m121 – connect real-life statements with probability

concepts (e.g., if I am one of five people in a group,the probability of being chosen is 1 out of 5);

5m122 A – predict probability in simple experiments and usefractions to describe probability;

6m113 A • compare experimental probability results withtheoretical results.


6m123 A – examine experimental probability results in thelight of theoretical results;

6m125 – show an understanding of probability in makingrelevant decisions (e.g., the probability of tossing ahead with a coin is not dependent on the previoustoss).

DescriptionStudents take turns rolling two numbered cubes and using the sum to move their counters across the gameboard. As students play River Crossing Game, they see which combinations of numbers are the most commonand begin to strategically place their counters.

The probability of rolling sums is investigated and reflected upon by the students in their math journal. Thisentry is assessed by the teacher using the Journal Rubric (attached to the culminating task).

GroupingsStudents Working In PairsStudents Working Individually

Teaching / Learning StrategiesCollaborative/cooperative LearningDemonstrationLearning Log/ Journal

AssessmentTeachers assess student understanding ofprobability concepts through the mathjournal response. Read to determine howwell Grade 5 and 6 students are able to:- use mathematical language to explainprobability- use charts/diagrams to communicate- understand probability concepts- use fractions to explain probability

Assessment StrategiesLearning LogQuestions And Answers (oral)



Demonstration of River Crossing:- Explain the rules of the game through a demonstration of River Crossing (with help from a volunteer). Theblackboard can be used with magnetic markers serving as boats. (Instructions for the game are outlined inBLM 10.1 River Crossing. A gameboard is also provided.)

Paired Work

Playing the Game:- Have each pair of students play the game twice.- Ask the students to share their ideas about strategy with the class.- Ask probing questions such as:


Making a Game of It! Subtask 10River Crossing


Resources

- How many ways can you roll 12? How many ways can you roll 11? Do you have a better chance of rolling11 or 12? Why?- How can you figure out which numbers will come up the most frequently?- Does anyone see a pattern in the number of combinations? What is it?

Individual Work

Math Journal:Ask each student to respond to the following prompts:What does River Crossing teach about probability? How can you make River Crossing into a morechallenging game?

Adaptations

River Crossing Instructions BLM10.1River .cwk

counters (e.g., centicubes, buttons) 12

numbered cubes 2

Notes to TeacherPlaying the Game:The first time students play this game, they will likely randomly select dock numbers for their counters. Afterstudents have played the game a few times, they will develop better strategies for deciding where theirboats should be placed to get them to the other side more quickly (with fewer rolls of the numbered cubes).It is at this point that they are ready to discuss their strategies with the class and be led through adiscussion on probability.

Extension:

Give the students the following investigation: If you were given three numbered cubes (with numbers oneto six on the sides), what would be the best docks to put your boats on. Support your answer withmathematical language and diagrams.

Teacher Reflections


Making a Game of It! Subtask 11Games Expo


Expectations5e1 A • communicate ideas and information for a variety of

purposes (e.g., to present and support a viewpoint)and to specific audiences (e.g., write a letter to anewspaper stating and justifying their position on anissue in the news);

5e2 A • use writing for various purposes and in a range ofcontexts, including school work (e.g., to summarizeinformation from materials they have read, to reflecton their thoughts, feelings, and imaginings);

5e7 A • revise and edit their work, seeking feedback fromothers and focusing on content, organization, andappropriateness of vocabulary for audience;

5m109 A • interpret displays of data and present theinformation using mathematical terms;

5m111 A • demonstrate an understanding of probabilityconcepts and use mathematical symbols;

5m120 A – evaluate data presented on tables, charts, andgraphs and use the information in discussion (e.g.,discuss patterns in the data presented in the cells ofa table that is part of a report on a scienceexperiment);

5m121 A – connect real-life statements with probabilityconcepts (e.g., if I am one of five people in a group,the probability of being chosen is 1 out of 5);

5m124 A – use a knowledge of probability to pose and solvesimple problems (e.g., what is the probability ofsnowfall in Ottawa during the month of April?).

6e1 A • communicate ideas and information for a variety ofpurposes (to inform, to persuade, to explain) and tospecific audiences (e.g., write the instructions forbuilding an electrical circuit for an audienceunfamiliar with the technical terminology);

6e7 A • revise and edit their work in collaboration withothers, seeking and evaluating feedback, andfocusing on content, organization, andappropriateness of vocabulary for audience;

6e19 A – frequently introduce vocabulary from other subjectareas into their writing;

6m109 A • interpret displays of data and present theinformation using mathematical terms;

6m110 A • evaluate data and make conclusions from the

DescriptionEach toy company (made up of two to four students) designs, field tests, and presents a game of chanceat a Games Expo. From the data generated in the field test of their game, students predict the probabilityof winning and determine the average set-up and playing time. This information is presented by the toycompany along with its game. The game and presentation are assessed for a number of datamanagement and probability skills, knowledge, and concepts using the Games Expo Rubric.

At this point, the students are asked to submit their math journal entry from River Crossing along with twoother entries (self-selected) that they believe demonstrate their understanding of data management andprobability concepts, skills, and knowledge. Students are encouraged to revise and edit their work (e.g.,clarifying or adding mathematical ideas). The Journal Rubric is used by the teacher for this assessment.

GroupingsStudents Working In Small GroupsStudents Working Individually

Teaching / Learning StrategiesBrainstormingCollaborative/cooperative LearningDemonstration

AssessmentThe teacher will be using two differentrubrics for the culminating task:1. Games Expo Rubric(Note: this rubric provides insufficientspace to list the expectations that arebeing assessed at this time. Additionalexpectations are: 5m120, 5m124, 6m106,6m109, and 6m112)2. Math Journal Rubric

Assessment StrategiesPerformance TaskQuestions And Answers (oral)Learning LogExhibition/demonstrationClassroom Presentation

Assessment Recording DevicesRubric




analysis of data;6m112 A • examine the concepts of possibility and probability;6m122 A – connect the possible events and the probability of

a particular event (e.g., in flipping a coin, there aretwo possibilities; in rolling a die, there are sixpossibilities);

6m125 A – show an understanding of probability in makingrelevant decisions (e.g., the probability of tossing ahead with a coin is not dependent on the previoustoss).

6m106 A • systematically collect, organise, and analyse data;

Teaching / LearningSmall Group (Toy Companies)

1. Reviewing the Design Process:- Introduce and review the design process with your students. (Note: There are many variations of thisprocess. One sample is provided in the Teacher Notes section.)- Present the design process on pieces of chart paper and hang in the class for easy reference.- Regularly question students on their progress as they work through the culminating task

2. Creating a Game:- Provide students with the criteria for the game of chance that they must design, construct, and present.a) The game must make use of a spinner, numbered cubes, or cards to be moved as pieces in the game.b) The game should be kept as simple as possible. The game should be considered a "mock-up" forpresentation purposes only. (It is assumed that the game and supporting materials will take no more thanthree 40-minute periods to prepare.)- Explain to students that they must use the information gathered and recorded from subtasks 4 and 7.

3. Presenting the Game - First Phase:- Explain that in the first phase of presentations each of the toy companies evaluate each other's games.They do this by playing the game and completing the Field Test Response Sheet (BLM11.1 Response). (Eachgame should be field tested by three or four different companies.)

4. Making Improvements:- Ask the creators of the game to use the data generated from the field test responses to make improvementson their games for the upcoming Games Expo.- Request that students keep a copy of their original game to compare with their upgraded version.

5. Games Expo - Second Phase:- Schedule each Toy Company's presentation. It is suggested that these presentations are made to the class.- Review the requirements of the presentation. Students need to explain:

- the object of the game- how the game relates to probability- how they incorporated suggestions from the field tests

- Assess the presentations using the Games Expo Rubric- Invite members of the community, school, and staff to sample the students' games in an Expo. This eventcan be held in the gym or library, for example. Visitors play the role of potential purchasers of the games andcomplete the Purchaser's Response Sheet (BLM11.2 Response) after sampling each game. (Theseresponses will be incorporated into the teacher's evaluation of the game.)

Individual Work:




Resources

Math Journal:- Ask students to submit their three journal entries. (Note: one of them must be the journal entry from subtask10: River Crossing.)Please Note: It is important to remember that the Revise and Edit category in the Journal Rubric primarilyfocuses on the students' revisions to and edits of their mathematical thinking. It is not intended to strictly focuson conventions of language.

AdaptationsThe culminating task can easily be adapted for exceptional students. Complexity of the game and length ofpresentation can easily be adapted. The students can also be given any number of accommodations includingextra time, a quiet space to work, assistance scribing their writing, and someone to read their text resources.

Grade 5 Journal Rubric


Games Expo Rubric

Form for Field Testing of the Games BLM11.1 Field Test.cwk

Purchaser's Response Form BLM11.2 Response.cwk

Bristol board 1

Notes to TeacherThe Design Process:Students should review the process before starting to design their game of chance. The design processlisted below is one of many that are available to support students.

Stage 1: Preparation for the Task (Understand the assignment, brainstorm, list questions, select a topic,divide your topic into smaller bits, and record timelines for each stage.)

Stage 2: Access the Resources You Need (Inquire about where to find resources and collaborate withothers.)

Stage 3: Create the Design (Draft, analyse, test, reflect.)

Stage 4: Presentation of the Product (Make a plan, practise, revise, present, and reflect.)

Teacher Reflections


Black Line Masters:


Appendices

Rubrics:

Resource List:

Unit Expectation List and Expectation Summary:



Resource List


Page 1

Rubric

Games Expo Rubric

This rubric is used to score the student's game andpresentation in the Culminating Activity.

2ST 11


This rubric is used to score each student's self-selected3 journal entries.

2ST 11


This rubric is used to score each student's self-selected3 journal entries.

2ST 11

Graph Rubric

This rubric is used to assess the students performancein graphing and explaining the message that their graphgives to the reader.

2ST 9


This rubric is used to assess the student's ability tocreate two types of graphs, their explanation ofintervals and their understanding of how graphs canshow the same data differently.

3ST 7


This rubric is used to assess the student's ability tocreate two types of graphs, their explanation ofintervals and their understanding of how graphs canshow the same data differently.

3ST 7

Blackline Master / File

Copyright Application FormBLM1.1 Copyright.cwkStudents record their Toy Company name and logo onthis sheet.

ST 1

Form for Field Testing of the GamesBLM11.1 Field Test.cwkStudents use this blackline master to collect informationfrom people who have field tested their game.

ST 11

Game Connection: Go-MokuBLM2.1 Japanese Tic-Tac-Toe.cwkThis is a one page instruction sheet for the Japanesegame of strategy called Go-Moku. It is similiar toTic-Tac-Toe since players alternate turns placing a tilein order to prevent the opponent from creating a row ofhis/her coloured tiles.

ST 2

Game Connectionsadditional games.cwkThese games can be used with the whole class or asextensions for small groups or individual students.

Unit

Instructions for Making SpinnersBLM6.1 Making Spinners.cwkTwo methods of making spinners are included in thisblackline master.

ST 6

Instructions for PlayingBLM8.1 Game Sticks.cwkInstructions for playing the Stick Game are providedhere.

ST 8

Investigating GraphsBLM3.2 InvestigatingGraphs.cwkThis blackline master assists students in theirinvestigations of the five graphs provided in BLM3.1Looking at Graphs.

ST 3

Looking at GraphsBLM3.1 Looking at Graphs.cwkProvided here are a series of five graphs: circle, bar,double bar, line and pictograph. Students investigatethese graphs in small groups, using BLM3.2Investigating Graphs to guide their discussions.

ST 3

Making PredictionsBLM6.3 Predictions.cwkThis blackline master includes a Grade 5 and Grade 6predictions page. Students make predictions, explaintheir thinking and create a tally on this page. Grade 6students are asked to indicate theoretical probability.

ST 6

Mia Hamm's StatisticsBLM9.2 Hamm.cwkStatistics for Mia Hamm are provided here.

ST 9

Observation ChecklistBLM6.5 Teacher Checklist.cwkThese Grade 5 and Grade 6 checklists are completedby the teacher as observations are being made. A ratingscale that parallels the four levels of achievement isprovided. Anecdotal notes should be used to supportthe ratings given.

ST 6

Written using the Ontario Curriculum Unit Planner 2.51 PLNR_01 March, 2001* Open Printed on Jul 23, 2001 at 1:10:27 AM Page D-1


Resource List


Page 2

Our SurveyBLM4.1 Our Survey.cwkThis blackline master is to be completed by each ToyCompany. It prompts students to include the audiencesurveyed, the survey question and the tally.

ST 4

Penny Flip Recording SheetBLM5.1 Penny Flip.cwkStudents write their predictions, tally their 30 flips andrecord their results on this recording sheet.

ST 5

Prompts for Pairs of StudentsBLM8.2 Reflection.cwkThese prompts are given to pairs of students in order toreflect on the Stick Game.

ST 8

Purchaser's Response FormBLM11.2 Response.cwkVisiting "purchasers" complete this form after they havetried out a game of chance.

ST 11

Rationale for Choice of GraphBLM7.1 My Choices.cwkThis blackline master includes a separate page for eachof Grade 5 and Grade 6 students. The students use thisblackline master to explain their choice of graph andtheir choice of intervals. Grade 6 students are expectedto compare their graphs and consider how a change inintervals would alter the graph.

ST 7

Resources to Support the UnitResources.cwkA bibliography of text, video and software resources.Some webites are also provided.

Unit

Results of the Spinner ExperimentBLM6.4 Results.cwkThis blackline master includes a page for Grade 5students and a page for Grade 6 students. Students areasked to explain their results and make a graph todisplay their data. Grade 6 students are asked toinvestigate the relationship between theoretcial andexperimental probability.

ST 6

River Crossing InstructionsBLM10.1River .cwkInstructions for the game River Crossing are included,along with a game board.

ST 10

Self-AssessmentBLM3.5 SelfAssessment.cwkThis blackline master is both a checklist for the studentto use as they complete their graph and a selfassessment tool.

ST 3

Spinner TemplatesBLM6.2 SpinnerTemplate.cwkTemplates for two spinners are provided here. Studentsuse one of the spinner templates to create their spinner.

ST 6

Tally SheetBLM3.3 Tally Sheet.cwkThis blackline master provides six sets of data relatedto games and game playing. Students use this data tocreate a graph for a specific audience.

ST 3

Task for Mia Hamm's StatisticsBLM9.4 HammInvestigation.cwkThis blackline master prompts students to makepredictions, investigate statistics and create twographs.

ST 9

Task for Wayne Gretzky's StatisticsBLM9.3 GretzkyInvestigation.cwkThis blackline master prompts students to investigatemean, median and mode, make predictions, investigatestatistics and create two graphs.

ST 9

Wayne Gretzky's StatisticsBLM9.1 Gretsky.cwkStatistics for Wayne Gretzky are provided here.

ST 9

What's It For?BLM3.4 What's it For.cwkThis sheet provides the students with seven differentscenarios for which a graph could be created.

ST 3

Material

10 cm x 10 cm squares of cardboard1

Each student will require a square of cardboard if theyare creating a spinner using Method #1.

per person

ST 6

Bristol board1

This bristol board will be used to create the logo andcompany banner.

per group

ST 1

Bristol board1

The Toy Companies may require bristol board in order toconstruct their game of chance.

per group

ST 11

buttons1

Students making a spinner using Method #2 will requireone button.

per person

ST 6

Cardboard or a three-fold display board1

This could be used to create an office wall for each toycompany. The group could use the backdrop to postbrainstorming ideas, display their data and to createsome privacy for their work site.

per group

ST 1

grid paper1

Students may require grid paper to complete their graph.per pair

ST 3

grid paper1

Students may request grid paper in order to make theirgraph.

per person

ST 6

grid paper1

Students will require grid paper to complete theirgraph(s).

per person

ST 7



Resource List


Page 3

grid paper2

Students will need grid paper to create their graphs.per person

ST 9

paper clips1

Each student will require one paper clip to create theirspinner, whether they are using Method #1 or #2.

per person

ST 6

pennies1

Students need one penny per pair.per pair

ST 5

tongue depressors12

Each team (pair) needs 12 sticks for the Stick Game.per pair

ST 8

Equipment / Manipulative

compass, large lids, masking tape1

These materials can be used by the students whochoose to make a circle graph.

per class

ST 3

counters (e.g., centicubes, buttons)12

Counters are needed to represent boats in the RiverCrossing game.

per person

ST 10

counters (e.g., toothpicks, cubes)10

These counters will be used in the Stick G ame. Theywill beneeded to keep track of the score.

per pair

ST 8

numbered cubes2

Each pair of students will need 2 numbered cubes toplay River Crossing.

per pair

ST 10


COPYRIGHT APPLICATION FORM

Proposed Company Name

Proposed Company Logo (please sketch)

Executives of the Company

The above company name and logo have been approved and the executives listed have exclusive rights to this material.

(authorized signature) (date)

BLM1.1 Copyright

Go-Moku

This game is an ancient game that has its origins in Japan. It is known as "Japanese tic-tac-toe" and is considered by many to be one of the world's greatest strategy games.

"Go-moku" means "five stones." It is played on the intersections of a traditional GO board with GO stone pieces (black and white stones or glass beads). The full name, "Go-moku Narabe," literally means "five stones in a row." In Japan, a more complex version of the game exists, known as Renju.

Instructions for play:

Each player uses either black or white "stones." In this version, players use a grid board that is at 19 cm x 19 cm. (The game can also be played on the blackboard using two colours of chalk.) The object of Go-moku is to create a row that has exactly five of the same coloured stones in a row. At the same time, players are trying to prevent their opponent from placing five of their stones in a row. This is done by blocking the opponent's stones by placing an opposite coloured stone. (Note: There can be more than five black and white stones in any row, but five consecutive stones of the same colour is the only way to win.)

The game begins with a "coin toss" to see who goes first. This player begins by placing one coloured stone anywhere on the board (on an intersection). The game alternates players until one player has successfully placed five of their stones in a row.

“Japanese Tic-Tac-Toe”

BLM2.1Japanese Tic-Tac-Toe

Game Connection

In this game, the player with the white stones is going next. Where should they go so that black doesn’t win?

Use of the Local Arena

FigureSkating

30%

FreeSkating

20%

SpecialEvents

Hockey

45%

5%

Most Popular Intramural Sports Played

Participation in Intramural Sports at P.T. Smythe School

10

20

30

40

50

Girls

Boys

Number of

Students

Time Spent Outside for Gym

Months of the School Year

1

2

3

4

5

6

S O N D J F M A M J

BOARD GAMES IN OUR CLASSROOMS

BLM3.1 Looking at Graphs

BLM3.1 Looking at Graphs

= 4 games

K to Gr. 3

Gr. 4 to 6

Gr. 7 to 8

Our Teachers’ Favourite Games

2 4 6 8 10 12 14 16 18

Number of Teachers

Word Games

Other Games

Board Games

Computer Games

BLM3.2 Investigating Graphs

What Is It About Graphs?

Names:

Look at each of the five graphs carefully.

1. What do you notice about all of the graphs that is the same? Why?

2. What differences do you see between the graphs? Explain carefully.

BLM3.3 Tally SheetTally Information!

One group of students collected a lot of information about games. The information is listed below.

Survey 3: Number of Games that are Used During ONE Indoor Recess

(in three classrooms)

Card Games Board Games

Individual Games Active Games

Survey 4: CHECKERS Survey

intermediate boys

junior boys

Say they are good at

CHECKERS

intermediate girls

junior girls

Say they are good at

CHECKERS

Survey 5: Number of Times the Balls are Signed Out (over three months)

April May June

Soccer balls

Basketballs

Softballs

week 1 week 2 week 3 week 4 week 1 week 2 week 3 week 4 week 1 week 2 week 3 week 4

0 1 3 1 4 5 4 10 10 8 8 4

2 4 6 4 4 3 4 6 5 5 6 3

0 0 2 0 3 4 3 2 4 4 5 3

likes chessnever played

chess dislikes chess

adults

kids

Survey 1: Chess Survey

Go Fish Crazy Eights

Snap Concentration

Survey 2: Forty Students in Primary Were Asked which of Four Games Is Their Favourite

You are making a graph forTHE CLASS NEWSLETTER.

Why might you be making this graph? What kind of graph will you use?

You are making a graph forTHE CLASS NEWSLETTER.


You are making a graph forTHE PRINCIPAL.


You are making a graph forTHE PRINCIPAL.


You are making a graph forA GAME COMPANY.


You are making a graph forA GAME COMPANY.


You are making a graph forYOUR TEACHER.


You are making a graph forYOUR TEACHER.


You are making a graph forA TOY STORE.


You are making a graph forA TOY STORE.


You are making a graph forA SCHOOL COACH.


You are making a graph forA SCHOOL COACH.


You are making a graph forTHE INTERMEDIATE

TEACHER.Why might you be making this graph?

What kind of graph will you use?

You are making a graph forTHE INTERMEDIATE

TEACHER.Why might you be making this graph?

What kind of graph will you use?

BLM3.4 What’s It For?

Student Self-Assessment Checklist

overall title for graph is included

labels, intervals and/or the legend are included

information is accurately displayed

the graph is easy to understand

The strengths of our graph are: Our graph could improve if we:

BLM 3.5 Self-Assessment

Student Self-Assessment Checklist

overall title for graph is included

labels, intervals and/or the legend are included

information is accurately displayed

the graph is easy to understand

The strengths of our graph are: Our graph could improve if we:

BLM 4.1 Our Survey

Our Survey

Name of Toy Company:

Our surveyed audience is

Approximate number of people who will be surveyed:

Our survey question is

Our tally:

BLM4.3 Tally Sheet

Talley Information!

One group of students collected a bunch of information about games. It is all listed below.

likes chessnever played

chessdislikes chess

adults

kids

intermediate boys

junior boys

Say they are Good at Scrabble

√√√

√ √

√√√√

√

√√√ √√√√√

√

√√√

√√√√

intermediate girls

junior girls

Say they are Good at Scrabble

√√√√

√√ √√√√√

√√√√

√√√√

√ √√

√√√

√√√√

√√√√√√√

Number of Games that are Used During ONE Indoor Recess (in three classrooms)

Card Games Board Games

Individual Games Active Games

BLM5.1 Penny Flip

Penny Flip Recording Sheet

1. Predict how many heads and tails you will get if you flip a penny 30 times.

PREDICTION: Heads Tails

2. Flip the penny 30 times.

Use this space to record your results:

3. Calculate your results.

RESULTS: Heads Tails

4. Add your results to the class tally sheet.

Making a SpinnerBLM 6.1 Making Spinners

First Steps:Choose spinner A or B. Colour the sections yellow (Y), red (R), and blue (B) as indicated on the spinner and cut out the spinner.

Method #1

You will need:- piece of circular cardboard for the base - 1 paper clip- sharp pencil or pen to poke a hole in the base - 1 butterfly clip- 1 grommet - scissors and glue

1. Glue the spinner circle to the cardboard.2. Poke a hole in the centre of the cardboard (and spinner circle) large enough that the grommet will fit into the hole. 3. Place the grommet through one circular end of the paperclip and then through the hole in the cardboard.4. Put the straight ends/prongs of the butterfly clip down through the grommet and cardboard.5. Open the butterfly clip against the back of the base. Spin the paperclip!

Method #2

You will need:- a piece of square cardboard (approx. 20 cm x 20 cm) - masking tape- one spinner top - red, yellow, and blue pencil crayons- scissors - 1 button- one paper clip - 1 ruler- a pencil

1. Draw lines diagonally across the back of the cardboard square. Where they meet is the centre of the square.

2. Unfold a paper clip by pulling out the middle section, bending it upward, and straightening it.

3. Poke the paper clip through the middle of the cardboard square and tape the paper clip to the back of the spinner.

4. Put a button on the paperclip so that it sits on top of the cardboard.

5. Put the centre of the paper spinner through the paper clip.

6. Fold the end of the paper clip down and wrap a small piece of tape around it.

7. In one corner of the cardboard square, draw a small arrow. This will be the pointer. To spin, hold the edge of the square with the fingers of one hand, and spin the spinner top with the other.

paper clip

the grommet sits in the whole in the cardboard

BLM 6.2 Spinners

SPINNER A

B

R Y

SPINNER B

Y

B R

B

Y

BR

B

Use either Spinner A or Spinner B (as directed by the teacher).

B

R Y

Y

B R

B

Y

BR

B

BB

Making Predictions About the Spinner Experiment (Gr. 5)

Record how many times you will spin your spinner:

1. What colour do you think will come up most frequently? _________________

How many times do you think this colour will be spun? ____________________

BLM6.3 Predictions

2. Use this space to keep track of your results as you spin your spinner.

Explain your thinking.

BLM6.3 Predictions

Making Predictions About the Spinner Experiment (Gr. 6)

Record how many times you will spin your spinner:

1. What colour do you think will come up most frequently? _________________

What is the theoretical probability for this colour? _____________________

2. Use this space to keep track of your results as you spin your spinner.

Explain your thinking.

Thinking About the Results of The Spinner Experiment (Gr. 5)

1. Use mathematical language to explain the results of your spinner experiment. Be sure to compare your prediction to the result.

BLM6.4 Results

2. Create a graph that will clearly display the data from your experiment.

BLM6.5 Teacher Checklist

Legend for Ratings1: struggling 2: learning3: consolidating 4: extending comments

Observation Checklist (Grade 5)

provides a reasonable prediction

explains rationale

for prediction

creates and uses

a tally

compares predictions

with results

creates an effective graph to

show data

uses fractions to

describe probability

My Choices (Grade 5)

My graph has intervals of ____________ because

My first graph is a ______________ graph.

BLM7.1 My Choices

I chose this type of graph because

My graph has intervals of ____________ because

My second graph is a ______________ graph.

I chose this type of graph because

BLM7.1 My Choices

BLM8.1 Game Sticks

Stick Game

Materials Required: -12 decorated game sticks (6 per player or team) - 1 container of 10 counters - 1 copy of the rules for game sticks

Rules of the Game:The game is played in pairs or small groups.

To find out which team will begin, one person from each team tosses six sticks. The team that has the most design sides facing up goes first.

A person on the first team tosses the sticks and takes counters as indicated by the way the sticks land. Teams alternate, with a different person tossing each time.

When no counters remain in the middle, the teams take the counters from each other when they toss a winning combination of sticks.

The game ends when one team has all the counters.

Scoring: Start with 10 counters in the middle.

1. If all six sticks land on the design side, the team takes three counters.

2. If all six sticks land on the plain side, the team takes two counters.

3. If the sticks split evenly so that three plain and three design sides are showing, the team takes 1 counter.

4. If the sticks land in any other combination, the team takes no counters.

For example, suppose that Team 1 has two plain and four design sides showing. It would take no counters. Then suppose Team 2s toss shows three plain and three design sides showing. Team 2 would take one counter.

What number of counters are players most likely to

collect on each turn? Why?

Do you think you had more tosses that resulted in taking

counters or not taking counters? Explain.

How could you find out which combinations of sticks are

most likely?

Describe another game that you like to play that involves probability, and explain how probability affects that game.

BLM8.2 Reflection

What number of counters are players most likely to

collect on each turn? Why?

Do you think you had more tosses that resulted in taking

counters or not taking counters? Explain.

What does the scoring for Native American Game Sticks

have to do with probability?

Describe another game that you like to play that involves probability, and explain how probability affects that game.

How could you find out which combinations of sticks are

most likely?

What does the scoring for Native American Game Sticks

have to do with probability?

Cut the boxes and distribute one prompt to each pair of students.

SEASON TEAM GAMES GOALS ASSISTS TOTAL POINTS

1979 - 80 Edmonton 79 51 86 137

1980 - 81 Edmonton 80 55 109 164

1981 - 82 Edmonton 80 92 120 212

1982 - 83 Edmonton 80 71 125 196

1983 - 84 Edmonton 74 87 118 205

1984 - 85 Edmonton 80 73 135 208

1985 - 86 Edmonton 80 52 163 215

1986 - 87 Edmonton 79 62 121 183

1987 - 88 Edmonton 64 40 109 149

1988 - 89 Los Angeles 78 54 114 168

1989 - 90 Los Angeles 73 40 102 142

1990 - 91 Los Angeles 78 41 122 163

1991 - 92 Los Angeles 74 31 90 121

1992 - 93 Los Angeles 45 16 49 65

1993 - 94 Los Angeles 81 38 92 130

1994 - 95 Los Angeles 48 11 37 48

1995 - 96 Los Angeles/

St. Louis 80 23 79 1021996 - 97 New York 82 25 72 97

1997 - 98 New York 82 23 67 90

1998 - 99 New York 70 9 53 62

TOTALS 1487 894 1963 2857

Wayne Gretzky’s Career Statistics BLM 9.1 Gretzky

Year Games Played Minutes Goals Assists Points

1987 7 369 0 0 0

1988 8 554 0 0 0

1989 1 40 0 0 0

1990 5 270 4 1 9

1991 28 1820 10 4 24

1992 2 136 1 0 2

1993 16 1304 10 4 24

1994 9 810 10 5 25

1995 21 1790 19 18 56

1996 23 1777 9 18 36

1997 16 1253 18 6 42

1998 21 1676 20 20 60

1999 13 1033 5 8 18

TOTALS 170 12 807 106 84 296

BLM9.2 Hamm

Mia Hamm Career Statistics

Investigating Wayne Gretzky’s Statistics

4. Calculate Wayne’s best year. Explain what statistics you are using to determine his best year.

1. Calculate the mean, mode, and median of Wayne’s past scoring.

mean: _______________ median: ________________ mode: ______________

2. Looking at the mean, median, and mode, predict how many goals he would get in his first year back.

I predict _________ goals because ____________________________________

________________________________________________________________

________________________________________________________________

BLM9.3 Gretzky Investigation

5. Create two graphs that show Wayne’s career. One should help support an argument “for” signing Wayne, and one should help convince the league not to sign him for the team.

6. Attach two statements to the graphs that explain:

a) Why you think that your graphs convey different messages to readers.

b) Why you chose the type of graph that you did.

Investigating Mia Hamm’s Statistics

3. Create two graphs that show Mia’s career. One should help support an argument “for” signing Mia, and one should help convince the league not to sign her for the team.

4. Attach two statements to the graphs that explain:

a) Why you think that your graphs convey different messages to readers.

b) Why you chose the type of graph that you did.

A famous North American soccer team has asked you to decide whether or not it should sign Mia Hamm. There are several young players to choose from and only a few spots available.

1. Look at Mia’s career statistics and determine her best year in scoring.

I determine that Mia’s best year was _______________________

because ________________________________________________________

2. Calculate her best year (don’t forget to look at how many minutes she played each year). Explain what statistics you are using to determine her best year.

BLM9.4 Hamm Investigation

Expectations for this Subtask to Assess with this Rubric:

Problem Solving- ability to solve problemswithout additional prompting

Understanding of concepts- defines two sets of data to suita purpose (to represent bias)- understanding which graph willrelay the desired message to thereader

Application of mathematicalprocedures- making two graphs with all ofthe component parts

Communication- using the language mean,median, mode appropriately- graphing data clearly, usingappropriate labels and titles- explanations of graphs usemathematical language

- needs a great deal ofprompting to enter into thegraphing problem

- graphs are simple and aremissing many components

- uses the terms mean,median, and modeinappropriately- graphs are hard to decipher- written explanations arevague

- is able to enter into thegraphing problem after oneor two simple prompts

- is able to choose one set ofappropriate data- can choose an appropriategraph to use but isn't sure ofwhy others shouldn't be used

- graphs are unclear andsome aspects of the graphmay be incomplete

- uses the terms mean,median, and mode correctlyin some cases- graphs are somewhat clear- written explanations requireoral clarification

- is able to enter into thegraphing problem withminimal prompting

- chooses two obvious setsof data for the graphs- chooses an appropriategraphing format to use andexplains his or her choice

- graphs are clear and easyto read

- uses the terms mean,median, and mode correctly- graphs are clear- written explanations areunderstandable

- is able to enter into thegraphing problem withoutprompting; may askquestions or clarify thoughtsas he or she extends his orher thinking

- chooses two sets of data thatare more discreet in theirmessage; more sophisticated- chooses an appropriategraphing format to use andexplains his or her choice

- graphs are well labelled,detailed, and organized, andkeep the reader in mind

- uses the terms mean,median, and mode correctly- graphs are clear anddetailed- written explanations areclear and concise

Level 1 Level 2 Level 3 Level 4

Graph Rubricfor use with Subtask 9 : What Does the Data Tell Us?

from the Grade 5/6 Unit: Making a Game of It!Student Name:Date:

- has much difficulty choosingwhich data to use fordifferent audiences- does not recognize thetypes of graphs that wouldbe appropriate for the data

5m118 – recognize that graphs, tables, and charts can present data with accuracy or bias;

5m114 – display data on graphs (e.g., line graphs, bar graphs, pictographs, and circle graphs) by hand and by using computer applications;

5m117 – calculate the mean and the mode of a set of data;

6m119 – recognize that different types of graphs can present the same data differently (e.g., a circle graph will show the relationship between the data and a part of the data,a bar graph will show the relationship between separate parts of the data);

6m118 – calculate the median of a set of data;

Category/Criteria

Written using the Ontario Curriculum Unit Planner 2.51 PLNR_01 March, 2001* Open Printed on Jul 23, 2001 at 1:17:45 AM Page E-1


Oral Presentation

Use of Data to Designthe Game

How Probability isFactored into the Gameand Explained

Organization of Timeand Materials (LearningSkills)

- presentation and answersto questions demonstrate alimited understanding of thesubject matter

- probability concepts are notconnected to the game, orany probability connectionsare not relevant

- no plan of organization

- organizes work with limitedcompetence

- presentation and answersto questions demonstrate abasic understanding of thesubject matter

- some references to thedata were made; the studenthas made a few connectionsbetween the data and his orher game

- probability concepts arevague and/or uncertain asthey are connected to thegame

- rudimentary plan oforganization

- organizes work withmoderate competence

- presentation and answersto questions demonstrate asolid understanding of thesubject matter

- many references to thedata were made; the studenthas made soundconnections between thedata and his or her game

- probability concepts areappropriately connected tothe game

- appropriate plan oforganization

- organizes work withconsiderable competence

- presentation and answersto questions demonstrate athorough understanding ofthe subject matter

- thoughtful references to thedata were made; the studenthas made insightfulconnections between thedata and his or her game

- probability concepts areappropriately connected andreferred to in other games

- logical and coherent plan oforganization

- organizes work with a highdegree of competence


Games Expo Rubric for use with Subtask 11 : Games Expo


- minimal references to thedata were made; the studentdoes not appear to makeconnections between thedata and his or her game

5e1 • communicate ideas and information for a variety of purposes (e.g., to present and support a viewpoint) and to specific audiences (e.g., write a letter to a newspaperstating and justifying their position on an issue in the news);

5m111 • demonstrate an understanding of probability concepts and use mathematical symbols;

6e1 • communicate ideas and information for a variety of purposes (to inform, to persuade, to explain) and to specific audiences (e.g., write the instructions for building anelectrical circuit for an audience unfamiliar with the technical terminology);

6m122 – connect the possible events and the probability of a particular event (e.g., in flipping a coin, there are two possibilities; in rolling a die, there are six possibilities);

Category/Criteria



Mathematics Concepts

To what extent do thejournal entries show anunderstanding of mathconcepts?

Mathematical Language

How well has the writerincorporated mathvocabulary into thejournal entries?

Clarity

How well has the writerexplained his/her ideas?

Revising/Editing

How effective are therevisions and edits thatwere made to thejournal entries?

- writing shows a limitedunderstanding ofconcepts due to partiallycomplete and unclearexplanations

- expressed thoughtsare incomplete and/ordisconnected

- revisions and edits dolittle to improve thequality of the journalentries; revisions andedits may be incomplete

- writing shows anuncertain understandingof concepts due toinaccurate or confusedexplanations

- some mathematicallanguage and symbols areused appropriately but maybe compromised by errorsor vagueness

- expressed thoughtsare uncertain; someideas are disconnected

- revisions and editsimprove some aspectsof the journal entries

- writing shows a solidunderstanding ofconcepts throughcomplete andappropriate explanations

- mathematicallanguage and symbolsare used appropriately

- expressed thoughtsare clear and connected

- revisions and edits areeffective and improvemany aspects of thejournal entries

- writing shows athorough understandingof concepts throughdetailed explanations

- mathematicallanguage and symbolsare used purposefullyand effectively

- expressed thoughtsare clear, connected,and concise

- revisions and edits areeffective and greatlyimprove the journalentries


Grade 5 Journal Rubricfor use with Subtask 11 : Games Expo


- mathematicallanguage is impreciseor inappropriate

5e1 • communicate ideas and information for a variety of purposes (e.g., to present and support a viewpoint) and to specific audiences (e.g., write a letter to a newspaperstating and justifying their position on an issue in the news);

5e7 • revise and edit their work, seeking feedback from others and focusing on content, organization, and appropriateness of vocabulary for audience;

5e9 • use and spell correctly the vocabulary appropriate for this grade level;

5m109 • interpret displays of data and present the information using mathematical terms;

5m111 • demonstrate an understanding of probability concepts and use mathematical symbols;

Category/Criteria



Mathematics Concepts

To what extent do thejournal entries show anunderstanding of mathconcepts?

Mathematical Language

How well has the writerincorporated mathvocabulary into thejournal entries?

Clarity

How well has the writerexplained his/her ideas?

Revising/Editing

How effective are therevisions and edits thatwere made to thejournal entries?

- writing shows a limitedunderstanding ofconcepts due to partiallycomplete and unclearexplanations

- expressed thoughtsare incomplete and/ordisconnected

- revisions and edits dolittle to improve thequality of the journalentries; revisions andedits may be incomplete

- writing shows anuncertain understandingof concepts due toinaccurate or confusedexplanations

- some mathematicallanguage and symbols areused appropriately but maybe compromised by errorsor vagueness

- expressed thoughtsare uncertain; someideas are disconnected

- revisions and editsimprove some aspectsof the journal entries

- writing shows a solidunderstanding ofconcepts throughcomplete andappropriate explanations

- mathematicallanguage and symbolsare used appropriately

- expressed thoughtsare clear and connected

- revisions and edits areeffective and improvemany aspects of thejournal entries

- writing shows athorough understandingof concepts throughdetailed explanations

- mathematicallanguage and symbolsare used purposefullyand effectively

- expressed thoughtsare clear, connected,and concise

- revisions and edits areeffective and greatlyimprove the journalentries


Grade 6 Journal Rubricfor use with Subtask 11 : Games Expo


- mathematicallanguage is impreciseor inappropriate

6e1 • communicate ideas and information for a variety of purposes (to inform, to persuade, to explain) and to specific audiences (e.g., write the instructions for building anelectrical circuit for an audience unfamiliar with the technical terminology);

6e7 • revise and edit their work in collaboration with others, seeking and evaluating feedback, and focusing on content, organization, and appropriateness of vocabularyfor audience;

6e19 – frequently introduce vocabulary from other subject areas into their writing;

6m110 • evaluate data and make conclusions from the analysis of data;

6m125 – show an understanding of probability in making relevant decisions (e.g., the probability of tossing a head with a coin is not dependent on the previous toss).

Category/Criteria


Expectationsfor this Subtask to Assess with this Rubric:

Application ofMathematicalProcedures

- create two different graphs

- use data from a graphicorganizer

Understanding ofConcepts

- explain choice of intervals

Communication inMathematics

- interpret displays of data

- describe and comparegraphs

- My graphs are unfinished.

- I used the datainappropriately in thegraphs.

- I was not able to interpretthe data that wasdisplayed.

- In my group, I had difficultydescribing my graphs andcomparing them usingmathematical language.

- My graphs are unclear orinconsistent (e.g., one iswell done; the other isinappropriate orincomplete).

- I used some of the dataappropriately in the graphs.

- I was uncertain of whythe intervals were chosen.

- I was able to interpretparts of the data that wasdisplayed.- In my group, I coulddescribe and comparesome aspects of my graphsusing mathematicallanguage.

- Both of my graphs areclear.

- I used most of the dataappropriately in the graphs.

- I had a good explanationfor my choice of intervals.

- I was able to interpretmost of the data that wasdisplayed.

- In my group, I did a goodjob describing andcomparing my graphs usingmathematical language.

- Both of my graphs aredistinctive.

- I used the dataappropriately in the graphs.

- I had a clear rationale formy choice of intervals. Imade connections to othergraphs in my explanation.

- I was able to interpret allof the data that wasdisplayed.

- I did an excellent jobdescribing and comparingmy graphs usingmathematical language.


Graph Rubric - Self Assessment (5)for use with Subtask 7 : Graphing the Data


- I was unable to explainwhy I chose the intervals,or why my explanation didnot make sense when youlook at the graph(s).

5m109 • interpret displays of data and present the information using mathematical terms;

5m110 • evaluate and use data from graphic organizers;

5m119 – construct labelled graphs both by hand and by using computer applications;

5m114 – display data on graphs (e.g., line graphs, bar graphs, pictographs, and circle graphs) by hand and by using computer applications;

5m116 – explain the choice of intervals used to construct a bar graph or the choice of symbols on a pictograph;

Category/Criteria


Expectationsfor this Subtask to Assess with this Rubric:

Application ofMathematicalProcedures

- create two different graphs

- use data from a graphicorganizer

Understanding ofConcepts- explain how choice ofintervals affect theappearance of data

- understand how graphsshow data differently

Communication inMathematics

- evaluate displays of data

- describe and comparegraphs

- My graphs are unfinished.

- I used the datainappropriately in thegraphs.

- I was not able to evaluatethe data that wasdisplayed.

- In my group, I had difficultydescribing my graphs andcomparing them usingmathematical language.

- My graphs are unclear orinconsistent (e.g., one iswell done, the other isinappropriate orincomplete).

- I used some of the dataappropriately in the graphs.

- I was uncertain of howthe intervals would changethe appearance of the data.

- I was able to explain afew basic ways that mygraphs show the datadifferently.

- I was able to evaluateparts of the data that wasdisplayed.- In my group, I coulddescribe and comparesome aspects of my graphsusing mathematicallanguage.

- Both of my graphs areclear.

- I used most of the dataappropriately in the graphs.

- I had a good explanationof how the intervals wouldchange the appearance ofthe data.

- I was able to explain howmy graphs show the datadifferently.

- I was able to evaluatemost of the data that wasdisplayed.

- In my group, I did a goodjob describing andcomparing my graphs usingmathematical language.

- Both of my graphs aredistinctive.

- I used the dataappropriately in the graphs.

- I had an excellentexplanation of how theintervals would change theappearance of the data. Imade connections to othergraphs in my explanation.- I clearly explained how mygraphs show the datadifferently.

- I was able to evaluate allof the data that wasdisplayed.

- I did an excellent jobdescribing and comparingmy graphs usingmathematical language.


Graph Rubric - Self Assessment (6)for use with Subtask 7 : Graphing the Data


- I was unable to explainhow the intervals wouldchange the appearance ofthe data.

- I could not explain how mygraphs show the datadifferently.

6m110 • evaluate data and make conclusions from the analysis of data;

6m119 – recognize that different types of graphs can present the same data differently (e.g., a circle graph will show the relationship between the data and a part of the data,a bar graph will show the relationship between separate parts of the data);

6m120 – construct line graphs, bar graphs, and scatter plots both by hand and by using computer applications;

6m121 – make inferences and convincing arguments based on the analysis of tables, charts, and graphs;

6m117 – explain how the choice of intervals affects the appearance of data (e.g., in comparing two graphs drawn with different intervals by hand or by using graphingcalculators or computers);

Category/Criteria


Expectation List

Selected


Page 1

Assessed

English Language---Writing• communicate ideas and information for a variety of purposes (e.g., to present and support a viewpoint) and to specific

audiences (e.g., write a letter to a newspaper stating and justifying their position on an issue in the news);1 15e1

• use writing for various purposes and in a range of contexts, including school work (e.g., to summarize information frommaterials they have read, to reflect on their thoughts, feelings, and imaginings);

1 15e2

• organize information to convey a central idea, using well-developed paragraphs that focus on a main idea and give somerelevant supporting details;

15e3

• revise and edit their work, seeking feedback from others and focusing on content, organization, and appropriateness ofvocabulary for audience;

15e7

English Language---Oral and Visual Communication• express and respond to ideas and opinions concisely, clearly, and appropriately; 15e48

Mathematics---Number Sense and Numeration– identify and investigate the use of number in various careers; 15m19

– identify and interpret the use of numbers in the media; 15m20

Mathematics---Data Management and Probability• interpret displays of data and present the information using mathematical terms; 1 25m109

• evaluate and use data from graphic organizers; 1 15m110

• demonstrate an understanding of probability concepts and use mathematical symbols; 1 35m111

• pose and solve simple problems involving the concept of probability. 15m112

– design surveys, collect data, and record the results on given spreadsheets or tally charts; 2 15m113

– display data on graphs (e.g., line graphs, bar graphs, pictographs, and circle graphs) by hand and by using computerapplications;

1 35m114

– explain the choice of intervals used to construct a bar graph or the choice of symbols on a pictograph; 1 15m116

– calculate the mean and the mode of a set of data; 15m117

– recognize that graphs, tables, and charts can present data with accuracy or bias; 15m118

– construct labelled graphs both by hand and by using computer applications; 1 25m119

– evaluate data presented on tables, charts, and graphs and use the information in discussion (e.g., discuss patterns in the datapresented in the cells of a table that is part of a report on a science experiment);

4 35m120

– connect real-life statements with probability concepts (e.g., if I am one of five people in a group, the probability of beingchosen is 1 out of 5);

3 15m121

– predict probability in simple experiments and use fractions to describe probability; 1 25m122

– use tree diagrams to record the results of simple probability experiments; 15m123

– use a knowledge of probability to pose and solve simple problems (e.g., what is the probability of snowfall in Ottawa duringthe month of April?).

1 15m124

The Arts---Visual Arts• produce two- and three-dimensional works of art that communicate a range of ideas (thoughts, feelings, experiences) for

specific purposes and to specific audiences;15a26

English Language---Writing• communicate ideas and information for a variety of purposes (to inform, to persuade, to explain) and to specific audiences

(e.g., write the instructions for building an electricalcircuit for an audience unfamiliar with the technical terminology);

1 16e1

• use writing for various purposes and in a range of contexts, including school work (e.g., to develop and clarify ideas, toexpress thoughts and opinions);

16e2

• revise and edit their work in collaboration with others, seeking and evaluating feedback, and focusing on content, organization,and appropriateness of vocabulary for audience;

16e7

– frequently introduce vocabulary from other subject areas into their writing; 16e19

English Language---Oral and Visual Communication• express and respond to a range of ideas and opinions concisely, clearly, and appropriately; 16e50

Mathematics---Number Sense and Numeration– identify the use of number in various careers; 16m21

– identify, interpret, and evaluate the use of numbers in the media; 16m22

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Expectation List

Selected


Page 2

Assessed

Mathematics---Data Management and Probability• systematically collect, organise, and analyse data; 4 16m106

• interpret displays of data and present the information using mathematical terms; 16m109

• evaluate data and make conclusions from the analysis of data; 2 26m110

• use a knowledge of probability to pose and solve problems; 16m111

• examine the concepts of possibility and probability; 1 26m112

• compare experimental probability results with theoretical results. 1 26m113

– design surveys, organize the data into self-selected categories and ranges, and record the data on spreadsheets or tallycharts;

2 16m114

– experiment with a variety of displays of the same data using computer applications, and select the type of graph that bestrepresents the data;

16m115

– explain how the choice of intervals affects the appearance of data (e.g., in comparing two graphs drawn with differentintervals by hand or by using graphing calculators or computers);

1 16m117

– calculate the median of a set of data; 16m118

– recognize that different types of graphs can present the same data differently (e.g., a circle graph will show the relationshipbetween the data and a part of the data, a bar graph will show the relationship between separate parts of the data);

1 26m119

– construct line graphs, bar graphs, and scatter plots both by hand and by using computer applications; 2 16m120

– make inferences and convincing arguments based on the analysis of tables, charts, and graphs; 16m121

– connect the possible events and the probability of a particular event (e.g., in flipping a coin, there are two possibilities; inrolling a die, there are six possibilities);

3 26m122

– examine experimental probability results in the light of theoretical results; 1 26m123

– use tree diagrams to record the results of systematic counting; 16m124

– show an understanding of probability in making relevant decisions (e.g., the probability of tossing a head with a coin is notdependent on the previous toss).

1 16m125

The Arts---Visual Arts• produce two- and three-dimensional works of art that communicate a range of ideas (thoughts, feelings, experiences) for

specific purposes and to specific audiences, using a variety of familiar art tools, materials, and techniques;16a25

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Expectation Summary


Selected Assessed

English Language5e1 11 5e2 11 5e3 1 5e4 5e5 5e6 5e7 1 5e8 5e9 5e105e11 5e12 5e13 5e14 5e15 5e16 5e17 5e18 5e19 5e205e21 5e22 5e23 5e24 5e25 5e26 5e27 5e28 5e29 5e305e31 5e32 5e33 5e34 5e35 5e36 5e37 5e38 5e39 5e405e41 5e42 5e43 5e44 5e45 5e46 5e47 5e48 1 5e49 5e505e51 5e52 5e53 5e54 5e55 5e56 5e57 5e58 5e59 5e605e61 5e62 5e63 5e64 5e65 5e66

French as a Second Language5f1 5f2 5f3 5f4 5f5 5f6 5f7 5f8 5f9 5f105f11 5f12 5f13 5f14 5f15 5f16 5f17 5f18

Mathematics5m1 5m2 5m3 5m4 5m5 5m6 5m7 5m8 5m9 5m105m11 5m12 5m13 5m14 5m15 5m16 5m17 5m18 5m19 1 5m20 15m21 5m22 5m23 5m24 5m25 5m26 5m27 5m28 5m29 5m305m31 5m32 5m33 5m34 5m35 5m36 5m37 5m38 5m39 5m405m41 5m42 5m43 5m44 5m45 5m46 5m47 5m48 5m49 5m505m51 5m52 5m53 5m54 5m55 5m56 5m57 5m58 5m59 5m605m61 5m62 5m63 5m64 5m65 5m66 5m67 5m68 5m69 5m705m71 5m72 5m73 5m74 5m75 5m76 5m77 5m78 5m79 5m805m81 5m82 5m83 5m84 5m85 5m86 5m87 5m88 5m89 5m905m91 5m92 5m93 5m94 5m95 5m96 5m97 5m98 5m99 5m1005m101 5m102 5m103 5m104 5m105 5m106 5m107 5m108 5m109 21 5m110 115m111 31 5m112 1 5m113 12 5m114 31 5m115 5m116 11 5m117 1 5m118 1 5m119 21 5m120 345m121 13 5m122 21 5m123 1 5m124 11

Science and Technology5s1 5s2 5s3 5s4 5s5 5s6 5s7 5s8 5s9 5s105s11 5s12 5s13 5s14 5s15 5s16 5s17 5s18 5s19 5s205s21 5s22 5s23 5s24 5s25 5s26 5s27 5s28 5s29 5s305s31 5s32 5s33 5s34 5s35 5s36 5s37 5s38 5s39 5s405s41 5s42 5s43 5s44 5s45 5s46 5s47 5s48 5s49 5s505s51 5s52 5s53 5s54 5s55 5s56 5s57 5s58 5s59 5s605s61 5s62 5s63 5s64 5s65 5s66 5s67 5s68 5s69 5s705s71 5s72 5s73 5s74 5s75 5s76 5s77 5s78 5s79 5s805s81 5s82 5s83 5s84 5s85 5s86 5s87 5s88 5s89 5s905s91 5s92 5s93 5s94 5s95 5s96 5s97 5s98 5s99 5s1005s101 5s102 5s103 5s104 5s105 5s106 5s107 5s108 5s109 5s1105s111 5s112 5s113 5s114 5s115 5s116 5s117 5s118 5s119 5s1205s121 5s122 5s123 5s124 5s125 5s126 5s127 5s128

Social Studies5z1 5z2 5z3 5z4 5z5 5z6 5z7 5z8 5z9 5z105z11 5z12 5z13 5z14 5z15 5z16 5z17 5z18 5z19 5z205z21 5z22 5z23 5z24 5z25 5z26 5z27 5z28 5z29 5z305z31 5z32 5z33 5z34 5z35 5z36 5z37 5z38 5z39 5z405z41 5z42 5z43 5z44 5z45 5z46 5z47 5z48

Health & Physical Education5p1 5p2 5p3 5p4 5p5 5p6 5p7 5p8 5p9 5p105p11 5p12 5p13 5p14 5p15 5p16 5p17 5p18 5p19 5p205p21 5p22 5p23 5p24 5p25 5p26 5p27 5p28 5p29 5p305p31 5p32 5p33 5p34 5p35 5p36 5p37 5p38 5p39 5p40

The Arts5a1 5a2 5a3 5a4 5a5 5a6 5a7 5a8 5a9 5a105a11 5a12 5a13 5a14 5a15 5a16 5a17 5a18 5a19 5a205a21 5a22 5a23 5a24 5a25 5a26 1 5a27 5a28 5a29 5a305a31 5a32 5a33 5a34 5a35 5a36 5a37 5a38 5a39 5a405a41 5a42 5a43 5a44 5a45 5a46 5a47 5a48 5a49 5a505a51 5a52 5a53 5a54 5a55 5a56 5a57 5a58 5a59 5a605a61 5a62 5a63 5a64 5a65 5a66 5a67 5a68 5a69

Written using the Ontario Curriculum Unit Planner 2.51 PLNR_01 March, 2001* Open Printed on Jul 23, 2001 at 1:10:50 AM Page G-1


Expectation Summary


Selected Assessed

English Language6e1 11 6e2 1 6e3 6e4 6e5 6e6 6e7 1 6e8 6e9 6e106e11 6e12 6e13 6e14 6e15 6e16 6e17 6e18 6e19 1 6e206e21 6e22 6e23 6e24 6e25 6e26 6e27 6e28 6e29 6e306e31 6e32 6e33 6e34 6e35 6e36 6e37 6e38 6e39 6e406e41 6e42 6e43 6e44 6e45 6e46 6e47 6e48 6e49 6e50 16e51 6e52 6e53 6e54 6e55 6e56 6e57 6e58 6e59 6e606e61 6e62 6e63 6e64 6e65 6e66

French as a Second Language6f1 6f2 6f3 6f4 6f5 6f6 6f7 6f8 6f9 6f106f11 6f12 6f13 6f14 6f15 6f16 6f17 6f18

Mathematics6m1 6m2 6m3 6m4 6m5 6m6 6m7 6m8 6m9 6m106m11 6m12 6m13 6m14 6m15 6m16 6m17 6m18 6m19 6m206m21 1 6m22 1 6m23 6m24 6m25 6m26 6m27 6m28 6m29 6m306m31 6m32 6m33 6m34 6m35 6m36 6m37 6m38 6m39 6m406m41 6m42 6m43 6m44 6m45 6m46 6m47 6m48 6m49 6m506m51 6m52 6m53 6m54 6m55 6m56 6m57 6m58 6m59 6m606m61 6m62 6m63 6m64 6m65 6m66 6m67 6m68 6m69 6m706m71 6m72 6m73 6m74 6m75 6m76 6m77 6m78 6m79 6m806m81 6m82 6m83 6m84 6m85 6m86 6m87 6m88 6m89 6m906m91 6m92 6m93 6m94 6m95 6m96 6m97 6m98 6m99 6m1006m101 6m102 6m103 6m104 6m105 6m106 14 6m107 6m108 6m109 1 6m110 226m111 1 6m112 21 6m113 21 6m114 12 6m115 1 6m116 6m117 11 6m118 1 6m119 21 6m120 126m121 1 6m122 23 6m123 21 6m124 1 6m125 11

Science and Technology6s1 6s2 6s3 6s4 6s5 6s6 6s7 6s8 6s9 6s106s11 6s12 6s13 6s14 6s15 6s16 6s17 6s18 6s19 6s206s21 6s22 6s23 6s24 6s25 6s26 6s27 6s28 6s29 6s306s31 6s32 6s33 6s34 6s35 6s36 6s37 6s38 6s39 6s406s41 6s42 6s43 6s44 6s45 6s46 6s47 6s48 6s49 6s506s51 6s52 6s53 6s54 6s55 6s56 6s57 6s58 6s59 6s606s61 6s62 6s63 6s64 6s65 6s66 6s67 6s68 6s69 6s706s71 6s72 6s73 6s74 6s75 6s76 6s77 6s78 6s79 6s806s81 6s82 6s83 6s84 6s85 6s86 6s87 6s88 6s89 6s906s91 6s92 6s93 6s94 6s95 6s96 6s97 6s98 6s99 6s1006s101 6s102 6s103 6s104 6s105 6s106 6s107 6s108 6s109 6s1106s111 6s112 6s113 6s114 6s115 6s116 6s117 6s118 6s119 6s1206s121 6s122 6s123 6s124

Social Studies6z1 6z2 6z3 6z4 6z5 6z6 6z7 6z8 6z9 6z106z11 6z12 6z13 6z14 6z15 6z16 6z17 6z18 6z19 6z206z21 6z22 6z23 6z24 6z25 6z26 6z27 6z28 6z29 6z306z31 6z32 6z33 6z34 6z35 6z36 6z37 6z38 6z39 6z406z41 6z42 6z43 6z44 6z45 6z46 6z47 6z48

Health & Physical Education6p1 6p2 6p3 6p4 6p5 6p6 6p7 6p8 6p9 6p106p11 6p12 6p13 6p14 6p15 6p16 6p17 6p18 6p19 6p206p21 6p22 6p23 6p24 6p25 6p26 6p27 6p28 6p29 6p306p31 6p32 6p33 6p34

The Arts6a1 6a2 6a3 6a4 6a5 6a6 6a7 6a8 6a9 6a106a11 6a12 6a13 6a14 6a15 6a16 6a17 6a18 6a19 6a206a21 6a22 6a23 6a24 6a25 1 6a26 6a27 6a28 6a29 6a306a31 6a32 6a33 6a34 6a35 6a36 6a37 6a38 6a39 6a406a41 6a42 6a43 6a44 6a45 6a46 6a47 6a48 6a49 6a506a51 6a52 6a53 6a54 6a55 6a56 6a57 6a58 6a59 6a606a61 6a62 6a63 6a64 6a65 6a66 6a67 6a68 6a69 6a706a71

Written using the Ontario Curriculum Unit Planner 2.51 PLNR_01 March, 2001* Open Printed on Jul 23, 2001 at 1:10:50 AM Page G-2


Page 1Unit Analysis

Assessment Recording Devices

10 Anecdotal Record2 Checklist1 Rating Scale3 Rubric

Assessment Strategies

1 Classroom Presentation2 Exhibition/demonstration10 Learning Log6 Observation4 Performance Task5 Questions And Answers (oral)2 Self Assessment

Groupings

6 Students Working As A Whole Class4 Students Working In Pairs7 Students Working In Small Groups10 Students Working Individually

Teaching / Learning Strategies

2 Brainstorming8 Collaborative/cooperative Learning7 Demonstration3 Direct Teaching5 Discussion1 Experimenting3 Graphing1 Inquiry8 Learning Log/ Journal1 Open-ended Questions

Analysis Of Unit Components

11 Subtasks102 Expectations 48 Resources112 Strategies & Groupings

-- Unique Expectations -- 10 Language Expectations 36 Mathematics Expectations 2 Arts Expectations

Resource Types

6 Rubrics 26 Blackline Masters 0 Licensed Software 0 Print Resources 0 Media Resources 0 Websites 12 Material Resources 4 Equipment / Manipulatives 0 Sample Graphics 0 Other Resources 0 Parent / Community 0 Companion Bookmarks

Written using the Ontario Curriculum Unit Planner 2.51 PLNR_01 March, 2001* Open Printed on Jul 23, 2001 at 1:11:01 AM Page H-1

grd 5:6 dm & probability

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