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MIFFLIN COUNTY SCHOOL DISTRICT
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MCSD Mathematics Curriculum
Probability and Statistics
Planned Instruction
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Title of Planned Instruction:
Probability and Statistics |
| Subject Area: Mathematics Grade Level:
Grades 11-12 |
| Prerequisites: Algebra II Course Description:
The focus of this course is to further develop topics in
probability and statistics. Probability and statistical concepts
previously learned will be enhanced and connected by daily
experiences with real life problems. All college bound students
are encouraged to take this course.
Required Time: 90 days
Major Text(s) and Resources: |
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Statistics and Probability in Modern Life,
Copyright 1997 by Harcourt Brace College Publishers |
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Names of District Subject Area Curriculum Writing Committee: |
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- R. Joseph Lauver - Lewistown High School
- Allen C. Muir - Lewistown High School
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Date of Board Approval: July 24, 2003 |
| Major Topics |
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- Collect data
- Represent data
- Analyze data
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- Make decisions about data
- Probability
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| Course Objectives and Performance Indicators |
Strand: 2.1
Standard: Numbers, Number Systems and Number Relationships
Course: Probability and Statistics |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.1.11A |
Use operations. |
Use properties of real
numbers to simplify expressions and solve equations. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.2
Standard: Computation and Estimation
Course: Probability and Statistics |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.2.11A |
Develop and use computation
concepts, operations, and procedures with real numbers in problem-solving
situations. |
Perform calculations that
require multiple procedures and operations involving real numbers. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.2.11B |
Use estimation to solve
problems for which an exact answer is not needed. |
Use estimation to solve
problems for which an exact answer is not needed. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.2.11C |
Construct and apply
mathematical models, including lines and curves of best fit, to estimate
values of related quantities. |
Construct and apply
mathematical models, including lines and curves of best fit, to estimate
values of related quantities |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.2.11D |
Describe and explain the
amount of error that may exist in a computation using estimates. |
Describe and explain the
amount of error that may exist in a computation using estimates. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.2.11E |
Recognize that the degree
of precision needed in calculating a number depends on how the results
will be used and the instruments used to generate the measure. |
Recognize that the degree
of precision needed in calculating a number depends on how the results
will be used and the instruments used to generate the measure. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.2.11F |
Demonstrate skills for
using scientific and graphing calculators. |
Demonstrate skills for
using scientific and graphing calculators. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.3
Standard: Measurement and Estimation
Course: Probability and Statistics |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.3.11A |
Select and use appropriate
units to the degree of accuracy required in particular measurement
situations. |
Select and use appropriate
units to the degree of accuracy required in particular measurement
situations. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.3.11C |
Demonstrate the ability to
produce measures with specified levels of precision. |
Demonstrate the ability to
produce measures of central tendency with specified levels of precision. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.4
Standard: Mathematical Reasoning and Connections
Course: Probability and Statistics |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.4.11A |
Use direct proofs, indirect
proofs or proof by contradiction to validate conjectures. |
Use postulates and theorems
to build proofs involving probability and statistics. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.4.11B |
Construct valid arguments
from stated facts. |
Explain the steps taken to
correctly solve a mathematical problem by listing properties and other
mathematical facts. Identify the steps needed to reach a conclusion when
given some facts. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.4.11C |
Determine the validity of
an argument. |
Determine if an answer is
reasonable by identifying reasons why (or why not) the answer makes sense.
Determine if the steps and supplied reasons for each step in an argument
are correct.
Reject or accept hypotheses |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.4.11E |
Demonstrate mathematical
solutions to problems. |
Demonstrate mathematical
solutions to problems. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.5
Standard: Mathematical Problem Solving and Communication
Course: Probability and Statistics |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.5.11A |
Select and use appropriate
mathematical concepts and techniques from different areas of mathematics
and apply them to solving non-routine and multi-step problems. |
Select, use, and display
all of the mathematical procedures that are necessary to the solution of a
problem situation and achieve the correct answer. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.5.11B |
Use symbols, mathematical
terminology, standard notation, mathematical rules, graphing and other
types of mathematical representations to communicate observations,
predictions, concepts, procedures, generalizations, ideas and results. |
Communicate all of the
mathematical procedures concepts, conclusions, etc. necessary to the
solution of a problem situation using correct and appropriate mathematical
representations. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.5.11C |
Present mathematical
procedures and results clearly, systematically, succinctly and correctly. |
Present all of the
procedures important to the solution of a problem in ways that are
understandable. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.5.11D |
Conclude a solution process
with a summary of results and evaluate the degree to which the results
obtained represent an acceptable response to the initial problem and why
the reasoning is valid. |
Explain how a problem was
solved and why the chosen procedures were used. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.6
Standard: Statistics and Data Analysis
Course: Probability and Statistics |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.6.11A |
Design and conduct an
experiment. Describe data as an example of a distribution using
statistical measures of center and spread. Organize and represent the
results with graphs. (Use standard deviation, variance and z-scores). |
Design and conduct an
experiment. Apply appropriate sampling techniques.
Construct a frequency distribution and its related graph.
Describe data by determining measures of central tendency and variance.
Determine standard deviations and z-scores. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.6.11B |
Use appropriate technology
to organize and analyze data taken from the local community. |
Organize data into a
frequency distribution and its related graph (scatter plot). Find lines
of best fit for the scatter plot.
Determine correlation coefficient for the line of best fit. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.6.11C |
Determine the regression
equation of best fit (e.g., linear, quadratic, exponential). |
Determine the regression
equation of best fit (e.g., linear, quadratic, and exponential). |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.6.11D |
Make predictions using
interpolation, extrapolation, regression and estimation using technology
to verify them. |
Make predictions using
interpolation, extrapolation, regression and estimation using technology
to verify them. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.6.11E |
Determine the validity of
the sampling method described in a given study. |
Determine validity and
reliability of sampling techniques. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.6.11F |
Determine the degree of
dependence of two quantities specified by a two-way table. |
Perform tests of
significance. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.6.11G |
Describe questions of
experimental design, control groups, treatment groups, cluster sampling
and reliability. |
Describe questions of
experimental design, control groups, treatment groups, cluster sampling
and reliability. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.6.11H |
Use sampling techniques to
draw inferences about large populations. |
Use sampling techniques to
draw inferences about large populations. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.6.11I |
Describe the normal curve
and use its properties to answer questions about sets of data that are
assumed to be normally distributed. |
Describe the normal curve
and use its properties to answer questions about sets of data that are
assumed to be normally distributed. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.7
Standard: Probability and Predictions
Course: Probability and Statistics |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.7.11A |
Compare odds and
probability. |
Use the counting principal.
Construct tree diagrams and sample spaces.
Find probability.
Find odds.
Compare probability and odds.
Solve problems involving odds. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.7.11B |
Apply probability and
statistics to perform an experiment involving a sample and generalize its
results to the entire population. |
Apply probability and
statistics to perform an experiment involving a sample and generalize its
results to the entire population. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.7.11C |
Draw and justify a
conclusion regarding the validity of a probability or statistical
argument. |
Draw and justify a
conclusion regarding the validity of a probability or statistical
argument. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.7.11D |
Use experimental and
theoretical probability distributions to make judgments about the
likelihood of various outcomes in uncertain situations. |
Use experimental and
theoretical probability distributions to make judgments about the
likelihood of various outcomes in uncertain situations. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.7.11E |
Solve problems involving
probability. |
Solve problems involving
permutations. Solve problems involving combinations.
Determine the probability in situations involving dependent and
independent events.
Determine the probability in situations involving mutually exclusive or
inclusive events.
Find conditional probabilities.
Use the binomial theorem to solve problems involving probabilities. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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District Recommended Instructional Approaches For
the Course
To Drive Teacher’s Instructional Activities |
- Whole group instruction
- Small group instruction
- Projects
- Class discussion
- Peer evaluation
- Teacher and peer conferencing
- Oral presentations
- Individual instruction
- Research
- Dramatization
- Role playing
- Independent reading
- Read aloud
- Directed reading-thinking activities
- Modeling process
- Games
- Self-reflection
- Self-evaluation
- Independent study
- Guest speaker
- Guest reading
- Writing activities
- Thematic units
- Notebooks
- Study guides
- Computer technology
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