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Course Title: AP Statistics                                                                                    Course Number:         38022

Department: Mathematics                                                                                        ADS Number:         20604133

Prerequisites: Successful completion of Algebra II

Length of Course:        One Year            Credit/PRI Area:       .50 per Semester/Mathematics or elective                   Grade Level(s):       11 - 12

Important Notes: It is not required, but strongly recommended, that the student purchase a TI83+ graphing calculator. The Advanced Placement Statistics
course is a basic introduction to statistics. The AP title is an indication that the course may be preparation for the AP exam but taking the exam is wholly

Advanced Placement Statistics introduces the student to the major concepts and tools for collecting, analyzing, and drawing conclusions from data
 using these four broad themes:
         1. Exploration: Observing patterns and departure from patterns
         2. Study design
         3. Producing models using probability theory and simulation
         4. Statistical inference
This course uses an interactive data collection approach using the text and lessons as resources and addresses the standards presented by the National
Council of Teachers of mathematics (NCTM). The student applies his/her knowledge of algebra and geometry to linear transformation of data,
conducting surveys, and analyzing the results. The student builds his/her own studies using both proper and improper data analysis techniques,
critiques studies conducted by other students and entitles, and makes suggested improvements.

References in parenthesis following each performance standard align with the State of New Mexico Mathematics Standards (NM) and the Albuquerque
Public Schools (APS) Mathematics Standards.

AP STATISTICS                                                                  14.1.8                                                       Albuquerque Public 03/04
The “Illustrations” column in the Program of Studies provides exemplars of the standards, strategies, and best practices suggested by Mathematics
departments in the Albuquerque Public Schools (APS).

The “Illustrations” column also incorporates a variety of assessments and “check for” items suggested by the mathematics departments in APS.
Assessments include: teacher evaluations of statistical studies using rubrics, short answer essay tests, homework assignments, AP exam, and criterion

   Until new adoptions: Larsen Farber Elementary Statistics
   Cartoon Guide to Statistics Harper Perennial 1993
   JMP Start Statistics Software
   Fathom Software
   At mathematics adoption: Introduction to Statistics and Data Analysis Peck Olsen Devore
   Statistics for the Utterly Confused McGraw Hill 2000


                                                                                                                 Approved by HSCA:

AP STATISTICS                                                                 14.2.8                                                      Albuquerque Public 03/04
CONTENT STANDARD: The student understands and uses mathematical processes.

BENCHMARK: The student uses problem solving, reasoning and proof, communication, connections, and representations, as appropriate, in all mathematical experiences.

 GRADE                           PERFORMANCE STANDARDS                                                                  ILLUSTRATIONS
 11 – 12
                                                                                         Note: Illustrations include suggested activities for attaining each
                                                                                               performance standard. A check () refers to a key feature
                                                                                               to look for while assessing student performance.

              1. Develops resourcefulness and perseverance in problem solving in         1, 4-10. The student, working in teams, plans and conducts product studies
                 mathematics and other disciplines (NM-4D; APS-1.1).                         that have long time duration. Using this study, he/she discusses how the
              2. Recognizes when to use previously learned strategies to solve new           statistics were analyzed, how he/she arrived at the conclusions, and
                 problems (NM-1C, 3B; APS-I.2).                                              presents the studies to the class and to the corporations involved in the
              3. Develops and uses strategies to solve given problems (NM-1C,1E, 3B;         studies. Other class members critique each other’s work.
                 APS-I-2).                                                                              all required components
              4. Monitors, discusses, and reflects on the processes of mathematical                     team work/peer support
                 problem solving (NM-1A, 2A; APS-I.4).                                                  effective communication
              5. Works in teams to share ideas, to develop and coordinate group                         problem-solving techniques
                 approaches to problems, and to communicate findings                                    analysis
                 (NM-2B; APS-I.8).
              6. Communicates mathematical thinking coherently and clearly to others     2, 3. The student utilizes Algebra II mathematics (matrices) to analyze
                 (NM-2B, 2C; APS-I-9).                                                       data and presents solutions to the class.
              7. Analyzes and evaluates mathematical thinking and strategies of others                 new problem-solving strategies
                 (NM-2D; APS-I.10).                                                                    relevance
              8. Relates applications to mathematical language in various modalities                   clarity and comprehension in communication
                 (NM-2B, 2C, 2C; APS-I.11).
              9. Identifies and connects functions with real-world applications
                 (NM-4E, 12D; APS-I.12).
             10. Recognizes and applies mathematics in contexts outside the
                 mathematics course (NM-6B; APS-I.15).

AP STATISTICS                                                                   14.3.8                                                            Albuquerque Public 03/04
CONTENT STANDARD: The student demonstrates number sense through experiences with meaningful mathematical problems tht focus on number
                    meaning, number relationships, place value, relative effect of operations, and multiple representations to communicate sound mathematical

BENCHMARK: The student understands rational, real, and complex numbers, and uses a variety of means, including technology, to solve problems in these number systems.

 GRADE                            PERFORMANCE STANDARDS                                                                     ILLUSTRATIONS
  11 - 12
                                                                                             Note: Although successful completion of Algebra II is required for this
                                                                                                   course, review and remediation of algebraic concepts has to take
                                                                                                   place on a regular basis for the student to accomplish performance
                                                                                                   tasks required by this course.

             1.   Develops a deeper understanding of very large and very small numbers       1, 2. The student uses statistical software to construct graphs and to analyze
                  (NM-5B; APS-II.1).                                                             variance (e.g., determination of a “p” value – the smallest significance level
                                                                                                 at which something is statistically significant).
             2.   Uses graphical representations to model numerical relationships                               use of technology
                  (NM-2C, 5D, 12B; APS-II.4).                                                                   process
                                                                                                                graphical representation
                                                                                                                accuracy

             3.   Applies ratios, proportions, and percents in more complex mathematical     3-5, 7. The student uses the correct methodology (e.g., matrices, probability
                  situations (NM-5C; APS-II.11).                                                distribution) to calculate standard deviation, measures of central tendency,
                                                                                                variance, and confidence intervals for his/her individual study, provided
             4.   Evaluates relationships between key components in a problem situation         studies or teacher-selected studies using equations, matrices, factorials, and
                  (NM-4B, 4C, 6D; APS-II.11).                                                   linear regression.

             5.   Develops fluency in operations with real numbers and matrices using                         accuracy
                  mental computation, paper and pencil, or technology (NM-2D, 4D, 13A;                        correct equations for data
                  APS-II.3 Late HS).                                                                          comprehension of “p” value

             6.   Develops a fundamental understanding of sequences and series               6. The student uses factorials to computer complex probability outcomes
                  (NM-3H; APS-II.6 Late HS).                                                    (e.g., odds of winning the Powerball).
                                                                                                               accuracy
             7.   Solves an application involving optimization (NM-13G; APS-II.7 LHS).                         formulas

AP STATISTICS                                                                       14.4.8                                                             Albuquerque Public 03/04
CONTENT STANDARD: The student identifies patterns and special features of data and events of chance through experiences with meaningful mathemeatical problems that
                    Focus on comparing, predicting, representing data, and making decisions to communicate mathematical understanding.

BENCHMARK: The student understands the characteristics of a well designed study, describes the difference between studies, and uses a variety of ways to interpret data.
           The student computes basic statistics and evaluates published statistics and representations of data. The student simulates probability situations and computes
           and interprets simple probability cases.

 GRADE                             PERFORMANCE STANDARDS                                                                         ILLUSTRATIONS
  11 - 12
             1.   Creates histograms, box plots, and scatter plots and uses them to display       1-3, 6, 9, 11, 12. Using the data from the last boy’s high school basketball
                  data (NM-10A; APS IV.1).                                                           game, the student creates charts and tables with regression lines to
                                                                                                     illustrate shooting percentages, correlation of time vs. shooting
             2.   Computes mean, median, mode, and identifies the merit of each                      percentage, from three-pointers, field goals, and free throws. The
                  (NM-10C, 10F; APS-IV.2).                                                           student finds the measures of central tendencies (e.g., mean, median, mode,
                                                                                                     interquartile range, skew) for each.
             3.   Identifies and uses statistical terms (NM-10B-D, 10F; APS-IV.3).                               calculations
                                                                                                                 completion of all tasks
                                                                                                                 neatness of graphs and tables
                                                                                                                 matching of data to tables and graphs

             4.   Defines sampling and recognizes its role (NM-10D; APS-IV.4).                    4, 5, 10, 14. Using student’s individual studies and studies from other sources,
                                                                                                      the student differentiates between proper sampling techniques and sampling
             5.   Constructs and draws inferences from charts, tables, and graphs                     techniques that have bias in them.
                  (NM-10A; APS-IV.5).                                                                           recognition of bias
                                                                                                                recognition of proper statistical techniques
             6.   Writes an equation of best-fit using a set of data points, and makes                          logical inferences
                  predictions based on the graph (NM-10B; APS-IV.6).

             7.   Uses simulations to create and interpret discrete probability distributions     7, 8, 13, 15-17. The student observes a teacher demonstration (ten students at a
                  (NM-11 A; APS-IV.7).                                                                time) of Black Jack hands (without gambling) using four decks of cards.
                                                                                                      He/she interprets probability distributions, probability of compound events,
             8.   Computes the probability of a compound event (NM-11D; APS-IV.8).                    fundamental counting principle, and predicts the probability of a particular
                                                                                                      setoff cards coming up next and the independence of those events.
             9.   Explains the differences among various kinds of studies and which types                        ability to calculate the probability of the next card
                  of inferences can be legitimately be drawn from each (NM-10A;                                  prediction of the probability of the succession of cards
                  APS-IV.1 Late HS).                                                                             understanding of probability principles

            10.   Recognizes the characteristics of well designed studies including the role
                  of randomness (NM-10E; APS-IV.2 LHS).

AP STATISTICS                                                                            14.5.8                                                            Albuquerque Public 03/04
 GRADE                             PERFORMANCE STANDARDS                                                               ILLUSTRATIONS
  11 - 12
            11.   Analyzes the effects of data transformations on measures of central
                  tendency and variability (NM-10C, 10 F; APS-IV.3 LHS).

            12.   For bivariate measurement data, creates and displays a scatter plot,
                  describes its shape, and determines the regression of the coefficients
                  (NM-10A, 10B; APS-IV.4 LHS).

            13.   Uses simulations to explore the variability of sample statistics from a
                  known population and to construct sampling distributions (NM-11A;
                  APS-IV.5 LHS).

            14. Evaluates published reports that are based on data by examining the
                design of the study, the appropriateness of the data analysis, and the
                validity of the conclusions (NM-10E; APS-IV.6 LHS).

CONTENT STANDARD: The student demonstrates an understanding of algebraic skills and concepts through experiences with meaningful mathematical problems that
                     focus on discovering, describing, modeling, and generalizing patterns and functions, representing and analyzing relationships, and finding and
                     supporting solutions.

AP STATISTICS                                                                         14.6.8                                                    Albuquerque Public 03/04
BENCHMARK: The student represents patterns with relations and functions, investigates rates of change, and symbolically manipulates numbers.

  GRADE                              PERFORMANCE STANDARDS                                                                       ILLUSTRATIONS
   11 - 12
                1.    Explains the meanings of and uses common algebraic symbols                    1-17. The student, through the construction of his study (teacher-approved),
                     (NM-13D, APS-V.7).                                                                creates his own real-life word problem that incorporates statistical
                2.    Identifies and uses algebraic terms such as variable, exponent, factor           formulas, variables, exponents, matrices, polynomials, radicals, rational
                      term, and function (NM-13D; APS-V.8).                                            expressions, order of operations, and graphical representations of data,
                3.    Uses order of operations and the commutative, associative, and                   including regression analysis. The student solves his own problem and
                      distributive axioms to simplify expressions (NM-4A, 13A; APS-V.9).               submits the results.
                4.    Translates a real-life problem into an expression, equation, inequality, or              variety of concepts
                      matrix as the first step (NM-13A; APS-V.11).                                             solution
                5.    Graphs linear equations and inequalities from given equations and from                   critical thinking, problem-solving skills
                      symbolic reasoning in the context of applied settings or presented data                  accuracy
                      (NM-12B, 13B; APS-V.12).                                                                 visuals
                6.    Applies the laws of exponents with integers to perform operations on                     use of technology
                      expressions (NM-5B, 13A; APS-V.14).                                                      reasonableness of conclusions
                7.    Adds, subtracts, multiplies, and divides polynomials with monomial                       presence of all required components
                      divisors using concrete objects, pictorial representation, and algebraic
                      manipulation (NM-2C, 4A; APS-V.15).
                8.    Simplifies radicals and numerical radicands and estimates their value
                      both mentally and with a calculator (NM-5A; APS-V.18).
                9.    Finds the sum, difference, product, and quotient of rational expressions
                      with monomial and polynomial numerators and denominators
                      (NM-13A; APS-V.20).
              10.    Solves equations involving rational expressions with monomial and
                     polynomial numerators and denominators (NM-13C; APS-V.21).
              11.    Solves word problems involving algebraic functions using appropriate
                     units, unit analysis, and precision (NM-1C, E, 9B, 12D; APS-V.22).
              12.    Analyzes functions of one variable by investigating rates of change,
                     intercepts, zero’s asymptotes, maximum/minimum, and local/ global
                     behavior (NM-12E, 13G; APS-V.2 LHS).

              13.    Creates systems of equations in two or three variables and solves them by
                     using the following algebraic processes; graphing by hand as well as
                     graphing with calculators, using algebraic methods such as linear
                     combination and substitution, applying basic matrix operations, and
                     inverse matrix properties (NM-13B, 13E; APS-V.5 LHS).

AP STATISTICS                                                                          14.7.8                                                             Albuquerque Public 03/04
  GRADE                             PERFORMANCE STANDARDS                                       ILLUSTRATIONS
   11 - 12
             14.   Describes a real-life problem or event algebraically and graphically using
                   various functions including linear, exponential power, rational square,
                   square root, cube and cube root (NM-12 A-C; APS-V.7 LHS).

             15.   Validates the reasonableness of conclusions (NM-3C; APS-V.9 LHS).

             16. Identifies linear, quadratic, polynomial, logarithmic, and exponential
                 functions from graphs (NM-12A, 12C, 13B; APS-V.10 LHS).

             17.   Applies the laws of exponents with real numbers to perform operations
                   on expressions (NM-5B, 13A, 13D; APS-V.16 LHS).

AP STATISTICS                                                                      14.8.8                       Albuquerque Public 03/04

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