· web viewthe aim of this course is to provide an introduction to the topics of statistics and...
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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
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
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
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
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
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
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
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
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:
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
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:
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