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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 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 Description:The aim of this course is to provide students with a basic understanding of the fundamental concepts of statistics and probability. The early portion of the course will cover six main introductory themes: the nature of probability and statistics, frequency distributions and graphs, data descriptions, probability and counting rules, discrete probability distributions, and the normal distribution. As the course progresses, students will be exposed to a few higher-level topics used in data analysis: confidence intervals, hypothesis testing, and linear regression. The students will have several opportunities to work from a project-based perspective—making many different real-life connections to statistics and probability. Completion of this course should give students 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 Unit 7: Confidence Intervals and Sample Size Unit 8: Hypothesis Testing Unit 9: Correlation and Regression Unit 10: Sampling and Simulation
Subject: Mathematics Course: Introductory Statistics & Probability
Suggested Timeline: 3 weeks
Unit Title: The Nature of Probability and Statistics
Unit 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 statistic
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/A
Misconceptions: 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
Competencies/Skills: Demonstrate knowledge of
statistical terms Differentiate between the two
Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration
Population Sample Descriptive Inferential Qualitative Quantitative 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
branches of statistics Identify types of data Identify the measurement level
for each variable Identify the four basic sampling
techniques Explain the difference between an
observational and experimental study
Explain how statistics can be used and misused
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 Approved supplemental resources like: USA TestPrep Approved online resources like: Khan Academy
Subject: Mathematics Course: Introductory Statistics & Probability
Suggested Timeline: 3 weeks
Unit Title: Frequency Distributions and Graphs
Unit 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/A
Misconceptions: 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
Competencies/Skills: Organize data using a frequency
distribution Represent data in frequency
distributions graphically using histograms, frequency polygons,
Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration Online remedial/enrichment videos Project: “Collecting & Organizing Data” –
Class limits Class midpoints Class width Cumulative frequency Histogram Frequency polygon Ogive Bar graph Pie graph Pareto chart Time series graph Stem-and-leaf plot
and ogives Represent data using bar graphs,
Pareto charts, time series graphs, and pie graphs
Draw and interpret and stem-and-leaf plot
Students will each visit the website of a popular restaurant of their choice. They will select several menu items and gather relevant nutritional information (calories, fat, ingredients, etc.). This information will then be classified according to data type, level of measurement, qualitative or quantitative, and discrete or continuous. Students will organize this data into frequency distribution tables and then construct appropriate statistical graphs to display the information visually.
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 Approved supplemental resources like: USA TestPrep Approved online resources like: Khan Academy
Subject: Mathematics Course: Introductory Suggested Timeline: 4 weeks
Statistics & ProbabilityUnit 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/A
Misconceptions: 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
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,
Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration Online remedial/enrichment videos
Unimodal Bimodal Multimodal Symmetric Skewed Modal class Weighted mean Range Variance Standard deviation Quartile Percentile Boxplot Interquartile range (IQR) Outlier Coefficient of variation Five-number summary z-score Empirical rule
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 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 Approved supplemental resources like: USA TestPrep
Approved online resources like: Khan Academy
Subject: Mathematics Course: Introductory Statistics & Probability
Suggested Timeline: 4 weeks
Unit Title: Probability and Counting Rules
Unit 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/A
Misconceptions: 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
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
Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration Online remedial/enrichment videos Project: “Games of Chance” – Students will
select and research different types of games of
Empirical Subjective Mutually exclusive Independent Law of large numbers Complement Conditional probability Fundamental counting rule Factorial Permutation Combination
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
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
chance. They will investigate and share the important details of each game relating to winning, losing, betting, strategies, variations, etc. A main area of focus for the students will be to make direct connections to several of the probability topics that have been covered in this unit. The students will be expected to use a combination of words, numbers, pictures, charts, and/or graphs as they communicate the descriptions of their games with each other.
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 Approved supplemental resources like: USA TestPrep Approved online resources like: Khan Academy
Subject: Mathematics Course: Introductory Statistics & Probability
Suggested Timeline: 4 weeks
Unit Title: Discrete Probability Distributions
Unit 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/A
Misconceptions: 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
Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration Online remedial/enrichment videos
standard deviation for the variable of a binomial distribution
Find probabilities for outcomes of variables using the multinomial, Poisson, and hypergeometric distributions
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 Approved supplemental resources like: USA TestPrep Approved online resources like: Khan Academy
Subject: Mathematics Course: Introductory Statistics & Probability
Suggested Timeline: 4 weeks
Unit Title: The Normal Distribution
Unit 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 The Central Limit Theorem
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 model
Important Standards Addressed in this Unit: N/A
Misconceptions: 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 Sampling error Sampling distribution Central limit theorem Standard error of the mean
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
Use the central limit theorem to
Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration Online remedial/enrichment videos Project: “Investigating Distributions” – The
students will each select a topic to research and gather data for (e.g. sports statistics, stock prices, income, populations, etc.). From this data, the students will calculate mean and standard deviation, as well as create a histogram. The histograms will then be analyzed for symmetry/skewness and modality. The students will make comparisons between their histograms and the normal distribution. The data used in this project will also be revisited in
solve problems involving sample means for large samples
the near future when class topics involve confidence intervals and hypothesis testing.
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 Approved supplemental resources like: USA TestPrep Approved online resources like: Khan Academy
Subject: Mathematics Course: Introductory Statistics & Probability
Suggested Timeline: 4 weeks
Unit Title: Confidence Intervals and Sample Size
Unit Overview/Essential Understanding: In Unit 7, the students will learn how to make a true estimate of a parameter, what is meant by the margin of error, and whether or not the sample size is large enough to properly represent the population. The very beginnings of inferential statistics will be explored with the introduction of confidence intervals.
Unit Objectives: At the end of this unit, students will have a strong understanding of and be able to independently work with:
Confidence intervals for the mean when σ is known and unknown Confidence intervals and sample size for proportions Confidence intervals for variances and standard deviations
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/A
Misconceptions: Confusion between the differences in confidence intervals for means and proportions Failure to appropriately justify all assumptions and conditions for inference
Concepts/Content: Assumptions Estimation Point estimate Confidence interval Confidence level Consistent estimator Unbiased estimator Relatively efficient estimator Interval estimate Margin of error Robust
Competencies/Skills: Find the confidence interval for
the mean when σ is known Determine the minimum sample
size for finding a confidence interval for the mean
Find the confidence interval for the mean when σ is unknown
Find the confidence interval for a proportion
Determine the minimum sample size for finding a confidence interval for a proportion
Find a confidence interval for a variance and standard deviation
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 Approved supplemental resources like: USA TestPrep Approved online resources like: Khan Academy
Subject: Mathematics Course: Introductory Statistics & Probability
Suggested Timeline: 4 weeks
Unit Title: Hypothesis Testing
Unit Overview/Essential Understanding: Unit 8 introduces students to a process called hypothesis testing. This will allow students to answer certain types of statistical questions and arrive at statistically backed conclusions. Three different methods of hypothesis testing will be explored and used throughout the unit.
Unit Objectives: At the end of this unit, students will have a strong understanding of and be able to independently work with:
The steps in hypothesis testing
Tests for a mean Tests for a proportion Tests for a variance or standard deviation Additional topics regarding hypothesis testing
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/A
Misconceptions: Confusion between the differences in the different types of tests for means and proportions Failure to appropriately justify all assumptions and conditions for inference
Concepts/Content: Null hypothesis Alternative hypothesis Hypothesis testing Test value Type I and II errors Alpha Beta One-tailed test Two-tailed test Critical value Critical region z test t test Level of significance P-value
Competencies/Skills: Understand the definitions used
in hypothesis testing State the null and alternative
hypotheses Find critical values for the z test State the five steps used in
hypothesis testing Test means when σ is known,
using the z test Test means when σ is unknown,
using the t test Test proportions, using the z test Test hypotheses, using confidence
intervals
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 Approved supplemental resources like: USA TestPrep Approved online resources like: Khan Academy
Subject: Mathematics Course: Introductory Statistics & Probability
Suggested Timeline: 4 weeks
Unit Title: Correlation and Regression
Unit Overview/Essential Understanding: The main themes of Unit 9 are correlation and regression. Students will collect and analyze data to determine if there is a linear relationship between two variables. If so, the students will then determine how strong that relationship is, as well as how to make predictions based on this relationship.
Unit Objectives: At the end of this unit, students will have a strong understanding of and be able to independently work with:
Scatter plots and correlation Regression Coefficient of determination and standard error of the estimate
Focus Standards Addressed in this Unit: CC.2.4.HS.B.2 – Summarize, represent, and interpret data on two categorical and quantitative variables
Important Standards Addressed in this Unit: N/A
Misconceptions: Attempting to fit a linear model to a curved relationship Extrapolating, or trying to make predictions beyond the bounds of the collected data
Concepts/Content: Independent variable Dependent variable Scatter plot Positive relationship Negative relationship Correlation Correlation coefficient Regression line Influential point Extrapolation Lurking variable Residual plot Standard error Coefficient of determination
Competencies/Skills: Draw a scatter plot for a set of
ordered pairs Compute the correlation
coefficient Test the hypothesis: Ho: p = 0. Compute the equation of the
regression line Compute the coefficient of
determination Compute the standard error of
the estimate Find a prediction interval
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 Approved supplemental resources like: USA TestPrep Approved online resources like: Khan Academy
Subject: Mathematics Course: Introductory Statistics & Probability
Suggested Timeline: 2 weeks
Unit Title: Sampling and Simulation
Unit Overview/Essential Understanding: In the 10th and final unit of this course, students will study various sampling techniques for gathering information from populations. There will also be some work with using simulation and random numbers to model real-life situations.
Unit Objectives: At the end of this unit, students will have a strong understanding of and be able to independently work with:
Common sampling techniques
Surveys and questionnaire design Simulation techniques
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/A
Misconceptions: Using biased or inappropriate methods for gathering a sample from a population Applying random numbers inaccurately when attempting to model real-life events
Concepts/Content: Random sample Biased sample Unbiased sample Systematic sample Stratified sample Cluster sample Convenience sample Multistage sampling Simulation technique
Competencies/Skills: Demonstrate a knowledge of the
four basic sampling methods Recognize faulty questions on a
survey and other factors that can bias responses
Solve problems, using simulation techniques
Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration Online remedial/enrichment videos Project: “Sampling and Surveys” – The students
will design and conduct surveys to gather information from their peers relating to a specific chosen topic (sports, music, politics, school, etc.). They will describe the appropriate sampling techniques and randomization strategies that they used during this process. Special attention will be paid to the design of the survey questions in order to avoid unnecessary bias whenever possible. The students will share the results of their surveys with the class and discuss how information like this could be used in a meaningful way by businesses and/or retailers.
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 Approved supplemental resources like: USA TestPrep Approved online resources like: Khan Academy