Download Probability Activity

Grade 7 - Statistics and Probability (Data Analysis)
PRESCRIBED LEARNING OUTCOMES
It is expected that students will develop and implement a plan for the collection, display, and
analysis of data, using measures of variability and central tendency.
It is expected that students will:
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formulate questions that explore whether or not a relationship exists in a real-world
context
select and justify appropriate methods of collecting data (designing and using
questionnaires, interviews, experiments, research)
display data by hand or by computer in a variety of ways, including circle graphs
read and interpret graphs that are provided
determine measures of central tendency for a set of data:
o mode
o median
o mean
determine measures of the distribution of a set of data:
o range
o extremes, gaps, and clusters
o quartiles
interpolate from data to make predictions
SUGGESTED INSTRUCTIONAL STRATEGIES
Statistics allow us to make a summary of what we know of the world and to make inferences
about things we do not know. Young students pose questions based on their immediate
environment. Students' investigations expand to include community and global issues. Often the
questions they wish to investigate are raised in social studies and science contexts. Statistics are
also used frequently in the world of sports.
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Have students formulate and implement a plan to pursue a question of interest to them,
such as:
o How does height relate to jumping ability?
o Does your pet prefer dry or moist food?
Discuss appropriate ways to collect and display data for different kinds of questions.
Their plan must include a method for collecting data (e.g., experimental measurement,
library research, survey forms), for organizing and graphing the data, and for drawing
conclusions or raising further questions from the investigation.
Using students' graphs, discuss with the class what information can be derived from them
such as mean, median, mode, and range.
Grade 7 - Statistics and Probability (Data Analysis)
SUGGESTED ASSESSMENT STRATEGIES
When students gather their own data, they are familiar with and interested in the information.
They develop a greater understanding of what it means to organize and summarize data and are
then better able to draw conclusions and to make predictions for new contexts.
Collect
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After a whole-class discussion, ask students to write to reflect on their reasoning,
including information about revisions they may have made. Look for evidence of logical
reasoning. For example, how does the student explain why the average is between the
highest and lowest values?
After students have had opportunities to display information in a variety of ways, ask
them to make a list of the decisions that need to be made when summarizing and
displaying data.
Work with the class to develop task specifications and a checklist or rating scale that
specifies criteria for scoring their investigations.
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Box Cars & One-Eyed Jacks
Constructing Ideas About Fractions, Decimals & Percents
Electrical Connections
Interactions 7
Junior High Probability Jobcards
Machine Shop
Mathematics From Many Cultures
Mathpower Seven
Maths Workshop
Minds on Math 7
Nelson Canadian School Mathematics Dictionary
Out of this World
The Sky's The Limit
Video
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Mathematics: What Are You Teaching My Child?
Software
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The Cruncher
Statistics Workshop
Games/Manipulatives
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D.I.M.E. Probability Pack A
D.I.M.E. Probability Pack B
Heads or Tails
Designed by: Tammy Hester
School: Gibbes Middle
Grade Level: 7
Subject: Mathematics
Core Curriculum Objective: Find and compare experimental and theoretical probabilities.
(7SP2-1)
South Carolina Curriculum Standards: VI. Probability and Statistics C. 3.
Overview: Students will experience hands-on how the number of trials of an experiment affects
the relationship between theoretical and experimental probabilities. Students will understand the
difference between theoretical and experimental probabilities.
Focus Question: If you were calling a toss in a football game, would you call heads or tails?
Why?
Time Frame: Two 50 minute periods
Resources:
Enough pennies for each student to have one
Website: shazam.econ.ubc.ca/flip/
Assessment: Students will design their own problem and determine the theoretical probability
and perform an experiment to determine the experimental probability. Students will write a report
about their findings and share with the class.
Day One
Activity One
The teacher should as the following question: "Suppose I flip this coin. Will it turn up heads or
tails?" Then, the teacher should toss a coin to see the result. Repeat the scenario. Next ask the
students what is the probability the next coin will be heads? Have students give explanations for
their answers.
Then pose this question to the students. "Suppose I flip all 10 coins, how many will land on heads
and how many will land on tails?" Allow several students to give their answers and reasons for
their answers.
Explain that the situation they have described is an example of a theoretical probability. Have
students add this term to their notebooks. Guide the students to see that a theoretical probability
is found by applying a formula.
Example: P(H)=1/2 1 is the number of ways to toss heads 2 is the number of possible outcomes
*****note****** tables for the following activities are provided
Activity Two
Conduct a simulation to find the experimental probability of a similar problem.
1. Go to website http://shazam.econ.ubc.ca/flip/
2. Flip the coin 25 times and fill in the table with the results.
3. Combine the results from your simulation with those from the other members of your class and
fill in the class data table.
After the tables are completed, compare the results from individual internet simulation with the
results obtained by the entire class. Explain why they are different through class discussion.
Add the term experimental probability to the vocabulary section of your notebook. Guide student
to the understanding that experimental probability is given by collecting data.
Activity Three
Now conduct the experiment using a penny. Flip the penny 25 times. Record the results in the
table. Then collect the results of the class and fill in the class table. Again, discuss the results.
Activity Four
In the journal section of the student's notebook have them explain how the theoretical, Internet
simulation, and actual coin toss probabilities compare with each other. Allow time for some
students to read their explanations.
Assessment:
1. Students are to make up a problem similar to the one in done in class.
2. Determine the theoretical probability.
3. Perform an experiment and determine the experimental probability.
4. Write a report about the experiment and the results.
5. Give an oral report to the class.
Rubric for the assessment provided in the lesson plan.
Name_______________________________ Date___________ Period_________
Tables for Internet Simulation Coin Toss
Website: shazam.econ.ubc.ca/flip/
Individual Internet Coin Toss Simulation
Number of
Heads
Number of
Tails
Total Number
of Flips
Probability
Heads
Probability
Tails
Class Data Internet Coin Toss Simulation
Number of
Heads
Number of
Tails
Total Number
of Flips
Probability
Heads
Probability
Tails
Name_______________________________Date____________ Period________
Tables for Actual Coin Toss Experiments
Individual Coin Toss
Number of
Heads
Number of
Tails
Total Number
of Flips
Probability
Heads
Probability
Tails
Class Data From Coin Toss
Number of
Heads
Number of
Tails
Total Number
of Flips
Probability
Heads
Probability
Tails
Rubric for Assessment of Individual Probability Problem
Rubric for Probability Problem
Name_________________________ Date _____________ Period _____
Required Item
20 points
15 points
10 points
5 points
Problem
stated
Correctly written,
free of errors
Correctly written,
one error
Problem is not a
probability
problem
Problem is not
clear, but
attempted
Theoretical
probability
Correctly given
with explanation
and formula
Correctly given,
missing
explanation or
formula
Incorrect, but
explanation or
formula attempted
Incorrect, no
explanation or
formula given
Experimental
Probability
Correctly given
with evidence and
explanation of
experiment
Correctly given ,
missing evidence
or explanation
Incorrect, but
evidence or
explanation
attempted
Incorrect, no
evidence or
explanation or
experiment
Title, and all 3
parts included w/
through
explanation and
evidence
All 3 parts
included, but
support lacking in
one area
All 3 parts
included, but
evidence poor in
more than one
area
One or more parts
are left out of the
report.
Overview of report
clear and all parts
presented.
3 to 5 minutes.
Overview of report
clear and all parts
presented. Time
frame not met.
Report is not clear
and one
component is left
out.
Report is not clear,
components left
out, less than 3
minutes.
Written report
Oral report
Subtotal
Total points
Final Grade