Download Roselle School District Grade 7 Pre-Algebra Honors Curriculum Unit

Roselle School District
Grade 7 Pre-Algebra Honors Curriculum
Unit 10
Essential Question(s)
How can you use probabilities to make predictions?
How can probabilities be calculated?
How does understanding probability affect the choices you make?
Enduring Understanding(s)
Probabilistic thinking develops notions of chance.
Understanding and utilizing probability can be very helpful in
predicting future events.
Common Core Standards, 2010
S&P 5. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger
numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither
unlikely nor likely, and a probability near 1 indicates a likely event.
S&P 6. 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.
S&P 7. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the
agreement is not good, explain possible sources of the discrepancy.
S&P 7a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of
events.
S&P 7b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
S&P 8a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which
the compound event occurs.
S&P 8b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described
in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.
S&P 8c. Design and use a simulation to generate frequencies for compound events.
W.7.2. Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and
analysis of relevant content.
Learning
Expectations
Activities/Resources
Student Strategies
Formative
Assessments
Technology
Infusion/
Resources
Explain that the
probability of an
event is the measure
of how likely it is that
the vent will occur is
a number between 0
and 1
Explain that a
probability near 1
indicates an unlikely
event, a probability
around ½ indicates
an event is neither
likely nor unlikely,
and a probability
near 1 indicates that
an event is likely
Have students create a list of events that have a probability of zero
and a different list of events that have a probability of one.
Interpret probabilities
as ratios, percents,
and decimals.
___ Watch the Brainpop video and take the quiz receiving a score of at
least 9 out of 10
http://www.brainpop.com/math/probability/independentanddependent
events/preview.weml
http://www.brainpop.com/math/dataanalysis/statistics/preview.weml
Play and analyze
probability-based
games, and discuss
the concepts of
fairness and expected
value.
Have students turn to a partner and compare their lists. Have a few
student volunteers put an event from their list on the Smart Board
Students will watch the video “Probability with Ben and Jerry” on
Youtube: http://www.youtube.com/watch?v=hUIvyKqamjg
Probability Activity Menu
Directions: Choose a variety of activities from the menu below. The activities
must total at least 10 points. Place a checkmark next to each box to show
which activities you will complete.
2 Points
___ Complete the Worksheet ( No work = No credit)
Watch the Brainpop video and take the quiz receiving a score of at
least 9 out of 10
http://www.brainpop.com/math/probability/compoundevents/prev
iew.weml
http://www.brainpop.com/math/probability/gametheory/preview.
weml
5 Points
___ Create a cartoon explaining probability and how to find the probability
of independent and dependent events and compound events, using
paper and colored pencils or online at:
http://www.makebeliefscomix.com/Comix/ or
Small group
instruction
Individualized
instruction
Choice activities
Chunking
information
Rephrasing of
questions
Working with partner
Do now
Quiz
Test
Oral questioning
Homework
http://www.b
rainpop.com/
math/probabil
ity/compound
events/previe
w.weml
http://www.b
rainpop.com/
math/probabil
ity/gametheor
y/preview.we
ml
http://www.b
rainpop.com/
math/probabil
ity/independe
ntanddepende
ntevents/prev
iew.weml
http://www.b
rainpop.com/
math/dataanal
ysis/statistics
/preview.wem
l
http://www.y
outube.com/
watch?v=hUI
vyKqamjg
http://www.readwritethink.org/files/resources/interactives/comic/
index.html
___ Create a worksheet with a separate answer key, including definitions
and sample problems for simple probability, compound probability,
independent and dependent events using real-world scenarios in word
problem format
___ Create a poster explaining probability and how to find the probability
of independent and dependent events and compound events with sample
problems and solutions included on the poster
8 Points (Individual or Group)
___ Create video for other students explaining what probability is, how to
solve problems related to simple and compound probability,
probability of independent and dependent events with specific
examples for each of the topics mentioned above
___ Create a Google Site or Power Point that students could use to help
review for a test on probability showing how to solve problems
related to simple and compound probability, independent and
dependent events with an instructional video clip included, sample
problems with solutions and an original problem of each type with a
separate answer key
___ Create a Probability Brochure that students could use to help review
for a test on probability showing how to solve problems related to
simple and compound probability, independent and dependent
events with an instructional video clip included, sample problems
with solutions and an original problem of each type with a separate
answer key
The probability of a
compound event is
the fraction of
outcomes in the
sample space for
which the compound
event occurs, just like
with simple events
Design and use a
simulation to
generate frequencies
for compound events
Show visual
representations of
sample spaces for
compound events
(Use organized lists,
use tables, use tree
diagrams)
Show a mathematical
algorithm for
determining the
probability of
compound events
Conduct an actual
experiment and
record the results
From the results,
predict the
approximate relative
frequency given the
probability
Students will conduct a simulation to determine the number of times
Ashante will take out a ball and a truck that are the same color given
the following scenario:
Ashante’s toy chest contains a blue, a red, a yellow, a brown and an
orange ball. It also has a blue and a white truck. Ashante takes out a
ball and a truck without looking. If Ashante does this 35 times, about
how many times can she expect to take out a ball and a truck of the
same color? Use a number cube and a coin to do a simulation. Assign
a number to each ball and a heads or tails to each truck. Make a table
to display your results.
Experimental Scenario:
TaNaiyah takes a 3-item true or false test. She guesses each of the
answers. How many correct answers can she expect to get? Before
conducting the simulation, make predictions as to the probability of
the events. Now, toss a coin three times, once for each item on the
test. Do this simulation 25 times and display your results in a bar
graph.
Experimental Scenario:
Each Thursday, a radio station randomly plays new releases 50% of
the time. What is the probability that 6 of the next 10 songs will be
new releases on any given Thursday?
Use a coin to simulate playing a new release. Let heads represent a
new release and tails represent a song that is not a new release.
Create a table in which you record the data you collect over five trials.
For each trial, toss the coint 10 times to represent playing the song 10
times.
In how many trials did heads appear 6 or more times?
Find the experimental probability that 6 of the next 10 songs on any
given Thursday will be new releases based upon the data you
collected from your simulation.
Why is tossing a coin a good way to simulate the situation?
What other methods could you use to simulate this situation? Which
methods are best? Explain your reasoning.
Small group
instruction
Individualized
instruction
Peer tutoring
Chunking
information
Rephrasing of
questions
Exit ticket
Journal entry
Do now
Quiz
Test
Oral questioning
Homework
Conduct an
experiment that
shows probability
that is not uniform
Develop probabilities
from that experiment
Explain why the
actual results of an
experiment might not
match the probability
Determine the
probability of an
event by assigning
equal probability to
all outcomes
Use that probability
to determine an
estimate of an
extrapolated
situation
Probability & Wheel of Fortune:
Probing Question: Why are contestants on Wheel of Fortune always
given R, S, T, L, N, and E as their first letter guesses in the bonus
round?
Performance Task I:
Scenario:
Studies have been done on use of the English language that indicates
that the most commonly used consonants are R, S, T, N, and L and the
most commonly used vowel is E. Select an adequate number of
paragraphs from a variety of sources or use the paragraphs given to
you by your teacher and count the occurrences of these letters and
organize your data in a chart or table using Excel or Microsoft Word
and graph your data using the most appropriate display of data.
Compare and contrast the results of your data collection experiment
with the claims of the studies. Based on your conclusions, critique
whether the consonants R, S, T, N, and L and the vowel E is a
reasonable approach when appearing on Wheel of Fortune and
present your findings to the class.
Performance Task II: (Optional Lesson)
Probing Question: What other three consonants and what vowel
should you select if you were a contestant on Wheel of Fortune in the
bonus round?
In the bonus round you are allowed to pick three more consonants
and one vowel. Using the same paragraphs as before, analyze the
letter frequency of the paragraphs and decide what three consonants
you should pick and what vowel if you made it to the bonus round of
Wheel of Fortune from the data you’ve collected.
Compare your data with another group’s data and present your
findings to the class.
(Performance-Based Curriculum: From Knowing to Showing pg. 50)
Summative Assessment Task
Small group
instruction
Individualized
instruction
Peer tutoring
Chunking
information
Rephrasing of
questions
Working with partner
Exit ticket
Journal entry
Do now
Quiz
Test
Oral questioning
Homework