AP STATISTICS: Unit 1 Exploring Data
Enduring understanding (Big Idea): Students will understand how to make sense of both categorical (qualitative) and quantitative data, whether in graphical or numerical forms.Essential Questions:
1. What is the difference between data and numbers?
2. What are a) a population, b) an individual and c) a distribution?
3. What is the distinction between quantitative and categorical variables
4. What are the accepted ways to display and analyze data?
BY THE END OF THIS UNIT:
Students will know:(See the AP Statistics Course Description page 7 for full details)
Exploring Data: Describing patterns and departures from patterns (20%–30%)
A Constructing and interpreting graphical displays of distributions of univariate data (dotplot, stemplot, histogram, cumulative frequency plot) Shape, Center, Spread, Clusters, Gaps, Outliers and other unusual features
B Summarizing distributions of univariate data: Measuring center: (median, mean) spread: (range, interquartile range, standard deviation); using boxplots and the effect of changing units on summary measures
C Comparing distributions of univariate data (dotplots, back-to-back stemplots, parallel boxplots): center and spread (within group, between group variation; 2 Comparing clusters and gaps; 3 Comparing outliers and other unusual features; 4 Comparing shapes
D See Units # 2 and 12 & E Exploring categorical data: Frequency tables and bar charts; Marginal and joint frequencies for two-way tables; Comparing distributions using bar charts / Students will be able to…
1. Identify the individuals and variables in a set of data
2. Classify variables as categorical (qualitative)
3. Identify units of measurement for a quantitative variable
4. Determine which measures of center and spread should be used for a given set of data and be able to use them
5. Compare distributions
6. Calculate variance and standard deviation
Vocabulary: Association, Bar graph (or Bar Chart), Categorical variable, Comparing Distributions, Conditional distribution, Counts (See Frequency below), Data, Distribution, Dotplots, Five Number Summary, Histograms, Individuals, Interquartile Range (IQR), Marginal distribution, Mean, Median, Outlier, Pie charts, Quantitative variable, Quartiles, Simpson's Paradox, Skewed Distributions, Standard Deviation, Stemplots, Symmetric Distributions, Two way table, Variable, Variance, Frequency (See Counts above), Relative Frequency, and Population.
Unit Resources:
· Use of Fathom is highly recommended (pricing has been greatly reduced)
http://www.keycurriculum.com/products/fathom
· Use Applets from: http://www.whfreeman.com/tps4e
http://www.rossmanchance.com/applets/
http://teachers.dadeschools.net/akoski/statsSyllabus1.htm
· Download the chapter glossary at (below) and give copies to your kids. http://bcs.whfreeman.com/tps4e/#628644__666335__
Learning Tasks: homework on page 1-7 of the Teacher's Edition
Performance Task: end the chapter with a "FRAPPY" (see Formative Assessments and Problem Task suggestions below)
Project: Characterizing Students
Unit Review Game: Jeopardy and Millionaire (PowerPoints) http://www.apstatsmonkey.com/StatsMonkey/TPS3e.html / Mathematical Practices in Focus (CCSS):
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
CORE CONTENT
Cluster Title: Summarize, represent, and interpret data on two categorical and quantitative variables (S-ID)Standards:
S.ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. (Also included in TPS4e Sections 5.2 & 5.3)
NCSCOC None
AP Stats IE1, 2, & 4 Exploring categorical data: 1 Frequency tables and bar charts; 2 Marginal and joint frequencies for two-way tables; 3 See Unit 5; and 4 Comparing distributions using bar charts
Cluster Title: Making Inferences and Justifying Conclusions (S-IC)
S.IC.6 Evaluate reports based on data
NCSCOC None
AP Stats IID Generalizability of results and types of conclusions that can be drawn from observational studies, experiments and surveys
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
AP STATISTICS: Unit 1 Exploring Data
Concepts and Skills to Master (on paper and with technology)Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
AP STATISTICS: Unit 1 Exploring Data
Introduction [Data Analysis: Making Sense of Data]· Identify the individuals and variables in a set of data
· Classify variables as categorical (qualitative) or quantitative
· Identify units of measurement for a quantitative variable / Section 1.1 [Analyzing Categorical Data]
· bar graphs and pie charts
· graphs: good and bad
· two-way tables and marginal distributions
· relationship between categorical variables: conditional distributions
· organizing a statistical problem
· Simpson's Paradox
SUPPORTS FOR TEACHERS
Critical Background KnowledgeThe common core standards require that probability and statistics are incorporated throughout a student's educational experience. However, it will take a while for that to propagate through the educational system; so assume no substantial prior relevant knowledge of probability and statistics and cover all of their fundamental aspects in our course.
Academic Vocabulary
From Introduction: Categorical variable, Data, Distribution, Individuals, Population, Quantitative Variable, Variable
From Sec 1.1 Association, Bar graph (or Bar Chart), Conditional distribution, Counts (See Frequency below), Frequency (See Counts above), Marginal distribution, Pie charts, Relative Frequency , Simpson's Paradox, Two way table
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
AP STATISTICS: Unit 1 Exploring Data
Suggested Instructional Strategies· Totally use collaborative group class arrangement and group assignment. For many of the class activities grade by groups (each student has a turn-in sheet) done collaboratively. Randomly select one turn-in sheet to grade for the group.
· For a great first day activity use First Day Activity
· Begin your course with the comprehensive statistical pre-assessment found at the ARTIST website as your first home-learning (homework) practice assignment. This is an excellent NSF funded resource with comparisons to national results. http://ore.gen.umn.edu/artist/tests/index.html Grade it as 100% for answering each question, independent of the correctness of the answer. You will know their statistics readiness and relative reasoning abilities . It is free (thanks NSF) and a great motivator for many students
· Although it is not part of the AP Statistics Curriculum, it is recommended that you administer (Day 2 is a great choice for a 100% grade) the North Carolina Early Math Placement Test (NCEMPT) to your students so that they realistically know their readiness for college and you will know their math readiness and relative math abilities . It is free (thanks UNC) and a great motivator for many students http://www.ncempt.org/welcome.jsp
· Rely on the Teachers' Edition and the Platinum Resource Binder
· The text is excellent and students should have their book (and their calculator) at each class. The challenge is how to inspire kids to read and study it. There should be class discussions during each class using material from the book and using the calculator. Consider assigning the next class' material as a prereading. Especially focus on the boxes labeled "AP Exam Common Error" in the margins (and also in Appendix A)
· With all students on their calculators and you on your projection calculator do Technology Corner 1.1 on page 16 using calculator lists (or other Technology)
· Do the "Hiring Discrimination" Activity on Page 5
· Have a Class Discussion of the Introduction's "Summary" on page 6
· Have a Class Discussion of Section 1.1's "Summary" on page 21
· The College Board has posted tremendously helpful material http://apcentral.collegeboard.com/apc/public/courses/teachers_corner/2151.html
in particular use: http://apcentral.collegeboard.com/apc/members/exam/exam_information/8357.html
· Copy the formula sheets and tables from the 2012 Questions, laminate them, and give them to your kids at the start of the course. Refer to these sheets continually and have the kids use them on every test and exam.
Useful directories for the released questions are at http://www.apstatsmonkey.com/StatsMonkey/AP_Review.html
for FR look for AP Index 11_12.xls for MC look for MC_Index.xls - Daren Starnes / Resources
· Textbook Correlation:
Chapter 1 Introduction (pages 1 - 7)
Section 1.1 (pages 8 - 26)
· Most of the PowerPoint slides on the Instructor's CD are very helpful.
· Use resources at
http://apstatsmonkey.com/StatsMonkey/Statsmonkey.html
· Monitor the AP Statistics List Serve [see Electronic Discussion Groups on http://apcentral.collegeboard.com/apc/public/courses/teachers_corner/2151.html ] soon to be an AP community see
https://epl.collegeboard.org/epl/login.do
Sample Formative Assessment Tasks
Skill-based tasks
· CHECK YOUR UNDERSTANDING (textbook pages 5, 14 and 17)
· Use assessments at http://www.stats4stem.org/
· Use Released Multiple Choice questions (see the last Suggested Instructional Strategy above for a link to the list of MC questions) The column "% correct " shows the global performance on the AP Exam for that question. Add a column to the spreadsheet to keep a record of the questions you used and when used. / Problem Tasks
· Students in groups should discuss and write down the solution of an AP Exam Free Response question, then compare it to the model solution, and [selected group(s)] should present their solutions to the class describing what they learned from their discussions
· See the last Suggested Instructional Strategy above for a list of released free response questions you can use (Do not use 2006 #1 until the end of Chapter 1.) Add a column to the spreadsheet to keep a record of the questions you used and when used.
CORE CONTENT
Cluster Title: Summarize, represent, and interpret data on a single count or measurement variables (S-ID)Standards:
S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).
S.ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
NCSCOS 2.01 Construct and interpret graphical displays of univariate data www.dpi.state.nc.us/curriculum/mathematics/scos/2003/9-12/72apstatistics
AP Stats IA Constructing and interpreting graphical displays of distributions of univariate data (dotplot, stemplot, histogram, cumulative frequency plot)
AP Stats IC Comparing distributions of univariate data (dotplots, back-to-back stemplots, parallel boxplots) [Comparing center and spread: within group, between group variation; Comparing clusters and gaps; Comparing outliers and other unusual features; and Comparing shapes]
Concepts and Skills to Master (on paper and with technology) Section 1.2 [Displaying Quantitative Data with Graphs]
· Dotplots
· Describing Shape
· Comparing Distributions / · Stemplots
· Histograms
· Using histograms wisely
SUPPORTS FOR TEACHERS
Critical Background KnowledgeSkills and concepts from section 1.1
Academic Vocabulary
Dotplots, stemplots, histograms, shape, center , spread, outliers, skewed, symmetric
Suggested Instructional Strategies
· Rely on the Teachers' Edition and the Platinum Resource Binder
· The text is excellent and students should have their book (and their calculator) at each class. The challenge is how to inspire kids to read and study it. There should be class discussions during each class using material from the book and using the calculator. Consider assigning the next class' material as a prereading. Especially focus on the boxes labeled "AP Exam Common Error" in the margins (and also in Appendix A)
· With all students on their calculators and you on your projection calculator do Technology Corner 1.2 on page 38 (or other Technology)
· Have a Class Discussion of Section 1.2's "Summary" on page 42
· The College Board has posted tremendously helpful material http://apcentral.collegeboard.com/apc/public/courses/teachers_corner/2151.html
in particular use: (Continued) http://apcentral.collegeboard.com/apc/members/exam/exam_information/8357.html
· Useful directories for the released questions are at
http://www.apstatsmonkey.com/StatsMonkey/AP_Review.html
(for FR look for AP Index 11_12.xls and for MC look for MC_Index.xls - Daren Starnes / Resources
· Textbook Correlation: Chapter 1 Section 2 (Pages 27 - 49)
· Most of the PowerPoint slides on the Instructor's CD are very helpful.
· Use resources at http://apstatsmonkey.com/StatsMonkey/Statsmonkey.html
· Monitor the AP Statistics List Serve [see Electronic Discussion Groups on http://apcentral.collegeboard.com/apc/public/courses/teachers_corner/2151.html ] (Continued)
soon to be an AP community see
https://epl.collegeboard.org/epl/login.do
Sample Formative Assessment Tasks
Skill-based tasks
· CHECK YOUR UNDERSTANDING (textbook pages 31 and 41)
· Use assessments at http://www.stats4stem.org/
· Use Released Multiple Choice questions (see the last Suggested Instructional Strategy above for a link to the list of MC questions) The column "% correct " shows the global performance on the AP Exam for that question. Add a column to the spreadsheet to keep a record of the questions you used and when used. / Problem Tasks
· Students in groups should discuss and write down the solution of an AP Exam Free Response question, then compare it to the model solution, and [selected group(s)] should present their solutions to the class describing what they learned from their discussions
· See the last Suggested Instructional Strategy above for a list of released free response questions you could use (Do not use 2006 #1 until the end of Chapter 1.) Add a column to the spreadsheet to keep a record of the questions you used and when used.
CORE CONTENT
Cluster Title: Summarize, represent, and interpret data on a single count or measurement variables (S-ID)Standards
S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).
S.ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
S.ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
NCSCOS 1.01 Summarize distributions of univariate data by determining and interpreting measures of center, spread, position, boxplots, and effects of changing units on summary measures. http://www.dpi.state.nc.us/curriculum/mathematics/scos/2003/9-12/72apstatistics
NCSCOS 2.01 Construct and interpret graphical displays of univariate data
NCSCOS 2.02 Compare distributions among sets of univariate data
NCSCOS 3.01 Analyze categorical data
AP Stats IB1-4 Summarizing distributions of univariate data [Measuring center: median, mean; Measuring spread: range, interquartile range, standard deviation; See Unit #2; Using boxplots]
AP Stats IC Comparing distributions of univariate data (dotplots, back-to-back stemplots, parallel boxplots) [Comparing center and spread: within group, between group variation; Comparing clusters and gaps; Comparing outliers and other unusual features; and Comparing shapes]
Concepts and Skills to Master (on paper and with technology) Section 1.3 [Describing quantitative data with numbers]
· Measuring center: The mean
· Measuring center: The median
· Comparing the mean and the median
· Measuring spread: The Interquartile Range (IQR)
· Identifying outliers / · The five number summary and box plots
· Measuring spread: The standard deviation
· Numerical summaries with technology
· Choosing measures of center and spread
SUPPORTS FOR TEACHERS