Download Grade 9 Probability - Ms. Ashley Vautour

Grade: 6
Unit: Statistics and Probability
Curriculum Outcome: GCO: Statistics and Probability (SP): Use experimental or theoretical
probabilities to solve problems
Student Learning Outcomes:
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Identify all outcomes of an experiment using probability
Know the difference between theoretical and experimental probability
Identify the theoretical probability outcomes in a probability experiment
Compare experimental probability results with the theoretical results
Common challenges with the concept:
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Problems distinguishing between experimental and theoretical probability
Problems reducing fractions
Problems distinguishing outcomes of consecutive trials
Problems making predictions
Problems understanding why multiple trials is best when performing experimental
probability
Materials: Dice, coin, bag, chocolate
Procedure:
1) Introduce ourselves to the class and state that we are going to be introducing probability. At
this point state the grade level and curriculum outcome. Also bring the students attention to the
smart board and explain the schedule of events for the class.
2) Refresh on theoretical probability. Start by asking probability questions related to a two sided
coin: Ask for the probability of:
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Flipping a heads (1/2)
Flipping a tails (1/2)
Flipping neither a head nor tails (0/2).
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Proceed by asking students if they know what type of probability this is. They should
reply with theoretical probability.
Ask the class, if everyone remembers theoretical probability from grade 5.
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3) Move into an example with more possible outcomes, such as a die. Ask for the probability of:
 Rolling a 3 (1/6)
 Rolling a 2 (1/6)
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Rolling any number (6/6)
4) Ask the students to take a minute and think of the formula they are using to calculate their
answers. Ask for a volunteer to write their answer on the white board and explain.
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Theoretical Probability: # of favourable outcomes / total # of possible outcome
Ask the class if everyone got the same answer and if not get the other students to also
write their answer and explain.
5) Ask the students to write out all the possible outcomes of ten trials when pulling chocolates
out of bag. Have a student write answers on the board; explain you’ll revisit the results later.
 Probability of grabbing a red chocolate (5/10)
 Probability of grabbing a chocolate (10/10)
 Probability of grabbing a blue chocolate (3/10)
 Probability of grabbing a yellow chocolate (2/10)
 Ask the students if everyone understood how we got those outcomes
6) Ask the class what they think probability is and when probability is important. Also ask the
class to give examples when probability occurs in everyday life.
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Probability- The measure of how likely an event is to occur.
Everyday occurrence- Lotto (1/14 million), pro-line, poker, bingo, coin toss at sports,
Hunger Games.
7) Describe to the class that it is often hard to depend on theoretical probability in the real life
situations, like the ones they described in step 5. Ask the class their opinion on this question.
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Theoretical can be used to determine the outcome of real life events but this percent is not
always accurate because it is dependent on the best possible outcome; this does not
always occur.
Explain that we must perform several trials to show this.
8) Ask the class what is meant by the term trial and give an example.
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In simple context the word trial means how many times you performed the experiment.
8) Re-cap. Explain again, where theoretical probability only provides the best possible outcomes;
we must collect our data using trials. Then ask the class what this type of probability is:
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Experimental Probability: This is the frequency of an event happening.
9) Ask the students to discuss a possible formula to represent experimental probability with the
person beside them. Proceed by asking if anyone from the class would like to go up to the white
board and explain the formula they use to represent experimental probability.
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Experimental Probability = Number of observed successful occurrences/Total number of
trials in the experiment
10) Bring the students attention back to the data they collected on the chocolates using
theoretical probability. Ask the students to perform10 trials using experimental probability.
Simply, get students to grab a chocolate out of the bag and record the colour. Do this three times.
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Get one student from each table to record the experimental probability of each colour
chocolate on the white board.
Ask the students if everyone understood how we got those numbers.
Bring the students attention to the difference in the results of the experimental probability
and the theoretical probability results.
- Likely not going to be same outcome
11) Discuss with the students what would happen as we perform more trials.
 The greater the number of trials, the closer the experimental probability approaches the
theoretical probability. This is why people rely on theoretical probability for games of
chance, but they cannot always depend on it because it is only the best possible outcome.
Before conducting experiments, students should predict the probability whenever
possible.
12) Have students do worksheet provided on probability. Circulate and help students as needed.
13) Go over the work sheet and obtain answers from students. Ask if anyone had any questions
regarding the work sheet.
14) Conclusion: give a brief over view of the two types of probability and what happens to the
experimental probability if we perform more trials. “What did u learn today”?
15) Tell the students tomorrow we will be forming different types of graphs to represent our data
collected from our theoretical and experimental probability and comparing them that way. For
homework they should think if which type of graph would best represent the information.
18) End with video on probability.
Practice Problems
1) You flip a coin. What is the probability of flipping heads?
2) You roll a six sided die. What is the probability of rolling a 5?
3) You pick a card at random:
4) You pick a marble at random:
5) You spin the spinner once:
what is the probability of picking odd?
what is the probability of picking red?
what is the probability of picking red?
6) You pick one card at random from a stack of: 5 green, 1 red, 2 blue, 1 yellow, 1 brown, 1
purple. What is the probability of choosing green?
7) You select a marble without looking and then put it back. If you do this 7 times, what is the
best prediction possible for the number of times you will pick a marble that is not yellow?
8) You select a marble without looking and then put it back. If you do this 10 times, what is the
best prediction possible for the number of times you will pick red or a purple marble?
9) There are five slices of pizza in a box: 2 pepperoni, 1 mushroom, and 2 eggplant. If you reach
into the box without looking and take a slice, what is the probability you will get pepperoni?
10) You toss two dice. Each time the two dice add up to an even number player A gets one point.
Each time they add up to an odd number player B gets one point. Is this a fair game? Explain.
Bonus:
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You toss two coins in the air. What is the probability of both coins landing on heads?
Explain.
To Make This Lesson Most Effective:
To make this lesson most effective; teachers should check in regularly with students for
understanding. They should also keep in mind common challenges students have with this topic
and learn ways to rephrase statements or questions so students clearly understand.
What Happens Next:
Next students should learn how to put this information in a graph to visually represent data. This
way they can clearly see the difference in results obtained through theoretical and experimental
probability. They could also perform more trials with objects that have more outcomes to further
their understanding that theoretical probability gives the most probably outcome, and that
experimental probability approaches theoretical when more trials are performed, but it may never
reach it.