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Fayetteville Public Schools 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. 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. |
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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).
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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).
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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).
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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).
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Correlation: Understanding
The learner will be able to comprehend the idea of correlation, the measure of the relationship between two variables (Master).
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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).
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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).
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Experiment: Study/Survey
The learner will be able to differentiate between observational studies, surveys, and experiments (Master).
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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).
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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).
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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).
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Probability: Create/Models
The learner will be able to create models using probability and simulation (Master).
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Probability: Comprehend/Apply
The learner will be able to comprehend and apply probability with relative frequency definition of probability (Master).
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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).
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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).
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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).
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Variate: Discrete/Define
The learner will be able to define a discrete random variable (Master).
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Continuous Random Variable: Understand
The learner will be able to comprehend the idea of a continuous random variable (Master).
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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).
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Probability: Comprehend/Apply
The learner will be able to comprehend and apply probability with simulation of binomial and geometric probability distributions (Master).
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Probability: Law of Large Numbers
The learner will be able to describe and apply the law of large numbers (Master).
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Central Limit Theorem: Understand
The learner will be able to describe and apply the Central Limit Theorem (Master).
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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).
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Distribution Tables: Apply
The learner will be able to apply normal distribution tables and formulate inferences from these tables (Master).
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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).
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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.
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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).
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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).
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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).
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