Download Making a Game of It!

Making a Game of It!
Gr. 5 / 6 Data Management and Probability
Including:
Creating A Toy Company
Tic-Tac-Toe
Learning About Graphs
Making A Good Game Of It
The Penny Flip Experiment
Spinner Experiment
Graphing the Data
Game Sticks
What Does the Data Tell Us?
River Crossing
Games Expo
An Integrated Unit for Grade 5/6
Written by:
Janice Mackenzie, Jane Moore, Dave Wing, Kevin Woollacott
July 2001
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
Acknowledgements
The developers are appreciative of the suggestions and comments from colleagues involved through the
internal and external review process.
Participating Lead Public School Boards:
Mathematics, Grades 1-8
Grand Erie District School Board
Kawartha Pine Ridge District School Board
Renfrew District School Board
Science and Technology, Grades 1-8
Lakehead District School Board
Thames Valley District School Board
York Region District School Board
Social Studies, History and Geography, Grade 1-8
Renfrew District School Board
Thames Valley District School Board
York Region District School Board
The following organizations have supported the elementary curriculum unit project through team building and
leadership:
The Council of Ontario Directors of Education
The Ontario Curriculum Centre
The Ministry of Education, Curriculum and Assessment Policy Branch
An Integrated Unit for Grade 5/6
Written by:
Janice Mackenzie, Jane Moore, Dave Wing, Kevin Woollacott
Education Centre
(705)742-9773
Kawartha Pine Ridge District School Board
[email protected]
Based on a unit by:
Janice Mackenzie, Jane Moore, Dave Wing, Kevin Woollacott
Education Centre
(705)742-9773
Kawartha Pine Ridge District School Board
[email protected]
This unit was written using the Curriculum Unit Planner, 1999-2001, which Planner was developed in the province of
Ontario by the Ministry of Education. The Planner provides electronic templates and resources to develop and share units
to help implement the new Ontario curriculum. This unit reflects the views of the developers of the unit and is not
necessarily those of the Ministry of Education. Permission is given to reproduce this unit for any non-profit educational
purpose. Teachers are encouraged to copy, edit, and adapt this unit for educational purposes. Any reference in this unit
to particular commercial resources, learning materials, equipment, or technology does not reflect any official
endorsements by the Ministry of Education, school boards, or associations that supported the production of this unit.
Written using the Ontario Curriculum Unit Planner 2.51 PLNR_01 March, 2001* Open Printed on Jul 23, 2001 at 1:09:56 AM
Unit Overview
Making a Game of It!
Page 1
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
Task Context
Students have been invited to participate in a Games Expo. In order to take part in the Expo, they first need to
investigate a variety of games of chance before creating their own unique game of chance and
presenting it at the Expo. "Purchasers" from various companies will evaluate the students' understanding of
data management and probability concepts, skills, and knowledge based on their oral and written
explanations.
Task Summary
In this unit, students will learn about data management and probability skills, concepts, and knowledge
through the exploration of a variety of traditional and non-traditional games. Some expectations from
Language and the arts are addressed and assessed within the unit. Connections to Social Studies can also
be made.
Each of the mathematics tasks is centred on the theme of "games," whether it be collecting, graphing, and
analysing data or investigating probability concepts. The subtasks are sequenced so that the students have
ample opportunity to learn about and practise the identified skills, concepts, and knowledge before their
performance is assessed in later subtasks. The investigations prepare students for the culminating task in
which they design and present their own game of chance.
A variety of assessment tools are used throughout the unit. These include observation, rubrics, and
checklists.
Throughout the unit students explain their mathematical thinking through the use of a math journal. Students
communicate their understanding of relevant mathematics skills, knowledge, and concepts. Each journal entry
is a response to one or more prompts outlined in the subtasks. Throughout the unit, the teacher will read the
journal entries to maintain an understanding of how well students are understanding concepts. At the end of
the unit, the students revise and edit their final journal entry and two additional self-selected entries that were
completed during the unit. These three entries are submitted for scoring by the teacher (using the Journal
Rubric).
Culminating Task Assessment
Each toy company (made up of two to four students) designs, field tests, and presents a game of chance at
a Games Expo. From the data generated in the field test of their game, students predict the probability of
winning and determine the average set-up and playing time. This information is presented by the toy company
along with its game. The game and presentation are assessed for a number of data 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 with two
other entries (self-selected) that they believe demonstrate their understanding of data management and
probability 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 Knowledge
Students 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
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Considerations
Notes to Teacher
Math Journal:
Students use a math journal throughout the unit in order write their ideas and reflect on what they are
learning. The Journal Rubric is provided to students at the beginning of the unit so that they can see what
they need to do to be successful. Wherever a journal entry is required, students are given a journal prompt
and 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 provided
does not assess students on conventions of language (e.g., spelling, grammar, and punctuation). They are
assessed on their ability to revise and edit their entries. Assessment should be focused on their mathematical
thinking. Students should be encouraged to clarify and in some cases extend their original thinking. The final
entry should be attached to the original entry so that the teacher can assess the student's ability to revise
and edit their mathematical thinking.
The math journal does not have to be a separate book. Students can use their math notebook for their
responses.
Using the Computer:
Computer applications can be utilized for the collection, sorting, and presentation of data. Students should be
taught how to use appropriate programs if they are not already familiar with them. Students can also use
Appleworks 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 easily
woven 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 board
games or active games (for use in a Phys-Ed class, for example). Games that would make good extensions
to subtasks are attached directly to those subtasks. Additional games are provided in Unit Wide Resources.
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List of Subtasks
Subtask List Page 1
Making a Game of It!
Gr. 5 / 6 Data Management and Probability
1
An Integrated Unit for Grade 5/6
Creating A Toy Company
Students are informed that they are the creative executives for a new toy company. Their job is to
investigate a variety of games, find out what the market (their peer group) likes, and ultimately develop
and 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 prompts
for their first entry. From this first entry the teacher is able to assess each student's level of
understanding of data management and probability skills, knowledge, and concepts.
2
Tic-Tac-Toe
Students 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 the game is predictable. After discussing strategy and how probability does or does
not 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 students
develop a survey.
Students reflect in their journals about games that involve strategy and chance.
3
Learning About Graphs
In 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 to
create 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.
4
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 toy
company's survey. A tracking sheet is provided for students to record information pertaining to their
survey (e.g., their survey question).
Students write a journal entry about surveys in the local community.
5
The Penny Flip Experiment
Students flip a penny a given number of times in order to explore the probability of getting heads or
tails. Each student creates a tally sheet and collects data which is later added to a class chart. The
teacher leads a discussion 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.
6
Spinner Experiment
In this subtask, students construct a spinner and make predictions about what they think will happen
when they spin a given number of times. Students record their spins in a self-constructed tally, and
then reflect on what happened in the experiment. The students will be assessed by the teacher on
their 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.
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List of Subtasks
Subtask List Page 2
Making a Game of It!
Gr. 5 / 6 Data Management and Probability
An Integrated Unit for Grade 5/6
7
Graphing the Data
In 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 is
self-assessed by the student using the Graph Rubric. (This subtask provides students with practice
before they are assessed on their ability to create graphs in Subtask 9.)
8
Game Sticks
In this game, each person (or team) uses 6 two-sided sticks (tongue depressors), which students
must first decorate. After the demonstration game, students record a few questions about probability
as it relates to the game and then play the game, a few times to answer their questions and test their
theories. In pairs, the students construct tree diagrams to determine the possible outcomes and
discuss their findings.
In their journals, students then respond to prompts about the activity.
9
What Does the Data Tell Us?
Students 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 are provided. The students must display one athlete's data in more than one way in order to
show bias. The student's graphs are assessed using a rubric.
10 River Crossing
Students take turns rolling two numbered cubes and using the sum to move their counters across the
game board. As students play River Crossing Game, they see which combinations of numbers are the
most 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).
11 Games Expo
Each toy company (made up of two to four students) designs, field tests, and presents a game of
chance at a Games Expo. From the data generated in the field test of their game, students predict the
probability of winning and determine the average set-up and playing time. This information is presented
by the toy company along with its game. The game and presentation are assessed for a number of
data 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 with
two other entries (self-selected) that they believe demonstrate their understanding of data
management and probability 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.
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Creating A Toy Company
Subtask 1
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
40 mins
Description
Students are informed that they are the creative executives for a new toy company. Their job is to investigate
a variety of games, find out what the market (their peer group) likes, and ultimately develop and 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 prompts for their
first entry. From this first entry the teacher is able to assess each student's level of understanding of data
management and probability skills, knowledge, and concepts.
Expectations
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• organize information to convey a central idea,
using well-developed paragraphs that focus on a
main idea and give some relevant supporting
details;
• use writing for various purposes and in a range of
contexts, including school work (e.g., to summarize
information from materials they have read, to reflect
on their thoughts, feelings, and imaginings);
• produce two- and three-dimensional works of art
that communicate a range of ideas (thoughts,
feelings, experiences) for specific purposes and to
specific audiences;
• use writing for various purposes and in a range of
contexts, including school work (e.g., to develop
and clarify ideas, to express thoughts and opinions);
• 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;
Groupings
Students Working In Small Groups
Students Working Individually
Students Working As A Whole Class
Teaching / Learning Strategies
Brainstorming
Learning Log/ Journal
Collaborative/cooperative Learning
Assessment
The teacher is able to read each journal
entry and make notes about the students'
understanding of data management and
probability concepts as they relate to games.
Reading the journals will allow the teacher to
decide which skills need to be emphasized
and which need to be attended to more
closely.
Assessment Strategies
Learning Log
Assessment Recording Devices
Anecdotal Record
Teaching / Learning
Whole 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 to
discover what makes them appealing. Once they complete a variety of investigations of games (background
research), 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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Creating A Toy Company
Subtask 1
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
40 mins
3. Instructions to the Group:
- Explain that each toy company will be inventing its own name and logo, and will be applying for copyright
protection for both.
- Introduce the concept of math journals. Explain that after many of the tasks, the students will be asked to
write in their math journals. Sometimes there will be specific prompts to follow, and sometimes the students
will 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 expectations
that 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 and
probability. 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 TV
broadcaster to have a good understanding of data management skills. Give examples wherever possible.
Adaptations
The journal prompts may be overwhelming for students with a learning disability. The teacher may wish to
give 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 simpler
prompts 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 information
in 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?
Resources
Copyright Application Form
BLM1.1 Copyright.cwk
Bristol board
1
Cardboard or a three-fold display board
1
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Creating A Toy Company
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
Subtask 1
40 mins
Notes to Teacher
Groupings:
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 logo
ideas. It also allows the teacher to prevent any inappropriate names or logos. The application also allows
the 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. In
the Notes to Teacher section at the front end of the unit, there is important information on the assessment
of 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 simulation
somewhat more real for the students. They can later be used for the presentation of the company's game in
the culminating task.
Teacher Reflections
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Tic-Tac-Toe
Subtask 2
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
40 mins
Description
Students 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 the
game is predictable. After discussing strategy and how probability does or does not 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 students develop a survey.
Students reflect in their journals about games that involve strategy and chance.
Expectations
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6m106
5e1
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5m121
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6m122
• interpret displays of data and present the
information using mathematical terms;
• systematically collect, organise, and analyse data;
• 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);
• express and respond to ideas and opinions
concisely, clearly, and appropriately;
– 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);
• 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 electrical circuit for an audience
unfamiliar with the technical terminology);
• express and respond to a range of ideas and
opinions concisely, clearly, and appropriately;
– 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);
Groupings
Students Working As A Whole Class
Students Working In Small Groups
Students Working Individually
Teaching / Learning Strategies
Demonstration
Discussion
Collaborative/cooperative Learning
Learning Log/ Journal
Assessment
Through observations the teacher will be
able to determine how well Grade 5 and 6
students are able to:
- use terminology such as chance, likely,
probability, fair, and possibility
- communicate ideas and information in a
group discussion
- respond to other students' opinions and
ideas concisely, clearly, and appropriately.
The teacher may wish to follow up on the
journal prompt responses. Consider creating
a class chart that lists games of chance,
games of strategy, and games involving
both chance and strategy.
Assessment Strategies
Learning Log
Observation
Assessment Recording Devices
Anecdotal Record
Teaching / Learning
Whole Group
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
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Tic-Tac-Toe
Subtask 2
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
40 mins
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 teacher
will 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, or
easy to understand). The students should make their list on a large piece of paper with their company name
at 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.
Adaptations
The journal prompts may be overwhelming for students with a learning disability. The teacher may wish to
give the student the prompts orally and scribe the responses, or allow the LD student access to the
computer.
Students who cannot cope with the complexity of the journal prompt may respond to a simpler prompt such
as:
- Write about what happened when the teacher played tic-tac-toe with the students.
Resources
Game Connection: Go-Moku
BLM2.1 Japanese Tic-Tac-Toe.cwk
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Tic-Tac-Toe
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
Subtask 2
40 mins
Notes to Teacher
Extension Idea:
Extend this activity by discussing how the game can be "set up" to ensure a tie (what has to happen?) or
by 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 the
classroom.
Teacher Reflections
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Learning About Graphs
Subtask 3
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
80 mins
Description
In 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 to create 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.
Expectations
5m110
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5m120
6m106
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6m119
6m120
• evaluate and use data from graphic organizers;
– display data on graphs (e.g., line graphs, bar
graphs, pictographs, and circle graphs) by hand and
by using computer applications;
– explain the choice of intervals used to construct a
bar graph or the choice of symbols on a pictograph;
– construct labelled graphs both by hand and by
using computer applications;
– 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 of
a table that is part of a report on a science
experiment);
• systematically collect, organise, and analyse data;
– 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
graphing calculators or computers);
– 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);
– construct line graphs, bar graphs, and scatter
plots both by hand and by using computer
applications;
Groupings
Students Working As A Whole Class
Students Working Individually
Students Working In Pairs
Teaching / Learning Strategies
Direct Teaching
Graphing
Discussion
Learning Log/ Journal
Open-ended Questions
Assessment
Teachers should question students through
informal conferences whenever possible and
record their observations. This is invaluable
formative assessment information that will
assist teachers in determining whether or not
students are learning new concepts.
Through questioning and observations the
teacher will be able to determine how well
Grade 5 and 6 students are able to:
- make comparisons between types of
graphs
- interpret data and make reasonable
choices about the type of graph to create
- explain their choice of a graph (e.g., "Why
didn't you use a _____ graph?")
- display data accurately on a graph
- explain their choice of intervals
- explain how their choice of intervals affects
the appearance of data (Grade 6)
- make comparisons between their graphs
and those made by other students
Teachers can observe student performance
through a variety of learning situations
including:
- discussions
- paired investigations of graphs
- development of the graph to meet the
required audience/purpose
- presentations of the graph and rationale
- written reflections in the math journal
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Learning About Graphs
Subtask 3
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
80 mins
In this subtask, students are asked to
assess their graph with their partner (BLM3.5
Self-Assessment). This assessment should
be attached to their graph.
Assessment Strategies
Exhibition/demonstration
Learning Log
Self Assessment
Questions And Answers (oral)
Assessment Recording Devices
Checklist
Anecdotal Record
Teaching / Learning
Day 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 BLM3.2
Investigating 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 following
prompts as discussion starters:
1. The pictograph and circle graphs have a legend. What is the purpose of the legends? Why don't the
other 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 no
spaces between are called histograms. Each bar in a histogram represents an interval or range such as
number 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 over
time. 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 how
a 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 think
tthe media uses these graphs most often?
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Learning About Graphs
Subtask 3
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
80 mins
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 purpose
of the graph and the audience who will be viewing it. They should be prepared to explain why they chose to
build the graph that they did.
- Students can refer to the graphs that were investigated previously if they need reminders about the
components 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 other
groups made? Were you satisfied with your graph?
Adaptations
Students who need accommodations in order to get their ideas on paper should be paired up with a student who
can assist in the written portion of the task. During the whole group discussion about graphing, put large diagrams
on the wall or blackboard. Also, be cognizant of the speed of the discussion, as it often takes learning disabled
students longer to formulate their ideas into verbal responses.
Resources
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
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Learning About Graphs
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
Subtask 3
80 mins
Notes to Teacher
Creating the Graph:
Students who choose to make a circle graph will need to have some method for making an appropriate
sized circle. They should be able to brainstorm possible solutions to this problem (e.g., compass, large lid, or
masking tape roll).
Teacher Reflections
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Making A Good Game Of It
Subtask 4
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
40 mins
Description
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 toy company's survey.
A tracking sheet is provided for students to record information pertaining to their survey (e.g., their survey
question).
Students write a journal entry about surveys in the local community.
Expectations
5m113
5m120
6m106
6m110
6m114
– design surveys, collect data, and record the
results on given spreadsheets or tally charts;
– 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 of
a table that is part of a report on a science
experiment);
• systematically collect, organise, and analyse data;
• evaluate data and make conclusions from the
analysis of data;
– design surveys, organize the data into
self-selected categories and ranges, and record the
data on spreadsheets or tally charts;
Groupings
Students Working As A Whole Class
Students Working In Small Groups
Students Working Individually
Teaching / Learning Strategies
Discussion
Direct Teaching
Inquiry
Learning Log/ Journal
Assessment
Through questioning and observations the
teacher will be able to determine how well
Grade 5 and 6 students are able to:
- use data management vocabulary in
discussions (e.g,. sample, population,
survey, and random sample)
- generate and discuss a selection of
appropriate survey questions
- design a survey with their small group
- create an appropriate tally chart
- tally their survey data
Students should also be asked to describe
their initial responses to the data. For
example:
Is the data as you predicted?
What do you find surprising?
Would you design the survey question
any differently if you had the chance to
do it again?
Teachers should observe student
understanding of surveying through a
variety of learning situations including
discussions, group decision making on the
nature of their survey, and written
reflections in the math journal.
Assessment Strategies
Learning Log
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Making A Good Game Of It
Subtask 4
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
40 mins
Observation
Assessment Recording Devices
Anecdotal Record
Teaching / Learning
Whole Group
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 think
were 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, subject
matter, 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 age
group (since the game of chance they will be developing will be for their age group and must also be
reflective 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 group
is 11- year-old students who live in X town, a random sample would be a selection of students from all over
town).
- 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 choose
from, 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 most
important factors or criteria of a good game. (keeping in mind the criteria they indicated as important in
subtask 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 up
to the teacher and students.
- Set a reasonable timeline for gathering the data. (The data is not required until Subtask 7, so the students
have a bit of time to gather their information.)
Individual Work
Math Journal:
Ask students to respond to the following prompt:
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Making A Good Game Of It
Subtask 4
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
40 mins
Who collects information in our local communities? Why do they collect it? Do you think this data
collection is important? Why?
Adaptations
Students who cannot cope with the complexity of the journal prompt may respond to a simpler prompt such
as:
What is a survey? What kind of worker might have to do a survey for their job?
Resources
Our Survey
BLM4.1 Our Survey.cwk
Notes to Teacher
Discussion on Surveys:
This discussion led by the teacher is very important for establishing mathematical terminology involved in
surveying (population, sample, random sample). It is also very important for students to understand that a
survey question must be decided upon and used consistently in order to collect accurate information.
Teacher Reflections
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The Penny Flip Experiment
Subtask 5
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
40 mins
Description
Students flip a penny a given number of times in order to explore the probability of getting heads or tails. Each
student creates a tally sheet and collects data which is later added to a class chart. The teacher leads a
discussion 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.
Expectations
5m111
5m113
5m120
5m121
5m122
6m106
6m112
6m113
6m114
6m122
6m123
• demonstrate an understanding of probability
concepts and use mathematical symbols;
– design surveys, collect data, and record the
results on given spreadsheets or tally charts;
– 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 of
a table that is part of a report on a science
experiment);
– 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);
– predict probability in simple experiments and use
fractions to describe probability;
• systematically collect, organise, and analyse data;
• examine the concepts of possibility and probability;
• compare experimental probability results with
theoretical results.
– design surveys, organize the data into
self-selected categories and ranges, and record the
data on spreadsheets or tally charts;
– 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);
– examine experimental probability results in the
light of theoretical results;
Groupings
Students Working As A Whole Class
Students Working In Pairs
Students Working Individually
Teaching / Learning Strategies
Demonstration
Experimenting
Collaborative/cooperative Learning
Discussion
Assessment
The teacher can read the student's math
journal to gather formative assessment data
on the student's understanding of
probability.
Through questioning and observations the
teacher will be able to determine how well
Grade 5 and 6 students are able to:
- use mathematical terminology appropriately
in discussions and in their writing (e.g.,
probability, chance, likely, possibility,
theoretical probability, experimental
probability)
- keep a tally of their results
- reflect on results in their tally and on the
class tally
Assessment Strategies
Observation
Questions And Answers (oral)
Learning Log
Assessment Recording Devices
Anecdotal Record
Teaching / Learning
Whole Group
Demonstration:
- Explain to the students that they will will be gathering data on the results of a number of penny flips.
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The Penny Flip Experiment
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
Subtask 5
40 mins
- 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 the
results 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 the
flips 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 math
journal 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 each
number 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 (20
tosses). Discuss this calculation. Have students calculate the experimental probability of the combined results
for 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 experimental
probability 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 the
theoretical results (what actually happened compared to what should have happened).
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The Penny Flip Experiment
Subtask 5
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
40 mins
Adaptations
Students with fine motor difficulties may have difficulty flipping the coin successfully. These students could tally
their partner's tosses using two different coloured blocks or by making tick marks on the blackboard using wide
chalk.
Resources
Penny Flip Recording Sheet
BLM5.1 Penny Flip.cwk
pennies
1
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The Penny Flip Experiment
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
Subtask 5
40 mins
Notes to Teacher
Flipping the Coins
It can get pretty noisy flipping coins, and pennies have a tendency to roll off desks. These problems can be
solved by lining shoeboxes or shoebox lids with felt and flipping the penny into the box or lid.
Theoretical and Experimental Probability - An Overview
It 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 in
60 penny flips, 30 flips would be heads, and 30 flips would be tails. Experimental probability is what we find
in 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 penny
flips there is only one favourable outcome if we are predicting heads) and the number of possible outcomes
as the denominator (for penny flips there are two possible outcomes: heads and tails). The theoretical
probability of flipping heads is 1/2. To figure out the theoretical probability of 60 flips, we would multiply 60
by 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 the
numerator (25), and use the number of trials as the denominator (60). The experimental probability is
therefore 25/60 or .42. (The theoretical probability is 1/2 or .50.) The experimental probability is fairly close
to the theoretical probability.
Understanding Probability
The probability of an event happening can be a number from 0 to 1. This number can be expressed as a
fraction, a percentage, or a decimal. (Note: Odds are given in a ratio. The odds of winning are expressed
as 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, the
probability 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
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Spinner Experiment
Subtask 6
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
40 mins
Description
In this subtask, students construct a spinner and make predictions about what they think will happen when
they spin a given number of times. Students record their spins in a self-constructed tally, and then reflect on
what happened in the experiment. The students will be assessed by the teacher on their 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.
Expectations
5m111 A • demonstrate an understanding of probability
concepts and use mathematical symbols;
5m113 A – 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 of
a table that is part of a report on a science
experiment);
5m122 A – predict probability in simple experiments and use
fractions to describe probability;
5m114 A – display data on graphs (e.g., line graphs, bar
graphs, pictographs, and circle graphs) by hand and
by 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
self-selected categories and ranges, and record the
data on spreadsheets or tally charts;
6m120
– construct line graphs, bar graphs, and scatter
plots both by hand and by using computer
applications;
6m122 A – 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);
6m123 A – examine experimental probability results in the
light of theoretical results;
Groupings
Students Working Individually
Teaching / Learning Strategies
Graphing
Learning Log/ Journal
Demonstration
Assessment
BLM6.5 Teacher Checklist is available for
teachers to use to assess the students'
understanding of selected data
management and probability concepts,
skills, and knowledge. Two checklists are
provided within the blackline master, one
for each grade. It is very important that
anecdotal comments be used as often as
possible to expand on the ratings given on
the Observation Checklist.
In addition to assessing the students'
written work, teachers should listen to
group or paired discussions (about the
two spinners). Observe to assess
whether students:
- realize that the spinners have the same
probability of spinning each colour
- understand why the results might be
different. (You need to spin many, many
times before the experimental results begin
to look more like the theoretical results.)
Ask questions of the Grade 6 students
about theoretical and experimental
probability. Phrase your questions to get at
the mathematical language of probability.
For example:
- I notice that you are going to spin 40
times and you predict that blue will be
landed on 20 times. How did you come
up with this number? (Student explains.)
Do you know what that is called?
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Spinner Experiment
Subtask 6
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
40 mins
(Theoretical probability.) What is
experimental probability then? (Student
explains.)
Note: This is formative assessment data.
Students will need a lot of experience with
using the terms theoretical and
experimental before they are given a
summative assessment.
Assessment Strategies
Performance Task
Learning Log
Assessment Recording Devices
Checklist
Anecdotal Record
Rating Scale
Teaching / Learning
Individual 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 BLM6.2
Spinner 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 could
be divided by grade).
- Ask students to complete the worksheet My Predictions (BLM6.3 Predictions). Go over the worksheet with
the group.
2. Reflecting on the Results:
- Ask the students to reflect on their findings on the worksheet Thinking About the Results of My Spinner
Experiment (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?
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Spinner Experiment
Subtask 6
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
40 mins
Adaptations
Students with specific learning disabilities in the area of mathematics may be able to take part in the task if it is
adapted 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. Have
the students conduct their experiments and keep track of each spin. Once they are done, ask them to explain
what they found. Have them repeat the experiment, asking them to make a new prediction. Observe to see if
the students make the same prediction or adapts it to reflect the results of their first experiment. Does the
student understand the idea of equal/unequal chance probability of landing on a certain colour?
Resources
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 Teacher
Possible Extensions:
1 a) Present the students with two different spinners that contain the numbers 2, 3, 4, and 5. Pose this
problem: if each participant gets five spins and the winner is determined by the highest sum of the five
numbers, 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
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Graphing the Data
Subtask 7
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
80 mins
Description
In 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 is self-assessed by the
student using the Graph Rubric. (This subtask provides students with practice before they are assessed on
their ability to create graphs in Subtask 9.)
Expectations
5m109 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
graphs, pictographs, and circle graphs) by hand and
by using computer applications;
5m116 A – explain the choice of intervals used to construct a
bar graph or the choice of symbols on a pictograph;
5m119 A – construct labelled graphs both by hand and by
using computer applications;
5m120 A – 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 of
a table that is part of a report on a science
experiment);
6m110 A • evaluate data and make conclusions from the
analysis of data;
6m117 A – 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
graphing calculators or computers);
6m119 A – 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 A – construct line graphs, bar graphs, and scatter
plots both by hand and by using computer
applications;
6m121 A – make inferences and convincing arguments based
on the analysis of tables, charts, and graphs;
Groupings
Students Working In Small Groups
Students Working Individually
Teaching / Learning Strategies
Collaborative/cooperative Learning
Graphing
Demonstration
Assessment
Students will use the Graph Rubric to assess
their two graphs as well as their discussions.
It will have been very important for the
students to have seen the rubric BEFORE
they begin the task. A review of the
expectations and rubric will help to focus
their work and their discussions.
The teacher should review the graphs and
the student self-assessment. Feedback will
be very important for the students since they
are assessed on many of these skills again
in Subtask 9.
Assessment Strategies
Performance Task
Self Assessment
Observation
Assessment Recording Devices
Rubric
Anecdotal Record
Teaching / Learning
Whole Group
Introducing the Task and Rubric:
- Explain that the task is done independently (for the most part) in order to see how well students can create
graphs without the support of peers.
- Review the task (compiling data, creating two graphs, reflecting on their graphs, discussing with a small
group, and assessing their work).
- Go over the rubric with the students. Point out the slight differences in the Grade 5 and Grade 6 rubrics.
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Graphing the Data
Subtask 7
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
80 mins
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 from
the 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 to
represent 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 to
explain 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.
Adaptations
This graphing activity should be done independently. Students with IEPs will have specific accommodations listed
for assessment tasks. These students may need assistance creating their graph (e.g., using a computer) or in
explaining 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 their
work as you go. The student can circle the description that best matches their performance.
Resources
Graph Rubric - Self Assessment (5)
Graph Rubric - Self Assessment (6)
Rationale for Choice of Graph
BLM7.1 My Choices.cwk
grid paper
1
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Graphing the Data
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
Subtask 7
80 mins
Notes to Teacher
Graphing the Data:
Some students may need to review the five types of graphs that were investigated in subtask 3. A small
group of students who want a "refresher" could be invited to get together for a 5- to 10-minute review. Use
BLM3.1 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 for
students 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 students
should be able to construct graphs using computer applications. If at all possible, students should be given
the opportunity to learn how to make graphs on the computer.
Teacher Reflections
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Game Sticks
Subtask 8
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
80 mins
Description
In this game, each person (or team) uses 6 two-sided sticks (tongue depressors), which students must first
decorate. After the demonstration game, students record a few questions about probability as it relates to the
game and then play the game, a few times to answer their questions and test their theories. In pairs, the
students construct tree diagrams to determine the possible outcomes and discuss their findings.
In their journals, students then respond to prompts about the activity.
Expectations
5m123
5m124
6m111
6m124
– use tree diagrams to record the results of simple
probability experiments;
– use a knowledge of probability to pose and solve
simple problems (e.g., what is the probability of
snowfall in Ottawa during the month of April?).
• use a knowledge of probability to pose and solve
problems;
– use tree diagrams to record the results of
systematic counting;
Groupings
Students Working In Pairs
Students Working In Small Groups
Teaching / Learning Strategies
Demonstration
Learning Log/ Journal
Collaborative/cooperative Learning
Discussion
Assessment
Through questioning and observations the
teacher will be able to determine how well
Grade 5 and 6 students are able to:
- use tree diagrams to record the possible
combinations of plain and patterned sticks
- use mathematical language in large and
small group discussions as well as in their
journal responses
Assessment Strategies
Observation
Learning Log
Questions And Answers (oral)
Assessment Recording Devices
Anecdotal Record
Teaching / Learning
Day 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.
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Game Sticks
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
Subtask 8
80 mins
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 language
of 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 they
will 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 affects
that 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 possible
outcomes.
- Repeat with a two-stick version of the game. What are the possible outcomes now? Ask the students how
they 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 following
prompts:
- 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?
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Game Sticks
Subtask 8
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
80 mins
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.
Adaptations
Be cognizant of student participation in large and small group discussions. Less confident students who may
or may not have specific exceptionalities will need additional prompts and perhaps additional time to formulate
their ideas and respond.
Students who cannot cope with the complexity of the journal prompt may respond to a simpler prompt such
as:
Did you have a good chance of winning the Stick Game? Why?
Resources
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 Teacher
Tree Diagrams
Tree diagrams are used to help show all combinations of items. For example, if an ice cream cone can have
three scoops of either strawberry (s), chocolate (c), or vanilla (v), a tree diagram can help show all of the
possible combinations. (Strawberry - sss, ssc, ssv, scc, svv, scv)
Rationale for this Activity
Stick Games provides students with the opportunity to discuss a game of chance where the probability of
winning is not immediately obvious. There is a considerable amount of investigative possibilities in this
subtask. The teacher is able to explore many levels (if desired) by looking at possible results when the
game uses five, four, or three sticks instead of six.
This activity also provides an authentic context for using tree diagrams. These diagrams help students to
sort out the possible outcomes of each toss in a visual format.
Teacher Reflections
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What Does the Data Tell Us?
Subtask 9
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
80 mins
Description
Students 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 are
provided. The students must display one athlete's data in more than one way in order to show bias. The
student's graphs are assessed using a rubric.
Expectations
5m19
5m20 A
5m114 A
5m117 A
5m118 A
5m119 A
5m120 A
6m21
6m22 A
6m110
6m118 A
6m119 A
6m115
– identify and investigate the use of number in
various careers;
– identify and interpret the use of numbers in the
media;
– display data on graphs (e.g., line graphs, bar
graphs, pictographs, and circle graphs) by hand and
by using computer applications;
– calculate the mean and the mode of a set of data;
– recognize that graphs, tables, and charts can
present data with accuracy or bias;
– construct labelled graphs both by hand and by
using computer applications;
– 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 of
a table that is part of a report on a science
experiment);
– identify the use of number in various careers;
– identify, interpret, and evaluate the use of
numbers in the media;
• evaluate data and make conclusions from the
analysis of data;
– calculate the median of a set of data;
– 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);
– experiment with a variety of displays of the same
data using computer applications, and select the
type of graph that best represents the data;
Groupings
Students Working In Small Groups
Students Working Individually
Students Working As A Whole Class
Teaching / Learning Strategies
Collaborative/cooperative Learning
Learning Log/ Journal
Direct Teaching
Assessment
Through questioning and observations the
teacher will be able to determine how well
Grade 5 and 6 students are able to:
- create two graphs that give different
messages (create bias)
- understand the concept of mean and
mode (and median - Grade 6)
- calculate mean and mode (and median Grade 6)
- explain their choice of graph; and
- use mathematical language in their
discussions and written work
The students' graphs are done individually
and are assessed by the teacher using the
Graph Rubric. Please note that only five
expectations will fit onto the rubric. In
addition, the following expectations are
assessed using the rubric: 5m20, 5m119,
5m120, and 6m22.
Assessment Strategies
Observation
Performance Task
Learning Log
Assessment Recording Devices
Rubric
Anecdotal Record
Teaching / Learning
Day One
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What Does the Data Tell Us?
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
Subtask 9
80 mins
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 cubes
together to represent the results of the first test. Ask eight other students to represent the scores for the
other tests using linking cubes. Stand the towers up side by side to show the differences in test results. Ask
students what the test mark would be if the total of all the test marks remained the same, but each student got
the same mark. Redistribute the cubes to make equal towers (13 cubes high). Explain that this is the average
score.
- 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 up
slightly).
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 scores
under 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 for
possible solutions. (Take the two middle numbers, 12 and 14. Add 12 and 14 together and divide by 2. The
new median would be 13 and therefore the answer is yes, the median would be affected by an additional
math 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 whole
group.
b) Ask the students if it would be accurate for a teacher to use the mean, median, or mode to predict what
the 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 and
whether 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
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What Does the Data Tell Us?
Subtask 9
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
80 mins
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 then
represent on a pair of graphs. The graphs must contain the data provided for the athlete, but show the data
differently or use certain portions of the data to convey two different messages; one to support signing the
athlete 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 two
athletes, but "get at" the same expectations.)
- Reinforce that in both cases students must create two graphs that display the athlete's career. They must
be the same type of graph. One of the two graphs must be able to support their recommendation (through the
manipulation of intervals on the graph).
- Each group must attach a brief written response which explains why they think their graphs convey
different messages to readers. The group must also explain its choice of graph (bar, line, pictograph, or
circle).
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.
Adaptations
Students who have specific learning disabilities will need to have significant support to complete the tasks
outlined. A strong partner who can scribe the discussions will be of particular importance. Graphing may need to
be done using a computer that already contains the data. The student is then able to manipulate the data.
Resources
Graph Rubric
Mia Hamm's Statistics
BLM9.2 Hamm.cwk
Wayne Gretzky's Statistics
BLM9.1 Gretsky.cwk
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What Does the Data Tell Us?
Subtask 9
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
80 mins
Task for Mia Hamm's Statistics
BLM9.4 HammInvestigation.cwk
Task for Wayne Gretzky's Statistics
BLM9.3 GretzkyInvestigation.cwk
grid paper
2
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What Does the Data Tell Us?
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
Subtask 9
80 mins
Notes to Teacher
Important 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 are
greater 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 has
been on the team since she was 15. She plays forward. Mia is a role model for young athletes around the
world.
Using Other Data:
Different data could be used to investigate mean, median, and mode and to discuss how bias is created
through the representation of data. For example, a student could research the data from a favourite athlete
and 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 to
the class along with their graphs. They could pretend they are making a convincing presentation to team
owners to convince them to sign or not to sign the athlete.
Wayne's Mean, Median, and Mode
1. Mean: The total for Wayne’s scoring over 20 years was 2857 (Divide 2857 by 20). His mean scoring per
season 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 of
graph that best represents the data
In this subtask, the students use handmade graphs. It is certainly preferable for students to be inputting
their data and producing a variety of graphs electronically. Students would be able to create a wider variety
of graphs. These graphs would also be helpful in discussions about bias.
Teacher Reflections
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River Crossing
Making a Game of It!
Subtask 10
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
40 mins
Description
Students take turns rolling two numbered cubes and using the sum to move their counters across the game
board. As students play River Crossing Game, they see which combinations of numbers are the most 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).
Expectations
5m111 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 use
fractions to describe probability;
6m113 A • compare experimental probability results with
theoretical results.
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);
6m123 A – examine experimental probability results in the
light of theoretical results;
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).
Groupings
Students Working In Pairs
Students Working Individually
Teaching / Learning Strategies
Collaborative/cooperative Learning
Demonstration
Learning Log/ Journal
Assessment
Teachers assess student understanding of
probability concepts through the math
journal response. Read to determine how
well Grade 5 and 6 students are able to:
- use mathematical language to explain
probability
- use charts/diagrams to communicate
- understand probability concepts
- use fractions to explain probability
Assessment Strategies
Learning Log
Questions And Answers (oral)
Assessment Recording Devices
Anecdotal Record
Teaching / Learning
Whole Group
Demonstration of River Crossing:
- Explain the rules of the game through a demonstration of River Crossing (with help from a volunteer). The
blackboard can be used with magnetic markers serving as boats. (Instructions for the game are outlined in
BLM 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:
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River Crossing
Making a Game of It!
Subtask 10
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
40 mins
- How many ways can you roll 12? How many ways can you roll 11? Do you have a better chance of rolling
11 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 more
challenging game?
Adaptations
Resources
River Crossing Instructions
BLM10.1River .cwk
counters (e.g., centicubes, buttons)
12
numbered cubes
2
Notes to Teacher
Playing the Game:
The first time students play this game, they will likely randomly select dock numbers for their counters. After
students have played the game a few times, they will develop better strategies for deciding where their
boats 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 a
discussion on probability.
Extension:
Give the students the following investigation: If you were given three numbered cubes (with numbers one
to six on the sides), what would be the best docks to put your boats on. Support your answer with
mathematical language and diagrams.
Teacher Reflections
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Games Expo
Subtask 11
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
280 mins
Description
Each toy company (made up of two to four students) designs, field tests, and presents a game of chance
at a Games Expo. From the data generated in the field test of their game, students predict the probability
of winning and determine the average set-up and playing time. This information is presented by the toy
company along with its game. The game and presentation are assessed for a number of data
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 with two
other entries (self-selected) that they believe demonstrate their understanding of data management and
probability 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.
Expectations
5e1 A
5e2 A
5e7 A
5m109 A
5m111 A
5m120 A
5m121 A
5m124 A
6e1 A
6e7 A
6e19 A
6m109 A
6m110 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 a
newspaper stating and justifying their position on an
issue in the news);
• use writing for various purposes and in a range of
contexts, including school work (e.g., to summarize
information from materials they have read, to reflect
on their thoughts, feelings, and imaginings);
• revise and edit their work, seeking feedback from
others and focusing on content, organization, and
appropriateness of vocabulary for audience;
• interpret displays of data and present the
information using mathematical terms;
• demonstrate an understanding of probability
concepts and use mathematical symbols;
– 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 of
a table that is part of a report on a science
experiment);
– 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);
– use a knowledge of probability to pose and solve
simple problems (e.g., what is the probability of
snowfall in Ottawa during the month of April?).
• 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 electrical circuit for an audience
unfamiliar with the technical terminology);
• revise and edit their work in collaboration with
others, seeking and evaluating feedback, and
focusing on content, organization, and
appropriateness of vocabulary for audience;
– frequently introduce vocabulary from other subject
areas into their writing;
• interpret displays of data and present the
information using mathematical terms;
• evaluate data and make conclusions from the
Groupings
Students Working In Small Groups
Students Working Individually
Teaching / Learning Strategies
Brainstorming
Collaborative/cooperative Learning
Demonstration
Assessment
The teacher will be using two different
rubrics for the culminating task:
1. Games Expo Rubric
(Note: this rubric provides insufficient
space to list the expectations that are
being assessed at this time. Additional
expectations are: 5m120, 5m124, 6m106,
6m109, and 6m112)
2. Math Journal Rubric
Assessment Strategies
Performance Task
Questions And Answers (oral)
Learning Log
Exhibition/demonstration
Classroom Presentation
Assessment Recording Devices
Rubric
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Games Expo
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
Subtask 11
280 mins
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 are
two possibilities; in rolling a die, there are six
possibilities);
6m125 A – 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).
6m106 A • systematically collect, organise, and analyse data;
Teaching / Learning
Small Group (Toy Companies)
1. Reviewing the Design Process:
- Introduce and review the design process with your students. (Note: There are many variations of this
process. 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" for
presentation purposes only. (It is assumed that the game and supporting materials will take no more than
three 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). (Each
game 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 improvements
on 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 event
can be held in the gym or library, for example. Visitors play the role of potential purchasers of the games and
complete the Purchaser's Response Sheet (BLM11.2 Response) after sampling each game. (These
responses will be incorporated into the teacher's evaluation of the game.)
Individual Work:
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Games Expo
Subtask 11
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
280 mins
Math Journal:
- Ask students to submit their three journal entries. (Note: one of them must be the journal entry from subtask
10: River Crossing.)
Please Note: It is important to remember that the Revise and Edit category in the Journal Rubric primarily
focuses on the students' revisions to and edits of their mathematical thinking. It is not intended to strictly focus
on conventions of language.
Adaptations
The culminating task can easily be adapted for exceptional students. Complexity of the game and length of
presentation can easily be adapted. The students can also be given any number of accommodations including
extra time, a quiet space to work, assistance scribing their writing, and someone to read their text resources.
Resources
Grade 5 Journal Rubric
Grade 6 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 Teacher
The Design Process:
Students should review the process before starting to design their game of chance. The design process
listed 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 with
others.)
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
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Appendices
Making a Game of It!
Gr. 5 / 6 Data Management and Probability
Resource List:
Black Line Masters:
Rubrics:
Unit Expectation List and Expectation Summary:
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Resource List
Page 1
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
Rubric
Blackline Master / File
Games Expo Rubric
ST 11
2
This rubric is used to score the student's game and
presentation in the Culminating Activity.
Copyright Application Form
ST 1
BLM1.1 Copyright.cwk
Students record their Toy Company name and logo on
this sheet.
Grade 5 Journal Rubric
ST 11
2
This rubric is used to score each student's self-selected
3 journal entries.
Form for Field Testing of the Games
ST 11
BLM11.1 Field Test.cwk
Students use this blackline master to collect information
from people who have field tested their game.
Grade 6 Journal Rubric
ST 11
2
This rubric is used to score each student's self-selected
3 journal entries.
Game Connection: Go-Moku
ST 2
BLM2.1 Japanese Tic-Tac-Toe.cwk
This is a one page instruction sheet for the Japanese
game of strategy called Go-Moku. It is similiar to
Tic-Tac-Toe since players alternate turns placing a tile
in order to prevent the opponent from creating a row of
his/her coloured tiles.
Graph Rubric
ST 9
2
This rubric is used to assess the students performance
in graphing and explaining the message that their graph
gives to the reader.
Graph Rubric - Self Assessment (5)
ST 7
3
This rubric is used to assess the student's ability to
create two types of graphs, their explanation of
intervals and their understanding of how graphs can
show the same data differently.
Graph Rubric - Self Assessment (6)
ST 7
3
This rubric is used to assess the student's ability to
create two types of graphs, their explanation of
intervals and their understanding of how graphs can
show the same data differently.
Game Connections
Unit
additional games.cwk
These games can be used with the whole class or as
extensions for small groups or individual students.
Instructions for Making Spinners
ST 6
BLM6.1 Making Spinners.cwk
Two methods of making spinners are included in this
blackline master.
Instructions for Playing
ST 8
BLM8.1 Game Sticks.cwk
Instructions for playing the Stick Game are provided
here.
Investigating Graphs
ST 3
BLM3.2 InvestigatingGraphs.cwk
This blackline master assists students in their
investigations of the five graphs provided in BLM3.1
Looking at Graphs.
Looking at Graphs
ST 3
BLM3.1 Looking at Graphs.cwk
Provided here are a series of five graphs: circle, bar,
double bar, line and pictograph. Students investigate
these graphs in small groups, using BLM3.2
Investigating Graphs to guide their discussions.
Making Predictions
ST 6
BLM6.3 Predictions.cwk
This blackline master includes a Grade 5 and Grade 6
predictions page. Students make predictions, explain
their thinking and create a tally on this page. Grade 6
students are asked to indicate theoretical probability.
Mia Hamm's Statistics
BLM9.2 Hamm.cwk
Statistics for Mia Hamm are provided here.
ST 9
Observation Checklist
ST 6
BLM6.5 Teacher Checklist.cwk
These Grade 5 and Grade 6 checklists are completed
by the teacher as observations are being made. A rating
scale that parallels the four levels of achievement is
provided. Anecdotal notes should be used to support
the ratings given.
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Resource List
Page 2
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
Our Survey
ST 4
BLM4.1 Our Survey.cwk
This blackline master is to be completed by each Toy
Company. It prompts students to include the audience
surveyed, the survey question and the tally.
Task for Wayne Gretzky's Statistics
ST 9
BLM9.3 GretzkyInvestigation.cwk
This blackline master prompts students to investigate
mean, median and mode, make predictions, investigate
statistics and create two graphs.
Penny Flip Recording Sheet
ST 5
BLM5.1 Penny Flip.cwk
Students write their predictions, tally their 30 flips and
record their results on this recording sheet.
Wayne Gretzky's Statistics
BLM9.1 Gretsky.cwk
Statistics for Wayne Gretzky are provided here.
Prompts for Pairs of Students
ST 8
BLM8.2 Reflection.cwk
These prompts are given to pairs of students in order to
reflect on the Stick Game.
Purchaser's Response Form
ST 11
BLM11.2 Response.cwk
Visiting "purchasers" complete this form after they have
tried out a game of chance.
Rationale for Choice of Graph
ST 7
BLM7.1 My Choices.cwk
This blackline master includes a separate page for each
of Grade 5 and Grade 6 students. The students use this
blackline master to explain their choice of graph and
their choice of intervals. Grade 6 students are expected
to compare their graphs and consider how a change in
intervals would alter the graph.
Resources to Support the Unit
Unit
Resources.cwk
A bibliography of text, video and software resources.
Some webites are also provided.
Results of the Spinner Experiment
ST 6
BLM6.4 Results.cwk
This blackline master includes a page for Grade 5
students and a page for Grade 6 students. Students are
asked to explain their results and make a graph to
display their data. Grade 6 students are asked to
investigate the relationship between theoretcial and
experimental probability.
River Crossing Instructions
ST 10
BLM10.1River .cwk
Instructions for the game River Crossing are included,
along with a game board.
Self-Assessment
ST 3
BLM3.5 SelfAssessment.cwk
This blackline master is both a checklist for the student
to use as they complete their graph and a self
assessment tool.
Spinner Templates
ST 6
BLM6.2 SpinnerTemplate.cwk
Templates for two spinners are provided here. Students
use one of the spinner templates to create their spinner.
Tally Sheet
ST 3
BLM3.3 Tally Sheet.cwk
This blackline master provides six sets of data related
to games and game playing. Students use this data to
create a graph for a specific audience.
Task for Mia Hamm's Statistics
BLM9.4 HammInvestigation.cwk
This blackline master prompts students to make
predictions, investigate statistics and create two
graphs.
ST 9
ST 9
What's It For?
ST 3
BLM3.4 What's it For.cwk
This sheet provides the students with seven different
scenarios for which a graph could be created.
Material
10 cm x 10 cm squares of cardboard
ST 6
1
per person
Each student will require a square of cardboard if they
are creating a spinner using Method #1.
Bristol board
ST 1
1
per group
This bristol board will be used to create the logo and
company banner.
Bristol board
ST 11
1
per group
The Toy Companies may require bristol board in order to
construct their game of chance.
buttons
ST 6
1
per person
Students making a spinner using Method #2 will require
one button.
Cardboard or a three-fold display board
ST 1
1
per group
This could be used to create an office wall for each toy
company. The group could use the backdrop to post
brainstorming ideas, display their data and to create
some privacy for their work site.
grid paper
ST 3
1
per pair
Students may require grid paper to complete their graph.
grid paper
ST 6
1
per person
Students may request grid paper in order to make their
graph.
grid paper
1
per person
Students will require grid paper to complete their
graph(s).
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ST 7
Resource List
Page 3
Making a Game of It!
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
grid paper
ST 9
2
per person
Students will need grid paper to create their graphs.
paper clips
ST 6
1
per person
Each student will require one paper clip to create their
spinner, whether they are using Method #1 or #2.
pennies
1
per pair
Students need one penny per pair.
ST 5
tongue depressors
ST 8
12
per pair
Each team (pair) needs 12 sticks for the Stick Game.
Equipment / Manipulative
compass, large lids, masking tape
1
per class
These materials can be used by the students who
choose to make a circle graph.
ST 3
counters (e.g., centicubes, buttons)
ST 10
12
per person
Counters are needed to represent boats in the River
Crossing game.
counters (e.g., toothpicks, cubes)
ST 8
10
per pair
These counters will be used in the Stick G ame. They
will beneeded to keep track of the score.
numbered cubes
ST 10
2
per pair
Each pair of students will need 2 numbered cubes to
play River Crossing.
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BLM1.1 Copyright
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)
BLM2.1Japanese Tic-Tac-Toe
Game Connection
“Japanese Tic-Tac-Toe”
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 Gomoku 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.
In this game, the player
with the white stones is
going next. Where
should they go so that
black doesn’t win?
BLM3.1 Looking at Graphs
Use of the Local Arena
Participation in Intramural
Sports at P.T. Smythe School
Figure
Skating
Hockey
Number
30
of
Students
Free
Skating
20
Special
Events
Girls
10
20%
5%
Boys
40
30%
45%
50
Most Popular Intramural Sports Played
Time Spent Outside for Gym
6
5
4
3
2
1
S
O
N
D
J
F
M
Months of the School Year
BOARD GAMES IN OUR CLASSROOMS
A
M
J
BLM3.1 Looking at Graphs
= 4 games
Gr. 7 to 8
Gr. 4 to 6
K to Gr. 3
Our Teachers’
Favourite Games
Word Games
Computer Games
Board Games
Other Games
2
4
6
8
10 12 14 16 18
Number of Teachers
Names:
BLM3.2 Investigating Graphs
What Is It About Graphs?
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 Sheet
Tally Information!
One group of students collected a lot of information about games. The information
is listed below.
Survey 2: Forty Students in
Primary Were Asked which of
Four Games Is Their Favourite
Survey 1: Chess Survey
never played
chess
dislikes chess
likes chess
Go Fish
Crazy Eights
Snap
Concentration
adults
kids
Survey 3: Number of Games that are Used
During ONE Indoor Recess
(in three classrooms)
Card Games
Board Games
Survey 4: CHECKERS Survey
Say they are
good at
CHECKERS
junior
boys
Individual Games
Say they are
good at
CHECKERS
intermediate
boys
junior
girls
intermediate
girls
Active Games
Survey 5: Number of Times the Balls are Signed Out (over three months)
May
April
June
week 1
week 2
week 3
week 4
week 1
week 2
week 3
week 4
week 1
week 2
week 3
week 4
Soccer
balls
0
1
3
1
4
5
4
10
10
8
8
4
Basketballs
2
4
6
4
4
3
4
6
5
5
6
3
Softballs
0
0
2
0
3
4
3
2
4
4
5
3
BLM3.4 What’s It For?
You are making a graph for
THE CLASS NEWSLETTER.
You are making a graph for
THE CLASS NEWSLETTER.
Why might you be making this graph?
What kind of graph will you use?
Why might you be making this graph?
What kind of graph will you use?
You are making a graph for
THE PRINCIPAL.
You are making a graph for
THE PRINCIPAL.
Why might you be making this graph?
What kind of graph will you use?
Why might you be making this graph?
What kind of graph will you use?
You are making a graph for
A GAME COMPANY.
You are making a graph for
A GAME COMPANY.
Why might you be making this graph?
What kind of graph will you use?
Why might you be making this graph?
What kind of graph will you use?
You are making a graph for
YOUR TEACHER.
You are making a graph for
YOUR TEACHER.
Why might you be making this graph?
What kind of graph will you use?
Why might you be making this graph?
What kind of graph will you use?
You are making a graph for
A TOY STORE.
You are making a graph for
A TOY STORE.
Why might you be making this graph?
What kind of graph will you use?
Why might you be making this graph?
What kind of graph will you use?
You are making a graph for
A SCHOOL COACH.
You are making a graph for
A SCHOOL COACH.
Why might you be making this graph?
What kind of graph will you use?
Why might you be making this graph?
What kind of graph will you use?
You are making a graph for
THE INTERMEDIATE
TEACHER.
You are making a graph for
THE INTERMEDIATE
TEACHER.
Why might you be making this graph?
What kind of graph will you use?
Why might you be making this graph?
What kind of graph will you use?
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:
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
Name of Toy Company:
Our Survey
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.
never played
chess
likes chess
dislikes chess
adults
Say they are
Good at
Scrabble
junior
intermediate
boys
boys
√√√
√
kids
√
√√√√
√
Number of Games that are Used During ONE Indoor Recess
(in three classrooms)
Card Games
Board Games
√√ √√
√√√
Active Games
√√
√
√√√√
Say they are
Good at
Scrabble
junior
intermediate
girls
girls
√√√√
Individual 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
4. Add your results to the class tally sheet.
Tails
BLM 6.1 Making Spinners
Making a Spinner
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.
the grommet sits in the
whole in the cardboard
Method #1
You will need:
- piece of circular cardboard for the base
- sharp pencil or pen to poke a hole in the base
- 1 grommet
- 1 paper clip
- 1 butterfly clip
- 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)
- one spinner top
- scissors
- one paper clip
- a pencil
- masking tape
- red, yellow, and blue pencil crayons
- 1 button
- 1 ruler
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.
paper clip
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.
BLM 6.2 Spinners
Use either Spinner A or Spinner B (as directed by the teacher).
SPINNER A
B
B
B
B
R
Y
R
Y
SPINNER B
B
B
R
R
Y
B
Y
B
B
Y
B
Y
R
B
R
B
BLM6.3 Predictions
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? ____________________
Explain your thinking.
2. Use this space to keep track of your results as you spin your spinner.
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? _____________________
Explain your thinking.
2. Use this space to keep track of your results as you spin your spinner.
BLM6.4 Results
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.
2. Create a graph that will clearly display the data from your experiment.
Observation Checklist (Grade 5)
Legend for Ratings
1: struggling
2: learning
3: consolidating
4: extending
explains
compares creates an
uses
provides a fractions to rationale creates predictions effective
and uses
for
with
reasonable describe
graph to
results
prediction probability prediction a tally
show data
BLM6.5 Teacher Checklist
comments
BLM7.1 My Choices
My Choices (Grade 5)
My first graph is a ______________ graph.
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
My graph has intervals of ____________ 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.
BLM8.2 Reflection
Cut the boxes and distribute one prompt to each pair of students.
What number of counters
are players most likely to
collect on each turn?
Why?
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.
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?
What does the scoring for
Native American Game Sticks
have to do with probability?
How could you find out which
combinations of sticks are
most likely?
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.
Describe another game that
you like to play that involves
probability, and explain how
probability affects that game.
Wayne Gretzky’s Career Statistics
BLM 9.1
Gretzky
TOTAL
POINTS
SEASON
TEAM
GAMES
GOALS
ASSISTS
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
102
1996 - 97
New York
82
25
72
97
1997 - 98
New York
82
23
67
90
1998 - 99
New York
70
9
53
62
1487
894
1963
2857
TOTALS
BLM9.2 Hamm
Mia Hamm Career Statistics
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
BLM9.3 Gretzky Investigation
Investigating Wayne Gretzky’s Statistics
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 ____________________________________
________________________________________________________________
________________________________________________________________
4. Calculate Wayne’s best year. Explain what statistics you are using to determine
his best year.
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.
BLM9.4 Hamm Investigation
Investigating Mia Hamm’s Statistics
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.
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.
Graph Rubric
for use with Subtask 9 : What Does the Data Tell Us?
from the Grade 5/6 Unit: Making a Game of It!
Student Name:
Date:
Expectations for this Subtask to Assess with this Rubric:
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
Level 1
Level 2
Level 3
Level 4
Problem Solving
- needs a great deal of
prompting to enter into the
graphing problem
- is able to enter into the
graphing problem after one
or two simple prompts
- is able to enter into the
graphing problem with
minimal prompting
- is able to enter into the
graphing problem without
prompting; may ask
questions or clarify thoughts
as he or she extends his or
her thinking
Understanding of concepts
- has much difficulty choosing
which data to use for
different audiences
- does not recognize the
types of graphs that would
be appropriate for the data
- is able to choose one set of
appropriate data
- can choose an appropriate
graph to use but isn't sure of
why others shouldn't be used
- chooses two obvious sets
of data for the graphs
- chooses an appropriate
graphing format to use and
explains his or her choice
- chooses two sets of data that
are more discreet in their
message; more sophisticated
- chooses an appropriate
graphing format to use and
explains his or her choice
Application of mathematical - graphs are simple and are
missing many components
procedures
- graphs are unclear and
some aspects of the graph
may be incomplete
- graphs are clear and easy
to read
- graphs are well labelled,
detailed, and organized, and
keep the reader in mind
Communication
- uses the terms mean,
median, and mode correctly
in some cases
- graphs are somewhat clear
- written explanations require
oral clarification
- uses the terms mean,
median, and mode correctly
- graphs are clear
- written explanations are
understandable
- uses the terms mean,
median, and mode correctly
- graphs are clear and
detailed
- written explanations are
clear and concise
- ability to solve problems
without additional prompting
- defines two sets of data to suit
a purpose (to represent bias)
- understanding which graph will
relay the desired message to the
reader
- making two graphs with all of
the component parts
- using the language mean,
median, mode appropriately
- graphing data clearly, using
appropriate labels and titles
- explanations of graphs use
mathematical language
- uses the terms mean,
median, and mode
inappropriately
- graphs are hard to decipher
- written explanations are
vague
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
Games Expo Rubric
for use with Subtask 11 : Games Expo
from the Grade 5/6 Unit: Making a Game of It!
Student Name:
Date:
Expectations for this Subtask to Assess with this Rubric:
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 newspaper
stating 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 an
electrical 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
Level 1
Level 2
Level 3
Level 4
Oral Presentation
- presentation and answers
to questions demonstrate a
limited understanding of the
subject matter
- presentation and answers
to questions demonstrate a
basic understanding of the
subject matter
- presentation and answers
to questions demonstrate a
solid understanding of the
subject matter
- presentation and answers
to questions demonstrate a
thorough understanding of
the subject matter
Use of Data to Design
the Game
- minimal references to the
data were made; the student
does not appear to make
connections between the
data and his or her game
- some references to the
data were made; the student
has made a few connections
between the data and his or
her game
- many references to the
data were made; the student
has made sound
connections between the
data and his or her game
- thoughtful references to the
data were made; the student
has made insightful
connections between the
data and his or her game
How Probability is
Factored into the Game
and Explained
- probability concepts are not
connected to the game, or
any probability connections
are not relevant
- probability concepts are
vague and/or uncertain as
they are connected to the
game
- probability concepts are
appropriately connected to
the game
- probability concepts are
appropriately connected and
referred to in other games
Organization of Time
and Materials (Learning
Skills)
- no plan of organization
- rudimentary plan of
organization
- appropriate plan of
organization
- logical and coherent plan of
organization
- organizes work with limited
competence
- organizes work with
moderate competence
- organizes work with
considerable competence
- organizes work with a high
degree of competence
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-2
Grade 5 Journal Rubric
for use with Subtask 11 : Games Expo
from the Grade 5/6 Unit: Making a Game of It!
Student Name:
Date:
Expectations for this Subtask to Assess with this Rubric:
5e1
5e7
• 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);
• 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
Level 1
Mathematics Concepts
- writing shows a limited
understanding of
concepts due to partially
complete and unclear
explanations
- writing shows an
uncertain understanding
of concepts due to
inaccurate or confused
explanations
- writing shows a solid
understanding of
concepts through
complete and
appropriate explanations
- writing shows a
thorough understanding
of concepts through
detailed explanations
- mathematical
language is imprecise
or inappropriate
- some mathematical
language and symbols are
used appropriately but may
be compromised by errors
or vagueness
- mathematical
language and symbols
are used appropriately
- mathematical
language and symbols
are used purposefully
and effectively
- expressed thoughts
are incomplete and/or
How well has the writer disconnected
explained his/her ideas?
- expressed thoughts
are uncertain; some
ideas are disconnected
- expressed thoughts
- expressed thoughts
are clear and connected are clear, connected,
and concise
To what extent do the
journal entries show an
understanding of math
concepts?
Mathematical Language
How well has the writer
incorporated math
vocabulary into the
journal entries?
Clarity
Revising/Editing
How effective are the
revisions and edits that
were made to the
journal entries?
Level 2
- revisions and edits do - revisions and edits
little to improve the
improve some aspects
quality of the journal
of the journal entries
entries; revisions and
edits may be incomplete
Level 3
- revisions and edits are
effective and improve
many aspects of the
journal entries
Level 4
- revisions and edits are
effective and greatly
improve the journal
entries
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-3
Grade 6 Journal Rubric
for use with Subtask 11 : Games Expo
from the Grade 5/6 Unit: Making a Game of It!
Student Name:
Date:
Expectations for this Subtask to Assess with this Rubric:
6e1
6e7
6e19
• 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
electrical circuit for an audience unfamiliar with the technical terminology);
• revise and edit their work in collaboration with others, seeking and evaluating feedback, and focusing on content, organization, and appropriateness of vocabulary
for audience;
– 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
Level 1
Mathematics Concepts
- writing shows a limited
understanding of
concepts due to partially
complete and unclear
explanations
- writing shows an
uncertain understanding
of concepts due to
inaccurate or confused
explanations
- writing shows a solid
understanding of
concepts through
complete and
appropriate explanations
- writing shows a
thorough understanding
of concepts through
detailed explanations
- mathematical
language is imprecise
or inappropriate
- some mathematical
language and symbols are
used appropriately but may
be compromised by errors
or vagueness
- mathematical
language and symbols
are used appropriately
- mathematical
language and symbols
are used purposefully
and effectively
- expressed thoughts
are incomplete and/or
How well has the writer disconnected
explained his/her ideas?
- expressed thoughts
are uncertain; some
ideas are disconnected
- expressed thoughts
- expressed thoughts
are clear and connected are clear, connected,
and concise
To what extent do the
journal entries show an
understanding of math
concepts?
Mathematical Language
How well has the writer
incorporated math
vocabulary into the
journal entries?
Clarity
Revising/Editing
How effective are the
revisions and edits that
were made to the
journal entries?
Level 2
- revisions and edits do - revisions and edits
little to improve the
improve some aspects
quality of the journal
of the journal entries
entries; revisions and
edits may be incomplete
Level 3
- revisions and edits are
effective and improve
many aspects of the
journal entries
Level 4
- revisions and edits are
effective and greatly
improve the journal
entries
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-4
Graph Rubric - Self Assessment (5)
for use with Subtask 7 : Graphing the Data
from the Grade 5/6 Unit: Making a Game of It!
Student Name:
Date:
Expectationsfor this Subtask to Assess with this Rubric:
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
Application of
Mathematical
Procedures
- create two different graphs
Level 1
Level 2
- My graphs are unfinished. - My graphs are unclear or
inconsistent (e.g., one is
- I used the data
well done; the other is
inappropriately in the
inappropriate or
graphs.
incomplete).
- use data from a graphic
organizer
- I used some of the data
appropriately in the graphs.
Understanding of
Concepts
- I was uncertain of why
the intervals were chosen.
- I was unable to explain
why I chose the intervals,
or why my explanation did
- explain choice of intervals not make sense when you
look at the graph(s).
Communication in
Mathematics
- interpret displays of data
- describe and compare
graphs
- I was not able to interpret
the data that was
displayed.
- I was able to interpret
parts of the data that was
displayed.
- In my group, I could
- In my group, I had difficulty describe and compare
describing my graphs and
some aspects of my graphs
comparing them using
using mathematical
mathematical language.
language.
Level 3
- Both of my graphs are
clear.
Level 4
- Both of my graphs are
distinctive.
- I used most of the data
- I used the data
appropriately in the graphs. appropriately in the graphs.
- I had a good explanation
for my choice of intervals.
- I had a clear rationale for
my choice of intervals. I
made connections to other
graphs in my explanation.
- I was able to interpret
most of the data that was
displayed.
- I was able to interpret all
of the data that was
displayed.
- In my group, I did a good
job describing and
comparing my graphs using
mathematical language.
- I did an excellent job
describing and comparing
my graphs using
mathematical language.
Written using the Ontario Curriculum Unit Planner 2.51 PLNR_01 March, 2001* Open Printed on Jul 23, 2001 at 1:17:54 AM Page E-5
Graph Rubric - Self Assessment (6)
for use with Subtask 7 : Graphing the Data
from the Grade 5/6 Unit: Making a Game of It!
Student Name:
Date:
Expectationsfor this Subtask to Assess with this Rubric:
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 graphing
calculators or computers);
Category/Criteria
Application of
Mathematical
Procedures
- create two different graphs
- use data from a graphic
organizer
Understanding of
Concepts
- explain how choice of
intervals affect the
appearance of data
- understand how graphs
show data differently
Communication in
Mathematics
- evaluate displays of data
- describe and compare
graphs
Level 1
Level 2
- My graphs are unfinished. - My graphs are unclear or
inconsistent (e.g., one is
well done, the other is
- I used the data
inappropriate or
inappropriately in the
incomplete).
graphs.
- I used some of the data
appropriately in the graphs.
Level 3
- Both of my graphs are
clear.
Level 4
- Both of my graphs are
distinctive.
- I used most of the data
- I used the data
appropriately in the graphs. appropriately in the graphs.
- I was uncertain of how
- I had a good explanation
the intervals would change of how the intervals would
the appearance of the data. change the appearance of
the data.
- I was able to explain a
- I could not explain how my few basic ways that my
- I was able to explain how
graphs show the data
graphs show the data
my graphs show the data
differently.
differently.
differently.
- I had an excellent
explanation of how the
intervals would change the
appearance of the data. I
made connections to other
graphs in my explanation.
- I clearly explained how my
graphs show the data
differently.
- I was not able to evaluate
the data that was
displayed.
- I was able to evaluate
most of the data that was
displayed.
- I was able to evaluate all
of the data that was
displayed.
- In my group, I did a good
job describing and
comparing my graphs using
mathematical language.
- I did an excellent job
describing and comparing
my graphs using
mathematical language.
- I was unable to explain
how the intervals would
change the appearance of
the data.
- I was able to evaluate
parts of the data that was
displayed.
- In my group, I could
- In my group, I had difficulty describe and compare
describing my graphs and
some aspects of my graphs
comparing them using
using mathematical
mathematical language.
language.
Written using the Ontario Curriculum Unit Planner 2.51 PLNR_01 March, 2001* Open Printed on Jul 23, 2001 at 1:17:54 AM Page E-6
Expectation List
Making a Game of It!
Page 1
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
Selected
Assessed
English Language---Writing
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 newspaper stating and justifying their position on an issue in the news);
• use writing for various purposes and in a range of contexts, including school work (e.g., to summarize information from
materials they have read, to reflect on their thoughts, feelings, and imaginings);
• organize information to convey a central idea, using well-developed paragraphs that focus on a main idea and give some
relevant supporting details;
• revise and edit their work, seeking feedback from others and focusing on content, organization, and appropriateness of
vocabulary for audience;
5e2
5e3
5e7
1
1
1
1
1
1
English Language---Oral and Visual Communication
5e48
• express and respond to ideas and opinions concisely, clearly, and appropriately;
1
Mathematics---Number Sense and Numeration
5m19
5m20
– identify and investigate the use of number in various careers;
– identify and interpret the use of numbers in the media;
1
1
Mathematics---Data Management and Probability
5m109
5m110
5m111
5m112
5m113
5m114
5m116
5m117
5m118
5m119
5m120
5m121
5m122
5m123
5m124
• interpret displays of data and present the information using mathematical terms;
• evaluate and use data from graphic organizers;
• demonstrate an understanding of probability concepts and use mathematical symbols;
• pose and solve simple problems involving the concept of probability.
– design surveys, collect data, and record the results on given spreadsheets or tally charts;
– display data on graphs (e.g., line graphs, bar graphs, pictographs, and circle graphs) by hand and by using computer
applications;
– explain the choice of intervals used to construct a bar graph or the choice of symbols on a pictograph;
– calculate the mean and the mode of a set of data;
– recognize that graphs, tables, and charts can present data with accuracy or bias;
– construct labelled graphs both by hand and by using computer applications;
– 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 of a table that is part of a report on a science experiment);
– 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);
– predict probability in simple experiments and use fractions to describe probability;
– use tree diagrams to record the results of simple probability experiments;
– use a knowledge of probability to pose and solve simple problems (e.g., what is the probability of snowfall in Ottawa during
the month of April?).
1
1
1
2
1
1
2
1
3
1
1
3
1
4
1
1
1
2
3
3
1
1
1
1
2
1
The Arts---Visual Arts
5a26
• produce two- and three-dimensional works of art that communicate a range of ideas (thoughts, feelings, experiences) for
specific purposes and to specific audiences;
1
English Language---Writing
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 an electrical
circuit for an audience unfamiliar with the technical terminology);
• use writing for various purposes and in a range of contexts, including school work (e.g., to develop and clarify ideas, to
express thoughts and opinions);
• revise and edit their work in collaboration with others, seeking and evaluating feedback, and focusing on content, organization,
and appropriateness of vocabulary for audience;
– frequently introduce vocabulary from other subject areas into their writing;
6e2
6e7
6e19
1
1
1
1
1
English Language---Oral and Visual Communication
6e50
• express and respond to a range of ideas and opinions concisely, clearly, and appropriately;
1
Mathematics---Number Sense and Numeration
6m21
6m22
– identify the use of number in various careers;
– identify, interpret, and evaluate the use of numbers in the media;
1
Written using the Ontario Curriculum Unit Planner 2.51 PLNR_01 March, 2001* Open Printed on Jul 23, 2001 at 1:10:43 AM Page F-1
1
Expectation List
Making a Game of It!
Page 2
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
Selected
Assessed
Mathematics---Data Management and Probability
6m106
6m109
6m110
6m111
6m112
6m113
6m114
6m115
6m117
6m118
6m119
6m120
6m121
6m122
6m123
6m124
6m125
• systematically collect, organise, and analyse data;
• interpret displays of data and present the information using mathematical terms;
• evaluate data and make conclusions from the analysis of data;
• use a knowledge of probability to pose and solve problems;
• examine the concepts of possibility and probability;
• compare experimental probability results with theoretical results.
– design surveys, organize the data into self-selected categories and ranges, and record the data on spreadsheets or tally
charts;
– experiment with a variety of displays of the same data using computer applications, and select the type of graph that best
represents the data;
– 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 graphing calculators or computers);
– calculate the median of a set of data;
– 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);
– construct line graphs, bar graphs, and scatter plots both by hand and by using computer applications;
– make inferences and convincing arguments based on the analysis of tables, charts, and graphs;
– 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);
– examine experimental probability results in the light of theoretical results;
– use tree diagrams to record the results of systematic counting;
– 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).
4
2
1
1
1
2
• 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;
2
2
1
1
1
1
1
1
2
2
3
1
1
1
The Arts---Visual Arts
6a25
1
1
2
1
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1
1
2
2
1
Expectation Summary
Selected
Making a Game of It!
Assessed
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
English Language
5e1
5e11
5e21
5e31
5e41
5e51
5e61
1
1
5e2
5e12
5e22
5e32
5e42
5e52
5e62
1
1
5e3
5e13
5e23
5e33
5e43
5e53
5e63
1
5e4
5e14
5e24
5e34
5e44
5e54
5e64
5e5
5e15
5e25
5e35
5e45
5e55
5e65
5e6
5e16
5e26
5e36
5e46
5e56
5e66
5e7
5e17
5e27
5e37
5e47
5e57
5f3
5f13
5f4
5f14
5f5
5f15
5f6
5f16
5f7
5f17
5m3
5m13
5m23
5m33
5m43
5m53
5m63
5m73
5m83
5m93
5m103
5m113
5m123
5m4
5m14
5m24
5m34
5m44
5m54
5m64
5m74
5m84
5m94
5m104
5m114
5m124
5m5
5m15
5m25
5m35
5m45
5m55
5m65
5m75
5m85
5m95
5m105
5m115
5m6
5m16
5m26
5m36
5m46
5m56
5m66
5m76
5m86
5m96
5m106
5m116
5m7
5m17
5m27
5m37
5m47
5m57
5m67
5m77
5m87
5m97
5m107
5m117
1
5e8
5e18
5e28
5e38
5e48
5e58
5e9
5e19
5e29
5e39
5e49
5e59
5e10
5e20
5e30
5e40
5e50
5e60
5f8
5f18
5f9
5f10
5m8
5m18
5m28
5m38
5m48
5m58
5m68
5m78
5m88
5m98
5m108
5m118
5m9
5m19
5m29
5m39
5m49
5m59
5m69
5m79
5m89
5m99
5m109
5m119
1
French as a Second Language
5f1
5f11
5f2
5f12
Mathematics
5m1
5m11
5m21
5m31
5m41
5m51
5m61
5m71
5m81
5m91
5m101
5m111
5m121
1
3
3
1
5m2
5m12
5m22
5m32
5m42
5m52
5m62
5m72
5m82
5m92
5m102
5m112
5m122
1
1
2
2
1
1
1
1
3
1
1
1
1
1
1
1
1
2
2
5m10
5m20
5m30
5m40
5m50
5m60
5m70
5m80
5m90
5m100
5m110
5m120
Science and Technology
5s1
5s11
5s21
5s31
5s41
5s51
5s61
5s71
5s81
5s91
5s101
5s111
5s121
5s2
5s12
5s22
5s32
5s42
5s52
5s62
5s72
5s82
5s92
5s102
5s112
5s122
5s3
5s13
5s23
5s33
5s43
5s53
5s63
5s73
5s83
5s93
5s103
5s113
5s123
5s4
5s14
5s24
5s34
5s44
5s54
5s64
5s74
5s84
5s94
5s104
5s114
5s124
5s5
5s15
5s25
5s35
5s45
5s55
5s65
5s75
5s85
5s95
5s105
5s115
5s125
5s6
5s16
5s26
5s36
5s46
5s56
5s66
5s76
5s86
5s96
5s106
5s116
5s126
5s7
5s17
5s27
5s37
5s47
5s57
5s67
5s77
5s87
5s97
5s107
5s117
5s127
5s8
5s18
5s28
5s38
5s48
5s58
5s68
5s78
5s88
5s98
5s108
5s118
5s128
5s9
5s19
5s29
5s39
5s49
5s59
5s69
5s79
5s89
5s99
5s109
5s119
5s10
5s20
5s30
5s40
5s50
5s60
5s70
5s80
5s90
5s100
5s110
5s120
5z3
5z13
5z23
5z33
5z43
5z4
5z14
5z24
5z34
5z44
5z5
5z15
5z25
5z35
5z45
5z6
5z16
5z26
5z36
5z46
5z7
5z17
5z27
5z37
5z47
5z8
5z18
5z28
5z38
5z48
5z9
5z19
5z29
5z39
5z10
5z20
5z30
5z40
Social Studies
5z1
5z11
5z21
5z31
5z41
5z2
5z12
5z22
5z32
5z42
Health & Physical Education
5p1
5p11
5p21
5p31
5p2
5p12
5p22
5p32
5p3
5p13
5p23
5p33
5p4
5p14
5p24
5p34
5p5
5p15
5p25
5p35
5p6
5p16
5p26
5p36
5p7
5p17
5p27
5p37
5p8
5p18
5p28
5p38
5p9
5p19
5p29
5p39
5p10
5p20
5p30
5p40
5a2
5a12
5a22
5a32
5a42
5a52
5a62
5a3
5a13
5a23
5a33
5a43
5a53
5a63
5a4
5a14
5a24
5a34
5a44
5a54
5a64
5a5
5a15
5a25
5a35
5a45
5a55
5a65
5a6
5a16
5a26
5a36
5a46
5a56
5a66
5a7
5a17
5a27
5a37
5a47
5a57
5a67
5a8
5a18
5a28
5a38
5a48
5a58
5a68
5a9
5a19
5a29
5a39
5a49
5a59
5a69
5a10
5a20
5a30
5a40
5a50
5a60
The Arts
5a1
5a11
5a21
5a31
5a41
5a51
5a61
1
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
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1
4
1
3
Expectation Summary
Selected
Making a Game of It!
Assessed
Gr. 5 / 6 Data Management and Probability An Integrated Unit for Grade 5/6
English Language
6e1
6e11
6e21
6e31
6e41
6e51
6e61
1
1
6e2
6e12
6e22
6e32
6e42
6e52
6e62
1
6e3
6e13
6e23
6e33
6e43
6e53
6e63
6e4
6e14
6e24
6e34
6e44
6e54
6e64
6e5
6e15
6e25
6e35
6e45
6e55
6e65
6e6
6e16
6e26
6e36
6e46
6e56
6e66
6e7
6e17
6e27
6e37
6e47
6e57
6f3
6f13
6f4
6f14
6f5
6f15
6f6
6f16
6m3
6m13
6m23
6m33
6m43
6m53
6m63
6m73
6m83
6m93
6m103
6m113
6m123
6m4
6m14
6m24
6m34
6m44
6m54
6m64
6m74
6m84
6m94
6m104
6m114
6m124
6m5
6m15
6m25
6m35
6m45
6m55
6m65
6m75
6m85
6m95
6m105
6m115
6m125
6m6
6m16
6m26
6m36
6m46
6m56
6m66
6m76
6m86
6m96
6m106
6m116
1
6e8
6e18
6e28
6e38
6e48
6e58
6e9
6e19
6e29
6e39
6e49
6e59
6f7
6f17
6f8
6f18
6f9
6f10
6m7
6m17
6m27
6m37
6m47
6m57
6m67
6m77
6m87
6m97
6m107
6m117
6m8
6m18
6m28
6m38
6m48
6m58
6m68
6m78
6m88
6m98
6m108
6m118
6m9
6m19
6m29
6m39
6m49
6m59
6m69
6m79
6m89
6m99
6m109
6m119
6m10
6m20
6m30
6m40
6m50
6m60
6m70
6m80
6m90
6m100
6m110
6m120
1
6e10
6e20
6e30
6e40
6e50
6e60
1
French as a Second Language
6f1
6f11
6f2
6f12
Mathematics
6m1
6m11
6m21
6m31
6m41
6m51
6m61
6m71
6m81
6m91
6m101
6m111
6m121
1
1
1
6m2
6m12
6m22
6m32
6m42
6m52
6m62
6m72
6m82
6m92
6m102
6m112
6m122
1
1
3
2
2
1
1
2
2
2
1
1
1
1
4
1
1
1
1
1
1
2
1
Science and Technology
6s1
6s11
6s21
6s31
6s41
6s51
6s61
6s71
6s81
6s91
6s101
6s111
6s121
6s2
6s12
6s22
6s32
6s42
6s52
6s62
6s72
6s82
6s92
6s102
6s112
6s122
6s3
6s13
6s23
6s33
6s43
6s53
6s63
6s73
6s83
6s93
6s103
6s113
6s123
6s4
6s14
6s24
6s34
6s44
6s54
6s64
6s74
6s84
6s94
6s104
6s114
6s124
6s5
6s15
6s25
6s35
6s45
6s55
6s65
6s75
6s85
6s95
6s105
6s115
6s6
6s16
6s26
6s36
6s46
6s56
6s66
6s76
6s86
6s96
6s106
6s116
6s7
6s17
6s27
6s37
6s47
6s57
6s67
6s77
6s87
6s97
6s107
6s117
6s8
6s18
6s28
6s38
6s48
6s58
6s68
6s78
6s88
6s98
6s108
6s118
6s9
6s19
6s29
6s39
6s49
6s59
6s69
6s79
6s89
6s99
6s109
6s119
6s10
6s20
6s30
6s40
6s50
6s60
6s70
6s80
6s90
6s100
6s110
6s120
6z3
6z13
6z23
6z33
6z43
6z4
6z14
6z24
6z34
6z44
6z5
6z15
6z25
6z35
6z45
6z6
6z16
6z26
6z36
6z46
6z7
6z17
6z27
6z37
6z47
6z8
6z18
6z28
6z38
6z48
6z9
6z19
6z29
6z39
6z10
6z20
6z30
6z40
Social Studies
6z1
6z11
6z21
6z31
6z41
6z2
6z12
6z22
6z32
6z42
Health & Physical Education
6p1
6p11
6p21
6p31
6p2
6p12
6p22
6p32
6p3
6p13
6p23
6p33
6p4
6p14
6p24
6p34
6p5
6p15
6p25
6p6
6p16
6p26
6p7
6p17
6p27
6p8
6p18
6p28
6p9
6p19
6p29
6p10
6p20
6p30
6a2
6a12
6a22
6a32
6a42
6a52
6a62
6a3
6a13
6a23
6a33
6a43
6a53
6a63
6a4
6a14
6a24
6a34
6a44
6a54
6a64
6a5
6a15
6a25
6a35
6a45
6a55
6a65
6a6
6a16
6a26
6a36
6a46
6a56
6a66
6a7
6a17
6a27
6a37
6a47
6a57
6a67
6a8
6a18
6a28
6a38
6a48
6a58
6a68
6a9
6a19
6a29
6a39
6a49
6a59
6a69
6a10
6a20
6a30
6a40
6a50
6a60
6a70
The Arts
6a1
6a11
6a21
6a31
6a41
6a51
6a61
6a71
1
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
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Unit Analysis
Page 1
Making a Game of It!
Gr. 5 / 6 Data Management and Probability
Analysis Of Unit Components
11
102
48
112
Subtasks
Expectations
Resources
Strategies & Groupings
-- Unique Expectations -10 Language Expectations
36 Mathematics Expectations
2 Arts Expectations
An Integrated Unit for Grade 5/6
Resource Types
6
26
0
0
0
0
12
4
0
0
0
0
Rubrics
Blackline Masters
Licensed Software
Print Resources
Media Resources
Websites
Material Resources
Equipment / Manipulatives
Sample Graphics
Other Resources
Parent / Community
Companion Bookmarks
Groupings
Assessment Recording Devices
6
4
7
10
10
2
1
3
Students Working As A Whole Class
Students Working In Pairs
Students Working In Small Groups
Students Working Individually
Anecdotal Record
Checklist
Rating Scale
Rubric
Teaching / Learning Strategies
Assessment Strategies
2
8
7
3
5
1
3
1
8
1
1
2
10
6
4
5
2
Brainstorming
Collaborative/cooperative Learning
Demonstration
Direct Teaching
Discussion
Experimenting
Graphing
Inquiry
Learning Log/ Journal
Open-ended Questions
Classroom Presentation
Exhibition/demonstration
Learning Log
Observation
Performance Task
Questions And Answers (oral)
Self Assessment
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