Curriculum Documents by Quarter - Mathematics Grade #

Unit of Study 1: Statistics
Standards
Essential Questions

Learning Objectives

 

§     construct and draw inferences from charts, tables, and graphs that summarize data from real-world situations;

§     use curve fitting to predict from data;

§     understand and apply measures of central tendency, variability, and correlation;

§     understand sampling and recognize its role in statistical claims;

§     design a statistical experiment to study a problem, conduct the experiment, and interpret and communicate the outcomes;

§     analyze the effects of data transformations on measures of central tendency and variability;

§     transform data to aid in data interpretation and prediction;

test hypotheses using appropriate statistics.

 

§     How do patterns and relationships help us understand mathematical situations?

§     How do we represent patterns and relationships in everyday life?

§     How can change be analyzed?

§     What are the measurable attributes of objects and what are the units, systems and processes of measurement?

§     How do you organize data to make it understandable?

§     How do you infer and evaluate predictions from data?

§     Which strategies and mathematical operations are used to solve problems?

§     How do we monitor and reflect on the process of mathematical problem solving?

§     How can mathematical thinking be organized and presented so that it can be shared with others?

§     How can we develop a mathematical language that is useful in the real world?

§     What are the relationships between mathematical concepts?

§     How can mathematics be used in other disciplines?

§     How is math used in the real world?

§     How can we use representations to model and interpret physical, social and mathematical phenomena?

 Vocabulary

  • ·        Random variable

    ·        Descriptive Statistics

    ·        Population

    ·        Sample

    ·        Hypothesis Testing

    ·        Inferential Statistics

    ·        Discrete vs. Continuous Variable

    ·        Nominal Level of Measurement

    ·        Ordinal Level of Measurement

    ·        Interval Level of Measurement

    ·        Ratio Level of Measurement

    ·        Random Sample

    ·        Systematic Sample

    ·        Stratified Sample

    ·        Cluster Sample

    ·        Observational Study vs. Experimental Study

    ·        Confounding Variable

    ·        Suspect Sample

    ·        Ambiguous Average

    ·        Changing the Subject

    ·        Detached Statistics

    ·        Implied Connections

    ·        Misleading Graphs

    ·        Faulty Survey Questions

    ·        Class Boundaries

    ·        Class Midpoint

    ·        Class Width

    ·        Cumulative Frequency

    ·        Frequency

    ·        Frequency Polygon

    ·        Histogram

    ·        Ogive

    ·        Pareto Chart

    ·        Pie Graph

    ·        Stem and leaf Plot

    ·        Time Series Graph

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 four basic sampling techniques

·         Explain the difference between an observational study and an experimental study

·         Explain how statistics can be used or misused

·         Explain the importance of computers and calculators in statistics

·         Organize data using frequency distributions

·         Represent data in frequency distributions graphically using histograms, frequency polygons, and ogives

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

·         Draw and interpret a stem and leaf plot

·         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 percentiles, deciles, and quartiles

Use the techniques of exploratory data analysis, including boxplots and five-number summaries, to discover various aspects of data.

Unit of Study 2:

 

§      Construct and draw inferences from charts, tables, and graphs that summarize data from real-world situations;

§      Understand and apply measures of central tendency, variability, and correlation;

§      Design a statistical experiment to study a problem, conduct the experiment, and interpret and communicate the outcomes;

§      Test hypotheses using appropriate statistics.

§      Develop an understanding of permutations and combinations as counting techniques.

§      know the characteristics of well-designed studies, including the role of randomization in surveys and experiments;

§      Understand histograms, parallel box plots, and scatterplots and use them to display data;

§      for univariate measurement data, be able to display the distribution, describe its shape, and select and calculate summary statistics;

§      Evaluate published reports that are based on data by examining the design of the study, the appropriateness of the data analysis, and the validity of conclusions;

§      Understand how basic statistical techniques are used to monitor process characteristics in the workplace.

§      Understand the concepts of sample space and probability distribution and construct sample spaces and distributions in simple cases;

§      Use simulations to construct empirical probability distributions;

§      Understand the concepts of conditional probability and independent events;

Understand how to compute the probability of a compound event.

 

What are different ways of representing, organizing, and relating numbers to mathematical operations?

 

How do we understand and represent patterns, relationships, and change?

 

How do we collect, organize, display, and analyze data?

 

Which strategies and mathematical operations are used to solve problems and arguments, and how can we develop and improve them?

 

How can mathematical thinking be effectively communicated to different audiences?

 

How are mathematical concepts related to one another, other disciplines, and to the real world?

 Vocabulary

  • ·      Box plot

    ·      Coefficient of Variation

    ·      Mean

    ·      Median

    ·      Midrange

    ·      Mode

    ·      Negatively skewed or left-skewed distribution

    ·      Positively skewed or right-skewed distribution

    ·      Quartile

    ·      Range

    Standard deviation

  • ·      Variance

    ·      z-score

    ·      classical probability

    ·      combination

    ·      permutation

    ·      conditional probability

    ·      dependent events

    ·      empirical probability

    ·      event

    ·      fundamental counting rule

    ·      independent events

    ·      mutually exclusive events

    ·      probability experiment

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.

·         Find the number of ways that r objects can be selected from n objects, using permutations.

·         Find the number of ways that r objects can be selected from n objects without regard to order, using the combination rule

·         Find the probability of an event, using the counting rules.

·         Construct a probability distribution for a random variable

·         Find the mean, variance, 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 Poisson, hypergeometric, and multinomial distributions.

·         Identify distributions as symmetrical or skewed

·         Identify the propierties of the 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 normal variable.

·         Find specific data values for given %, using the standard normal distribution.

·         Use the central limit theorem to solve problems involving sample means for large samples.

Use the normal approximation to compute probabilities for a binomial variable.

Unit of Study 3:

 

 

Vocabulary

Skills

Unit of Study 4:

 

 

Vocabulary

Skills

 

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