Fayetteville Public Schools
Mathematics Curriculum

Mathematics - AP Statistics

Mathematics

The vision is that students will be avid mathematical problem solvers, will communicate mathematically (listen, speak, read, write, and reflect), will reason mathematically using basic and higher-order thinking skills concurrently, and will make connections within mathematics as well as between mathematics and other disciplines.

Incorporating technology in instruction is imperative in order to empower students to keep pace with the information age and to be competitive in the job market; it will enhance and provide flexibility in the learning environment. Calculators and computers are essential tools for learning and doing mathematics at all grade levels. Students should be able to solve practical problems, investigate patterns, explore strategies, and focus on the process of solving problems rather than on tedious computation unrelated to applications.

The Mathematics curriculum for Fayetteville Public Schools incorporates national and state standards as well as standards derived from the Mathematics section of the state benchmark -course exams, the Stanford Achievement Test, Version 9, the SAT and the ACT.
The Benchmark Exams are criterion-referenced exams administered at the end of grades 4, 6, and 8 and designed to test proficiency of students in Arkansas Mathematics Content Standards and Student Learning Expectations.
The Algebra I and Geometry End of Course Tests are criterion-referenced tests administered at the end of each course.

Arkansas' Learning Standards and Student Learning Expectations are defined in the Arkansas Curriculum Frameworks (http://arkedu.state.ar.us/frameworks), discipline-based documents which clearly describe what students must know and be able to do in the area of Mathematics at three critical levels: grades 4, 8, and 12. The rigorous academic content standards and the student learning expectations within each document provide the focus for instruction for each local school district, without rigidly prescribing every element of the local curriculum. Student demonstration of the standards and learning expectations within the Arkansas Frameworks is the anchor for the entire education system, with instructional programs, state-level assessments, professional development, school improvement planning, teacher/administrator licensure, and accountability sharing the common goal of improved student learning and performance around these standards.


The Frameworks establish the basis for a challenging program of study that will increase student achievement in mathematics. The content standards may be expanded and enhanced at the discretion of local school systems, but may not be deleted or replaced.

AP Statistics

Each grade level or course curriculum designates competencies and objectives necessary to develop students' understanding and use of mathematical concepts and skills through increasingly complex mathematical experiences. The goal of each grade level or course curriculum is to narrow the focus of instruction and student learning in order to allow students' to engage in learning the competencies and objectives in depth through a variety of contexts. The grade level or course curricula have been vertically aligned to prepare students for proficiency at the state benchmark levels.


Probability/Statistics

    Data Analysis: Summarize/Distributions
The learner will be able to summarize distribution of univariate data and accurately determine and apply: measure of center (mean, median, mode), measures of spread (range, interquartile range, standard deviation), and measures of position (quartiles, percentiles, standardized scores) (Master).
Bloom's Source
Comprehension 2001-2002 AP Statistics, College Board
  
    Data Analysis: Interpret/Distributions
The learner will be able to interpret and compare graphical representations of distributions of univariate data (dotplots, stemplots, boxplots, histograms, frequency tables) focusing on center and spread, clusters, outliers, and other unusual features and shapes (Master).
Bloom's Source
Evaluation 2001-02 AP Statistics--College Board
  
    Data: Univariate/Summary Measures
The learner will be able to study the effect of changing units on summary measures in order to summarize distributions of univariate data (Master).
Bloom's Source
Knowledge 2001-02 AP Statistics--College Board
  
    Probability Distribution: Comprehend
The learner will be able to comprehend normal distributions through their properties, models for distributions of measurements, and tables of standard normal probability (Z) (Master).
Bloom's Source
Comprehension 2001-02 AP Statistics--College Board
  
    Correlation: Understanding
The learner will be able to comprehend the idea of correlation, the measure of the relationship between two variables (Master).
Bloom's Source
Comprehension 2001-02 AP Statistics--College Board
  
    Data Analysis: Investigate/Bivariate
The learner will be able to investigate bivariate data by studying patterns in scatterplots, residual plots, outliers, influential points, performing logarithmic and power transformations to achieve linearity, determining least squares regression lines, and finding correlation coefficients (Master).
Bloom's Source
Analysis 2001-02 AP Statistics--College Board
  
    Data: Study/Categorical
The learner will be able to study categorical data using frequency tables, marginal and joints frequencies for two-way tables, and conditional relative frequencies and association (Master).
Bloom's Source
Knowledge 2001-02 AP Statistics--College Board
  
    Experiment: Study/Survey
The learner will be able to differentiate between observational studies, surveys, and experiments (Master).
Bloom's Source
Analysis 2001-02 AP Statistics--College Board
  
    Data Collection: Comprehend/Compare
The learner will be able to comprehend and compare strategies of data collection including census, sample survey, designed experiment, and observational study (Master).
Bloom's Source
Analysis 2001-02 AP Statistics--College Board
  
    Sample Surveys: Comprehend
The learner will be able to comprehend principles, strategies, and difficulties in sample surveys including simple random sampling and systematic sampling, sampling error (the variation inherent in a survey), stratifying to reduce variation, cluster sampling, and sources of bias (Master).
Bloom's Source
Comprehension 2001-02 AP Statistics--College Board
  
    Experiments: Comprehend
The learner will be able to comprehend principles, strategies, and difficulties in designed experiments including the following: confounding variables, control groups, placebo effects, blinding, randomization, replication, paired comparisons, treatments, and experimental units (Master).
Bloom's Source
Comprehension 2001-02 AP Statistics--College Board
  
    Probability: Create/Models
The learner will be able to create models using probability and simulation (Master).
Bloom's Source
Application 2001-02 AP Statistics--College Board
  
    Probability: Comprehend/Apply
The learner will be able to comprehend and apply probability with relative frequency definition of probability (Master).
Bloom's Source
Application 2001-02 AP Statistics--College Board
  
    Probability Distributions: Apply
The learner will be able to apply a knowledge and familiarity of the normal, binomial, and exponential distributions in obtaining solutions to problems where these distributions are involved (Master).
Bloom's Source
Application 2001-02 AP Statistics--College Board
  
    Probability Function: Density/Area
The learner will be able to interpret the probability of an event as the area of the region under the graph of a probability density function connected to the random variable (Master).
Bloom's Source
Analysis, Evaluation 2001-02 AP Statistics--College Board
  
    Probability: Use/Determine
The learner will be able to apply the concepts of independent and mutually exclusive events, and use the addition, multiplication, and conditional probability rules to determine the probability of events (Master).
Bloom's Source
Application 2001-02 AP Statistics--College Board
  
    Variate: Discrete/Define
The learner will be able to define a discrete random variable (Master).
Bloom's Source
Knowledge 2001-02 AP Statistics--College Board
  
    Continuous Random Variable: Understand
The learner will be able to comprehend the idea of a continuous random variable (Master).
Bloom's Source
Comprehension 2001-02 AP Statistics--College Board
  
    Random Variable: Determine/Mean
The learner will be able to determine the mean and standard deviation of a random variable and the mean and standard deviation for the sums and differences of independent random variables (Master).
Bloom's Source
Analysis 2001-02 AP Statistics--College Board
  
    Probability: Comprehend/Apply
The learner will be able to comprehend and apply probability with simulation of binomial and geometric probability distributions (Master).
Bloom's Source
Application 2001-02 AP Statistics--College Board
  
    Probability: Law of Large Numbers
The learner will be able to describe and apply the law of large numbers (Master).
Bloom's Source
Comprehension, Application 2001-02 AP Statistics--College Board
  
    Central Limit Theorem: Understand
The learner will be able to describe and apply the Central Limit Theorem (Master).
Bloom's Source
Application 2001-02 AP Statistics--College Board
  
    Sampling: Comprehend/Simulate
The learner will be able to comprehend and simulate sampling distributions for sample proportion, sample mean, difference between two independent sample proportions, and difference between two independent sample means (Master).
Bloom's Source
Synthesis 2001-02 AP Statistics--College Board
  
    Distribution Tables: Apply
The learner will be able to apply normal distribution tables and formulate inferences from these tables (Master).
Bloom's Source
Evaluation 2001-02 AP Statistics--College Board
  
    Statistical Analysis: Hypotheses
The learner will be able to write null and alternate hypotheses for studies, differentiate between one and two-sided test, compute appropriate test statistics, determine p-values, come to appropriate conclusions, and describe those conclusions effectively (Master).
Bloom's Source
Evaluation 2001-02 AP Statistics--College Board
  
    Statistics: Test Significance
The learner will be able to appropriately apply tests for significance to include the following: large sample tests for a proportion, a mean, a difference between two proportions, and a difference between two means (unpaired and paired); Chi-square test for goodness of fit, homogeneity of proportions, and independence; single sample and two sample t-procedures; and inference for slope of least squares line.
Bloom's Source
Evaluation 2001-02 AP Statistics--College Board
  
    Sample: Determine/Interpret
The learner will be able to determine and interpret large sample confidence intervals for a proportion, a mean, a difference between two proportions, a difference between two means, and the slope of the least squares line (using a z or t distribution) (Master).
Bloom's Source
Evaluation 2001-02 AP Statistics--College Board
  
    Confidence Intervals: Sample Size
The learner will be able to figure out the correct sample size that is necessary for a desired margin of error (Master).
Bloom's Source
Analysis 2001-02 AP Statistics--College Board
  
    Data: Develop/Study
The learner will be able to develop a study by clarifying a question and deciding upon a strategy of data collection and analysis (Master).
Bloom's Source
Synthesis 2001-02 AP Statistics--College Board
  

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