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Evaluating Student Learning: Preparing to Report:
Unit 11 Probability
This unit provides an opportunity to report on the Statistics and Probability strand.
Master 11.4: Unit Summary: Probability provides a comprehensive format for recording and summarizing
evidence collected.
Here is an example of a completed summary chart for this Unit:
Key:
1 = Not Yet Adequate
2 = Adequate
3 = Proficient
4 = Excellent
Strand:
Statistics and
Probability
Reasoning;
Applying
concepts
Accuracy of
procedures
Problem
solving
Communication
Overall
Ongoing Observations
3
2
2
3
2/3
3
Strategies Toolkit
(Lesson 5)
3
Work samples or
portfolios; conferences
3
3
2
3
3
Show What You Know
3
3
3
3
3
Unit Test
3
2
2
3
2/3
Unit Problem
At the Pet Store!
3
2
3
3
3
Achievement Level for reporting
3
Recording
How to Report
Ongoing Observations
Use Master 11.2 Ongoing Observations: Probability to determine the most consistent level
achieved in each category. Enter it in the chart. Choose to summarize by achievement
category, or simply to enter an overall level.
Observations from late in the unit should be most heavily weighted.
Strategies Toolkit
(problem solving)
Use PM 1: Inquiry Process Check List with the Strategies Toolkit (Lesson 5). Transfer
results to the summary form. Teachers may choose to enter a level in the Problem solving
column and/or Communication.
Portfolios or collections of
work samples; conferences,
or interviews
Use Master 11.1 Unit Rubric: Probability to guide evaluation of collections of work and
information gathered in conferences. Teachers may choose to focus particular attention on
the Assessment Focus questions.
Work from late in the unit should be most heavily weighted.
Show What You Know
Master 11.1 Unit Rubric: Probability may be helpful in determining levels of achievement.
#2 and 6 provide evidence of Reasoning; Applying concepts; #3 and 6 provide evidence of
Accuracy of procedures; #1, 3, 4, and 5 provide evidence of Problem solving; #4, 5, and 6
provide evidence of Communication.
Unit Test
Master 11.1 Unit Rubric: Probability may be helpful in determining levels of achievement.
Part A provides evidence of Reasoning; Applying concepts; Part B provides evidence of
Accuracy of procedures; Part C provides evidence of Problem solving; all parts provide
evidence of Communication.
Unit performance task
Use Master 11.3 Performance Assessment Rubric: At the Pet Store!. The Unit Problem
offers a snapshot of students’ achievement. In particular, it shows their ability to synthesize
and apply what they have learned.
Student Self-Assessment
Note students’ perceptions of their own progress. This may take the form of an oral or
written comment, or a self-rating.
Comments
Analyze the pattern of achievement to identify strengths and needs. In some cases,
specific actions may need to be planned to support the learner.
Learning Skills
Ongoing Records
PM 4: Learning Skills Check List
PM 10: Summary Class Records: Strands
PM 11: Summary Class Records: Achievement Categories
PM 12: Summary Record: Individual
Use to record and report throughout a reporting period, rather
than for each unit and/or strand.
Use to record and report evaluations of student achievement over
several clusters, a reporting period, or a school year.
These can also be used in place of the Unit Summary.
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Master 11.1
Date
Unit Rubric: Probability
Not Yet
Adequate
Adequate
Proficient
Excellent
limited understanding;
may be unable to:
– use concepts and
language of
probability to describe
events (e.g.,
best/worst;
more/equally/less
likely)
– explain and justify the
results of probability
experiments
– demonstrate that
results of an
experiment are not
affected by such
factors as age, skill,
experience
some understanding;
partially able to:
– use concepts and
language of
probability to describe
events (e.g.,
best/worst;
more/equally/less
likely)
– explain and justify the
results of probability
experiments
– demonstrate that
results of an
experiment are not
affected by such
factors as age, skill,
experience
shows understanding;
able to:
– use concepts and
language of probability
to describe events
(e.g., best/worst;
more/equally/less
likely)
– explain and justify the
results of probability
experiments
– demonstrate that
results of an
experiment are not
affected by such
factors as age, skill,
experience
thorough understanding;
in various contexts, able
to:
– use concepts and
language of probability
to describe events
(e.g., best/worst;
more/equally/less
likely)
– explain and justify the
results of probability
experiments
– demonstrate that
results of an
experiment are not
affected by such
factors as age, skill,
experience
limited accuracy; often
makes major
errors/omissions in:
– listing possible
outcomes
– predicting outcomes
– using fractions to
describe probability
partially accurate;
makes frequent minor
errors/ omissions in:
– listing possible
outcomes
– predicting outcomes
– using fractions to
describe probability
generally accurate;
makes few errors/
omissions in:
– listing possible
outcomes
– predicting outcomes
– using fractions to
describe probability
accurate; rarely makes
errors/omissions in:
– listing possible
outcomes
– predicting outcomes
– using fractions to
describe probability
may be unable to use
appropriate strategies
to conduct experiments
and solve problems
involving probability
with limited help, uses
some appropriate
strategies, with partial
success, to conduct
simple experiments and
solve problems
involving probability
successfully uses
appropriate strategies to
conduct experiments
and solve problems
involving probability
successfully uses
appropriate, often
innovative, strategies to
conduct experiments
and solve problems
involving probability;
may introduce some
complexity into the
experiment
• explains reasoning
and procedures clearly
using appropriate
vocabulary (e.g.,
certain, outcome,
probable, experiment)
unable to explain
reasoning and
procedures clearly
partially explains
reasoning and
procedures
explains reasoning and
procedures clearly
explains reasoning and
procedures clearly,
precisely, and
confidently
• presents work clearly
(including recording
experimental results)
work is often unclear
presents work with
some clarity
presents work clearly
presents work clearly
and precisely
Reasoning; Applying
concepts
• shows understanding
of probability by
appropriately:
– using concepts and
language of
probability to
describe events and
predictions (e.g.,
best/worst;
more/equally/less
likely)
– explaining the
results of probability
experiments
– demonstrating that
results of an
experiment are not
affected by such
factors as age, skill,
and experience
Accuracy of
procedures
• accurately:
– lists all possible
outcomes of an
experiment (single
event)
– makes reasonable
predictions about the
likelihood of events
– uses fractions to
describe probability
Problem-solving
strategies
• conducts experiments
to solve problems
involving the
probability of single
events and predicts
the results
Communication
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Master 11.2
Date
Ongoing Observations: Probability
The behaviours described under each heading are examples; they are not intended to be an exhaustive list of all
that might be observed. More detailed descriptions are provided in each lesson under Assessment for Learning.
STUDENT ACHIEVEMENT: Probability *
Student
Reasoning;
Applying concepts
 Uses concepts and
language of
probability to
describe events
 Explains results of
probability
experiments
 Demonstrates that
results of an
experiment are due
to chance
Accuracy of
procedures
 Lists all possible
outcomes of an
experiment
 Makes reasonable
predictions
 Uses fractions
correctly to describe
probability
Problem solving
 Successfully uses
appropriate
strategies to
conduct
experiments and
solve problems
involving probability
(single event)
Communication
 Explains procedures
and reasoning
clearly
 Records results
clearly
* Use locally or provincially approved levels, symbols, or numeric ratings.
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Master 11.3
Date
Unit Problem: At the Pet Store!
Not Yet
Adequate
Adequate
Proficient
Excellent
shows little
understanding; may be
unable to analyze or
explain:
– differences between
predicted probabilities
and actual events
– procedures used to
determine
probabilities and
calculate the number
of each kind of fish
shows partial
understanding; offers
some reasonable
analysis and
explanation of:
– differences between
predicted probabilities
and actual events
– procedures used to
determine
probabilities and
calculate the number
of each kind of fish
shows understanding by
offering reasonable
analyses and
explanation of:
– differences between
predicted probabilities
and actual events
– procedures used to
determine
probabilities and
calculate the number
of each kind of fish
shows thorough
understanding by giving
in-depth and insightful
analyses and
explanations of:
– differences between
predicted probabilities
and actual events
– procedures used to
determine
probabilities and
calculate the number
of each kind of fish
limited accuracy; major
errors or omissions in
determining:
– the number of fish of
each colour
– the number of
fish/cubes of each
colour that are
needed to match
given probabilities
– the number of fish of
each type needed to
match the
probabilities chosen
somewhat accurate;
frequent minor errors/
omissions in
determining:
– the number of fish of
each colour
– the number of
fish/cubes of each
colour that are
needed to match
given probabilities
– the number of fish of
each type needed to
match the
probabilities chosen
generally accurate; few
errors/ omissions in
determining:
– the number of fish of
each colour
– the number of
fish/cubes of each
colour that are
needed to match
given probabilities
– the number of fish of
each type needed to
match the
probabilities chosen
accurate; rarely makes
errors/omissions in
determining:
– the number of fish of
each colour
– the number of
fish/cubes of each
colour that are
needed to match
given probabilities
– the number of fish of
each type needed to
match the
probabilities chosen
may be unable to
choose and use
appropriate strategies
to:
– solve problems
involving probability
– use probabilities to
design the
composition of a fish
tank
with limited help, uses
some appropriate
strategies, with partial
success, to:
– solve problems
involving probability
– use probabilities to
design the
composition of a fish
tank
successfully uses
appropriate strategies
to:
– solve problems
involving probability
– use probabilities to
design the
composition of a fish
tank
successfully uses
appropriate, and often
innovative, strategies to:
– solve problems
involving probability
– use probabilities to
design the
composition of a fish
tank (may introduce
some complexity)
• explains reasoning and
procedures clearly,
including appropriate
terminology
(e.g., more/equally/less
likely; outcome)
unable to explain
reasoning and
procedures clearly
partially explains
reasoning and
procedures
explains reasoning and
procedures clearly
explains reasoning and
procedures clearly,
precisely, and
confidently
• records data and
presents work clearly
work is presented with
little clarity
work is presented with
some clarity
presents work clearly
presents work clearly
and precisely
Reasoning; Applying
concepts
• shows understanding
by analyzing and
explaining:
– differences between
predicted
probabilities and
actual events
– procedures used to
determine
probabilities and
calculate the number
of each kind of fish
Accuracy of
procedures
• accurately determines:
– the number of fish of
each colour, given
the probability
fractions and total
number (Part 1)
– the number of fish
(cubes) needed to
represent the listed
probabilities
(expressed in
fractions) (Part 2)
– the number of fish of
each type needed to
match the
probabilities chosen
(Part 3)
Problem-solving
strategies
• chooses and carries
out appropriate
strategies, including
using tables and
diagrams, to:
– solve problems
involving probability
– use probabilities to
design the
composition of a
fish tank
Communication
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Master 11.4
Date
Unit Summary: Probability
Review assessment records to determine the most consistent achievement levels for the assessments conducted.
Some cells may be blank. Overall achievement levels may be recorded in each row, rather than identifying
levels for each achievement category.
Most Consistent Level of Achievement*
Strand:
Statistics and Probability
Reasoning;
Applying
concepts
Accuracy of
procedures
Problem
solving
Communication
Overall
Ongoing Observations
Strategies Toolkit
(Lesson 5)
Work samples or
portfolios; conferences
Show What You Know
Unit Test
Unit Problem
At the Pet Store!
Achievement Level for reporting
*Use locally or provincially approved levels, symbols, or numeric ratings.
Self-Assessment:
Comments: (Strengths, Needs, Next Steps)
30
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Master 11.5
Date
To Parents and Adults at Home …
Your child’s class is starting a mathematics unit on probability. As adults, we use
ideas of probability in everyday life when we estimate the likelihood of risks and
predict future events. Many decisions, from carrying an umbrella to buying extra life
insurance, are based on our understanding of probability.
In this unit, your child will:
 Use the language of probability.
 Conduct experiments and predict results.
 Use fractions to describe probability.
 Use probability to pose and solve problems.
Probability concepts can be practised at home as well as at school. Here are some
suggestions for activities you can do at home:
 Listen to weather forecasts with your child. Use words such as likely, unlikely,
probable, and improbable to talk about the next day’s weather. Compare the
actual weather to the forecast weather. Help your child understand that
meteorologists use past weather patterns to tell us what is probable, rather
than certain, in the future.
 Play board and card games with your child. Compare games that depend on
chance (for example, snakes and ladders) with games that depend on skill (for
example, chess). Look for games that combine chance and skill.
 Talk with your child about superstitions. For instance, you might help your child
realize that wishing hard or having a “lucky number” does not influence the
cards you are dealt in a game.
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Master 11.6
32
Date
Blank Spinners
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Master 11.7
Date
Additional Activity 1:
Match My Meaning!
Work with a partner. Carefully cut apart these cards.





certain
will definitely
happen
impossible
cannot happen
possible
could happen
probable
is likely
to happen
improbable
is unlikely
to happen
Place all the cards face down.
Take turns flipping over 2 cards.
If the cards match (word and meaning), keep them and take another turn.
The winner is the player who collects the most cards.
Play 5 rounds. The grand winner is the player who wins the most rounds.
Take It Further:
Write about a situation that can be described using the words on the cards.
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Master 11.8
Date
Additional Activity 2:
Animal Draw
Work with a partner.
 Look at the animal names listed here. What fraction of the list are
cats? Insects? Birds? Fish?
Cougar
Lion
Tiger
Panther
Beetle
Fly
Mosquito
Ladybug
Crow
Eagle
Salmon
Tuna
 Cut apart the animal names and place them in a bag.
 You will pull out an animal name without looking, then replace it in the bag.
 Make a prediction. In 30 tries, about how many times do you expect to draw a
cat? An insect? A fish? A bird?
 Shake up the bag. Reach in and pull out a name without looking.
Record your result and replace the name. Make 30 draws in all.
 Did your actual draws match your prediction? Explain.
Take It Further:
Find as many different equivalent fractions as possible to express the probability of
drawing an insect.
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Master 11.9
Date
Additional Activity 3:
Fold Your Tents!
Work with a partner.
You will need 20 matching squares of paper about 2 cm by 2 cm and a tray.
 Fold each piece of paper in half to make a small “tent.”
 Stand all your tents on a tray. Each tent should have the fold facing up.
 Shake the tray so that all the tents fall off and land on the floor.
 What fraction of the tents have landed fold up?
What fraction landed lying on one side?
What fraction landed standing on one end?
 Repeat the experiment 4 more times.
 Record your results each time.
 Based on your results, predict what fraction of the tents will land fold up after
your next toss.
 Toss the tents once more. Count the tents that landed fold up.
Did your actual results match your prediction? Explain.
Take It Further:
Predict the fraction of the tents that will land fold up after the 10th and 20th tosses.
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Master 11.10
Date
Additional Activity 4:
Robot Roundup
Imagine you are in charge of a robot factory.
Each robot needs 2 arms, 2 wheels, and a box-shaped body.
Both arms must be the same colour. Both wheels must be the same colour.
For each component, you have the colour choices shown here:
Arms:
Wheels:
Body:
yellow or blue
green or purple
red or black or grey
 List the outcomes to find out how many different robots you can make.
 Draw and colour one of the robots.
 If you picked the components without looking, what are the chances you would
create a grey robot with blue arms and purple wheels?
Take It Further:
Add another component (for example, a control panel in gold or silver) and work out
how many different robots can now be produced.
36
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Master 11.11a
Date
Step-by-Step 1
Lesson 1, Question 6
Step 1
Yellow is more likely, so there are more __________ sectors than red.
Red is more likely, so there are more ___________ sectors than blue.
Look at the first spinner on Master 11b. It has 8 sectors.
How many sectors will you colour yellow? ____ red? ____ blue? ____
Colour the spinner.
Is there a different way to colour the spinner? Explain.
_______________________________________________________
Step 2
Blue and green are equally likely.
They cover _______ sectors.
Yellow is more likely. It covers _______ sectors.
Look at the second spinner on Master 11b. It has 5 sectors.
How many sectors will you colour blue? ___ green? ___ yellow? ___
Colour the spinner.
Is there a different way to colour the spinner? Explain.
_______________________________________________________
Step 3
Yellow is certain.
Are there any blue sectors? _____ Are there any red sectors? _____
Look at the third spinner on Master 11b. It has 10 sectors.
Yellow covers _____ of the sectors.
Colour the spinner.
Is there a different way to colour the spinner? Explain.
_______________________________________________________
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Master 11.11b
38
Date
Spinners for Lesson 1, Question 6
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Master 11.12
Date
Step-by-Step 2
Lesson 2, Question 4
Vicki scores a point if the pointers land on the same colour.
Alastair scores a point if the pointers land on different colours.
Make the spinners identical for each case.
Step 1
Vicki will win if the spinners are mostly one colour. Choose 2 colours.
Colour the spinners so that Vicki is more likely to win.
Step 2
Alastair will win if each spinner has 4 different colours. Choose 4 colours.
Colour the spinners so that Alastair is more likely to win.
Step 3
The game is fair if the pointers are equally likely to land on the same colour
or a different colour. Choose 2 colours. Colour the spinners so that Vicki
and Alastair have equal chances of winning.
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Master 11.13
Date
Step-by-Step 3
Lesson 3, Question 2
Step 1
What are the possible outcomes when Dave tosses a coin?
_________________ or _________________
Step 2
Dave tosses heads 12 times out of 20.
So, Dave got tails 20 – _______ = _______ times
Step 3
What fraction of the tosses were heads?
What fraction of the tosses were tails?
Step 4
20
20
How many times would you expect Dave to get heads
in 20 tosses? _____
What fraction of the tosses would be heads? _____
How do Dave’s results compare with what you expected?
_______________________________________________________
_______________________________________________________
40
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Master 11.14
Date
Step-by-Step 4
Lesson 4, Question 2
Step 1
What are the possible outcomes of tossing 3 coins?
Complete this table.
First Coin
Second Coin
Third Coin
Heads
Heads
Heads
Heads
Heads
Tails
Heads
Tails
Heads
Tails
Tails
Tails
Tails
Tails
Tails
Step 2
How many different outcomes are possible? ________
Step 3
If a game is fair, each player has an equal chance of winning.
How can we divide the number of possible outcomes into 2 equal parts?
_______________________________________________________
Step 4
Look at the table in Step 1.
How many outcomes include at least 2 heads? ________
How many outcomes include at least 2 tails?________
Make up a fair game with 3 coins.
Player A gets a point if ____________________________________.
Player B gets a point if ____________________________________.
How do you know this game is fair?
_______________________________________________________
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Master 11.15a
Date
Unit Test: Unit 11 Probability
Part A
1. Use the words likely, unlikely, probable, improbable, impossible, or certain to
describe each event.
a) The sun will rise tomorrow. ______________________
b) You will dig to the centre of the Earth. ______________________
c) You will win a gold medal at the Olympics. ______________________
d) You will sleep tonight. ______________________
2. Eric has red, green, yellow, and blue marbles.
He wants to give Andrea 2 marbles.
What possible colour combinations can he give her?
3. Colour this spinner so that green is more likely than blue and blue is
more likely than red.
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Master 11.15b
Date
Unit Test continued
Part B
4. Ruby will use this spinner to
choose a flavour of ice cream.
e) What is the probability that Ruby will choose strawberry ice cream?
__________________________________________________________
f) Which flavours have equal chances of being chosen?
__________________________________________________________
g) Just for fun, Ruby spun the spinner 40 times. Here are her results:
Chocolate 8, Vanilla 10, Strawberry 17, Butterscotch 5
Are these results what you would expect? Explain.
__________________________________________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
__________________________________________________________
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Master 11.15c
Date
Unit Test continued
Part C
5. Design a fair game of chance for 2 players. Use a 2-colour counter and a number
cube. Each player should have a different way of scoring a point. Explain how
you know your game is fair.
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
44
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Master 11.16
Date
Sample Answers
Unit Test – Master 11.15
Part A
1. a) Certain
b) Impossible
c) Improbable or unlikely
d) Likely or probable
2. Red/green, red/yellow, red/blue, green/yellow,
green/blue, yellow/blue
3. Students should colour the spinner so that green
covers the greatest area (for example, 4 ).
8
The blue area is smaller than green but larger
than red (for example, 3 ).
8
Red covers the smallest area (for example, 1 ).
8
Part B
4. a) 3
8
b) Chocolate and vanilla
c) These results are what I would expect. They
are close to the predicted probabilities, even
though they don’t match them exactly. My
predicted probabilities were: chocolate and
vanilla should each be about 2 of 40, or 10.
8
Strawberry should be about
3
8
of 40, or 15.
Butterscotch should be about 1 of 40, or 5.
8
Part C
5. Players take turns tossing the counter and
rolling the number cube. Player A scores a
point if the counter is red and the number cube
shows an even number. Player B scores a
point if the counter is white and the number
cube shows an odd number. I know this game
is fair because there is an equal number of
ways for each player to score.
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Extra Practice Masters 11.17–11.19
Go to the CD-ROM to access editable versions of these Extra Practice Masters.
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