probability and statistics curriculum pacing guide 2012-2013 · 2012-07-18 · probability and...

Probability and Statistics – Curriculum Pacing Guide – 2012-2013

Anderson School District Five Copyright July 1, 2012

The mathematical processes provide the framework for teaching, learning, and assessing in all high school mathematics core courses. Instructional programs should be built around these processes.

Standard DA-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

Indicators

DA-1.1 Execute procedures to conduct simple probability experiments and collect data by using manipulatives (including spinners, dice, cards, and coins)

DA-1.2 Execute procedures to find measures of probability and statistics by using tools such as handheld computing devices, spreadsheets, and statistical software

DA-1.3 Execute procedures to conduct a simulation by using random number tables and/or technology (including handheld computing devices and computers)

DA-1.4 Design and conduct a statistical research project and produce a report that summarizes the findings

DA-1.5 Apply the principles of probability and statistics to solve problems in real-world contexts

DA-1.6 Communicate a knowledge of data analysis and probability by using mathematical terminology appropriately

DA-1.7 Judge the reasonableness of mathematical solutions on the basis of the source of the data, the design of the study, the way the data are displayed, and the way the data are analyzed

DA-1.8 Compare data sets by using graphs and summary statistics


First Nine Weeks


Unit 1 – Terms AB – 5 days

Indicators Essential Tasks Activities Resources

DA-4.2 Compare descriptive and inferential statistics.

Differentiate between descriptive and inferential statistics.

1. Random Rectangles Lab 2. Farm Activity 3. Newspaper Activity

Chapter 1

DA-4.3 Classify a variable as either discrete or continuous and as either categorical or quantitative

Identify and classify variables as discrete or continuous and qualitative or quantitative.

DA-4.1 Classify a variable as either a statistic or a parameter

Distinguish between a statistic and a parameter.

DA-2.1 Classify a data-collection procedure as a survey, an observational study, or a controlled experiment.

Identify and classify methods of data collection as a survey, an observational study, or a controlled experiment

DA-2.2, 2.3

Compare various random sampling techniques (including simple, stratified, cluster, and systematic). Analyze a data-collection procedure to classify the technique used as either simple cluster, systematic, or convenience sampling.

Compare various random sampling techniques including simple, stratified, cluster, and systematic.

DA-2.4 Critique data-collection methods and describe how bias can be controlled.

Define bias and explain how you can minimize it.

DA-2.5 Judge which of two or more possible experimental designs will best answer a given research question.

Evaluate experimental designs


First Nine Weeks


Unit 2 – Tables and Graphs AB – 5 days


DA-3.2

Organize and interpret data by using pictographs, bar graphs, pie charts, dot plots, histograms, time-series plots, stem-and-leaf plots, box-and-whiskers plots, and scatterplots.

Construct dot plots, pictograph, time-series, circle graphs, bar graphs, dot plots, Pareto charts, categorical frequency distribution, and stem and leaf plots. Construct frequency distribution, histogram, frequency polygon, and ogive.

1. Lab: Qualitative vs. Quantitative

2. Stock Tracker Activity

Chapter 2

DA-3.3

Select appropriate graphic display(s) from among pictographs, bar graphs, pie charts, dot plots, histograms, time-series plots, stem-and-leaf plots, box-and-whiskers plots, and scatterplots when given a data set or problem situation.

DA-3.4

Represent frequency distributions by using displays such as categorical frequency distributions/Pareto charts, histograms, frequency polygons, and cumulative frequency distributions/ogives.

DA-4.8 Classify a distribution as either symmetric, positively skewed, or negatively skewed

Describe the skewness and symmetry of a graph


First Nine Weeks


Unit 3 – Measures of Central Tendency, Variation, and Position AB – 10 days


DA-4.4

Use procedures and/or technology to find measures of central tendency (mean, median, and mode) for given data.

Determine the mean, median, mode, and midrange of a data array by hand and using graphing calculator. Determine the range, variance, and standard deviation of a data array by hand and using graphing calculator. Determine the mean, median, and mode for ungrouped and grouped data by hand. (Show on graphing calculator after test)

1. Hand Span Lab 2. Unit 2 and 3 Project

Chapter 2

DA-4.6

Use procedures and/or technology to find measures of spread (range, variance, standard deviation, and interquartile range) and outliers for given data.

Determine the variance and standard deviation for ungrouped and grouped data by hand. (Show on graphing calculator after test)

DA-4.7

Use procedures and/or technology to find measures of position (including median, quartiles, percentiles, and standard scores) for given data.

Determine z-scores and discuss and apply the empirical rule

DA-4-10 Use a knowledge of the empirical rule to solve problems involving data that are distributed normally.


First Nine Weeks




DA-4.6

Use procedures and/or technology to find measures of spread (range, variance, standard deviation, and interquartile range) and outliers for given data. Determine quartiles, percentiles, and

Interquartile range.

Chapter 2

DA-4.7


DA-3.2


Draw box-and-whisker plots and determine outliers

DA-3.3



First Nine Weeks




DA-4.6

Use procedures and/or technology to find measures of spread (range, variance, standard deviation, and interquartile range) and outliers for given data.

DA-4.9 Explain the significance of the shape of a distribution.

DA-4.5

Predict the effect of transformations of data on measures of central tendency, variability, and the shape of the distribution.

Predict the effect of transformations of data on measures of central tendency, variability, and the shape of the distribution.

Review and First Nine Weeks Test


First Nine Weeks



Second Nine Weeks


Unit 4 – Descriptive Analysis and Presentation of Bivariate Data AB – 7 days


DA-3.2


Constructing contingency tables and scatter plots for bivariate data. Classify a scatterplot by shape including linear, quadratic, and exponential.

1. Guess My Age 2. M & M Lab 3. Cooling Coffee

Chapter 3

DA- 3.3


DA-3.5 Classify a scatterplot by shape (including linear, quadratic, and exponential).

DA-3.6 Classify graphically and analytically the correlation between two variables as either positive, negative, or zero.

Describe the linear correlation between two variables as positive, negative, or no correlation. Determine and explain the correlation coefficient. DA- 3.9

Explain the meaning of the correlation coefficient r.


Second Nine Weeks


Unit 4 – Descriptive Analysis and Presentation of Bivariate Data AB – 7 days


DA-3.7

Carry out a procedure to determine an equation of a trend line for a scatterplot exhibiting a linear pattern by using visual approximation. Determine the line of best fit with

visual approximation and technology and understand the meaning of the y-intercept and the slope

Chapter 3 DA-3.8

Carry out a procedure using technology to determine a line of best fit for a scatterplot exhibiting a linear pattern.

DA- 3.10 Use interpolation or extrapolation to predict values based on the relationship between two variables.

Make predictions using the line of best fit by using interpolation or extrapolation


Second Nine Weeks


Unit 5 – Counting Rules AB – 5 days


DA-5.1 Construct a sample space for an experiment and represent it as a list, chart, picture, or tree diagram.

Display sample spaces

1. Turkey 2. nPr/nCr Activity

Chapter 4

DA-3.1

Use manipulatives, random number tables, and technology to collect data and conduct experiments and simulations.

DA-5.2 Use counting techniques to determine the number of possible outcomes for an event.

Determine the probability of an event using counting rules (permutations) with and without replacement. Determine the probability of an event using combinations. Determine whether a probability problem is a permutation or a combination and solve it.

DA- 3.1


Review and Second Nine Weeks Exam (if test before Holiday Break)


Second Nine Weeks


Unit 6 – Probability AB – 7 days


DA-5.12 Understand the law of large numbers.

Use the Law of Large Numbers in probability experiments.

1. Is This Game Fair? 2. M & M 3. Let’s Race

Chapter 4

DA-3.1


DA-5.7

Carry out a procedure to compute simple probabilities and compound probabilities (including conditional probabilities).

Determine the theoretical probability of an event. Compare theoretical and experimental probabilities.

DA-5.9 Compare theoretical and experimental probabilities.

DA-5.5 Use the concept of complementary sets to compute probabilities.

Use the concept of complementary sets to compute probabilities.

DA-5.4 Categorize two events either as mutually exclusive or as not mutually exclusive of one another.

Categorize two events either as mutually exclusive or as not mutually exclusive of one another. Use the addition rule to find the probability of mutually exclusive events.

DA-5.2 Use counting techniques to determine the number of possible outcomes for an event.

Classify events as either dependent or independent. Use the multiplication rule to find the probability of independent and dependent events. DA- 5.3

Classify events as either dependent or independent.


Second Nine Weeks


Unit 6 – Probability AB – 7 days



DA-5.7

Carry out a procedure to compute simple probabilities and compound probabilities (including conditional probabilities).

Find conditional probability

Chapter 4 DA- 5.13 Carry out a procedure to compute conditional probability by using two-way tables.

DA-5.8 Use a procedure to find geometric probability in real-world contexts.

Use a procedure to find geometric probability in real-world contexts.

Review and Second Nine Weeks Exam (if test at end of nine weeks)


Second Nine Weeks



Third Nine Weeks


Unit 7 – Probability Distribution AB – 3 days


DA-5.10 Construct and compare theoretical and experimental probability distributions. Identify random variables. Determine

the probability distribution of a discrete random variable and graph.

Chapter 5

DA-4.3 Classify a variable as either discrete or continuous and as either categorical or quantitative.

SC DA-5.11

CCSS

S-MD.1

S-MD.2

S-MD.3

S-MD.4

Use control charts to determine whether a process is in control. (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. (+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. (+) Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. (+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.

Determine the mean, variance, and standard deviation of a discrete probability distribution. Use procedures to find the expected value of discrete random variables and construct meaning within contexts.


Third Nine Weeks


Unit 8 – Binomial Distribution AB – 4 days


DA-5.6 Use the binomial probability distribution to solve problems.

Determine the probability of a specific number of trials from a binomial experiment using graphing calculators for a real world problem. Determine the mean and standard deviation of a binomial distribution.

Chapter 5


Third Nine Weeks


Unit 9 – Normal Probability Distributions AB – 8 days


DA-4.10 Use a knowledge of the empirical rule to solve problems involving data that are distributed normally.

Identify properties of a normal distribution and find the area under the standard normal curve using tables and graphing calculators.

Chapter 6 DA-4.7


Determine the z-score for a given probability.

Solve real life applications involving the normal distributions (finding area, probability, and cut-off scores)


Third Nine Weeks


-

Unit 10 – Sample Variability AB – 5 days


Forming a sampling distribution of means and ranges.

Chapter 7

Constructing a sampling distribution of sample means and proportions using the central limits theorem.

Applications involving the central limits theorem.

Review and Third Nine Weeks Test


Fourth Nine Weeks


Unit 11 – Confidence Intervals and Minimum Sample Size AB – 6 days


CCSS S-MD.5a

S-MD.5b

Find the expected payoff for a game of chance. Evaluate and compare strategies on the basis of expected values.

Determine the confidence interval for the mean for a large sample.

1. Baseball Project

Chapter 8

Determine the minimum sample size for a large sample (z)

Determine the confidence interval for the mean of a small sample.

1. M & M Lab

Chapter 9 Determine the confidence interval for a proportion.

Determine the minimum sample size for a proportion.

Determine the confidence interval for a variance and standard deviation (chi-squared).


Fourth Nine Weeks


Unit 12 – One-Sample Hypothesis Testing AB – 6 days


CCSS S-MD.5a

S-MD.5b


Understanding the techniques of hypothesis testing.

Chapter 8 Investigate type I and type II errors.

Perform hypothesis testing for a large sample size

Perform hypothesis testing for a large sample size using the p-value

Chapter 9

Perform hypothesis testing for a small sample size

Perform hypothesis testing for a proportion

Perform hypothesis testing for chi-squared.


Fourth Nine Weeks


Unit 13 – Two-Sample Hypothesis Testing AB – 5 days


CCSS S-MD.5a

S-MD.5b


Perform hypothesis testing for the mean using the p-value.

Chapter 10

With time permitting you can do more two-sample tests.


Fourth Nine Weeks


Unit 14 – Quality Control AB – 3 days


DA-4.11 Use control charts to determine whether a process is in control.

Use control charts to determine whether a process is in control. (x-bar, r-bar, p-bar, c-bar charts)

Bluman 2nd Ed., Ch. 11

Review and Final Exam

Teacher needs to address Indicator DA-2.6 throughout units. DA-2.6: Generate a research question and design a statistical study to answer a given research question.

probability and statistics curriculum pacing guide 2012-2013 · 2012-07-18 · probability and...

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