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Mix It Up: Correlated Mathematics and Science
Texas State University – San Marcos
Correlated Lesson Plan
File Name: Probability_Physics_Rutherford’s Gold Foil-5-272011.docx
Lesson Title: Rutherford’s Gold Foil
Targeted Grade Band:
4
5
6
7 X 8
9
10
11
12
Targeted Mathematics Strand:
Targeted Science Strand:
Algebra
Earth Science
Agriculture
Geometry
Life Science
Technology
Space Science
X Measurement
X Probability
X Physics
Statistics
Chemistry
Quantitative Reasoning
Scientific Investigation and Reasoning
Total Estimated Time for This Lesson: 1 hour
Prerequisites: Students should be able to use experimental and theoretical probability to make
predictions and analyze and evaluate scientific explanations.
Attachments:
Title
File Name
Activity #1: Trials
Trials.docx
Activity #2: Using A Probability Model to
Determine the Diameter of a Marble Indirectly
Rutherford’s Gold Foil.docx
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Mix It Up: Correlated Mathematics and Science
Texas State University – San Marcos
Correlated Lesson Plan
I.
LearningObjectivesandStandardsAlignment
Mathematics Learning Objectives
National Mathematics
TEKS
Standards
At the end of
this lesson,
students will be
able to
D
Understand
the effect of
statistics on
empirical
determination
of probability
R
Determine
the diameter
of an object
Texas CCRS
7.10A
8.11AB
V. B. 1.
VI. A.
VI. C. 1.
8.8 C
IV. C. 2.
Science Learning Objectives
At the end of
this lesson,
students will
be able to
National Science
Standards
Describe the
atom as a
system in
terms of its
properties
and the
properties of
its parts.
A
B
At the end
of this
lesson,
students
will be
able to
N/A
National Education
Technology
Standards
At the end
of this
lesson,
students
will be
able to
N/A
National
Agriculture, Food
and Natural
Resources Career
Cluster Content
Standards
TEKS
8.3AB
Texas CCRS
VII. B.
Technology Standards
TEKS
Texas CCRS
Agriculture Standards
TEKS
Texas CCRS
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Mix It Up: Correlated Mathematics and Science
Texas State University – San Marcos
Correlated Lesson Plan
II.
Materials
Activity #1: Trials
Item
Quantity (per student or per group)
Student Materials
1 coin per group
1 per group
Instructor Materials
Coin
Worksheet: Trials
Activity #2: Using a Probability Model to Determine the Diameter of a Marble Indirectly
Item
Quantity (per student or per group)
Student Materials
Meter Stick
3 per group
Marbles of same size
10 marbles per group
Worksheet: Using a Probability Model to
1 per student
Determine the Diameter of a Marble Indirectly
Instructor Materials
Computer
1 per instructor
Projector
1 per instructor
III.
References
Merriam-Webster Online Dictionary
http://www.merriam-webster.com/
Molecular Expressions – The Rutherford Experiment (Java Applet)
http://micro.magnet.fsu.edu/electromag/java/rutherford/
Merriam-Webster Word Central
http://www.wordcentral.com/
Interactive Coin Toss
http://www.shodor.org/interactivate/activities/Coin/
TAKS Released Items
http://www.tea.state.tx.us/student.assessment/taks/items/
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Mix It Up: Correlated Mathematics and Science
Texas State University – San Marcos
Correlated Lesson Plan
IV.
TermsandDefinitions
Math Term
Radius
Diameter
Probability
Trials
Science Term
Atomic Radius
Electron Cloud
Nucleus
Definition
a line segment
extending from the
center of a circle or
sphere to the
circumference or
bounding surface
a chord passing through
the center of a figure or
body
the ratio of the number
of outcomes in an
exhaustive set of
equally likely outcomes
that produce a given
event to the total
number of possible
outcomes - the chance
that a given event will
occur
one of a number of
repetitions of an
experiment
Definition
a line segment
extending from the
center of the smallest
particle of an element
that can exist either
alone or in combination
to the circumference or
bounding surface
the system of electrons
surrounding the nucleus
of an atom
the positively charged
central portion of an
atom that comprises
nearly all of the atomic
mass and that consists
of protons and usually
neutrons
Source
Merriam-Webster Online Dictionary
Merriam-Webster Online Dictionary
Merriam-Webster Online Dictionary
Merriam-Webster Online Dictionary
Source
Merriam-Webster Online Dictionary
Merriam-Webster Online Dictionary
Merriam-Webster Online Dictionary
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Mix It Up: Correlated Mathematics and Science
Texas State University – San Marcos
Correlated Lesson Plan
Repel
Alpha particle
Gold Foil
Diffraction
V.
A.
B.
C.
D.
E.
VI.
to force away or apart
or tend to do so by
mutual action at a
distance
a positively charged
nuclear particle
identical with the
nucleus of a helium
atom that consists of
two protons and two
neutrons and is ejected
at high speed in certain
radioactive
transformations —
called also alpha, alpha
radiation, alpha ray
A thin foil made of gold
metal
Merriam-Webster Online Dictionary
the bending or
spreading of a beam of
light especially when
passing through a
narrow opening or by
the edge of an object;
also : similar changes
in other waves (as
sound waves)
Merriam-Webster Word Central
Merriam-Webster Online Dictionary
Molecular Expressions – The
Rutherford Experiment (Java Applet)
LanguageIssues
Same Word, Different Meanings
Different Word, Same Meanings
Supposedly interchangeable words
Homonyms
Words with variety of meanings in different contexts
ParallelConcepts
The terms radius and diameter are used to describe parts of 3-dimensional shapes and
to describe parts of an atom.
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Mix It Up: Correlated Mathematics and Science
Texas State University – San Marcos
Correlated Lesson Plan
VII.
Misconnections
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Mix It Up: Correlated Mathematics and Science
Texas State University – San Marcos
Correlated Lesson Plan
VIII. SequencingoftheLesson
Procedures
Introduction/Set:
Notes
Have students watch The Rutherford Experiment
simulation from the Molecular Expressions website
http://micro.magnet.fsu.edu/electromag/java/rutherford/
either in class or for pre-homework.
They should read and then discuss the experiment
before proceeding. The simulation should be projected
during this discussion.
Activity 1: Trials
What is happening to the particles when they scatter?
Diffraction
What is gold foil? A thin foil made of gold metal.
As the slit width is increased what happens to the alpha
particles? The particles collide with the gold nuclei and
scatter.
How did this experiment help scientist understand
atomic structure? The experiment found that the mass
of an atom is concentrated in the nucleus and an atom
is composed of largely empty space.
This activity demonstrates how the number of trials
affects the measured probability in an experiment.
What is the probability when flipping a coin that it will
land on heads? 50% (the probability for tails is the
same).
This is true because there are two possible outcomes,
each equally likely to happen.
Group students and give each group a coin and
worksheet.
Each group should flip its coin ten times, and record
the number of heads and number of tails on the
worksheet provided.
Ask each group to report their results, and on the board.
See the example below.
Group #
#of heads
#of tails
1
3
7
2
4
6
Total
35%
65%
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Mix It Up: Correlated Mathematics and Science
Texas State University – San Marcos
Correlated Lesson Plan
Most groups will not have seen five heads and five
tails.
Combine the results for all the groups. The result will
be much closer to 50% heads and 50% tails. Discuss
how as the number of trials increases, the experimental
results come closer to the theoretical probability.
After each group reported their results how many total
coin flips occurred? # of groups*# of flips = Total #
Let’s take a look at what happens when you flip a coin
1000 times.
Go to the coin tossing applet. Enter the number of
tosses and display the results in table form.
Activity 2: Using a Probability Model
to Determine the Diameter of Marble
Indirectly
Students will set up and conduct the experiment
according to the “Using a Probability Model to
Determine the Diameter of a Marble Indirectly”
worksheet.
By comparing the measured probability to the
predicted probability, the students can determine the
diameter of the marbles (all the same) without actually
measuring them.
The derivation proceeds as follows (Question #4 on
worksheet):
The experimentally determined probability of a
collision is given by
P = H/T
Where P is the probability of a collision occurring, H is
the number of hits, and T is the number of trials.
Remind students of the coin flipping activity when
addressing the probability of collision in this
experiment.
For Question #5
The theoretical probability requires a little thought.
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Mix It Up: Correlated Mathematics and Science
Texas State University – San Marcos
Correlated Lesson Plan
Referring to the picture given in the lesson, we note
that if the shooter marble is within a radius of center of
a target marble, there will be a collision. This makes
the effective target width twice the diameter of the
marble. The theoretical probability of a collision is
then the ratio of the net target width to the overall
width of the shooting apparatus. In other words,
P = 2ND/W
Where N is the number of target marbles, D is the
marble diameter, and W is the width of the shooting
area (1 meter in this case). Equating the two
expressions for probability gives:
H/T = 2ND/W
Solving for the diameter gives
D = HW/2NT
The same procedure was used to determine the
diameter of gold nuclei without actually seeing them.
Summary:
This lesson used an activity to demonstrate how
empirical measurements can be used to determine
probability, and also simulated the famous Rutherford
gold foil experiment. Instead of shooting alpha
particles at a thin piece of gold foil, we rolled a marble
at a row of target marbles. The shooter marble is
analogous to the alpha particle, and the row of marbles
is analogous to the nuclei of atoms in the gold foil.
Rutherford stated “It was as surprising as if I’d shot a
bullet at a bit of tissue paper and had it fly back to hit
me.” The idea that the atom is mostly empty space,
and there is apparently an extremely dense and small
mass at the center of it that is capable of deflecting and
even scattering a fast moving alpha particle back
toward the “gun” was the surprise. The likelihood of
this happening has to do with probability.
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Mix It Up: Correlated Mathematics and Science
Texas State University – San Marcos
Correlated Lesson Plan
4.
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Mix It Up: Correlated Mathematics and Science
Texas State University – San Marcos
Correlated Lesson Plan
Key:
1. C
2. B
3. B
4. C
5. B
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