Download Statistics Curriculum - Williamsport Area School District

Williamsport Area School District
Mathematics
Grade(s): 12
Course Title:
Statistics
Unit
Unit Title
1
Introduction to Statistics
Duration
(Days)
15
Descriptive Statistics
26
Probability
17
Discrete Probability Distributions
26
Normal Probability Distributions
23
6
Confidence Intervals
20
7
Hypothesis Testing with One Sample
22
CA
College Algebra Review
(Between Unit 3 and 4)
15
2
3
4
5
Statistics
Williamsport Area School District
Unit 1: Introduction to Statistics
Days: 15
Big Idea: Look at a sample and make inferences about a population.
Unit Essential Question:
What is the difference between a population and a sample?
How can we take a representative sample?
Concept
Concept Title
1.1
1.2
1.3
An Overview of Statistics
Data Classification
Data Collection and Experimental Design
Duration
(Days)
2
2
11
Statistics
Concept 1.1
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
An Overview of Statistics
What is the difference between a population and a sample?
data, statistics, population, sample, parameter, statistic, descriptive statistics,
inferential statistics
Descriptor
Days
1.1.A Distinguish between a population and a sample.
0.5
1.1.B
Distinguish between a parameter and a statistic.
1.1.C
Determine the difference between descriptive and
inferential statistics.
0.5
1
Resources:
Assessment Sources:
Whiteboard Practice
Color Cards
Exit Ticket
Homework
Quiz 1.1-1.2
Unit Assessment
Notes:
Page 3
Statistics
Concept 1.2
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
Data Classification
What is the difference between qualitative and quantitative data?
qualitative data, quantitative data
Descriptor
1.1.A Distinguish between qualitative and quantitative data.
Resources:
Fast Food Data Assignment
Assessment Sources:
Color Cards
Exit Ticket
Quiz 1.1-1.2
Unit Assessment
Fast Food Data Assignment connects lessons 1.2 and 1.3.
Additional day for review/quiz.
Notes:
Days
1
Page 4
Statistics
Concept 1.3
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Resources:
Assessment Sources:
Notes:
Williamsport Area School District
Data Collection and Experimental Design
How did the creators of Scrabble decide how many of each letter to include
in their game?
observational study, experiment, treatment, control group, experimental
units, placebo, simulation, survey, confounding variable, blinding, doubleblind experiment, randomization, completely randomized design, blocks,
randomized block design, matched-pairs design, sample size, replication,
census, sampling, sampling error, random sample, simple random sample,
stratified sample, cluster sample, systematic sample, convenience sample
Descriptor
Days
1.1.A Collect data through an observational study, and
1
experiment, a simulation, or a survey.
1.1.B
Generate Random Numbers
2
1.1.C
Create a sample using random sampling, cluster sampling,
systematic sampling, stratified sampling, and convenience
sampling.
4
1.1.D
Design a statistical study.
2
Countries in the UN Activity
Generating Random Numbers Activity
Redesigning Scrabble Activity
Coke vs. Pepsi or Regular vs. Diet Soda Activities
Milgram’s Obedience Experiment Activity
Whiteboard Practice
Exit Ticket
Homework
Unit Assessment
Two additional days for review and test.
Page 5
Statistics
Williamsport Area School District
Unit 2: Descriptive Statistics
Days: 26
Big Idea: Display data using frequency tables, pie charts, bar graphs, dot plots, stem-and-leaf plots,
and
box and whisker plots. Describe the data sets using measures of center and spread.
Unit Essential Question:
How can we represent and describe a data set?
Concept
Concept Title
2.1
2.2
2.3
2.4
2.5
Frequency Distributions and Their Graphs
More Graphs and Displays
Measures of Central Tendency
Measures of Variation
Measures of Position
Duration
(Days)
4
7
4
5
6
Statistics
Concept 2.1
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Resources:
Assessment Sources:
Williamsport Area School District
Frequency Distributions and Their Graphs
How can I create a graph of a frequency distribution?
center, variability, shape, frequency distribution, classes, intervals,
frequency, midpoint, relative frequency, cumulative frequency, frequency
histogram, class boundaries. Relative frequency histogram, cumulative
frequency histogram, ogive
Descriptor
Days
2.1.A Construct a frequency table, frequency histogram,
4
polygon, relative frequency histogram, and a
cumulative frequency histogram.
Book Notes 2.1
Olympic Medal Count Frequency Table
Frequency Histograms (N-gram) Activity
Frequency Graphs P-M-I
Quiz 2.1-2.2
Homework
Unit Assessment
Notes:
Page 7
Statistics
Concept 2.2
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
More Graphs and Displays
How can I display data?
Stem-and-leaf plot, stem, leaf, dot plot, pie chart, Pareto chart, paired data
sets, scatter plot, time series, time series chart
Descriptor
Days
2.2.A Graph and interpret stem-and-leaf plots, dot plots, pie
5
charts, Pareto charts, and scatter plots.
2.2.B
Use a graphing calculator to create a histogram.
Resources:
Graphs and Displays Jigsaw Activity
Assessment Sources:
Presentations
Quiz 2.1-2.2
Homework
Unit Assessment
One Extra day for quiz.
Notes:
1
Page 8
Statistics
Concept 2.3
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
Measures of Central Tendency
How can we describe the center of a data set?
measure of central tendency, median, mode, bimodal, outlier, gaps, weighted
mean, mean of a frequency distribution, symmetric, uniform, rectangular,
skewed left, negatively skewed, skewed right, positively skewed
Descriptor
Days
2.3.A Find the mean, median, and mode of a population and
3
sample.
2.3.B
Describe the shape of a distribution.
Resources:
Creating Data Sets Activity
Assessment Sources:
KWL Chart
Exit Ticket
Quiz 2.3-2.4
Homework
Unit Assessment
1
Notes:
Page 9
Statistics
Concept 2.4
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
Measures of Variation
How can we quantify the quality of guesses?
range, deviation, sum of squares, population variance, population standard
deviation, sample variance, sample standard deviation, empirical rule
Descriptor
Days
2.4.A Determine how far predicted values are from actual
3
values.
2.4.B
Describe the variation of a data set.
Resources:
Guessing Ages Activity
Assessment Sources:
Group Presentations
Exit Ticket
Quiz 2.3-2.4
Homework
Unit Assessment
2
Notes:
Page 10
Statistics
Concept 2.5
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
Measures of Position
Where does your height fall in comparison to others?
fractiles, quartiles, first quartile, second quartile, third quartile, box-andwhisker plot, five-number summary, percentiles, standard score, z-score
Descriptor
Days
2.5.A Construct and analyze box-and-whisker plots.
1
2.5.B
Describe the position of a data point using quartiles.
1
2.5.C
Describe the position of a data point using percentiles.
1
2.5.D
Describe the position of a data point using a standard
score.
1
Resources:
Percentile and Z-Score of Heights Activity
Assessment Sources:
Whiteboard Practice
Exit Ticket
Homework
Unit Assessment
Two additional days for review and unit test.
Notes:
Page 11
Statistics
Williamsport Area School District
Unit 3: Probability
Days: 17
Big Idea: Solve simple probability, compound probability, and counting problems.
Unit Essential Question:
How can we find the probability of simple and compound events?
How can we find the number of possible arrangements with and without
regard to order?
Concept
Concept Title
3.1
3.2
Basic Concepts of Probability and Counting
Conditional Probability and the
Multiplication Rule
The Addition Rule
Additional Topics in Probability and
Counting
3.3
3.4
Duration
(Days)
2
6
3
6
Page 12
Statistics
Concept 3.1
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
Basic Concepts of Probability and Counting
What is the difference between theoretical and experimental probability?
Probability experiment, outcome, sample space, event, simple event,
classical probability, theoretical probability, empirical probability, statistical
probability, law of large numbers, subjective probability, complement of
event E
Descriptor
Days
3.1.A Find the probability of a simple event.
1
3.1.B
Resources:
Assessment Sources:
Describe and find the probability of the compliment of
an event.
Dice Activity (Theoretical vs. Experimental Probability)
1
Exit Ticket
Homework
Unit Assessment
Notes:
Page 13
Statistics
Concept 3.2
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
Conditional Probability and the Multiplication Rule
What is the probability that an honest person fails a lie detector test?
conditional probability, independent, dependent, multiplication rule
Descriptor
Days
3.2.A Find the probability that an event will occur given that
4
another event already occurred.
3.2.B
Resources:
Assessment Sources:
Determine whether an event is independent or
dependent.
Lie Detectors/Colored Dots Activity
Water and Soda Probabilities Activity
Color Cards
Exit Ticket
Quiz 3.2
Homework
Unit Assessment
2
Notes:
Page 14
Statistics
Concept 3.3
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
The Addition Rule
How much information do we need to determine how many students are
female or blue is their favorite color?
mutually exclusive, addition rule,
Descriptor
Days
3.3.A Determine whether two event are mutually exclusive
1
or not mutually exclusive.
3.3.B
Find the probability of mutually exclusive events.
Resources:
Favorite Color Probability Activity
Assessment Sources:
Color Cards
Exit Ticket
Homework
Unit Assessment
2
Notes:
Page 15
Statistics
Concept 3.4
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
Additional Topics in Probability and Counting
What is the probability of winning Powerball?
permutation, factorial, permutation of n objects taken r at a time,
distinguishable permutations, combination, combinations of n objects taken r
at a time
Descriptor
Days
3.4.A Find the number of ways several objects can be
2
arranged or grouped.
3.4.B
Resources:
Assessment Sources:
Notes:
Use counting principles to find probabilities.
2
Powerball Activity (Part I)
Monty Hall Problem
Probability Games
Find Someone Who Can…
Exit Ticket
Homework
Unit Assessment
Two additional days for review and unit assessment.
Monty Hall Problem and Probability Games were used right before winter
break.
Power Activity (Part II) is in Unit 4.
Page 16
Statistics
Williamsport Area School District
Unit 4: Discrete Probability Distributions
Days: 26
Big Idea: Solve probability problems using the binomial, geometric, and Poisson distributions.
Unit Essential Question:
What are probability distributions and how can we use them?
Concept
Concept Title
4.1
4.2
4.3
Probability Distributions
Binomial Distributions
More Discrete Probability Distributions
Duration
(Days)
10
8
8
Page 17
Statistics
Concept 4.1
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
Probability Distributions
What is a probability distribution?
random variable, discrete continuous, discrete probability distribution,
expected value
Descriptor
Days
4.1.A Distinguish between discrete random variables and
2
continuous random variables.
4.1.B
Resources:
Assessment Sources:
Find the mean, variance, standard deviation, and
expected value of a probability distribution.
Probability Distribution with Two Dice
Powerball Expected Value
Deal or No Deal Expected Value
Exit Tickets
8
Notes:
Page 18
Statistics
Concept 4.2
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
Binomial Distributions
What is the binomial probability distribution?
binomial experiment, binomial probability distribution,
Descriptor
4.2.A Determine if a probability experiment is a binomial
experiment.
4.2.B
Find binomial probabilities.
4.2.C
Resources:
Assessment Sources:
Find the mean, variance, and standard deviation of a
binomial probability distribution
Baseball Binomial Activity
Days
2
5
1
Clicker Practice
Exit Tickets
Quiz 4.2
Notes:
Page 19
Statistics
Concept 4.3
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
More Discrete Probability Distributions
What are the geometric and Poisson probability disributions?
geometric distribution, Poisson distribution
Descriptor
4.3.A Find probabilities using the geometric distribution.
4.3.B
Resources:
Assessment Sources:
Notes:
Find probabilities using the Poisson distribution.
Days
4
2
Geometric Baseball Activity
Golden Ticket
Clicker Practice
Exit Tickets
Word-Wall Matching
Unit Assessment
Two additional days for unit review and assessment
Page 20
Statistics
Williamsport Area School District
Unit 5: Normal Probability Distributions
Days: 23
Big Idea: Use the normal distribution solve probability problems.
Unit Essential Question:
How can we apply the normal distribution to probability problems?
What is a sampling distribution and how can we use it?
Concept
Concept Title
5.1
Introduction to Normal Distributions and the
Standard normal Distribution
Normal Distributions: Finding Probabilities
Normal Distributions: Finding Values
Sampling Distributions and the Central Limit
Theorem
Normal Approximations to Binomial
Distributions
5.2
5.3
5.4
5.5
Duration
(Days)
4
4
3
5
7
Page 21
Statistics
Concept 5.1
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
Introduction to Normal Distributions and the Standard Normal Distribution
How can I find the area under the standard normal curve?
continuous probability distributions, normal distribution, normal curve,
probability density function, standard normal distribution,
Descriptor
Days
5.1.A Interpret graphs of normal probability distributions.
1
5.1.B
Find areas under the standard normal curve.
Resources:
Mind Map
Assessment Sources:
Clicker Practice
Exit Tickets
Quiz 5.1
3
Notes:
Page 22
Statistics
Concept 5.2
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
Normal Distributions: Finding Probabilities
How can I find probabilities using the normal distribution?
5.2.A
Resources:
Assessment Sources:
Descriptor
Find probabilities for normal distributed variables.
Days
4
Height Activity
Mind Map
Exit Ticket
Quiz 5.2
Notes:
Page 23
Statistics
Concept 5.3
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
Normal Distributions: Finding Values
How can I find the data value that corresponds to a given probability?
x-value
5.3.A
Descriptor
Find a z-score given the area under the normal curve.
5.3.B
Transform a z-score to an x-value.
5.3.C
Resources:
Assessment Sources:
Find a specific data value of a normal distribution
given the probability.
Airplane Seat Pitch Activity
Mind Maps
Clicker Practice
Exit Tickets
Days
1
1
1
Notes:
Page 24
Statistics
Concept 5.4
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
Sampling Distributions and the Central Limit Theorem
What is a sampling distribution?
Sampling distribution, sampling distribution of sample means, standard error
of the mean, Central Limit Theorem
Descriptor
Days
5.4.A Find sampling distributions and verify their properties.
2
5.4.B
Resources:
Assessment Sources:
Use the Central Limit Theorem to find the probability
of a sample mean.
Sampling Number Activity
Mind Maps
Clicker Practice
Exit Tickets
Quiz 5.4
3
Notes:
Page 25
Statistics
Concept 5.5
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
Normal Approximations to Binomial Distributions
How can I approximate binomial probabilities with the normal distribution?
continuity correction
5.5.A
Descriptor
Decide when a normal distribution can approximate a
binomial distribution.
5.5.B
Find continuity corrections.
5.5.C
Resources:
Assessment Sources:
Notes:
Use normal distribution to approximate binomial
probabilities.
Mind Maps
Days
1
1
3
Clicker Practice
Exit Tickets
Quiz 5.5
Unit Assessment
Three extra days for unit review and assessment.
Page 26
Statistics
Williamsport Area School District
Unit 6: Confidence Intervals
Days:
Big Idea: Find the margin of error in a sample and construct confidence intervals for
parameters.
Unit Essential Question:
How can we estimate a population parameter using sample statistics?
Concept
Concept Title
6.1
Confidence Intervals for the Mean (Large
Samples)
Confidence Intervals for the Mean (Small
Samples)
Confidence Intervals for Population
Proportions
6.2
6.3
Duration
(Days)
6
6
6
Page 27
Statistics
Concept 6.1
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
Confidence Intervals for the Mean (Large Samples)
point estimate, interval estimate, level of confidence, sampling error, margin
of error, confidence interval,
Descriptor
Days
6.1.A Find a point estimate and a margin of error.
2
6.1.B
Construct and interpret a confidence interval for the
population mean with a large sample.
2
6.1.C
Determine the minimum sample size required when
estimated a population mean.
2
Resources:
Assessment Sources:
Add
Notes:
Page 28
Statistics
Concept 6.2
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
Confidence Intervals for the Mean (Small Samples)
t-distribution, degrees of freedom,
Descriptor
6.2.A Interpret and use the t-distribution.
6.2.B
Construct and interpret a confidence interval for the
population mean with a small sample.
Days
3
3
Resources:
Assessment Sources:
Add
Notes:
Page 29
Statistics
Concept 6.3
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
Confidence Intervals for Population Proportions
population proportion
Descriptor
Find a point estimate for a population proportion.
Days
2
6.3.B
Construct and Interpret a confidence interval for a
population proportion.
2
6.3.C
Determine the minimum sample size required when
estimating a population proportion.
2
6.3.A
Resources:
Assessment Sources:
Add
Notes:
‘
Page 30
Statistics
Williamsport Area School District
Unit 7: Hypothesis Testing with One Sample
Days:
Big Idea:
Unit Essential Question:
How can we test a claim about a parameter?
Concept
Concept Title
7.1
7.2
Introduction to Hypothesis Testing
Hypothesis Testing for the Mean (Large
Samples)
Hypothesis Testing for the Mean (Small
Samples)
Hypothesis Testing for Proportions
7.3
7.4
Duration
(Days)
9
4
4
3
Page 31
Statistics
Concept 7.1
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
Introduction to Hypothesis Testing
Statistical hypothesis, null hypothesis, alternative hypothesis, type I error,
type II error, level of significance, test statistic, P-value, left-tailed test,
right-tailed test, two-tailed test
Descriptor
Days
7.1.A Introduction to hypothesis testing.
1
7.1.B
State a null and alternative hypothesis
1
7.1.C
Identify and interpret Type I and Type II error.
1
7.1.D
Determine whether to use a one-tailed or a two-tailed
statistical test.
1
7.1.E
Calculate the P-value of a statistical test.
3
7.1.F
Make and interpret a decision based on the results of a
statistical test.
1
7.1.G
Write a claim for a hypothesis test.
1
Resources:
Assessment Sources:
Add
Notes:
Page 32
Statistics
Concept 7.2
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
Hypothesis Testing for the Mean (Large Samples)
z-test for a mean, test statistic, standardized test statistic, rejection region,
critical value,
Descriptor
Days
7.2.A Find and interpret a P-value for a test about a
2
population mean.
7.2B
Find and interpret critical values and rejection regions.
2
Resources:
Assessment Sources:
Add
Notes:
Page 33
Statistics
Concept 7.3
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
Hypothesis Testing for the Mean (Small Samples)
t-test for a mean, test statistic, standardized test statistic
Descriptor
7.3.A Find critical values using the t-distribution.
7.3.B
Use a t-test to perform a test about a population mean.
Days
2
2
Resources:
Assessment Sources:
Add
Notes:
Page 34
Statistics
Concept 7.4
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
Hypothesis Testing for Proportions
z-test for a proportion, test statistic, standardized test statistic,
Descriptor
7.4.A Perform a z-test for a population proportion.
Days
3
Resources:
Assessment Sources:
Add
Notes:
Page 35
Statistics
Williamsport Area School District
Additional Information:
Include College Algebra Review Unit after Unit 3. Students will work in small groups and be
responsible for organizing resources on a specific algebra topic. This is intended as a review of key
algebra concepts prior to students taking college placement exams. (Approximately 15 days)
Page 36