```Probability Unit Grade 5
Overall Expectations:
• represent as a fraction the probability that a specific outcome will occur in a simple probability
experiment, using systematic lists and area models.
Specific Expectations:
– determine and represent all the possible outcomes in a simple probability experiment (e.g., when
tossing a coin, the possible outcomes are heads and tails; when rolling a number cube, the possible
outcomes are 1, 2, 3, 4, 5, and 6), using systematic lists and area models (e.g., a rectangle is divided into
two equal areas to represent the outcomes of a coin toss experiment).
– represent, using a common fraction, the probability that an event will occur in simple games and
probability experiments (e.g., “My spinner has four equal sections and one of those sections is coloured
red. The probability that I will land on red is ¼.”)
– pose and solve simple probability problems, and solve them by conducting probability experiments
and selecting appropriate methods of recording the results (e.g., tally chart, line plot, bar graph…?)
Big Ideas:
 The likelihood an outcome will occur can be described as impossible, unlikely, likely, or certain.
 A fraction can describe the probability of an event occurring. The numerator is the number of
outcomes favourable to the event; the denominator is the total number of possible outcomes.
 A tree diagram is an efficient way to find all possible combinations of outcomes of an event that
consists of two or more simple events.
 The results of probability experiments often differ from the theoretical predictions. As we repeat an
experiment, actual results tend to come closer to predicted probabilities.
 In probability situations, one can never be sure what might happen next.
 Sometimes a probability can be estimated by using an appropriate model and conducting an
experiment.
 An experimental probability is based on past events, and a theoretical probability is based on
analyzing what could happen. An experimental probability approaches a theoretical one when
enough random samples are used.
In this unit:
Students use probability vocabulary (impossible, unlikely, likely, certain) to describe the likelihood of
different outcomes in a variety of situations.
Students find the number of possible outcomes of an event and describe the probability of a particular
outcome as a fraction of all possible outcomes. They use tree diagrams, tables, area models, systematic
lists and other graphic organizers to record and count all possible outcomes of an event. Students
predict the probability that an outcome will occur. They conduct probability experiments and compare
actual results to predicted results. (source: Math Makes Sense 5, Unit 11)
Why Are These Concepts Important?
Throughout their lives, students will make decisions in situations involving uncertainty. The abilities to
understand, calculate, and predict probabilities are valuable life skills that refine and extend basic
intuitions about chance events. The work students do in this unit will help prepare them for later studies
of probability theory, data analysis, and statistics. (source: Math Makes Sense 5, Unit 11)
Success Criteria and Misconceptions
Success Criteria:
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I can use vocabulary to clearly talk
(likelihood, outcome, possibility,
impossible, possible, unlikely, likely,
certain, probability, probable,
improbable, odds, chances,
outcomes, combinations,
permutations)
I can pose and solve simple
probability problems, and solve
them by conducting probability
experiments
I can figure out (determine) all of
the possible outcomes of a
probability experiment
I can show (represent) the results in
different ways (circle graph, table,
tree diagram?, )
I can use fractions to show the
probability that an event will occur
in simple games and probability
experiments
Success Criteria for Problem Solving:
 I will highlight the important
information in the word problem
 I can make a K/W/H chart to help
me find out what the question is
 I will choose a strategy to help me
solve the problem
 I will try my strategy (carry out the
plan)
 I will check to see if my answer is
reasonable
 I will use math language to justify my
ESL Strategies
Illustrate a poster. Next to each colour (or
possible outcome) print the appropriate
probability statement: This outcome is likely.
This outcome is unlikely, and so on.
Possible misconceptions:
Some students may feel they have a “lucky” number or
colour that is more likely to be chosen. How to Help:
Encourage students to discuss the concept of chance.
Remind them that events are not controlled by thoughts
or feelings. (from MMS)
Students may think outcomes are influenced by magic,
luck, outside forces such as wind, or preference.
Students may think: past events influence present
probabilities, for example, if they flip heads three times,
they may think they are due for tails. How to Help: Point
out that the probability never changes.
Some students may think middle values are more likely
than the extremes. Students may think it is more likely to
roll a 3 or 4 on a die than it is to roll a 1 or 6. In fact, when
rolling one die, all six numbers are equally likely.
(However, if you roll a pair of dice, middle values are
most likely—for example, with a pair of dice, rolling a 7 is
much more likely than rolling a 2 or 12.) How to Help: Use
a systematic list to show the difference.
Students may over-generalize from a small sample. For
example, a student may flip a coin 10 times and get 3
heads. The student may predict that if you flip the same
rather than 50. How to Help: It is important to
demonstrate that with larger sample sizes, experimental
results tend to approach theoretical probability. (source:
Explorelearning.com)
One of the most common is that past events influence
present probabilities. For example, if you are rolling a
normal six-sided die and it’s been a long time since
you’ve rolled a 1, you may think you are “due” for a 1.
But the probability of rolling a 1 never changes; it is
always 1 out of 6.
Students may over-generalize from a small sample. For
example, a student may flip a coin 10 times and get 3
heads. The student may predict that if you flip the same
rather than 50. It is important to demonstrate that with
larger sample sizes, experimental results tend to
approach theoretical probability.
Note: “Probability is associated with games and gambling, but it also underlies many of the major
decisions made by governments, companies and other decision-makers.” (Explorelearning.com) Be
sensitive to the fact that some Christians, such as Baptists, prohibit playing games of chance.
Lesson 1 – Diagnostic and Launch – Grade 5 Probability – Sandra Van Elslander
Curriculum Expectations:
Overall: represent as a fraction the probability that a specific outcome will occur in a simple probability
experiment, using systematic lists and area models.
Specific:
– pose and solve simple probability problems, and solve them by conducting probability experiments and
selecting appropriate methods of recording the results.
– represent, using a common fraction, the probability that an event will occur in simple games and
probability experiments.
To pre-teach vocabulary.
To solve a simple probability problem and express
the answer as fraction, and in other ways using
appropriate vocabulary.
To identify prior knowledge and areas of need
(diagnostic assessment).
Learning Goal:
Solve a simple probability problem. Use vocabulary
from the book (including possible, probably, and
impossible) to show the answer in different ways.
Part 1 Before, Minds On or
Student Success Criteria:
Brainstorm words about probability: Question: When
you think about probability, what words come to
mind? (Activate prior knowledge/ assess knowledge
I can use vocabulary to clearly talk about
probability experiments.
Happen by Bruce Goldstein.
I can use fractions to show the probability that an
event will occur.
I can pose and solve simple probability problems.
Highlight vocabulary and add words and definitions
to the chart as they occur in the text.
Questions:
From text: What’s a possibility? Could this ball knock
down 12 pins in one roll? Why?
If one of these fish swims under the bridge, what kind
of fish will it be? Will this bee land on a white flower?
Will this butterfly land on one of the purple flowers?
What colour gumball will you probably get? What
prize are you most likely to get? What other prizes
are probable? Which prize is improbable?
Part 2 – During, Work on It
questions using probability language. Students work
with a partner to record their answers in as many
ways possible on white paper.
“If the cat pounces on one ball of yarn, what color
will it probably be?” What other color is possible?
Can you think of a color that’s impossible for this cat
to get? (There’s 3 blue and one yellow). With your
Strategies:
 Make a picture
 Use the words from the chart
 Use a fraction
 Use a circle graph
 Use a table
 Use a pictograph
 Express the answer as a ratio
Tools:
 Paper, pencils, markers
 Pre-printed vocabulary words and
definitions, chart paper, tape
partner, show the answer in as many ways you can.
other ways can you also show the answer?

Clipboard with class list for anecdotal
comments and noting areas of need
Questions:
How many balls of yarn are there? How many of
them are blue? How many are yellow? What do
What probability words can you use to explain your
thinking?
Part 3 – After, Congress
Misconceptions:
Highlight 3 chosen pieces of work to show a variety
of vocabulary words and a variety of ways of
Fractions: Invert the numerator and denominator.
The denominator is not the whole (for example 1
yellow 3 blue expressed as 1/3).
Make a chart of the ways students come up with
(fraction, circle graph, table, tallies, etc.)
Expressions and idioms in language apply to math,
i.e. “nothing is impossible.”
Congress Questions:
How do you know what is probable, possible and
impossible?
Preference (i.e., the cat likes blue, red parrots talk
more), magic, luck, or other outside factors, such as
wind, influence outcomes.
Can you tell me what (vocabulary word) means?
What does the fraction tell us?
How are these two ways of showing the answer
alike?
What does not affect the outcome, mathematically
speaking? (address misconceptions – magic, luck,
wind, etc.)
Extension: There are three small balls of yarn and
one big one. What other questions could you ask?
Answer questions on page 15 (a dog and 9 various
biscuits).
Vocabulary: Spin the Big Wheel!
Vocabulary
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Certain – definite.
o
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If an outcome is certain, it will happen every time.
Impossible – unable to occur.
o
If an outcome is impossible, it can never happen.

Outcome – a possible result of a trial.

Probability – a number between zero and one that states how likely an outcome is.

o
A probability of 0 means that the event is impossible.
o
A probability of 1 means that the event is certain.
o
A probability of
Sample space – the set of all possible outcomes of a trial.
o

2
means that the event will occur about 2 out of every 3 trials.
3
For example, if you are flipping a coin, the sample space has two outcomes:
Trial – a test of something, an experiment.
o
For example, a trial could be flipping a coin once or spinning a wheel once.
o
In general, the more trials you do, the more reliable your results will be.
Lesson 2 – Spin the Big Wheel – Grade 5 Probability – Sandra Van Elslander
Curriculum Expectations:
Overall: represent as a fraction the probability that a specific outcome will occur in a simple probability
experiment, using systematic lists and area models.
Specific:
– determine and represent all the possible outcomes in a simple probability experiment
– pose and solve simple probability problems, and solve them by conducting probability experiments and
selecting appropriate methods of recording the results.
– represent, using a common fraction, the probability that an event will occur in simple games and
probability experiments.
Solve a probability problem: Students spin the wheel
to explore concepts o probability, certainty, and
impossibility and design their own wheels.
-Understand that experimental results will not exactly
match theoretical probability.
Learning Goal:
I can say if an event will be certain, likely/ probable,
unlikely/improbable or impossible.
I can do an experiment and record the results in a
table and circle graph and as a fraction.
Part 1 Before, Minds On or
Student Success Criteria:
Student Exploration page 1– as a whole class on
projector. Review vocabulary: certain, impossible,
outcome, probability, sample space (set of all
possible outcomes), trial
I can use vocabulary to clearly talk about
probability experiments.
Which wheel gives you the best chances of
winning? Why did you choose that wheel?
Warm-up:
How many sections in the wheel divided into?
How many sections result in a small prize?
How many sections result in a big prize?
What fraction of the wheel says “big prize?”
Spin the wheel. What did you win?
Click clear. 10 kids are going to spin the wheel.
How many do you think will win a big prize?
Click 10 and press go.
How many players won a small prize, a big prize, no
prize?
How do the results compare to what you thought
would happen?
I can pose and solve simple probability problems by
doing probability experiments.
I can use fractions to show the probability that an
event will occur.
-I can show the results in different ways (circle
graph, table)
Part 2 – During, Work on It
Strategies:
Page 2 – Activity A: Individually on computers in the
library.
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Tools:
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(See attached Student Exploration sheets)
Questions 4 and 5 are open – students design their
own wheels and test the results.
If time, students complete Activity B and on-line
Use a circle graph
Use a table
Express the answer as a fraction
Student exploration sheet, pencils
Chart paper and markers
Chart of learning goals
assessment.
Part 3 – After, Consolidation
Misconceptions:
In class – Whole group discussion, refer to learning
goals.
Fractions: Invert the numerator and denominator.
The denominator is not the whole (for example 1
yellow 3 blue expressed as 1/3).
-I can pose… by doing probability experiments
-I can show the results in different ways (circle
graph, table)
Questions:
How do you know if an event will be certain, likely/
probable, unlikely/improbable or impossible?
What did the wheel you designed look like in 4A – It
is certain you will win a big prize? 4B – It is impossible
you will win a big prize? (A few students can come
up and draw their wheels on the program using the
5. Describe the wheel you designed. Can you
describe it using fractions? How did your predictions
compare to your results? What do you think would
happen if you did 100 more trials? 1000 more trials?
Did you display the results in a table or circle graph?
Why?
Go over assessment questions as a whole class using
If a few results are the same in a row, I am due for a
different result.
Name: ______________________________________
Date: ________________________
Student Exploration: Spin the Big Wheel!
Vocabulary: certain, impossible, outcome, probability, sample space, trial
Prior Knowledge Questions (Do these BEFORE using the Gizmo.)
Walking through the fair, the carnies tempt you to try your luck at their booth. “Step right up, step
right up. Spin the wheel and win a prize, there’s nothing to it!”
1. Which wheel gives you the best chance of winning? _______________________________
2. Why did you choose that wheel? _______________________________________________
_________________________________________________________________________
Gizmo Warm-up
The Spin the Big Wheel! Gizmo™ allows you to test your luck
and try to win a prize. First, observe the wheel.
1. How many sections is the wheel divided into? _______
2. How many sections result in a small prize? _______
How many sections result in a big prize? _______
3. Spin the wheel by dragging it sideways. What did you win? __________________________
4. Click Clear. Then, in the top right corner, next to Players, click 10 and press Go.
How many players won a small prize? _______
Big prize? _______
No prize? _______
Activity A:
What is the most
likely outcome?
 Be sure that Run the game is selected at the top.
 Make sure you still have the original wheel (4
sections – 2 No prize, 1 Big prize, 1 Small prize). If
The carnies make it sound like everyone will win. But what is really the most likely outcome?
1. The sample space of an experiment is the set of all possible outcomes, or results.
A. What is the sample space of the given wheel? ______________________________
___________________________________________________________________
B. Which outcome do you think is most likely? ________________________________
2. What do you think will happen if you spin the wheel once? __________________________
Spin the wheel. What happened? __________________ Is that what you predicted? _____
3. Click Clear. Select 100 Players, and click Go. Each spin is called a trial.
A. How many players won a small prize? ______ Big prize? ______ No prize? ______
B. Based on this, what is the most likely outcome? _____________________________
4. Select Design the game. Here you can design your own wheel. First, set the number of
Spinner sections with the up and down arrows. Then click any section to change the prize.
A. An outcome is certain if it always
happens. Design a wheel on which it is
certain that you will win a big prize.
Sketch this to the right, on Wheel A:
B. An outcome is impossible if it cannot
happen. Design a wheel on which it is
impossible that you will win a big prize.
Sketch this to the right, on Wheel B:
5. Design and sketch two wheels. Predict the most
likely outcomes. Test each prediction with 100
spins, and record the most common outcomes.
Wheel 1 prediction: ________ Actual: ________
Wheel 2 prediction: ________ Actual: ________
Activity B:
Probability of
winning
 Click Clear.
 Select Design the game.
The dancing monkey is on strike, so the fair needs a new booth. You are
in charge of designing a new attraction called “Spin the Big Wheel!”
1. Design a wheel. It should have all 3 possible outcomes: No prize,
Big prize, and Small prize. Draw your wheel to the right. (Label your
sections B for Big prize, S for Small prize, or N for No prize.)
2. The probability of an outcome is a number between 0 and 1. If the
probability is 0, the outcome is impossible. If the probability is 1, the
outcome is certain. Look at your wheel.
A. Which outcome do you think is most probable? _____________________________
B. Which outcome do you think is least probable? _____________________________
3. Turn on Make your own sign. The first sign reads: “Probability of winning a prize: # / #.”
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Set the denominator of the fraction to the total number of sections.

Set the numerator to the number of sections that will win a prize.
Click Submit to show your sign to the inspector. What is the probability of winning? ______
4. Select Run the game, and choose Circle graph to view the results.
A. If 100 people spin your wheel, how many do you think will win something? ________
B. Select 100 players, and click Go. When they have finished spinning, add up the Small
prize and Big prize winners. How many total winners were there? _________
C. How close was your prediction? _________________________________________
D. Look at the circle graph. How does the circle graph compare to the wheel? ________
___________________________________________________________________
5. Click Go until the Total players reaches 1,000. How does the circle graph compare to the
wheel now? _______________________________________________________________
Activity C:
Making wheels
 Click Clear.
 Select Design the game.
 Check that Make your own sign is turned on.
Your spinning wheel was so successful that fairs from all over the country are ordering them! Your
job now is to design wheels to fulfill your orders and satisfy your customers.
1. The Main Street Fair wants all 3 outcomes – Big prize, Small prize, and No prize – to have the
same probability. Sketch 3 different possible wheels below. (Use the Gizmo to help.)
2. Design 3 different signs that describe these wheels and click Submit. List them below.
_________________________________________________________________________
_________________________________________________________________________
3. Select Run the game. Test each of your wheels with 100 players. What were the results?
Wheel A
Wheel B
Wheel C
No Prize
Small Prize
Big Prize
4. Main St. Fair thinks your wheel is broken – the 3 outcomes (Big, Small, and No prize) are not
coming out exactly equal. Your wheel maker says that’s normal – the numbers should be
close to each other but probably not exactly equal. Who do you think is right? Explain.
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
Arwyn Carpenter - Lesson #3 * Colleen please mark this one
Lost Socks Part 1 (from Guide to Effective Instruction- DM & P Grades 4-6)
Overall: Represent as a fraction the probability that a specific outcome will occur in a simple probability
experiment, using systematic lists and area models.
Specific: Represent, using a common fraction, the probability that an event will occur in simple games
and probability experiments.
Task: Consider the sock problem, estimate
probability of getting a matching pair, carry out an
experiment based on the problem, record results,
revisit initial question with new insight.
Learning Goal: understand how to use results of
an experiment where there are two possible
outcomes to determine if the probability of
obtaining a desirable outcome will be likely,
equally likely or unlikely.
Part 1 Activate Prior Knowledge
Show quote: "Chance has no memory", and have
them discuss meaning. Review probability
language.
Student Success Criteria:
- I can use probability words to make predictions
and discuss this problem
- I understand that recording results during this
experiment will help me determine the probability
- I chose a tool to help me record my results in an
organized way
- I communicated my thinking with my partner and
Answer questions below with one of these words:
certain, likely, equally likely, unlikely, impossible
1- When I flip a coin it will land heads up.
2- Our class will have Phys. Ed next week.
3- When I roll a die it will land on an even number.
4- When I roll a die it will land on a 3.
5- When I roll a die it will land on a 7.
Part 2- Work on It - Present the problem:
"Suppose you have two pairs of socks lying loose in
a drawer, one blue pair and one green pair. You
reach in without looking and pick two socks.
Which outcome is more likely: the two socks will
match or the two socks will not match?"
Give students a minute to consider and tally on the
board the students' predictions of whether they
think it will be likely, equally likely or unlikely that
they will pull out a matching pair.
Give pairs of students a paper bag with two sets of
coloured tiles, ask them to try the experiment 30
times and record their results on paper.
Questions:
"Do you think one of you will have a better
probability than the other at getting matching
pairs?"
"Does your recording show the total number of
matches, non-matches and total number of trials?"
Part 3 – Consolidation
Have Gallery Walk to compare methods of keeping
track of results. How did people record their data?
What categories did people choose? Were there
Strategies:
 Use prior probability knowledge to make
reasonable predictions
 Consider the best tool for recording
collected data
 Carry out probability experiment to test
prediction
 Use questioning strategy to consider
reason for finding more mismatched pairs
Tools:
 Paper/markers
 Paper bags
 Coloured tiles
Misconceptions:
- students will think that because there are equal
numbers of blue and green socks, that a matching
outcome will be equally likely.
some that confused you? Which method most
clearly showed the results?
Ask, "Based on what you found, would you like to
their thinking using probability language.
Congress Question:
Why are we seeing more mismatched pairs than
matched?
- students will view experiment as a competition
against each other, distracting them from the
concept of probability
- students will not understand that both two blues
and two greens constitute matching pairs, and so
do not need to be recorded in different categories
Arwyn Carpenter - Lesson #4
Lost Socks Part 2 (from Guide to Effective Instruction- DM & P Grades 4-6)
Overall: Represent as a fraction the probability that a specific outcome will occur in a simple probability
experiment, using systematic lists and area models.
Specific: Determine and represent all the possible outcomes in a simple probability experiment using
systematic lists
Task/Problem Now that students see that it is
more likely that the pair of socks will be
mismatched, their task is to figure out why.
Again considering the sock problem, students are
asked to list all the possible combinations when
two socks are picked without looking. Then they
are asked to find the fraction that expresses the
probability of finding a matching pair, given that
the numerator represents the number of times
they list a desirable outcome and the denominator
represents the total number of possible outcomes.
Learning Goal: Understand how to create a
systematic list of all possible outcomes in a given
problem and how to use this to determine
probability as a fraction.
Part 1 Activate Prior Knowledge
Look again at outcome results from previous
lessons sock experiment
Student Success Criteria:
- I used a think aloud strategy to share my ideas.
- I apply my previous knowledge about fractions to
help conceive my approach.
- I created a clear method of organizing my data.
- I made sense of my data and was able to explain
it using probability words
Questions:
Why do you think most students got a result of
more mismatched than matched pairs of socks?
Understand that the fraction representing
probability will be desirable outcomes over
possible outcomes.
Can you think of a way to record all the possible
outcomes?
Part 2- Work on It
Sketch four socks on the board, two in one colour
and two in another colour. Identify each sock by
writing the numbers 1, 2, 3 or 4 beneath them.
Say, "Can you think of a way to list all the possible
outcomes?" Listen to their ideas and suggest they
use pairs of numbers to list all the possible
combinations when two socks are picked without
looking. Model the process for two of the
combinations (1-2; 1-3) then ask students to find
all the other combinations.
Questions:
Strategies:
* determine probability based on the experiment
* use prior knowledge of fractions, remembering
that the numerator is the part and the
denominator is the whole.
* remember from previous learning that the
greater the denominator, the smaller the part.
Tools:
 Paper/markers
"What fraction represents the probability of
finding a matching pair?"
Part 3 – Consolidation
Think/Pair/Share to discuss how they listed their
possible outcomes. Ask them to share how they
determined the probability as a fraction
Misconceptions:
* When organizing results students make
categories for "likely", "unlikely" and "equally
likely", rather than "matching" and "unmatching"
Congress Questions:
"How did you ensure that you had counted all the
possible outcomes?"
"How would you explain to a friend that when
pulling out two socks without looking, it is likely
that socks will be mismatched?"
*When listing outcomes students don't realize that
the matching pair 1-2 is the same as 2-1.
* Students mistakenly see 1-1 or 2-2 for example
as possible outcomes.
* When it comes to making a fraction they confuse
single outcome with total number of instances of
desirable outcome.
Assessment FOR Learning Observation & Interview
Lost Socks
Learning Goal: Use of Fractions to Express Probability
•
•
You have two pairs of socks loose in a drawer, one blue pair and
one green pair. Without looking pick two socks. Which outcome is
more likely: the two socks will match or the two socks will not
match?
Can you express the probability of finding a matching pair as a
fraction?
Seating Plan
Mathematical Thinking
A. Discussing socks combinations
in terms of probability
B. Understand they are gathering
info to help determine
predictability of likelihood
C. Logical list of outcomes logical
D. Re-strategizing based on
results
Meesha/Sandy
Mohamed/ Mikhail
Maxwell/Anya
Michael/Keagan
Kaelan/Aayana
Joey/Kara
Jamoree/Cory
Max/Faisal
Nicole/Sripiraba
Byan/ Housam
E. Conceptualizing possible
outcomes with drawings or
numbers
F. Use previous understanding of
fractions to find fraction to show
probability
Misconceptions
Problem Solving Strategies
1.
2.
3.
4.
Used "matching" "unmatching" for tally (organized list)
Made systematic list for all possible outcomes
Counted desirable outcomes
Created fraction with desirable outcomes over possible outcomes
a. Students will presume the
two outcomes are equally
likely.
b. Students see problem as a
competition to achieve more
matches.
c. Students cheat to achieve
the results they want.
d. Students pair a #1 with a
#1, not realizing you don't put
the sock back in after you've
pulled it.
e. Students pair 1-2 and then
count 2-1 as a different
possibility.
Probability – Lesson 5
Name: John Hong
Lesson Title: Two Dice Roll
Date: April 23, 2014
Learning Goal (Curriculum Expectations)
1) Students will solve simple probability problems, and solve them by conducting probability
experiments and selecting appropriate methods of recording the results (e.g., talyl chart, line plot,
bar graph).
Student Success Criteria
1) I can predict a probability outcome.
2) I can solve simple probability problems.
3) I can use probability language when speaking or writing about probability outcomes.
4) I can record my results using a line plot.
Lesson Components
Before
1. Open up the conversation and ask the students to name some things or situations in life that are
probable (e.g., It’s going to get hot in the summer).
2. Discuss the meaning of probability terms such as certain, impossible, likely, unlikely, somewhat
likely, most likely, equally likely, etc.
3. Ask the students: “If you roll two dice and add the two numbers on each roll, what sum will
come up most often?”
4. Ask the students to make a prediction and write it down in their workbooks. Then start the
experiment.
5. Hand out 2 regular dice along with paper, and two different coloured pencils for recording.
Part 1: Instruct the students to record the sums of the rolls until one of the numbers is recorded 3
times (using one of the coloured pencils) in a line plot (Refer students to the line plot anchor chart).
Part 2: Tell the students to continue the experiment (recording the results with the other coloured
pencil) until one of the sums is rolled a total of 15 times.
6. Remind students to label their line plot where appropriate.
During
1. Observe how students organize and label their line plot. Look for omissions made or for students
who might be struggling with the activity.
2. Observe their addition skills (e.g., counting on, doubling, making ten facts).
3. Observe statements or realizations expressed by the students (e.g., “There are more ways to
make the sum of 7”).
4. Challenge and discuss any misconceptions (e.g., “It’s all luck” or “My favourite number is 3”).
After (Consolidation)
1. Have students compare the results of the experiment with their own prediction.
2. Have students compare the results of Part 1(first sum to be rolled 3 times) with Part 2 (first sum to
be rolled 15 times).
3. Have students compare their results with other students.
4. Add up everyone’s results on chart paper and have students compare it with their own results
(Part 1 and Part 2).
5. Have a class discussion about what they discovered.
6. Ask students “Did the results of Part 1 and Part 2 differ? Why or why not? Did the results of Part 1
and Part 2 differ from the total class result? Why or why not?” (Discuss the misconception: overgeneralization from a small sample).
7. Discuss any theories, strategies, surprises, misconceptions, or difficulties they might have had.
These discussions should lead to figuring out what all the possible sums are when rolling two dice.
8. Figure out all the possible sums or outcomes with the students.
9. Once all the outcomes are written on chart paper, show or project the picture of all the
possible outcomes.
After (Highlights and Summary)
1. Students will reflect and write in their journal about what they have learned using probability
language (e.g., likely, unlikely, highly likely, equally likely, etc.)
2. Ask them “Why do you think some of the sums rolled many more times than other sums?” or “Do
you think all numbers had the same chance of being rolled?” Have them explain using words,
images, or numbers.
Other Activities
1) Ask students to record the probability of each sum being rolled in fractions, decimals, or
percentages (Gr. 5/6).
2) Ask students to display their results using an appropriate graph.
3) Do the same experiment but with one 6-sided die and one octahedron die.
Resources used: The Ontario Curriculum (Mathematics 2005), A Guide to Effective Instruction,
Prabability Games (Creative Publishers)
Probability- Lesson 6
Name: John Hong
Lesson Title: One Die and Quarter Roll
Date: April 23, 2014
Learning Goal (Curriculum Expectations)
1) Students will solve simple probability problems, and solve them by conducting probability
experiments and selecting appropriate methods of recording the results (e.g., tall chart, line plot, bar
graph).
2) Students will determine and represent all the possible outcomes in a simple probability experiment
using systematic lists and area models (e.g., T-chart).
Student Success Criteria
1) I can predict a probability outcome.
2) I can use probability language when speaking or writing about probability outcomes.
3) I can solve simple probability problems.
4) I can tally and record my results using a T-chart.
5) I can represent all possible outcomes using a rectangle (divided into parts).
Lesson Components
Before
1. As in the Two Dice Roll lesson, ask the students to make probability statements about real situations
(e.g., It is certainly raining today, the Toronto Maple Leafs may win their game tonight).
2. Discuss probability terms such as certain, impossible, likely, unlikely, somewhat likely, most likely,
equally likely, etc.
3. Ask the students: “What are the possible outcomes when you flip a coin? ( Heads or tails) Then ask:
“What are the possible outcomes when you roll a die?” (1,2,3,4,5,6).
4. Ask: “If you roll a regular die and flip a quarter 48 times, what coin side and number will come up
most often?”
4. Ask the students to make a prediction and write it down.
5. Hand out a regular die, a quarter, a T-chart and pencil for recording.
6. Organize students into pairs or into small groups.
7. Instruct students to organize and label their T-chart where appropriate (Ask them: “How will you
record the results? What are the possible outcomes?”).
8. Start the experiment.
During
1. Observe how students organize and label their T-chart. Look for omissions made or for students
who might be struggling with the activity. Notice if students list all outcomes first in their T-chart or if
they record the outcomes as they come up.
2. Observe statements or realizations expressed by the students (e.g., ”They all have an equal
chance”).
3. Discuss misconceptions (e.g., “It’s all luck” or “Heads and 6 have the best chance”).
4. Check to see if students are flipping the coin and rolling the die properly and fairly.
After (Consolidation)
1. Have students compare the results of the experiment with their own prediction.
2. Have students compare their results with other students.
3. Add up everyone’s results on chart paper and have students compare it with their own results.
4. Have a class discussion about what they discovered.
5. Ask students: Did your results differ from the total class result? Why or why not?” (Discuss the
misconception: over-generalization from a small sample).
7. Discuss any theories, strategies, surprises, misconceptions, or difficulties they might have had.
8. Figure out all the possible outcomes with the students.
After (Highlights and Summary)
1. Hand out grid paper and ask the students to represent all the possible outcomes in a rectangle
and label each outcome.
2. Ask the students to reflect and write in their journal about what they have learned from the
experiment. Encourage the use of probability language (e.g., likely, unlikely, equally likely, etc.).
Other Activities
1) Roll two regular dice, record how often even numbers come up in a chart. First make a prediction,
roll the dice 36, then 72 times. Compare the results for 36 rolls with 72 rolls. Compare the results with
own prediction and whole class result.
2) Roll an octahedron die 40 times, predict most often outcome, record results in a chart, show results
using fractions.
Resources used: The Ontario Curriculum (Mathematics 2005), A Guide to Effective Instruction,
Prabability Games (Creative Publishers)
Probability – Lesson 7
Adapted from: Math Makes Sense Unit 11, Lesson 4
Lesson Title: Tree Diagrams
Name: Candace Minifie
Date: April 26, 2014
Big Ideas
1. A tree diagram can be used to display the possible outcomes in an event that consists of two or
more simple events.
2. A tree diagram can be used to count outcomes.
Learning Goal (Curriculum Expectations)
✔ Students understand that calculating the probability of an event requires counting the total
number of possible outcomes.
✔ Students use a tree diagram to count all possible outcomes in a situation with many different
outcomes.
Student Success Criteria
I can use a tree diagram to count the total number of possible outcomes.
I can calculate the probability of an event.
Lesson Components
Before
1. Show students a coin, a number cube, and a 2-colour counter.
• How many outcomes are possible when we toss this number cube? What are they?
(6; 1, 2, 3, 4, 5, and 6)
• How many outcomes are possible when we flip this coin? What are they? (2; heads and tails)
• How many outcomes are possible when we toss this counter? What are they? (2; red and white)
During
Materials: You will need a coin, a number cube labelled 1 to 6, and a 2-colour counter.
Guiding Question: What are all the possible outcomes of rolling the number cube, tossing the coin,
and tossing the counter?
2. Ask one student to roll the number cube, another to toss the coin, and a third to toss the counter.
3. Record the results.
4. Repeat the experiment 10 times.
Ask: How many different outcomes did we find?
Ask: How can we be sure that we have found all of the outcomes?
Ongoing Assessment: Observe and Listen
As students work, ask questions, such as:
• What combinations of outcomes have you found? (heads, 5, red; tails, 4, red; heads, 2, white)
• How are you keeping track of what you have found? (In a table. I list all the outcomes that have
heads in one column and all the outcomes with tails in another.)
• Have you found all the possible outcomes? (No, other combinations could happen.)
Watch to see students sort their results and look for ways to determine other possible outcomes.
Encourage any reasonably efficient way to organize the outcomes.
Misconceptions
Students launch into producing various possible outcomes without organizing their work.
How to Help: Help students begin a tree diagram by focusing on one of the variables in the
situation. Talk through the process of deciding what each branch should represent.
After (Consolidation)
Engage students in discussing the following questions:
1. Did everyone find the same outcomes? Explain.
2. Did everyone record their results in the same way? If not, what were the differences? Explain.
3. What patterns did you see in your results?
4. Select 2 or 3 students to present their work.
• How many different combinations are possible? (24)
• How do you know you have found them all? (I used a pattern: first I listed heads and red with
every number from 1 to 6, and then I listed heads and white, and so on.)
If no one used a tree diagram, explain that there is another efficient way to figure out possible
combinations. Model drawing a tree diagram on the board. Invite students to help you fill in the
diagram once they get the hang of it.
• How does a tree diagram help us list all possible outcomes? (It shows that we have included every
choice for the combined outcome.)
• How can you find the probability that the student has purple socks? (I can count all the
combinations that include purple socks (4), and the total number of possible outcomes (12) to
make a fraction that tells the probability:
4
12
.)
1) Have students make up a simple restaurant menu and create a story problem about the possible
combinations of meals, drinks, and desserts. They should pose their problem to other students who
are finished early.
2) Omar’s class is painting pottery. Students can choose to paint a bowl, a plate, or a mug.
They can use blue, green, yellow, or purple paint.
a)
b)
c)
Use a tree diagram to show all the different pieces of pottery Omar could make.
What fraction of the choices are mugs?
What is the probability that a student will paint a yellow mug?
Probability Unit: Culminating Activity / Lesson 8
Lesson Title: Paper Bag Probability STEM Design Challenge
Big Ideas
Name: Candace Minifie
Date: April 25, 2014
1) A fraction can describe the probability of an event occurring. The numerator is the number of
outcomes favourable to the event; the denominator is the total number of possible outcomes.
Learning Goal (Curriculum Expectations)
1) Students will collect and organize data and display the data using charts and graphs, including
broken-line graphs.
2) Students will demonstrate an understanding that a fair game offers both players equal chances
of winning.
3) Students will demonstrate the ability to use a list or table of outcomes to identify all possible
outcomes.
Student Success Criteria
1) I can collect data.
2) I can organize data into a chart or graph.
3) I understand the concept of a fair game.
4) I can identify all possible outcomes in an experiment.
Lesson Components
Before
1. Invite students to the carpet and ask them to bring their pencil with them. Ask them to turn to a
partner and talk about how they think their pencils were made. Ask them to try to identify the
step-by-step process that goes into making each of their pencils. Students will likely have a variety
of pencil types which will make for a rich conversation with opportunities to compare design
processes.
2. Write the title: Design Process on chart paper or on a white board.
3. Invite students to list all of the steps in the process of designing a pencil.
4. Introduce the book In The Bag! Margaret Knight Wraps it Up! by Monica Kulling
5. Let students know that In the Bag! is a book about an inventor. Ask them to listen carefully to the
steps that the inventor went through to bring their idea to light.
6. After reading, revisit the step-by-step design process co-created earlier. Compare it to the
process Margaret went through to design the machine that mass-produced paper bags. I hope
that students would add in the patenting process.
During
Introduce the Paper Bag Probability design challenge.
Design Challenge: Your class has been asked to host this year’s Probability Palooza.
__________(teacher’s name) needs your help to prepare the probability games for the event.
Criteria:
Each probability game must:
- be original
- ensure that players have an equal chance of winning
- identify all of the possible outcomes
Constraints:
You may only use the materials provided.
Materials:
brown paper bag
variety of small items in a variety of colours (i.e., marbles, candies, counters, bingo chips, buttons,
nuts and bolts – to go with the theme of the text)
pencil and eraser
markers and pencil crayons
ruler
Introduce the Steps for S.T.E.M. Success:
Steps for S.T.E.M. Success
What have others done?
What are the constraints?
For this culminating activity, students can think about the experiments that they have completed
within this unit. In this early stage we want to activate students’ prior knowledge and get them
2. Imagine:
What are some solutions?
Brainstorm ideas
Choose the best idea
In step 2, students begin to generate ideas and ultimately select their best idea. In young children,
I find this often translates as their “favourite” idea.
3. Plan:
Draw a picture
Make a list of materials
For this design challenge, the picture that they will be creating will take the form of a tree
diagram. They will use the tree diagram to determine all of the possible outcomes.
4. Create:
Next, they actually create their probability game and test it out. They will want to record results in
an organized manner.
5. Improve:
Reflect and share findings
Make changes to make it better
In step 5, students can share the results of their experiment in small groups or with a partner, or
have two or three students try out the game. Students can give feedback on the probability
game.
Retest!
If students make any changes to their games, they will want to retest their game and record the
results again. I suggest doing at least three trials so that they have data to compare.
After (Consolidation)
Probability Palooza! Divide the class into three groups. Have one group set up their games and the
students from the other two groups are the players. Cycle through the groups until everyone has
had a chance to play and have their games played.
After (Highlights and Summary)
Take Probability Palooza! on the road! Have your students take their games to another class or
invite another class in to play the games.
Performance Assessment Rubric:
Name:
Date:
Level 1
Level 2
Level 3
Level 4
• with assistance,
chooses and
carries out a
limited range of
appropriate
strategies, with
little success
• chooses and
carries out some
appropriate
strategies, with
partial success
• chooses and
successfully
carries out
appropriate
strategies
• chooses and
successfully
carries out
effective
strategies
• uses
• limited ability to
probabilities to
design a fair
design a fair
game
game
Understanding of concepts
• shows
• shows very
understanding
limited
by providing
understanding
reasonable
by giving
explanations of:
inappropriate
explanations of:
• some ability to
design a fair
game
• successfully
designs a fair
game
• effectively
designs a fair
game
• shows limited
understanding
giving
appropriate but
incomplete
explanations of:
• shows
understanding
by giving
appropriate
explanations of:
• shows thorough
understanding
by giving
appropriate and
complete
explanations of:
• differences
between
predicted
probabilities and
actual results
• differences
between
predicted
probabilities and
actual results
• differences
between
predicted
probabilities and
actual results
• differences
between
predicted
probabilities and
actual results
• how
• how
• how
probabilities and probabilities and probabilities and
number of
number of
number of
outcomes can
outcomes can
outcomes can
be determined
be determined
be determined
Application of mathematical procedures
• uses
• limited
• somewhat
appropriate
accuracy
accurate
procedures to
accurately
• major errors or
• several minor
calculate
omissions in
errors or
probabilities
calculating
omissions in
using fractions
probabilities
calculating
probabilities
Communication
• provides a
• presentation
• presentation
clear
and discussion
and discussion
presentation and are unclear and
are partially clear
explanation of
imprecise
and precise
results
• how
probabilities and
number of
outcomes can
be determined
• how
probabilities and
number of
outcomes can
be determined
• generally
accurate
• accurate
• few errors or
omissions in
calculating
probabilities
• very few or no
errors or
omissions in
calculating
probabilities
• presentation
and discussion
are generally
clear and
precise
• presentation
and discussion
are clear,
precise, and
confident
• uses language
of probability
(e.g., likely,
probable,
outcome)
• uses
appropriate
mathematical
terms
• uses the most
appropriate
mathematical
terminology
Problem Solving
• chooses and
carries out
appropriate
strategies,
including tables
and diagrams
• differences
between
predicted
probabilities and
actual results
• uses few
appropriate
mathematical
terms
• uses some
appropriate
mathematical
terms
Resource List
A Guide to Effective Instruction
Explorelearning.com
Good Questions: Great Ways to Differentiate Mathematics Instruction, Second Edition
Canadian Edition of Elementary and Middle School Mathematics, by John A. Van de Walle and Sandra Folk.
Big Ideas from Dr. Small - Grades K-3, 4-8, 9-12
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