PROBABILITY AND STATISTICS - Elmwood Park …

1 APPROVED BY BOARD OF EDUCATION APRIL 29, 2014 Elmwood PARK PUBLIC SCHOOLS PROBABILITY & STATISTICS GRADE: 11 & 12 Prerequisite: Algebra 2 Credits: ABSTRACT This half year, two and one half credit course is to allow students the opportunity to study higher level mathematics dealing with the concepts and methods of both descriptive and inferential STATISTICS in addition to using PROBABILITY as a tool for predicting the statistical characteristics of collected data. This one semester course is designed for students with a wide variety of future vocational and educational ambitions. It aims to give students an understanding of the most significant concepts of PROBABILITY and STATISTICS , and to enable students to be wiser users and more critical consumers of statistical data. Key topics include measures of central tendency, graphical and statistical displays and analysis, ( , frequency tables and scatter plots), random samplings, basic PROBABILITY , normal distributions, confidence intervals and tests of significance.

2 Due to the nature of the course, all problems allow students to apply statistical techniques to real world situations and career oriented applications. Extensive technology usage is recommended through the use of calculators and computers. A prerequisite for this course is the successful completion of Algebra I, Geometry and Algebra II. In preparation for the state assessments, students will be given formative and summative assessments throughout the course. Course content is aligned with the appropriate Common Core State Standards. APPROVED BY BOARD OF EDUCATION APRIL 29, 2014 Elmwood PARK PUBLIC SCHOOLS Unit 1: Data Collection 15 Days Stage 1 Desired Results Established Goals 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.

3 (+) Use matrices to represent and manipulate data, , to represent payoffs or incidence relationships in a network. Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the PROBABILITY that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. Understand STATISTICS as a process for making inferences about population parameters based on a random sample from that population. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

4 Enduring Understanding What is STATISTICS ? What does random mean? How can data be collected / measured? Can a sample misrepresent a population? Essential Questions How is STATISTICS used in the real world? What is a population? APPROVED BY BOARD OF EDUCATION APRIL 29, 2014 Elmwood PARK PUBLIC SCHOOLS What types of samples can be used to collect data? How can a random sample be obtained? How can errors be avoided or corrected? What is the best type of experiment design for a given study? Stage 2 Assessment Evidence Performance tasks Pre-Assessment Quizzes and tests(Summative assessment) Other Evidence Checkpoint exercises Homework Oral questioning, closure, Projects Do-Nows/Exit tickets ( Formative assessment) Resources Graphing Calculators Manipulatives(when applicable) Math Literature A wide variety of Online Resources Teacher Generated Materials Stage 3 Skills and Topics Define STATISTICS Understand the process of STATISTICS Distinguish between qualitative and quantitative variables Distinguish between discrete and continuous data Distinguish between an observational study and an experiment Obtain a simple random sample Understand sources of error in sampling Understand and apply the process of experiment design APPROVED BY BOARD OF EDUCATION APRIL 29, 2014 Elmwood PARK PUBLIC SCHOOLS Applications of the various types of experiments Cross Curricular and Differentiation Shortened Tests Extended time Small group instruction Technology integration Reading Science Business Unit 2.

5 Organizing and Summarizing Data 45 Days Stage 1 Desired Results Established Goals 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. Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the PROBABILITY that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.

6 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. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. Represent data with plots on the real number line (dot plots, histograms, and box plots). APPROVED BY BOARD OF EDUCATION APRIL 29, 2014 Elmwood PARK PUBLIC SCHOOLS CC Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems CC Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, , graph paper, tracing paper, or geometry software.

7 Specify a sequence of transformations that will carry a given figure onto another. Enduring Understanding How can qualitative data be summarized? Why are graphs and plots useful to represent data? How should quantitative data be organized for understanding? What do measures of central tendency and dispersion help us understand? How can data points be compared within a set? Essential Questions What is qualitative data? What is quantitative data? How are frequency and relative frequency different? What is the difference between mean and median? Can one number greatly affect and entire set of data? Why are grouped data measures estimates? What do percentiles mean? (Think SAT) Why is the boxplot a great set summary tool? Stage 2 Assessment Evidence Performance tasks Pre-Assessment Quizzes and tests(Summative assessment) Other Evidence Checkpoint exercises APPROVED BY BOARD OF EDUCATION APRIL 29, 2014 Elmwood PARK PUBLIC SCHOOLS Homework Oral questioning, closure, Projects Do-Nows/Exit tickets ( Formative assessment) Resources Graphing Calculators Manipulatives(when applicable)

8 Math Literature A wide variety of Online Resources Teacher Generated Materials Stage 3 Skills and Topics Construct frequency and relative frequency distributions from qualitative data Construct bar graphs and pie charts Summarize discrete and continuous data in tables Construct histograms of discrete and continuous data Draw stem and leaf plots Identify the shape of a distribution Construct frequency polygons and ogives Create frequency and relative frequency tables Understand causes of misleading graphical representations of data Determine mean, median, and mode from raw data Use measures of central tendency to identify the shape of a distribution Compute the range, standard deviation, and variance of a data set Apply the Empirical Rule and Chebyshev s Theorem Compute measures of central tendency and dispersion for grouped data Apply z-scores, percentiles, and quartiles to data Check for outliers Visually represent data using boxplots APPROVED BY BOARD OF EDUCATION APRIL 29, 2014 Elmwood PARK PUBLIC SCHOOLS Cross Curricular and Differentiation Shortened Tests Extended time Small group instruction Technology integration Reading, Science Business APPROVED BY BOARD OF EDUCATION APRIL 29, 2014 Elmwood PARK PUBLIC SCHOOLS Unit 3: Bivariate Data 15 Days Stage 1 Desired Results Established Goals Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

9 Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Informally assess the fit of a function by plotting and analyzing residuals. Fit a linear function for a scatter plot that suggests a linear association. Compute (using technology) and interpret the correlation coefficient of a linear fit. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Enduring Understanding How can bivariate data be collected and organized? How can a regression line be used to gain more information about a data set? Why are predictions based on data necessary? Essential Questions How can bivariate data be graphed by hand, on the calculator, and using a computer or tablet?

10 What does r tell us about the relation between variables? Do linear models work indefinitely? How can a regression model be used to make predictions? Stage 2 Assessment Evidence Performance tasks Pre-Assessment Quizzes and tests(Summative assessment) Other Evidence Checkpoint exercises APPROVED BY BOARD OF EDUCATION APRIL 29, 2014 Elmwood PARK PUBLIC SCHOOLS Homework Oral questioning, closure, Projects Do-Nows/Exit tickets ( Formative assessment) Resources Graphing Calculators Manipulatives(when applicable) Math Literature A wide variety of Online Resources Teacher Generated Materials Stage 3 Skills and Topics Draw and interpret scatter diagrams Compute and interpret the linear correlation coefficient Find the least squares regression line Interpret the slope and y-intercept of the least squares regression line Interpolate and extrapolate data based on the least squares regression line Compute and interpret the coefficient of determination Perform residual analysis on a regression model Identify influential observations Cross Curricular and Differentiation Shortened Tests Extended time Small group instruction Technology integration Reading, Science Business APPROVED BY BOARD OF EDUCATION APRIL 29, 2014 Elmwood PARK PUBLIC SCHOOLS Unit 4.