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District Overview The mathematics curriculum provides sequential and comprehensive K-12 instruction in a collaborative, student-centered learning environment that fosters critical thinking, creativity, skillful problem-solving, and effective communication in order to enable all students to adapt to an ever-changing, global society and increase college and career readiness. An emphasis has been placed on conceptual understanding, higher-order thinking, and problem solving skills to prepare students for 21 st century careers. This is further embedded through the integrated use of technology into daily lessons. Instruction focuses on meaningful development of mathematical ideas at each grade level where students are given the opportunity to explore, engage, and take risks with content as they build and expand their knowledge and understanding of mathematics. Students will experience mathematics as a coherent and useful subject within the context of real- life situations. In all, the curriculum aims to reach high standards while encouraging curiosity and building confidence in a collaborative atmosphere. Introductory Statistics & Probability Course Description The aim of this course is to provide an introduction to the topics of statistics and probability. Six main themes will be covered in this course: the nature of probability and statistics, frequency distributions and graphs, data descriptions, probability and counting rules, and the normal distribution. Completion of this course should give the student enough of a fundamental background to enroll in other statistical courses on the college level. Introductory Statistics & Probability Units: Unit 1: The Nature of Probability and Statistics Unit 2: Frequency Distributions and Graphs Unit 3: Data Description Unit 4: Probability and Counting Rules Unit 5: Discrete Probability Distributions Unit 6: The Normal Distribution

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Page 1:  · Web viewThe aim of this course is to provide an introduction to the topics of statistics and probability. Six main themes will be covered in this course: the nature of probability

District OverviewThe mathematics curriculum provides sequential and comprehensive K-12 instruction in a collaborative, student-centered learning environment that fosters critical thinking, creativity, skillful problem-solving, and effective communication in order to enable all students to adapt to an ever-changing, global society and increase college and career readiness. An emphasis has been placed on conceptual understanding, higher-order thinking, and problem solving skills to prepare students for 21st century careers. This is further embedded through the integrated use of technology into daily lessons. Instruction focuses on meaningful development of mathematical ideas at each grade level where students are given the opportunity to explore, engage, and take risks with content as they build and expand their knowledge and understanding of mathematics. Students will experience mathematics as a coherent and useful subject within the context of real-life situations. In all, the curriculum aims to reach high standards while encouraging curiosity and building confidence in a collaborative atmosphere.

Introductory Statistics & Probability Course DescriptionThe aim of this course is to provide an introduction to the topics of statistics and probability. Six main themes will be covered in this course: the nature of probability and statistics, frequency distributions and graphs, data descriptions, probability and counting rules, and the normal distribution. Completion of this course should give the student enough of a fundamental background to enroll in other statistical courses on the college level.

Introductory Statistics & Probability Units: Unit 1: The Nature of Probability and Statistics Unit 2: Frequency Distributions and Graphs Unit 3: Data Description Unit 4: Probability and Counting Rules Unit 5: Discrete Probability Distributions Unit 6: The Normal Distribution

Page 2:  · Web viewThe aim of this course is to provide an introduction to the topics of statistics and probability. Six main themes will be covered in this course: the nature of probability

Subject: Mathematics

Course:Intro Stat & Prob

Suggested Timeline: 2 weeks

Unit Title: The Nature of Probability and StatisticsUnit Overview/Essential Understanding: In Unit 1, students will be introduced to many important terms and ideas in the world of statistics. They will practice identifying and classifying many different types of data, as well as discuss the main methods for gathering data. The unit finishes with having the students investigate several uses and misuses of statistics in the real world. Unit Objectives: At the end of this unit, students will have a strong understanding of and be able to independently work with:

Descriptive and inferential statistics Variables and types of data Data collection and sampling techniques Observational and experimental studies Uses and misuses of statistics

Focus Standards Addressed in this Unit: CC.2.4.HS.B.1 – Summarize, represent, and interpret data on a single count or measurement variable

Important Standards Addressed in this Unit:N/AMisconceptions:

General confusion between discrete and continuous types of data Knowing when to use (and when not to use) different sampling techniques Being aware of common misuses of statistics in advertising

Concepts/Content: Data Statistics Probability Variable Population Sample Descriptive Inferential Qualitative Quantitative

Competencies/Skills: Demonstrate knowledge of

statistical terms Differentiate between the two

branches of statistics Identify types of data Identify the measurement level

for each variable Identify the four basic sampling

techniques

Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration Online remedial/enrichment videos

Page 3:  · Web viewThe aim of this course is to provide an introduction to the topics of statistics and probability. Six main themes will be covered in this course: the nature of probability

Discrete Continuous Level of measurement Random sample Stratified sample Cluster sample Systematic sample Observational study Experimental study Treatment Control group Hawthorne effect Placebo effect Confounding variable

Explain the difference between an observational and experimental study

Explain how statistics can be used and misused

Assessments: informal questioning in-class formative assessments review of homework periodic quizzes unit test

Interdisciplinary Connections:N/A

Additional Resources: Elementary Statistics: A Step-By-Step Approach textbook USA TestPrep

Subject: Mathematics

Course:Intro Stat & Prob

Suggested Timeline: 3 weeks

Page 4:  · Web viewThe aim of this course is to provide an introduction to the topics of statistics and probability. Six main themes will be covered in this course: the nature of probability

Unit Title: Frequency Distributions and GraphsUnit Overview/Essential Understanding: In Unit 2, students will start to learn what to do with raw data after it has been collected. They will create frequency distribution tables to being to organize data in a meaningful way. Once organized, the data can then be put into several different visual displays or graphs. The students will not only learn how to create each different type of data display, but also how to choose which one would be appropriate for given situations.Unit Objectives: At the end of this unit, students will have a strong understanding of and be able to independently work with:

Organizing data Histograms, frequency polygons, and ogives Other types of graphs

Focus Standards Addressed in this Unit: CC.2.4.HS.B.5 – Make inferences and justify conclusions based on sample surveys, experiments, and observational studies

Important Standards Addressed in this Unit:N/AMisconceptions:

Making miscalculations with constructing frequency distributions Using the wrong scales and/or data for the x- and y-axes on graphs Choosing the wrong type of visual display to present data

Concepts/Content: Class Frequency Raw data Categorical frequency distribution Grouped frequency distribution Class boundaries Class limits Class midpoints Class width Cumulative frequency Histogram Frequency polygon Ogive Bar graph

Competencies/Skills: Organize data using a frequency

distribution Represent data in frequency

distributions graphically using histograms, frequency polygons, and ogives

Represent data using bar graphs, Pareto charts, time series graphs, and pie graphs

Draw and interpret and stem-and-leaf plot

Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration Online remedial/enrichment videos

Page 5:  · Web viewThe aim of this course is to provide an introduction to the topics of statistics and probability. Six main themes will be covered in this course: the nature of probability

Pie graph Pareto chart Time series graph Stem-and-leaf plot

Assessments: informal questioning in-class formative assessments review of homework periodic quizzes unit test

Interdisciplinary Connections:N/A

Additional Resources: Elementary Statistics: A Step-By-Step Approach textbook USA TestPrep

Subject: Mathematics

Course:Intro Stat & Prob

Suggested Timeline: 4 weeks

Unit Title: Data Descriptions

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Unit Overview/Essential Understanding: Unit 3 will have students summarizing the central tendency of data. Examples of this will involve mean, median, and mode, among other methods. The students will also use range, variance, and standard deviation to summarize the variation of data. Percentiles, quartiles, and z-scores will help students to measure the position of data values in the set.Unit Objectives: At the end of this unit, students will have a strong understanding of and be able to independently work with:

Measures of central tendency Measures of variation Measures of position Exploratory data analysis

Focus Standards Addressed in this Unit: CC.2.4.HS.B.3 – Analyze linear models to make interpretations based on data

Important Standards Addressed in this Unit:N/AMisconceptions:

Arithmetic errors when calculating measures of central tendency Mistakes when calculating variance and standard deviation on a calculator Misinterpreting how to handle outliers in a data set

Concepts/Content: Mean Median Mode Midrange Parameter Statistic Unimodal Bimodal Multimodal Symmetric Skewed Modal class Weighted mean Range Variance

Competencies/Skills: Summarize data using measures

of central tendency such as the mean, median, mode, and midrange

Describe data using measures of variation such as the range, variance, and standard deviation

Identify the position of a data value in a data set using various measures of position such as z-scores, percentiles, and quartiles

Use the techniques of exploratory data analysis including boxplots and five-number summaries to

Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration Online remedial/enrichment videos

Page 7:  · Web viewThe aim of this course is to provide an introduction to the topics of statistics and probability. Six main themes will be covered in this course: the nature of probability

Standard deviation Quartile Percentile Boxplot Interquartile range (IQR) Outlier Coefficient of variation Five-number summary z-score Empirical rule

discover various aspects of data

Assessments: informal questioning in-class formative assessments review of homework periodic quizzes unit test

Interdisciplinary Connections:N/A

Additional Resources: Elementary Statistics: A Step-By-Step Approach textbook USA TestPrep

Subject: Mathematics

Course:Intro Stat & Prob

Suggested Timeline: 4 weeks

Unit Title: Probability and Counting RulesUnit Overview/Essential Understanding: In Unit 4, the students will learn about the basics of probability—in particular, the three types: classical, empirical, and subjective. They will

Page 8:  · Web viewThe aim of this course is to provide an introduction to the topics of statistics and probability. Six main themes will be covered in this course: the nature of probability

work with situations involving mutually exclusive (and non-mutually exclusive) events and the addition rules. There will also be work with independent (and dependent) events and the multiplication rules. The unit finishes with the students working with several of the counting rules and how they relate to probability situations.Unit Objectives: At the end of this unit, students will have a strong understanding of and be able to independently work with:

Sample spaces and probability The addition rules for probability The multiplication rules and conditional probability Counting rules Probability and counting rules

Focus Standards Addressed in this Unit: CC.2.4.HS.B.4 – Recognize and evaluate random processes underlying statistical experiments

Important Standards Addressed in this Unit:N/AMisconceptions:

Misunderstandings involving the concepts of mutually exclusive events and independent events Confusion over whether a situation involves permutations or combinations Difficulty turning a real-life situation into a probability problem

Concepts/Content: Probability Sample space Outcome Event Tree diagram Venn diagram Classical Empirical Subjective Mutually exclusive Independent Law of large numbers Complement Conditional probability Fundamental counting rule

Competencies/Skills: Determine sample spaces and find

the probability of an event, using classical probability or empirical probability

Find the probability of compound events using the addition rules

Find the probability of compound events using the multiplication rules

Find the conditional probability of an event

Find the total number of outcomes in a sequence of events using the fundamental counting rule

Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration Online remedial/enrichment videos

Page 9:  · Web viewThe aim of this course is to provide an introduction to the topics of statistics and probability. Six main themes will be covered in this course: the nature of probability

Factorial Permutation Combination

Find the number of ways that r objects can be selected from n objects using the permutation rule

Find the number of ways that r objects can be selected from n objects using the combination rule

Find the probability of an event using the counting rules

Assessments: informal questioning in-class formative assessments review of homework periodic quizzes unit test

Interdisciplinary Connections:N/A

Additional Resources: Elementary Statistics: A Step-By-Step Approach textbook USA TestPrep

Subject: Mathematics

Course:Intro Stat & Prob

Suggested Timeline: 3 weeks

Unit Title: Discrete Probability DistributionsUnit Overview/Essential Understanding: Unit 5 will have students working with discrete probability distributions, in particular the values that random variables can assume and the corresponding probabilities of these values. The students will also work to find the mean, variance, standard deviation, and expectation of these discrete random variables. Several other types of distributions will be discussed as well in this unit: binomial, multinomial, Poisson, and hypergeometric.Unit Objectives:

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At the end of this unit, students will have a strong understanding of and be able to independently work with: Probability distributions Mean, variance, standard deviation, and expectation The binomial distribution Other types of distributions

Focus Standards Addressed in this Unit: CC.2.4.HS.B.6 – Use the concepts of independence and conditional probability to interpret data

Important Standards Addressed in this Unit:N/AMisconceptions:

Difficulty creating a probability distribution from real-life information Arithmetic errors when calculating mean, variance, standard deviation, and expectation Confusion over which type of probability distribution is relevant to a certain situation

Concepts/Content: Random variable Discrete probability distribution Expected value Binomial distribution Binomial experiment Multinomial distribution Poisson distribution Hypergeometric distribution

Competencies/Skills: Construct a probability

distribution for a random variable Find the mean, variance, standard

deviation, and expected value for a discrete random variable

Find the exact probability for X successes in n trials of a binomial experiment

Find the mean, variance, and standard deviation for the variable of a binomial distribution

Find probabilities for outcomes of variables using the multinomial, Poisson, and hypergeometric distributions

Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration Online remedial/enrichment videos

Assessments: informal questioning in-class formative assessments

Page 11:  · Web viewThe aim of this course is to provide an introduction to the topics of statistics and probability. Six main themes will be covered in this course: the nature of probability

review of homework periodic quizzes unit test

Interdisciplinary Connections:N/A

Additional Resources: Elementary Statistics: A Step-By-Step Approach textbook USA TestPrep

Subject: Mathematics

Course:Intro Stat & Prob

Suggested Timeline: 2 weeks

Unit Title: The Normal DistributionUnit Overview/Essential Understanding: In Unit 6 the students will learn all about the normal model and the normal distribution. They will use the normal distribution to describe a variety of different variables, and also use it to solve a wide variety of different problems.Unit Objectives: At the end of this unit, students will have a strong understanding of and be able to independently work with:

Normal distributions Applications of the normal distribution

Focus Standards Addressed in this Unit:

Page 12:  · Web viewThe aim of this course is to provide an introduction to the topics of statistics and probability. Six main themes will be covered in this course: the nature of probability

CC.2.4.HS.B.7 – Apply rules of probability to compute probabilities of compound events in a uniform probability modelImportant Standards Addressed in this Unit:N/AMisconceptions:

Accidently trying to apply the normal model to a skewed or non-normal distribution Mistakes with calculating z-scores and/or finding their corresponding percentages

Concepts/Content: Symmetric distribution Skewed distribution Normal distribution z-score Standard normal distribution

Competencies/Skills: Identify distributions as

symmetric or skewed Identify the properties of a

normal distribution Find the area under the standard

normal distribution, given various z values

Find probabilities for a normally distributed variable by transforming it into a standard variable

Find specific data values for given percentages using the standard normal distribution

Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration Online remedial/enrichment videos

Assessments: informal questioning in-class formative assessments review of homework periodic quizzes unit test

Interdisciplinary Connections:N/A

Additional Resources: Elementary Statistics: A Step-By-Step Approach textbook USA TestPrep