AP Statistics
Syllabus
Primary Textbook
Yates, Daniel S.; Moore, David S.; Starnes, Daren S. The Practice of Statistics 4th
edition. New York, New York: W. H. Freeman and Co., 2003
Course Description:
Statistics is the science of data. The purpose of this course is to introduce the
students to the major concepts and tools needed for collecting, analyzing, and drawing
conclusions from data. This course concentrates on four broad conceptual themes:
exploring data, planning a study (collecting data), probability (anticipating patterns in
data), and statistical inference based on data.
This course is an active learning experience. Students analyze data with
calculators and computers. They conduct classroom experiments, carry out individual
and group projects, and perform stimulations involving probability concepts. Students
are required to write a statistical report reporting their conclusions based on their data.
Course Overview
AP Statistics at our school is equivalent to a one-semester college course in
introductory statistics. To develop effective statistical communication skills, students are
required to prepare frequent written and oral analyses of real data. Early in the year,
students observe the effects of random phenomena and use Fathom frequently to view the
long-term outcomes. Students are taught both elementary probability theory and
combinatorial theory, but the emphasis for the probability section is placed on probability
modeling. Students use graphical and numerical techniques to study patterns and
departures from patterns. They use descriptive statistics to illustrate characteristics of
data sets and from observing these characteristics the student makes informed
speculations about the relationship of variables. A clear difference between association
and causation is developed by many examples encountered with these problems. The
students analyze sample surveys and experiments to further clarify the difference
between association and causation. Learners hypothesize about a population parameter,
create their own surveys and experiments, observe the effects of bias and determine the
best inference procedures. Once the population parameter is chosen, and inference model
selected, students work using probability modeling to determine if their acquired statistics
provide enough evidence to make conclusions about the respected populations. The
statistics course will teach students to communicate methods, results, and interpretations
using the vocabulary of statistics.
Use of Technology
Graphing calculators and computers are used throughout the course of the
program to assist students in solving problems, interpreting output, visualizing
distributions, and observe random behavior. Programs utilized are Fathom statistical
software and Microsoft Excel. Students observe Minitab statistical software output and
use various applets, ie Normal Distributions, to observe statistical theory in action. The
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school provides each student with a TI-84 plus for use during the academic year.
Students are expected to bring their calculators to all classes and be proficient with their
use and graphing capabilities. The students have access to two computer labs with both
Excel and Fathom software and TI-Connect. The instructor uses an interactive white
board technology, SmartBoard, during lectures, so the students may have access to visual
computer output and applets during most lectures.
Course Outline
I.
Exploring Data: Describing patterns and departures from patterns
A. Constructing and interpreting graphical displays of the distribution of
univariate data
1. Students construct and interpret graphical displays of univariate
data using histograms, stem-leaf plots, dotplots, boxplots and
ogives.
B. Summarizing distributions of univariate data
1. They observe and describe characteristics of the center and
spread, clusters and gaps, outliers and unusual features and
overall shape. The student will summarize the univariate data
distribution using measures of center (mean and median), using
measures of spread (range, IQR, standard deviation) and
measures of position (z-scores, 5 number summary, and
percentiles). They observe the effects of changing units on the
above descriptors and discuss the meaning of “resistance”.
C. Comparing distributions of univariate data
1. Students use dotplots, same axis histograms, back-to-back
stemplots and parallel boxplots to compare center and spread
within individual groups and compared groups. They also
transcribe comparisons of clusters and gaps, outliers and unusual
features and shapes of the individual groups.
D. Exploring bivariate data
1. Students analyze patterns in scatterplots using both TI
calculators, Excel and Fathom. They examine the distribution of
the explanatory and response variables for correlation and
linearity and explore the concept of error. Several technology
uses are employed to discover the least squares regression line
and the effect of outliers and influential points. Students use
residual plots to help determine linearity and use logarithmic and
power transformations to achieve linearity in nonlinear data sets.
E. Exploring categorical data
1. Students use frequency tables, bar charts, segments bar charts
and pie charts to help describe qualitative data sets. They use
marginal and joint frequencies and conditional relative
frequencies to explore the idea of independence and associations.
Additionally, students use segmented bar charts and side by side
bar charts to compare categorical data sets.
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II.
Sampling and Experimentation: Planning and conducting a study.
A. Methods of data collection
1. Students discuss and describe the difference between various
data collection methods: census, sample survey, experiments and
observational studies.
B. Planning and conducting surveys
1. Students plan and conduct their own surveys with an emphasis
placed on what question about their population would they like
answered and the best survey type to be employed for their
study. They discuss the benefits of reducing bias by SRS, but are
encouraged to see the positive uses of systematic, stratification,
and cluster sampling.
C. Planning and conducting experiments
1. Students observe the characteristics of a well-designed and wellconducted experiments and discuss in depth what errors can
occur and the devastating results of poorly conducted and
analyzed experiments. Students learn the building blocks of
experimental design, the importance of complete randomization,
and the purpose of varied treatments, control groups, random
assignments and replication of the experimental units. Students
discuss Hawthorne effect, placebo effect and the effects of
blinding. Additionally, they discover the benefits of blocking,
and matched pair and the importance of randomization within
these methods.
D. Generalizability of results and types of conclusions from the above
methods
1. Students discuss the importance of cause and effect versus
association that can be derived from studies and experiments.
An emphasis is put on the fact that one can never be 100% sure
and how many pharmaceutical companies now pay the price for
incorrect conclusions.
III.
Anticipating patterns: Exploring random phenomena using probability and
simulation.
A. Probability
1. Students use Activstats to explore the idea of long run frequency
and the Law of Large numbers. We devote several lessons to
elementary probability including set theory, probability theory
(additional rule, multiplication rule, conditional probability and
independence) and combinatorial theory. Following
combinations, students examine Bernoulli trials and Poisson
distributions. Included in the Bernoulli trials are binomial
distributions, geometric distributions and hyper geometric
distributions. Accordingly, they determine the mean and
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variance of probability models (including the Bernoulli and
Poisson) and the results of transformations to the random
variable that the distribution describes. Students use their TI
calculators and random number tables to simulate the behavior of
probability models and draw conclusions about random behavior.
B. Combining independent random variables
1. Students discuss the effects of independence on random variables
and using the “Pythagorean Theorem” of random variables,
determine the basis behind adding variance. Students write
frequently about combining and finding the difference between
independent and dependent random variables.
C. The normal distribution
1. Students examine many distributions in this class, but none is
more emphasized than the normal distribution. Students collect
and examine many data sets and observe the properties of the
normal curve. They are taught the use of both their TI calculator
and the z-table for predicting areas and values. Students use the
normal model for area descriptions.
D. Sampling distributions
1. Students examine through tactile manipulatives, Fathom, and
Java applets the sampling distribution of sample means and
sample proportions. Further exploration using these methods
allows the students visually attest to the results of these
distributions and the sample size increases, allowing
comprehension of the Central Limit Theorem on the basic level.
Confirming that two populations are independent, students
examine and have discussions about the difference between two
independent sample proportions and two independent sample
means. Students realize the importance of the student tdistribution in describing data sets with unknown population
variances and examine the uses of chi-square distributions.
IV.
Statistical Inference: Estimating population parameters and testing hypothesis
A. Estimation
1. Students determine the criteria of an unbiased estimator for
population parameters and how the variability of poor samples
affects those results. Through the use of applets, Fathom and
calculator activities, students examine the logic of confidence
intervals in estimating a population parameter, the meaning of
what a confidence interval actually is, describe in context of a
given problem what their acquired confidence interval says about
their parameter estimate and properties of a confidence interval.
Students use probability notation, tables and calculators to define
large sample confidence intervals for proportion and mean and
for difference between two proportions and two means. Students
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examine error of the least squares regression line and determine
confidence intervals for slopes about said lines using Fathom and
TI calculators.
B. Tests of Significance
1. Students discourse about the meaning of “significance” and what
it means to be statistically significant. They practice writing null
and alternative hypothesis, examine the importance of the pvalue as the likelihood of getting a result as extreme as the one
acquired. Perform one and two tailed tests and discuss the Power
of the test and the likelihood of a Type I and Type II error, what
these errors mean in context of the problem and how to reduce
said errors while keeping Power strong. Students learn the
importance of having the correct conditions before exploring the
use of a model with inferential prediction. Students perform a
series of inference testing including t-test for means, z-test for
means when sigma is known, matched pair t-test for difference of
means, t-test for difference of means for independent
populations, z-test for proportions, and z-test for difference of
proportions. Students additionally discuss the idea of pooling
data and post AP exam, explore f-distribution for that purpose.
Students perform chi-square tests for goodness of fit for one way
tables and homogeneity and independence for two-way tables.
Additionally, students test the slope for least square regression
lines to determine if the line is statistically suitable for the model.
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Material Covered by Section
I.
Designing Studies – Chapter 4 (12 days)
• Section 4.1 – Sampling and Surveys
o Convenience Sampling
o Simple Random Sample
o Voluntary Response Sample
o Systematic Sampling
o Cluster Sample
o Stratified Random Sample
o Undercoverage
o Non-response
o Response Bias
• Section 4.2 – Experiments
o Observational vs. Experimental
o Lurking variable
o Confounding
o Random Assignment
o Blocking
o Matched Pairs
• Section 4.3 – Using Studies Wisely
o Causation
o Inference
o Cause and effect
II.
Exploring Data – Chapter 1 (9 days)
• Section 1.1 – Analyzing Categorical Data
o Frequency table
o Pie charts
o Bar graphs
o Two way table
o Conditional distribution
o Association
• Section 1.2 – Displaying Quantitative Data with Graphs
o Dotplot, stemplot, histogram
o Shape, center, spread, outliers
o Skewed
• Section 1.3 – Displaying Quantitative Data with Numbers
o Mean, median
o Quartiles
o Outlier
o Variance and standard deviation
o Spread and variability
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III.
Modeling Distributions of Data – Chapter 2 (7 days)
• Section 2.1 – Describing Location in a Distribution
o Percentiles
o Z-scores
o Transforming data
o Density curve
o Mean and standard deviation of density curve
• Section 2.2 – Normal Distributions
o Normal distribution
o 68-95-99.7 Rule
o Standard normal distribution
o Using tables for z-scores
IV.
Describing Relationships – Chapter 3 (7 days)
• Section 3.1 – Scatterplots and Correlation
o Exploratory and response variable
o Direction, form, strength
o Correlation variable, r
• Section 3.2 – Least Squares Regression
o Regression line
o Residuals and standard deviation of residuals
o Residual plot
o Coefficient of determination r2
o Extrapolation
V.
Probability – Chapter 5 (8 days)
• Section 5.1 – Randomness, Probability and Simulation
o Law of large numbers
o Probability is a number between 0 and 1
o Simulations
• Section 5.2 – Probability Rules
o Sample space and events
o Compliment rule
o Addition rule for mutually exclusive events
o General addition rule
o Union, intersection
• Section 5.3 – Conditional Probability and Independence
o Conditional probability
o Independent events
o General multiplication rule
o Conditional probability formula
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VI.
Random Variables – Chapter 6 (10 days)
• Section 6.1 –Discrete and Continuous Random Variables
o Probability distribution
o Discrete and continuous random variable
o Mean of a random variable
o Expected value
o Variance and standard deviation of random variable
• Section 6.2 –Transforming and Combining Random Variables
o Linear transformations
o Shape, center, spread
• Section 6.3 –Binomial and Geometric Random Variables
o Binomial setting
o Normal approximation
o Geometric distribution
VII.
Sampling Distributions – Chapter 7 (10 days)
• Section 7.1 – Sampling Distributions
o Parameter
o Population distribution
o Unbiased and biased estimator
• Section 7.2 – Sample Proportions
o Mean and standard deviation of sampling distribution for
proportions
o Normal approximation
• Section 7.3 – Sample Means
o Central Limit Theorem
o Mean and standard deviation of sampling distribution for means
VIII.
Estimating with Confidence – Chapter 8 (11 days)
• Section 8.1 – Confidence Intervals
o Confidence level
o Point estimator
o Margin of error
• Section 8.2 – Estimating a Population Proportion
o Standard error
o Conditions
o Confidence interval for p
• Section 8.3 – Estimating a Population Mean
o One sample t-interval
o Degrees of freedom
o Robust
o Confidence interval for means
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IX.
Testing a Claim – Chapter 9 (9 days)
• Section 9.1 – Significant Tests
o One-sided and two-sided test
o Null/alternative hypothesis
o P-value
o Type I and II error
o Power
o Statistically significant
• Section 9.2 – Tests about a Population Proportion
o Test statistic
o One sample z-test for proportions
o Assumptions
• Section 9.3 – Tests about a Population Mean
o One sample t-test
o Paired data
o Assumptions
X.
Comparing Two Populations – Chapter 10 (7 days)
• Section 10.1 – Comparing Two Proportions
o Confidence intervals for two proportions (two-sample z-interval)
o Significance tests for two proportions (two-sample z-test)
o Pooling
• Section 10.2 – Comparing Two Means
o Confidence intervals for two means (two-sample t-interval)
o Significance tests for two means (two-sample t-test)
o Degrees of freedom
XI.
Inference Distributions of Categorical Data – Chapter 11 (8 days)
• Section 11.1 – Chi-Squared Goodness of Fit Test
o Chi-squared goodness of fit
o Chi-squared distribution
o Observed and expected counts
o Components
• Section 11.2 – Inference for Relationships
o Chi-squared test for homogeneity
o Chi-squared test for independence/association
o Expected counts
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XII.
More About Regression – Chapter 12 (8 days)
• Section 12.1 – Inference for Linear Regression
o t-interval for slope
o t-test for slope
o Conditions for finding population regression line
• Section 12.2 – Transforming to Achieve Linearity
o Power model
o Exponential model
o Logarithm
Chapter Timelines/Agenda
Chapter 4:
Designing Studies
Day
Lesson Objective
Homework
1
Welcome to AP Stat!
Activity: Dolphin Therapy
Calculator Form
2
Activity: Dolphin Therapy (Cont'd)
Read and Take Notes (R&TN): 4.1
3
Activity: Dolphin Therapy (Cont'd)
Go over Summer Assignment
R&TN: 4.1
Activity Permission Slip
4
Section 4.1
Page 226, #1-9 odd, 13, 19
5
Section 4.1 (Cont'd)
Page 228, #21-25, 29, 31, 35,
Review for Quiz
6
Quiz: 4.1
Activity: Chocolate Lovers!
R&TN: 4.2
7
Activity: Chocolate Lovers! (Cont'd)
Section 4.2
Chocolate Lover! Activity Questions
Page 253, #45, 49, 51, 59, 61, 63
8
Section 4.2 (Cont'd)
Page 256, #69, 73, 77, 79, 85, 89
9
Free Response Practice Problem
R&TN: 4.3
10
Section 4.3
Page 268, #102, 103, 105, 107, 111
11
Test Review
Review for Test
12
Test
R&TN: 1.1
10
Chapter 1:
Exploring Data
Day
Lesson Objective
Homework
1
Activity: M&M's
R&TN: 1.2
Take notes on 1.0 and 1.1
2
Finish M&M's Activity
Practice Problems: 1.0 & 1.1 (page 7, #3 & 5;
page 22-26, #11, 14, 17, 19, 21, 25)
Review for Quiz
Take notes on 1.2
3
Quiz: 1.0/1.1
Activity: US Presidents
HW 1.2 - page 42, #37, 39, 45, 49, 51
4
Activity: US Presidents Activity
Gather Data for Pulse Rates
HW 1.2 - page 46, #55, 59, 65, 67, 69-73 odd
5
Finish US Presidents
Project Pulse Rates on Fathom
R&TN 1.3
Project: Finish Pulse Rates
6
Notes: 1.3
Project: Finish Pulse Rates
HW 1.3 - page 70, #79, 81, 89, 93, 99, 106
7
Quiz 1.2/1.3
Work on Pulse Rate Activity
Project: Pulse Rates due tomorrow
8
Free Response Practice Problem
Test Review
Review for Test
9
Test
R&TN: 2.1
11
Chapter 2:
Modeling Distributions of Data
Day
Lesson Objective
Homework
1
Activity: Don't Crap Out
Take notes on 2.1
2
Finish Activity
Practice Problems: 2.1 (page 105, #1, 5, 7, 9,
11, 15, 19, 21, 27, 31)
R&TN: 2.2
3
Quiz: 2.1
Notes: 2.2
HW 2.2 day 1 - page 131, #41-47 odd, 51
4
Finish Notes: 2.2
Activity: Now you zee it
HW 2.2 day 2 - page 131, #54, 55, 59, 63, 65
5
Finish Activity: Now you Zee it!
Practice Problems
Finish Practice Problems
6
Free Response Practice Problem
Test Review
Review for Test
7
Test
R&TN: 3.1
Chapter 3:
Describing Relationships
Day
Lesson Objective
Homework
1
Activity: Missing M&M's
Take notes on 3.1
2
Finish Activity
Practice Problems: 3.1 (page 158, #1, 5, 7,
13, 15, 21)
R&TN: 3.2
3
Quiz: 3.1
Notes: 3.2
HW 3.2 day 1 - page 191, #37, 39, 45, 47, 72,
73
4
Continue Notes: 3.2
Activity: Case Closed - Baseballs
HW 3.2 day 2 - page 191, #53, 55, 63, 65, 75,
77
5
Quiz - 3.2
Finish Activity
Finish Activity
6
Free Response Practice Problem
Test Review
Review for Test
7
Test
R&TN: 5.1
12
Chapter 5:
Probability
Day
Lesson Objective
Homework
1
Activity: Don't Get Bumped off the Plane!
Take notes on 5.1
2
Practice Problems: 5.1 (page 294, #1, 7, 9,
13, 17, 23, 25)
R&TN: 5.1 AND Take notes on 5.2
3
Practice Problems: 5.2 (page 309, #43, 45,
49, 51, 53, 56)
R&TN 5.3 AND study for quiz 5.1-5.2
4
Quiz (5.1-5.2)
Activity: Probability Rules!
Finish Activity
5
Notes: 5.3
Practice Problems: 5.3 (page 329, #67, 73,
77, 79, 87, 89, 93, 101)
Finish Practice Problems 5.3
6
Free Response Practice Problem
Begin Reviewing for Test
7
Test Review
Review for Test
8
Test
R&TN: 6.1
Chapter 6:
Random Variables
Day
Lesson Objective
Homework
1
Activity: NJ Pick 4 – “Roll”anda Vega
Take notes on 6.1
2
Activity: That was Not Expected!
Practice Problems: 6.1 (page 353, #3, 5, 7, 11,
15, 25)
R&TN: 6.2 AND Finish Practice Problems
3
Notes: 6.2
Practice Problems: 6.2 (page 378, #37, 45, 49,
51, 55, 59)
Finish Practice Problems
4
Activity: Televisions
Activity: Meaner Means and Variating
Variances
Finish Activity AND Study for Quiz
5
Quiz 6.1-6.2
Begin Notes: 6.3
R&TN: 6.3
6
Finish Notes: 6.3
Practice Problems: 6.3 (page 403, #71, 73a, 75,
79, 85, 87, 95, 99)
Finish Practice Problems
7
Activity: Under Pressure - Free Throw
Percentage
Finish Activity
8
Activity: Hot Streaks - Free Throw Percentage
Finish Activity
9
Free Response Practice Problem
Test Review
10
Test
R&TN: 7.1
13
Chapter 7:
Sampling Distributions
Day
Lesson Objective
Homework
1
Activity: German Tanks
Research German Tanks online
2
Finish Activity: German Tanks
Symbol Review
Begin Notes: 7.1
German Tanks Reflection
3
Finish Notes: 7.1
Practice Problems: 7.1 (page 428, #3, 7, 9,
15, 17, 19)
Finish Practice Problems AND Study for
Quiz
4
Quiz 7.1
Activity: Sampling Variability
R&TN: 7.2 AND Take notes on 7.2
5
Practice Problems: 7.2 (page 439, #29, 31,
35, 37, 39)
R&TN: 7.3
6
Notes: 7.3
Practice Problems: 7.3 (page 454, #49, 53,
55, 59, 61)
Finish Practice Problems
7
Activity: Penny For Your Thought
Finish Activity
8
Chapter Review
Begin reviewing for test
9
Free Response Practice Problem
Test Review
10
Test
R&TN: 8.1
14
Chapter 8:
Estimating with Confidence
Day
Lesson Objective
Homework
1
Activity: You Look Confident!
Begin Notes: 8.1
R&TN: 8.1, Finish Taking Notes on 8.1
2
Practice Problems: 8.1 (page 481, #1, 5, 9, 11,
15, 17, 19)
Finish Practice Problems AND
R&TN: 8.2
3
Activity: The Steps to Confidence!
Takes notes on 8.2
4
Practice Problems: 8.2 (page 496, #27, 31, 36,
38, 43, 47)
Finish Practice Problems
5
Activity: Drop the (Cigarette) Butt!
Study for Quiz
6
Quiz 8.2
7
Activity: Words of the TIME(S)!
R&TN: 8.3 AND Finish Activity
8
Notes 8.3
Practice Problems: 8.3 (55, 57, 63, 67, 73)
9
Special Problem: An Intro to Question 6
problems…
Finish Special Problem
10
Free Response Practice Problem
Test Review
11
Chapter 8 Test
R&TN: 9.1
15
Chapter 9:
Testing a Claim
Day
Lesson Objective
Homework
1
Activity: Great Free-Throw Shooter
Notes: 9.1
Finish Taking Notes on 9.1
2
Activity: Types of Errors
Practice Problems: 9.1 (page 546, #1, 3, 7, 11,
13, 19, 23)
Finish Practice Problems AND
R&TN: 9.2
3
Activity: Spinning Heads
Finish Activity
4
Practice Problems: 9.2 (page 562, #33, 35, 37,
41, 45, 49, 55)
Study for Quiz (9.1-9.2) AND
R&TN: 9.3
5
Quiz 9.1-9.2
Activity: I got the Power…Reading Power
Finish Activity
6
Practice Problems: 9.3 (page 587, #63, 65, 69,
73, 75, 77, 85, 91)
Finish Practice Problems
7
Free Response Practice Problem
Begin Test Review
8
Test Review
Test Review
9
Chapter 9 Test
R&TN: 10.1
Chapter 10:
Comparing Two Populations or Groups
Day
Lesson Objective
Homework
1
Activity: Truth or D.A.R.E - Part 1
Notes: 10.1 (2 sample z-interval)
Practice Problems: 10.1 - Part 1 (page 621,
#1, 5, 7, 11, 13)
2
Activity: Truth or D.A.R.E - Part 2
Notes: 10.2 (2 sample z-test)
Practice Problems: 10.1 - Part 2 (page 621,
#15, 17, 19, 21, 27)
3
Quiz 10.1
A discussion about Power
R&TN: 10.2
4
Activity: Snapple "Real Fact" #789 – Part 1
Notes: 10.2 (2 sample t-interval)
Practice Problems: 10.2 - Part 1 (page 651,
#39, 43, 45, 47, 49)
5
Activity: Snapple "Real Fact" #789 – Part 2
Notes: 10.2 (2 sample t-test)
Practice Problems: 10.2 - Part 2 (page 651,
#51, 57, 59, 61-64, 65 use Ho: diff=5)
6
Free Response Practice Problem
Test Review
7
Chapter 10 Test
R&TN: 11.1
16
Chapter 11:
Inference Distributions of Categorical Data
Day
Lesson Objective
1
Activity: Melts in your Brain, Not in your Hands
Begin Practice Problems 11.1
2
Activity: Hang Up and Drive
Practice Problems: 11.1 (page 692, #1, 3, 5,
9, 17)
3
Finish Activity: Hang Up and Drive
FREE
RESPONSE PRACTICE PROBLEM - Question
6
R&TN: 11.2 AND Study for Quiz
4
Quiz 11.1
Start Activity: Wine and Music
Part 1 of Activity
5
Finish Activity: Wine and Music
Practice Problems: 11.2 - Part 1 (page 724,
#527, 29, 31, 37, 39, 41)
6
Activity: Students Who Smoke
Practice Problems: 11.2 - Part 2 (page 724,
#45, 49, 51, 53, 57)
7
Free Response Practice Problem
Test Review
8
Chapter 11 Test
R&TN: 12.1
Chapter 12:
Homework
More About Regression
Day
Lesson Objective
Homework
1
Intro Activity: SAT ESSAY
R&TN: 12.1
2
Activity: Ants in Your Pants
Practice Problems: 12.1 - Part 1 (page 759,
#3, 5, 7, 9, 11)
3
Activity: Crying and IQ
Practice Problems: 12.1 - Part 2 (page 759,
#13 & 19)
4
Quiz 12.1
R&TN: 12.2
5
Activity: Go Fish
Practice Problems: 12.2 - Part 1 (page 786,
#35, 37)
6
Activity: How Many Transistors do you Have?
Practice Problems: 12.2 - Part 2 (page 786,
#39, 41)
7
Free Response Practice Problem
Test Review
8
Test
17