Download Probability and Statistics Activity: Mystery Bags TEKS: (3.13

Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Probability and Statistics
Activity:
Mystery Bags
TEKS:
(3.13) Probability and statistics. The student solves problems by
collecting, organizing, displaying, and interpreting sets of data.
The student is expected to:
(C) use data to describe events as more likely than, less likely than,
or equally likely as.
(3.14) Underlying processes and mathematical tools. The student
applies Grade 3 mathematics to solve problems connected to everyday
experiences and activities in and outside of school.
The student is expected to:
(A) identify the mathematics in everyday situations; and
(C) select or develop an appropriate problem-solving plan or
strategy, including drawing a picture, looking for a pattern,
systematic guessing and checking, acting it out, making a table,
working a simpler problem, or working backwards to solve a
problem; and
(3.15) Underlying processes and mathematical tools. The student
communicates about Grade 3 mathematics using informal language.
The student is expected to:
(A)
explain and record observations using objects, words, pictures,
numbers, and technology; and
Note: Portions of this lesson address TEKS at other grade levels as well;
however, the intent of the lesson fits most appropriately at the grade level
indicated.
Overview:
Students will be given four Mystery Bags, each containing 10 tiles. Each
bag will have a certain number of blue tiles and a certain number of red
tiles. Students will draw twenty-five times (with replacement) from each
bag and record their data. Then, students will share their data with the
other students in their group. Next, each group will create a likelihood line
and write down where each bag belongs. They will also explain why they
placed the bags where they did. Groups will then discuss their results
with the class.
Materials:
Color tiles (red and blue)
Paper bags (4 per group – See Procedure 1 for details on preparing the
bags.)
Markers
Chart paper
What’s in the Bag? – Handout/Transparency 1a
Probability and Statistics
Mystery Bags
Grade 3
Page 1
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
What’s in the Bag? (Sample Data) – Handout/Transparency 1b
Mystery Bags Group Recording Sheet – Handout/Transparency 2
I’m Seeing Red! – Handout/Transparency 3
I’m So Blue! – Handout/Transparency 4
Our Predictions… ! – Handout/Transparency 5
Our Predictions, Revisited… ! – Handout/Transparency 6
It’s Your Turn to Spin – Handout/Transparency 7
Grouping:
4 students per group
Time:
1 to 2 hours
Lesson:
1.
Procedures
Prior to the lesson, create a set of mystery
bags for each group of students.
Notes
Each set should be prepared as follows:
Bag 1: Place 10 blue tiles
Bag 2: Place 8 blue tiles and 2 red tiles
Bag 3: Place 5 blue and 5 red tiles
Bag 4: Place 2 blue and 8 red tiles
2.
Tell the students: I have assembled a set of
Mystery Bags for each of the groups. The
four bags contain 10 tiles each, in
combinations of red and blue. The actual
distribution of red tiles and blue tiles in each
bag is a secret, though. Your job is to collect
some data to try to predict how many blue
tiles and how many red tiles are in each bag.
You are NOT allowed to look in the bags!
Ask for a volunteer to help you model the
activity (drawing with replacement) for the
class.
Give the volunteer one of the Mystery Bags
(1, 2, 3, or 4). The student should draw one
tile from the bag, and then record the
outcome in the appropriate Mystery Bag’s
column on Handout/Transparency 1a. Then,
the student should place the tile back into the
bag and shake the bag to randomly distribute
the tiles. Go through two or three draws to
make sure that each student in the class
Probability and Statistics
Mystery Bags
Grade 3
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Mathematics TEKS Refinement 2006 – K-5
Procedures
understands that the tiles are to be replaced
after each draw and that the outcome from
each draw should be recorded on the
recording sheet.
3.
Tarleton State University
Notes
Have students get into groups of 4.
Distribute a copy of What’s in the Bag? (see
Handout/Transparency 1a) to each student.
Distribute a set of four Mystery Bags to each
group.
See Procedure 1 for notes on
assembly of the bags.
Each student in the group should get a
Mystery Bag and draw (with replacement) 25
times from the bag, recording the outcome
each time on the recording sheet.
Then, each student in the group should get a
different bag and repeat until he or she has
completed 25 draws from each bag in the
set.
4.
A sample of student data is
provided on
Handout/Transparency 1b.
After each student has recorded the results
from all four bags, distribute one copy of
Mystery Bags Group Recording Sheet –
Handout/Transparency 2 to each group of
students.
Have all the students within each small
group record their data on this group
recording sheet.
5.
Discuss with students how to describe the
results of the experiment using the following
labels.
•
•
•
•
•
Impossible
Less likely than
Equally likely as
More likely than
Certain
Probability and Statistics
Mystery Bags
The probability of an event is a
number between 0 and 1. The
number represents the chance
that an event will happen. If an
event is certain to occur, its
probability is 1. If an event is
impossible, then the probability is
0.
Terms applied to the
comparison of the probabilities
of two events:
Grade 3
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Mathematics TEKS Refinement 2006 – K-5
Procedures
Tarleton State University
Notes
An event A is more likely to occur
than another event, B, if the
probability of the first event, P(A),
is greater than the probability of
the second, P(B).
An event A is less likely to occur
than another event, B, if the
probability of the first event, P(A),
is less than the probability of the
second, P(B).
An event A is equally likely to
occur as another event, B, if the
probability of the first event, P(A),
is equal to the probability of the
second, P(B).
Example:
A bag contains 12 balls (3 red, 1
blue, 2 green, 4 yellow, and 2
orange). If you reach into the bag
without looking:
(1) it is more likely that you will
pick a yellow ball than a blue
ball since P(yellow) > P(blue)
4
1
>
or
;
12 12
(2) it is less likely that you will
pick a green ball than a red
ball since P(green) < P(red) or
2
3
;
<
12 12
(3) it is equally likely that you will
pick a green or orange ball
since P(green) = P(orange) or
2
2
.
=
12 12
6.
Distribute Handouts/Transparencies 3 and 4
(I’m Seeing Red! and I’m So Blue!).
For each of the four Mystery Bags, have
each group write the number of the bag
Probability and Statistics
Mystery Bags
Grade 3
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Mathematics TEKS Refinement 2006 – K-5
Procedures
above each appropriate label on the
likelihood lines on Handouts/Transparencies
3 and 4. Then, have each group complete
the sentences to justify their classifications.
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Notes
Finally, have each group of students predict
how many tiles of each color are in the bags.
Groups should record their predictions on
Handout/Transparency 5. Remind groups
that they are NOT allowed to look into the
bags yet!
7.
Have each group present their likelihood
lines on Handouts/Transparencies 3 and 4 to
the class.
8.
After each group has presented, ask the
entire class the following questions:
1) How are the results for the two likelihood
lines the same? Different?
2) Were the individual results the same as
the group results? Why or why not?
3) Did all the groups place the bags under
the same labels? Why or why not?
4) What might cause the results to be
different? Same?
5) Can you predict exactly how many tiles of
each color are in the bags based on the
class data?
9.
Ask: Now that you have heard each group
present its results to the class, do you wish
to revise your predictions for the number of
red tiles and the number of blue tiles in each
bag? If so, record your new predictions on
Handout/Transparency 6.
10.
Finally, have the students look in the bags to
check their predictions. How close was the
entire class to the exact answer? Discuss
the results.
11.
As students reflect on the lesson, have them
write a sentence or two explaining each of
Probability and Statistics
Mystery Bags
Grade 3
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Mathematics TEKS Refinement 2006 – K-5
Procedures
the following descriptions:
•
•
•
•
•
Tarleton State University
Notes
impossible
less likely than
equally likely as
more likely than
certain
Homework:
Have students complete It’s Your Turn to Spin (Handout/Transparency
7). Students will color in each spinner on the homework sheet and
write a sentence explaining what description each spinner might
represent (impossible, less likely than, equally likely as, more likely
than, or certain) using the colors they have selected.
Assessment:
Have the students give real-life examples of events that might be
described in each of the following ways:
• impossible
• less likely than
• equally likely as
• more likely than
• certain
Extensions:
Have students get into groups and create activities to demonstrate
each of the following descriptions:
• impossible
• less likely than
• equally likely as
• more likely than
• certain
Resources:
North Carolina Department of Public Instruction, I. (2006, August1).
Mathematics: Instructional Resources. Retrieved September 21,
2006, from
http://community.learnnc.org/dpi/math/archives/instructional_resources
Probability and Statistics
Mystery Bags
Grade 3
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Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
What’s In the Bag?
Select a bag. Draw one tile from the bag, record its color on the chart below, and then
replace the tile. Repeat the process until you have drawn 25 times from that bag.
Then, select another bag and repeat the process. Continue until you have drawn 25
times from each of the mystery bags in your set.
Draw
#
BAG
1
BLUE
BAG
1
RED
BAG
2
BLUE
BAG
2
RED
BAG
3
BLUE
BAG
3
RED
BAG
4
BLUE
BAG
4
RED
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Totals
Handout/Transparency 1a
Probability and Statistics
Mystery Bags
Grade 3
Page 7
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
What’s In the Bag? (Sample Data)
Select a bag. Draw one tile from the bag, record its color on the chart below, and then
replace the tile. Repeat the process until you have drawn 25 times from that bag.
Then, select another bag and repeat the process. Continue until you have drawn 25
times from each of the mystery bags in your set.
Draw
#
BAG
1
BLUE
1
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
25
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Totals
BAG
1
RED
BAG
2
BLUE
BAG
2
RED
BAG
3
BLUE
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
5
11
BAG
4
RED
X
X
X
0
BAG
4
BLUE
X
X
X
X
X
X
X
X
X
X
X
X
20
BAG
3
RED
X
X
X
14
4
X
X
X
X
X
X
X
X
X
X
21
Handout/Transparency 1b
Probability and Statistics
Mystery Bags
Grade 3
Page 8
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Mystery Bags
Group Recording Sheet
Record the number of blue tiles and the number of red tiles
in each bag for each person in your group.
STUDENT
NAME
Bag 1
Bag 2
Bag 3
Bag 4
BLUE RED
BLUE RED
BLUE RED
BLUE RED
TOTAL
Handout/Transparency 2
Probability and Statistics
Mystery Bags
Grade 3
Page 9
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
I’m Seeing Red!
After recording your group’s data, identify which label on the likelihood line best describes the probably of drawing a red
tile compared to the probability of drawing a blue tile for each of the four Mystery Bags. You may have some labels that
are not used at all. In addition, any single label might describe more than one bag.
Bag #
Bag #
Bag #
Bag #
Bag #
________
________
________
________
________
Red is
Impossible
Red is Less
Likely than Blue
Red is
Equally Likely
as Blue
Red is More
Likely than Blue
Red is
Certain
Justifications for our Answers:
We placed Bag # 1 where we did because _____________________________________________________________.
We placed Bag # 2 where we did because _____________________________________________________________.
We placed Bag # 3 where we did because _____________________________________________________________.
We placed Bag # 4 where we did because _____________________________________________________________.
Handout/Transparency 3
Probability and Statistics
Mystery Bags
Grade 3
Page 10
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
I’m So Blue!
After recording your group’s data, identify which label on the likelihood line best describes the probably of drawing a blue
tile compared to the probability of drawing a red tile for each of the four Mystery Bags. You may have some labels that
are not used at all. In addition, any single label might describe more than one bag.
Bag #
Bag #
Bag #
Bag #
Bag #
________
________
________
________
________
Blue is
Impossible
Blue is Less
Likely than Red
Blue is
Equally Likely
as Red
Blue is More
Likely than Red
Blue is
Certain
Justifications for our Answers:
We placed Bag # 1 where we did because _____________________________________________________________.
We placed Bag # 2 where we did because _____________________________________________________________.
We placed Bag # 3 where we did because _____________________________________________________________.
We placed Bag # 4 where we did because _____________________________________________________________.
Handout/Transparency 4
Probability and Statistics
Mystery Bags
Grade 3
Page 11
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Our Predictions…
Based on your group’s data, predict how many blue tiles and red
tiles are contained in each of the four Mystery Bags.
Bag 1
Bag 2
Bag 3
Bag 4
10
10
10
10
Predicted
number of
blue tiles
Predicted
number of
red tiles
Total
number of
tiles
Handout/Transparency 5
Probability and Statistics
Mystery Bags
Grade 3
Page 12
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Our Predictions, Revisited…
After hearing each group in your class present its results, do you
wish to revise your group’s prediction about the number of blue
tiles and the number of red tiles in each bag? If so, record your
new predictions below.
Bag 1
Bag 2
Bag 3
Bag 4
10
10
10
10
Predicted
number of
blue tiles
Predicted
number of
red tiles
Total
number of
tiles
Handout/Transparency 6
Probability and Statistics
Mystery Bags
Grade 3
Page 13
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
NAME: ________________
It’s Your Turn to Spin
For each spinner, color it with your choice of colors and then write a sentence
explaining what description each spinner might represent (impossible, less likely than,
equally likely as, more likely than, or certain) using the colors you selected.
Handout/Transparency 7
Probability and Statistics
Mystery Bags
Grade 3
Page 14