Download Probability and Statistics Activity: What`s the Difference? TEKS: (7.10

Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Probability and Statistics
Activity:
What’s the Difference?
TEKS:
(7.10) Probability and statistics. The student recognizes that a physical
or mathematical model can be used to describe the experimental and
theoretical probability of real-life events.
The student is expected to:
(B) find the probability of independent events.
(7.11) Probability and statistics. The student understands that the way a
set of data is displayed influences its interpretation.
The student is expected to:
(A) select and use an appropriate representation for presenting and
displaying relationships among collected data, including line
plot, line graph, bar graph, stem and leaf plot, circle graph, and
Venn diagrams, and justify the selection; and
(7.13) Underlying processes and mathematical tools. The student
applies Grade 7 mathematics to solve problems connected to everyday
experiences, investigations in other disciplines, and activities in and
outside of school.
The student is expected to:
(A) identify and apply mathematics to everyday experiences, to
activities in and outside of school, with other disciplines, and
with other mathematical topics;
Overview:
This lesson gives students the opportunity to work with familiar objects
(number cubes) to answer something other than the usual question about
possible sums of the numbers on top when the cubes are tossed. After
playing the game, Remove One, students compute the experimental
probability for each difference. Then students study a sample space and
compute the theoretical probabilities. The lesson ends with a discussion
about the differences between experimental and theoretical probability.
Remove One was adapted from a PBS Teacher Source Mathline lesson
of the same name.
Materials:
Transparencies 1-4
Transparencies of Handouts 1 & 2
1 pair of number cubes for each pair of students
15 chips per student
Handout 1 Remove One for each student
Handout 2 Sample Space for each student
Paper and pencil for each student
TI-73 calculator (Optional)
Probability and Statistics
What’s the Difference?
Grade 7
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Mathematics TEKS Refinement 2006 – 6-8
Grouping:
2 to 4 students per group
Time:
90 minutes
Tarleton State University
Lesson:
Procedures
(5 minutes) Use Transparency 1 to
introduce the lesson. Give students about
one minute to think about the possible
differences between the two numbers on top
of the number cubes. Then allow them time
to discuss their thoughts with their partner
before having a whole group discussion.
Notes
Use questions similar to the
following ones to help students
share their thinking about the
possible differences.
(15 minutes) Use Transparency 2 and a
transparency of Handout 1 to introduce the
game, Remove One. Give each student 15
chips and Handout 1 Remove One. Explain
that they may place their chips anywhere on
the number line. Once the students have
their chips in place, toss the number cubes,
call out the two numbers and ask students
for the difference. The first student to remove
all of his or her chips is the winner and the
game is over.
Briefly discuss with students how
the game will be played. Do one
or two tosses to model the
procedure before beginning the
game.
3.
(10-15 minutes) Call out the differences
which were tossed and have students place
an x on their number line to construct a line
plot to represent the frequency distribution of
the differences. Have students use the line
plot to compute the experimental probability
of each difference.
Possible questions:
Which differences occurred most
often? Why do you think this
happened?
What differences occurred least
often? Why do you think this
happened?
4.
(10-15 minutes) Distribute copies of
Handout 2 Sample Space or if you prefer,
allow students to create one. (If you choose
to have them create one, more time will be
needed for this section of the lesson.) Have
the students compute the theoretical
probability of each possible difference.
Possible questions:
How many different outcomes are
there?
Does every outcome produce a
different difference?
What patterns do you notice?
1.
2.
What would be the smallest
possible difference? How do you
know?
What would be the largest
possible difference? How do you
know?
Keep a record of the all
differences tossed to use to
analyze the game in the next step.
Be sure students understand that
Probability and Statistics
What’s the Difference?
Grade 7
Page 2
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Procedures
Notes
(1,2) and (2,1) are different
outcomes. Use different colored
number cubes to model that a 1
on the “red” cube and a 2 on a
“white” cube is different from a 2
on the “red” cube and a 1 on the
“white” cube.
5.
(10-15 minutes) Allow the students to place
their chips on the number line and play the
game again.
Possible questions:
Will you place your chips on
different numbers this time? Why
or why not?
6.
(10-15 minutes) Record the data from each
group on Transparency 3.
Possible questions:
How does the experimental
probability of your group data
compare to the theoretical
probability computed from the
sample?
How does the experimental
probability of the class data
compare to the theoretical
probability computed from the
sample?
What would happen if we played
Remove One fifty times and
recorded the differences? Would
the probabilities of each difference
come closer to the theoretical
probability? Why or why not?
Use questions like those on Transparency 4
to discuss the differences between the
experimental and theoretical probability in
this situation. Call attention to the difference
between the experimental probabilities of
each set of small group data compared to
the experimental probability using the whole
class data recorded on Transparency 3.
Suppose every 6th grade math
class in the school played
Remove One and we collected all
the differences. Would those
probabilities come closer to the
theoretical probability? Why or
why not?
7.
(5 minutes) Student Reflection:
Which do you think is more reliable –
experimental or theoretical probability? Why?
Homework:
Suppose we tossed two number cubes and multiplied the two numbers
Probability and Statistics
What’s the Difference?
Grade 7
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Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
on top. Would there be more possible products than there were
differences? What are the possible products? Which product would
occur most frequently and why? Use a sample space to confirm your
answers. Compute the probability of each product. Is the probability of
getting an even product greater or less than the probability of getting
an odd product? Explain your answer.
Assessment:
Suppose we played Remove One again, but this time we computed
the sum of the two numbers on top. How would you line up your chips
on your number line to be a winner? Explain your answer.
Extensions:
1. Have each pair of students use the Dice feature of the TI-73 to
generate 25 tosses and record the difference for each toss. Have
students compute the probability of each difference based on the
25 tosses. Discuss how these experimental probabilities compare
to the theoretical probability computed from their sample spaces.
Collect the outcomes for all groups and compute the probability of
each difference again based on this larger set of data. Discuss how
these probabilities compare to the probabilities generated from 25
tosses and to the theoretical probability from the sample spaces.
2. Create a circle graph to represent the theoretical probability of the
possible differences.
Resources:
What are the chances? (http://nces.ed.gov/nceskids/probability/)
This website allows students to choose the number of times the die
will roll and then shows the student a bar graph of the outcomes.
There is a link to an explanation of probability.
Probability and Statistics
What’s the Difference?
Grade 7
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Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
What’s the Difference?
Suppose you toss a pair of number
cubes and compute the difference
between the two numbers on top. What are the
possible answers?
Transparency 1
Probability and Statistics
What’s the Difference?
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Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
Remove One
Place your 15 chips anywhere on the number line. You
may remove a chip if it is located on the number that
represents the resulting difference when the number
cubes are tossed. The winner is the first person to
remove all the chips from their number line.
Transparency 2
Probability and Statistics
What’s the Difference?
Grade 7
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Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
What’s the Difference?
Group Data
0
1
2
3
4
5
Group 1
Group 2
Group 3
Group 4
Group 5
Group 6
Group 7
Group 8
Group 9
Group 10
TOTAL
Transparency 3
Probability and Statistics
What’s the Difference?
Grade 7
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Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
What’s the Difference?
1.
What patterns do you notice in the
sample space for this situation?
2.
What was the experimental probability of tossing
a difference of 1 when we played Remove One?
3.
According to your sample space, what is the
theoretical probability of tossing a difference of
1?
4.
Compare the experimental probability and
theoretical probability of getting each possible
difference.
Transparency 4
Probability and Statistics
What’s the Difference?
Grade 7
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Probability and Statistics
What’s the Difference?
Handout 1
0
1
Mathematics TEKS Refinement 2006 – 6-8
2
3
Remove One
4
5
Grade 7
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Tarleton State University
Mathematics TEKS Refinement 2006 – 6-8
Tarleton State University
What’s the Difference?
Sample Space
(1,1)
(1,2)
(1,3)
(1,4)
(1,5)
(1,6)
(2,1)
(2,2)
(2,3)
(2,4)
(2,5)
(2,6)
(3,1)
(3,2)
(3,3)
(3,4)
(3,5)
(3,6)
(4,1)
(4,2)
(4,3)
(4,4)
(4,5)
(4,6)
(5,1)
(5,2)
(5,3)
(5,4)
(5,5)
(5,6)
(6,1)
(6,2)
(6,3)
(6,4)
(6,5)
(6,6)
Handout 2
Probability and Statistics
What’s the Difference?
Grade 7
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