MATHEMATICS
Grade 4/5 – Bothwell Elementary
Tanya Winship
University of British Columbia
STATISTICS AND
PROBABILITY
Tanya Winship |1
Table of Contents
Unit Rationale
Guiding Goals
Assessment
Curriculum Connections
Unit Timeline
Unit Overview
Extensions and Adaptations
2
2
3
4
7
8
14
Tanya Winship |2
Statistics and Probability
Grade Level: 4/5
Timeline: 3 weeks
Unit Rationale
This unit focuses on Prescribed Learning Outcomes in Mathematics for both grades 4 and 5. The unit itself may
vary slightly in order to meet these outcomes for each grade. This unit will largely be an introductory unit to
the topic and will allow students to begin to understand what probability is and how statistics are used. The
basic premise for the unit is to allow students to make connections to other areas of mathematics (rates,
percentages, fractions, and data). This unit will be based on a number of hands-on, interactive activities that
may be different than traditional math lessons; students will engage in experimentation and exploration and
will determine if reality matches up to mathematical assumptions.
Guiding Goals
The Prescribed Learning Outcomes for this unit vary between grades 4 and 5 (as described below).
The guiding goals for this unit have been taken from the BC Ministry of Education curriculum document.
Grade Four
D1 demonstrate an understanding of many-to-one correspondence
D2 construct and interpret pictographs and bar graphs involving many-to-one correspondence to draw
conclusions
Grade Five
D1 differentiate between first-hand and second-hand data
D2 construct and interpret double bar graphs to draw conclusions
D3 describe the likelihood of a single outcome occurring using words such as impossible, possible, certain
D4 compare the likelihood of two possible outcomes occurring using words such as less likely, equally likely, more likely
Tanya Winship |3
Assessment
Assessment for this unit will surround participation and understanding on in-class activities. There will also be
required completion and understanding through worksheets, textbook work, a group project, quizzes, and a
final test.
I will use the following questions to guide my assessment:
- Can the student distinguish between events that are likely or unlikely, possible or impossible, probable
or improbable, certain or uncertain?
- Can the student use the terminology of probability appropriately when describing his or her thinking
about activities in the unit?
- Can the student interpret measures if chance in real-world contexts, such as understanding the
implication of a weather report that indicates an 80 percent chance of rain or knowing that 50-50
means the chance of winning is the same for both teams?
- Can the student assign numerical probabilities to outcomes – for example, that the probability of
getting heads when a penny is tossed 1 out of 2 (1/2) or 50 percent, or that the chance of drawing a
yellow tile from a bag out of four tiles, one yellow, one blue, one green, and one red, is 1 out of 4 (1/4)
or 25 percent?
- Can the student interpret and use statistical data to make conjectures about probability activities?
- Can a child formulate theories about the probabilities of situations, such as “This is more likely
because…” or “They’re equally likely because…”?
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Curriculum Connections
Gr. 4 – Mathematics
Prescribed Learning Outcomes
It is expected students will be able to…
Suggested Achievement Indicators
D1 demonstrate an understanding of many‐to‐one correspondence
 compare graphs in which different intervals or
D2 construct and interpret pictographs and bar graphs involving many‐
to‐one correspondence to draw conclusions
correspondences are used and explain why the interval or
correspondence was used
 compare graphs in which the same data has been displayed
using one‐to‐one and many‐to‐one correspondences, and
explain how they are the same and different
 explain why many‐to‐one correspondence is sometimes
used rather than one‐to‐one correspondence
 find examples of graphs in which many‐to‐one
correspondence is used in print and electronic media, such
as newspapers, magazines and the Internet, and describe
the correspondence used
 identify an interval and correspondence for displaying a
given set of data in a graph and justify the choice
 create and label (with categories, title, and legend) a
pictograph to display a given set of data using many‐to‐one
correspondence, and justify the choice of correspondence
used
 create and label (with axes and title) a bar graph to display
a given set of data using many‐to‐one correspondence, and
justify the choice of interval used
 answer a given question using a given graph in which data
is displayed using many‐to‐one correspondence
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Gr. 5 – Mathematics
Prescribed Learning Outcomes
It is expected students will be able to…
Suggested Achievement Indicators
D1 differentiate between first-hand and second-hand data
 explain the difference between first-hand and second-hand data
 formulate a question that can best be answered using first-hand
data and explain why
 formulate a question that can best be answered using second-hand

D2 construct and interpret double bar graphs to draw conclusions





D3 describe the likelihood of a single outcome occurring using
words such as
 impossible
 possible
 certain




data and explain why
find examples of second-hand data in print and electronic media,
such as newspapers, magazines, and the internet
determine the attributes (title, axes, intervals, and legend) of
double bar graphs by comparing a given set of double bar graphs
represent a given set of data by creating a double bar graph, label
the title and axes, and create a legend without the use of
technology
draw conclusions from a given double bar graph to answer
questions
provide examples of double bar graphs used in a variety of print
and electronic media, such as newspapers, magazines, and the
internet
solve a given problem by constructing and interpreting a double
bar graph
provide examples of events that are impossible, possible, or
certain from personal contexts
classify the likelihood of a single outcome occurring in a
probability experiment as impossible, possible, or certain
design and conduct a probability experiment in which the
likelihood of a single outcome occurring is impossible, possible, or
certain
conduct a given probability experiment a number of times, record
the outcomes, and explain the results
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D4 compare the likelihood of two possible outcomes occurring using
words such as
 less likely
 equally likely
 more likely
 identify outcomes from a given probability experiment which are



less likely, equally likely, or more likely to occur than other
outcomes
design and conduct a probability experiment in which one
outcome is less likely to occur than the other outcome
design and conduct a probability experiment in which one
outcome is equally as likely to occur as the other outcome
design and conduct a probability experiment in which one
outcome is more likely to occur than the other outcome
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Unit Timeline
MONDAY
TUESDAY
WEDNESDAY
THURSDAY
FRIDAY
March 31st
April 1st
April 2nd
April 3rd
April 4th
Lesson 1:
Interpreting Graphs
Lesson 2: Statistics,
What are they and
how are they used?
Lesson 3: Statistics,
Connecting them to
the Real World
Lesson 4: Connecting
Statistics to Probability
Lesson 4 (cont’d)
April 7th
April 8th
April 9th
April 10th
April 11th
Lesson 5: Stations
Lesson 5 (cont’d)
Lesson 6: Language
of Probability, Single
Outcomes
Lesson 7: Comparing
Outcomes
Lesson 8: Review
April 14th
April 15th
April 16th
April 17th
April 18th
Lesson 8 (cont’d)
Lesson 9: Create a
Chance Game
Lesson 10: Wrap-Up
Unit Test
NO SCHOOL
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Unit Overview
Topic
1
Interpreting
Graphs: A
Review
Learning
Outcomes
(SWBAT)
Activities
- apply prior
knowledge of
bar/line graphs
Show students a number of graphs (line
graph, bar graph, pie chart). Ask
students what they can tell from each
graph.
SMARTBoard
Demonstrate different ways to collect
information.
Worksheet
- illustrate
different ways
to share
information
2
Statistics:
What are
they and
how are they
used?
- apply prior
knowledge of
bar/line graphs
- illustrate
different ways
to share
information
- explain how
and why they
collected their
data
Materials
Examples of
various graphs
Assessment
 observation of
participation
 worksheet
Writing tools
Worksheet on graphing (collecting and
analyzing data, completing graphs).
Explain what “statistics” are, connect to
prior knowledge of graphing.
Colouring tools
Writing tools
Graph paper
Each student should then come up with
a question and 3-4 possible responses to
ask their classmates (i.e. What is your
favourite colour?) Students will then go
around and survey their classmates.
After they have surveyed the entire
class, they must create a graph that
represents the data they have
collected.
Time permitting, students will share their
findings with the class.
Colouring tools
 participation
and
completion of
survey
 accurate
completion of
corresponding
graph
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Topic
3
Statistics:
Connecting
them to the
Real World
Learning
Outcomes
(SWBAT)
- understand
how and why
statistics are
used (census,
development)
- draw
connections to
the real world
4
Connecting
Statistics to
Probability
- access prior
knowledge re:
fractions
- understand
the difference
between
statistics and
probability
Activities
Materials
Use real-life examples to get students to
think about statistics, such as census,
weather information, development of
new buildings.
 contribution
of ideas to
class
discussion
 completed
worksheet
 journal entry
Worksheet on real-life examples/journal
entry.
Provide examples of questions (such as
those asked by the students when
collecting data). Without the data,
what were the chances that I would
pick “pink” (for example)? Explain that
chance connects to the number of
options available, like a fraction. The
“chance” of choosing something is
related to the number of each choice
compared to the total number of
options.
Assessment
Question
examples
(student work)
 accurate
completion of
work
SMARTBoard
Worksheet (or
textbook)
Writing tools
Do some examples as a class using the
SMARTBoard.
5
Connecting
Statistics to
Probability
(cont’d)
- understand
the difference
between
statistics and
probability
Worksheet or textbook work.
Review work from previous day. Address
any issues or questions. Collect work to
be checked.
Instruction sheets
for each station
5 decks of cards
 participation in
activities
 completion of
workbook
(must be
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Topic
Learning
Outcomes
(SWBAT)
- demonstrate
knowledge by
completing a
number of
activities
Activities
Explain today’s activity: we are going to
do some activities surrounding chance.
Will the results match the chance? (i.e.
If I roll a die 6 times, will I get each of the
possible results?) Have students write
down their predictions.
Explain that students will be divided into
5 groups and will move from station to
station. At each station, they will
complete a chance activity and record
their results. Divide students into 5
groups.
Each station will include a card
explaining the activity, explain the
“rules,” and provide the probability for
each outcome. Students must record
the outcome (as provided) and their
results. {For this activity, each probability
should be 1/total.}
Station 1: Draw a card from a deck.
What are the odds the card is red?
Black?
Station 2: Pull a ball out of a bag. What
are the odds the ball is a specific
colour?
Station 3: Spinners – What are the odds I
will land on a specific number/colour?
Materials
5 bags with 4
different
coloured balls
5 spinners with
pointers or paper
clips
5 dice
5 coins
Workbook
Writing tools
Assessment
handed in and
must be neatly
recorded)
 predictions
 exit slips
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Topic
Learning
Outcomes
(SWBAT)
Activities
Materials
Assessment
Station 4: Dice – What are the odds I will
roll each number?
Station 5: Heads or Tails – If I flip a coin,
what are the odds that I will get heads?
Tails?
After the students have spent 10
minutes at each station, bring the
students back to their seats. Ask the
students what surprised them the most?
The least? What were their results? Did
any of their results match the predicted
outcome?
6
Language of
Probability:
Single
Outcomes
- accurately
describe
outcomes as
possible,
impossible,
improbable, or
probable
Students should then complete an exit
slip, sharing one of their aha moments
from the day (answering one of the
above questions). Students should hand
in their workbook (including predictions
and exit slips).
Give each student a die. Ask the
students to roll a 7. What about a 0?
Students may need to try, but most will
inherently respond, “it’s impossible!”
Introduce the terms possible, impossible,
and probable, explaining what each
one means. Brainstorm with students
situations in which the outcome would
be impossible, probable, possible, or
improbable.
Dice, one for
each student
SMARTBoard
Worksheet (or
textbook)
Writing tools
 contribution to
brainstorm
activity
 accurate
completion of
work
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Topic
7
Language of
Probability:
Compared
to Other
Outcomes
Learning
Outcomes
(SWBAT)
- use equally
likely, less likely,
or more likely to
describe
possible
outcomes
- understand
when they
would use likely,
unlikely, or
equally likely
compared to
when to use
impossible,
possible,
probable
Activities
Worksheet or textbook work, labelling
outcomes as probable, improbable,
possible, or impossible.
Show students a number of spinners. Ask
students what the possible outcomes
are for each of them. See if students
can recognized that if the pieces are
not equal (the same size) or if there are
more of one number or colour, the
chances of landing on that piece are
higher.
Explain to students that in the last class’
activity, each of the possible outcomes
was “equally likely” to occur.
Give each group a spinner and see if
they can accurately label it as equally
likely or not. If it is not equally likely, what
is it?
Ask students to share their thoughts.
Explain that outcomes may be more
likely or less likely than others based on
circumstances. Brainstorm some things
that may be more likely or less likely to
occur.
Worksheet or textbook work, labelling
outcomes as unlikely, equally likely, or
more likely.
Materials
Assessment
5-8 spinners,
each with
different possible
outcomes
 contribution
to class
discussion
 participation
in spinner
activity
 accurate
completion of
work
SMARTBoard
(with spinners on
notebook)
Worksheet (or
textbook)
Writing tools
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Topic
8
9
10
Review of
Probability
Create a
Chance
Game
Wrap-Up
Learning
Outcomes
(SWBAT)
- use time wisely
to review
concepts and
material
- complete
review
package
- work with
others to create
a game that
demonstrates
understanding
of chance
- complete all
work for unit
Activities
Materials
Assessment
Students should use this time to ask
questions, confirm understanding, and
review information. Students will
complete a review package, to be
handed in in advance of the unit test.
Once students have completed their
review package, they may work in
groups (up to 3 people) to create a
game of chance.
Review package
 completion
of review
package (to
be graded)
The game must have a set of rules and
should include a section in the rules that
explains why or how it is a game of
chance.
Materials for
games
Students must complete their review
package. Students may continue to
work on their games of chance.
- engage in
further chance
Students who are finished will be free to
games/activities play each others’ games.
11
Unit Test
- demonstrate
knowledge of
all concepts
Students who have completed their
review package will also use this time to
work with the teacher to conference
about areas they may need more help
with.
Students will write the unit test, exploring
topics of both statistics (data) and
probability or chance.
Writing tools
Colouring tools
Review package
Outlines for
board games
 application
of knowledge
towards
creation of
game
Writing/Colouring
tools
Chance games
Review package
Writing tools
Unit Test
Writing tools
 graded unit
test
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Extensions and Adaptations
There is some time built into this unit should lessons be longer than anticipated.
Quizzes may also be used to assess students’ understanding as we go through the
unit. The completion of the group project (create a game of chance) is negotiable
and may not be used for assessment purposes.
In order to address students who may require adaptations or modifications, they will
be addressed on an individual basis. Students with IEPs will be considered in regards
to completion of the overall unit.
As the grade 4s are not required to learn probability, this will be taken into
consideration when assigning a final grade for the unit. It also may affect their unit
test, which will place a heavier emphasis on statistics and use of data.