Our team focused on the following standards for our learning cycle: Approximate the probability of a
chance event by collecting data on the chance process that produces it and observing its long-run
relative frequency, and predict the approximate relative frequency given the probability. Relate the
results of an experiment to the theoretical relative frequency of an event (7.SP.6).
The mathematics in our learning cycle is about: predicting, experimenting, recording results, multiple
representations, ratios and proportions.
Our goal statement is: Students will relate the results of an experiment to the theoretical relative
frequency of an event (7.SP.6)
Our develop understanding task is: Activity: Where will it land?
Instructions: Students will make a prediction before each activity. Students will roll a dice, spin a spinner
and flip a coin 10 times and record results. The students will then be instructed to get in a group of 3-4
and combine their data and compare the group results with their individual results. The class will then
come together to share and combine group results to get a final class result. Students will then be led in
a discussion (See questioning below).
In our develop-understanding task, we wish to surface ideas such as: experimental probability and
comparing small samples to larger samples within the experiment. Students will compare
predictions/expectations to actual events.
Anticipation:
Grouping: individual, small groups (3-4), whole group
Tools: spinner, dice, coin, poster/marker for each kid
Prior knowledge: ratios, percent, writing numbers and fractions, recording data
Vocabulary: theoretical probability, experimental probability
Errors: forget to record data, lose count, write the ratio incorrectly heads/tails instead
of heads/total, record blue and black as b, b or bl, bl, unorganized data
Anticipation Chart – Probability Task
Strategy
Who and
What
Order
Table/Chart
Tally Marks
Pictorial
Numerical
Other
Questions to ask during individual/group working:
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What are you recording?
What does this tally/number represent?
What are your labels?
Questions to ask during class discussion:
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Compare the individual data and the whole class data?
What do you think will happen if you roll/spin/toss 100, 200, 1000 times?
Why?
What affects the change in the probability?
Are results different than predicted?
Why?
Talk about theoretical and experimental vocabulary
Bring up the mathematical notation for writing probability and how to correctly say
it P(event)
The solidify task we chose is:
To experiment with larger numbers and further the students understanding of theoretical probability,
follow this link:
http://nlvm.usu.edu/en/nav/frames_asid_186_g_3_t_1.html?open=activities&from=grade_g_3.html
(national library of virtual manipulatives…….nlvm)
Students will experiment with large numbers of spins on a spinner, can experiment with more/different
colors as well as sample size. (Some worksheet and questioning should follow and occur after the
activity and relate back to the develop task and further understanding and lead into the solidify task).
Questioning:
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What did you notice when there were more/less colors?
If we spun a spinner more times, what would you expect to happen?
Is there a way to figure/estimate/solve for a larger number of outcomes?
How?
The solidify goal: Student will experiment with large number events to relate experimental and
theoretical probability.
The practice task we chose is: Practice Task 1
The practice goal is: Students will complete problems relating to theoretical probability and theoretically
probability.
Optional ideas: (Work in progress…..sorry for the poor copy, we didn’t have access to a scanner)
1. Probability lab (What’s the chance?)
2. Mathematics teaching in the Middle School March 2012, pg 426 (www.nctm.org)
Hunger Games: What’s the chance?
Where Will It Land?
Flipping a penny:
If you flip a coin 10 times, guess how many times it will land on heads? ____
Flip the coin 10 times then record your results and observations in any way you
would like.
How close to your guess were you? Explain why you think your guess was close or
not close.
If you spin a spinner 10 times, estimate how many times will it land on red? _____
Spin your spinner 10 times then record your results and observations in any way
you would like.
How close to your estimate were you? Explain why you think your guess was close
or not close.
If you roll a die 10 times, predict how many times will you roll a 3? _____
Roll your die 10 times then record your results and observations in any way you
would like.
How close to your prediction were you? Explain why you think your guess was close
or not close.
Practice Task 1
1. What is the probability of choosing a king from a standard deck of playing cards?
2. What is the probability of choosing a green marble from a jar containing 5 red, 6 green and 4 blue
marbles?
3. What is the probability of choosing a marble that is not blue in problem 2?
4. What is the probability of getting an odd number when rolling a single 6-sided die?
5. What is the probability of choosing a jack or a queen from a standard deck of 52 playing cards?
6. What is the probability of landing on an odd number after spinning a spinner with 7 equal sectors
numbered 1 through 7?
7. What is the probability of getting a 7 after rolling a single die numbered 1 to 6?
8. What is the probability of choosing a queen, a king or an ace from a standard deck of playing cards?
9. What is the probability of choosing the letter i from the word probability?
10. What is the sample space for choosing a letter from the word probability?
11. Explained what you learned about experimental and theoretical probability.
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What’s the Chance?
Hunger Games: What’s the Chance?