Documents
User Generated
Resources
Learning Center

# Strand Receptive Language Listening and Viewing.doc

VIEWS: 1 PAGES: 8

• pg 1
```									APS                      DISTRICT HIGH SCHOOL MATHEMATICS CURRICULUM FRAMEWORK

Course Title: AP Statistics                                                                                    Course Number:         38022

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
optional.

COURSE DESCRIPTION:
Advanced Placement Statistics introduces the student to the major concepts and tools for collecting, analyzing, and drawing conclusions from data
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
STRATEGIES:
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).

ASSESSMENTS:
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
quizzes.

SUGGESTED TEXTBOOKS AND INSTRUCTIONAL MATERIALS:
   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

SUGGESTED TITLES/AUTHORS WEB SITES:

Approved by HSCA:

AP STATISTICS                                                                 14.2.8                                                      Albuquerque Public 03/04
STRAND I: GLOBAL MATHEMATICAL PROCESSES
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.

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
STRAND II: NUMBER SENSE AND OPERATIONS
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
thinking.

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

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

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
STRAND III: DATA ANALYSIS, STATISTICS, AND PROBABILITY
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.

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
 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
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).

STRAND IV: PATTERNS, FUNCTIONS, AND ALGEBRAIC CONCEPTS
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.

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).
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
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

```
To top