mcs6-8math. web viewmathematical practice(s): ... level of thinking: applying. ... estimate the...

SandHills Regional Education Consortium

Domain: Statistics and Probability Mathematical Practice(s):3. Construct viable arguments and

critique the reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.

Level of Thinking:AnalyzingEvaluatingCreating

Grade Specific Standard: 7.SP.1 Use random sampling to draw inferences about a population. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Information Technology Standard: 7.TT.1 Use technology and other resources for assigned tasks.Clarifying Objectives: Use a random sample to gain information about a population by examining a sample of the population that represents the total population. Justify the validity of the sample population.Task Analysis Vocabulary Explain that random sampling tends to

produce representative samples and support valid inferences.

Identify correct population sector for taking a given sample population

Experiment with random samples to infer data results

Identify the appropriate audience for a given sample group

Demonstrate examples of representative bias and insufficient samples.

Infer valid statistics about a population based on random sampling.

Draw conclusions about a population. Understand that statistics can be used to gain

information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population.

ReviewDataExperimentGeneralizationInferenceMisleadingPopulationSurveyOutcomeGraphsPrediction

InstructRandom samplingRepresentative samplesStatisticsBias/unbiasedSample spaceRepresentative biasValidity

Instructional Resources:

Notes and Additional Information:

Anson County ~ Bladen County ~ Columbus County ~ Cumberland County ~ Ft. Bragg ~ Harnett County ~ Hoke CountyLee County ~ Montgomery County ~ Moore County ~ Richmond County ~ Robeson County ~ Scotland County ~ Whiteville City

Copyright (2012) – No portion of this document can be reproduced or used without the express permission of the Executive Director of the SandHills Regional Educational Consortium

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Domain: Statistics and Probability Mathematical Practice(s):3. Construct viable arguments and


Level of Thinking:ApplyingAnalyzing

Grade Specific Standard: 7.SP.2 Use random sampling to draw inferences about a population. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

Information Technology Standard: 7.TT.1 Use technology and other resources for assigned tasks.

Clarifying Objectives: Collect and use multiple samples of atypical data to answer questions about a population.Task Analysis Vocabulary Generate multiple samples (or simulated

samples) of the same size to gauge the variation in estimates or predictions.

Describe likenesses and differences between multiple samples.

Explain variation in random samples. Make predictions based on possible

outcomes and from compiled data. Draw inferences from multiple samples about

unknown characteristics of interest. Apply the principles of probability to solve

problems in real world contexts. Use data from a random sample to draw

inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

ReviewEstimateOutcomes

InstructMultiple samplesSimulated samplesPredict and gaugeVariationRandom samplesInferencesProbabilityDataEventPopulationGenerateEstimateConclusion





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Domain: Statistics and Probability Mathematical Practice(s):2. Reason abstractly and

quantitatively.3. Construct viable arguments and



Grade Specific Standard: 7.SP.3 Draw informal comparative inferences about two populations. Informally assess the degree of visual overlap of two numerical data distributions with similar variability, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.Information Technology Standard: 7.TT.1 Use technology and other resources for assigned tasks.Clarifying Objectives: Compare mean, median and mode of two populations and graph it on a dot plot. Summarize your observations.Task Analysis Vocabulary Represent and draw conclusions for 2 data

sets using a table, graph, dot plot, and box plot.

Calculate, compare, and interpret the mean, median, upper quartile, lower quartile, and inter-quartile range for two sets of data.

Calculate Mean Absolute Deviation Analyze and summarize data sets, including

initial analysis of variability. Analyze the variability of the median

compared to the inter-quartile range. Analyze the variability of the mean compared

to the mean absolute deviation Create a set of data that has a given mean

absolute deviation and assess for overlap. Informally assess the degree of visual overlap

of two numerical data distributions with similar variability, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

ReviewAnalyzeCalculateCentral tendencies: mean, median, modeDataData setSummarizeInterpret

InstructUpper quartile, lower quartile, inter-quartile rangeMean absolute deviationVariabilityBox and whisker plotDot plot (see unpacking example)





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Domain: Statistics and Probability Mathematical Practice(s):2. Reason abstractly and quantitatively.3. Construct viable arguments and



Grade Specific Standard: 7.SP.4 Draw informal comparative inferences about two populations. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.Information Technology Standard: 7.TT.1 Use technology and other resources for assigned tasks.Clarifying Objectives: Compare two populations using measures of center and variability to draw informal inferences.Task Analysis Vocabulary Recall how to determine the measures of

central tendencies from characteristics of a random sample. (ex. one random sample of height of people at a football game)

Determine measure of central tendencies from characteristics of several random samples. (ex. three random samples of height of people at a football game.)

Manipulate data to generate data that has given measures of central tendencies and variability

Compare two sets of data using measures of center and variability

Draw informal comparative inferences about two populations

Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

ReviewDataRandom samplePopulationMeasures of center: mean, median, mode

InstructMeasure of variabilityComparative inference





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critique the reasoning of others.5. Model with mathematics.6. Use appropriate tools strategically.7. Look for and make use of structure.8. Look for and express regularity in

repeated reasoning.


Grade Specific Standard: 7.SP.5 Investigate chance processes and develop, use, and evaluate probability models. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

Information Technology Standard: 7.TT.1 Use technology and other resources for assigned tasks.Clarifying Objectives: Analyze and evaluate the likelihood that an event will occur.Task Analysis Vocabulary Explain how the probability of an event is

expressed as a fraction. Explain the meaning of the numerator and

denominator of a fraction in terms of the event. (ex. P(black) = 3/4 3 black marbles out of 4 marbles total)

Represent the probability of events that are impossible, unlikely, likely and certain using rational numbers from 0 to 1.

Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

ReviewNumeratorDenominatorFractionProbability

InstructChance eventLikelyUnlikely





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Domain: Statistics and Probability Mathematical Practice(s):1. Make sense of problems and

persevere in solving them.1. Reason abstractly and quantitatively.2. Construct viable arguments and

critique the reasoning of others.3. Model with mathematics.4. Use appropriate tools strategically.5. Attend to precision.


Grade Specific Standard: 7.SP.6 Investigate chance processes and develop, use, and evaluate probability models. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.Information Technology Standard: 7.TT.1 Use technology and other resources for assigned tasks.Clarifying Objectives: Collect data from probability experiments in increasing number of trials and compare the experimental probabilities to the theoretical probabilitiesTask Analysis Vocabulary Define theoretical probability and proportions Design, perform, and collect data on a chance

event Analyze data from tables (frequency), graphs

and plots to determine probabilities of an event

Use probability to predict outcomes of long-run or repeated/ larger events

Organize collected data from experiments performed in tables, graphs, and plots.

Use a variety of experiments to explore the relationship between experimental and theoretical probabilities and the effect of the sample size on this relationship.

Compare theoretical and experimental probability using the “Law of Large Numbers.”

Use theoretical probability and proportions to make approximate predictions.

Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

ReviewDataProbability

InstructChance eventPredictionsLaw of Large NumbersSimple EventCompound EventRelative FrequencyExperimental ProbabilityTheoretical ProbabilityTrials





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critique the reasoning of others.4. Model with mathematics.5. Attend to precision.

Level of Thinking:AnalyzingEvaluating

Grade Specific Standard: 7.SP.7 Investigate chance processes and develop, use, and evaluate probability models. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

Information Technology Standard: 7.TT.1 Use technology and other resources for assigned tasks.Clarifying Objectives: Using theoretical probability, predict frequencies of outcomes and determine the probability of a simple event. Develop a model to demonstrate your understanding.Task Analysis Vocabulary Predict frequencies of outcomes based on

theoretical probability Recognize an appropriate design to conduct

an experiment with simple probability events. Develop a probability model to predict

outcomes based on a series of random events (experimental probability).

Use a variety of experiments to explore the relationship between experimental and theoretical probabilities and the affect of sample size on this relationship.

Recognize the frequency of outcomes based on theoretical probability.

Compare outcomes from theoretical to experimental probability.

Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

ReviewFrequencyEqually likelyOutcome

InstructUniform probabilitySkewedTheoretical probabilityDesignExperimentsExperimental probability





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Grade Specific Standard: 7.SP.7 Investigate chance processes and develop, use, and evaluate probability models. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?Information Technology Standard: 7.TT.1 Use technology and other resources for assigned tasks.Clarifying Objectives: Using theoretical probability, predict frequencies of outcomes and determine the probability of a simple event. Develop a model to demonstrate your understanding.Task Analysis Vocabulary Compare frequency of events based on a

mode. Develop a uniform probability model by

assigning equal probability to all outcomes and use it to determine probability of events.

Develop a non-uniform probability model by assigning unequal probability to all outcomes

Explain and justify discrepancy of events from observed frequencies.

Compare probability from models to observed frequencies

Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

Review

InstructUniform probability modelNon-uniform probability modelRelative frequencyTheoretical and experimental probabilityFrequencyDiscrepanciesCompound eventSample spaceProbability modelChance processApproximateJustify





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critique the reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in

repeated reasoning.


Grade Specific Standard: 7.SP.8 Investigate chance processes and develop, use, and evaluate probability models. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.Information Technology Standard: 7.TT.1 Use technology and other resources for assigned tasks.Clarifying Objectives: Use a random sample to gain information about a population by examining a sample of the population that represents the total population. Justify the validity of the sample population.Task Analysis Vocabulary Define and describe a compound event. Use tree diagrams and frequency tables to

model compound events. Determine the number of possible outcomes

of a given situation and list the possibilities Determine the probability of compound events

and express it as a fraction of outcomes in the sample space

Make predictions based on theoretical probabilities or experimental results.

Calculate the probability of a compound event representing it as a fraction.

Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

ReviewProbabilityCompound eventFractionOutcomesSample spacePredictions

InstructTheoretical and experimental probabilityTree diagramsFrequency tables PermutationsCombinations





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Grade Specific Standard: 7.SP.8 Investigate chance processes and develop, use, and evaluate probability models. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.Information Technology Standard: 7.TT.1 Use technology and other resources for assigned tasks.Clarifying Objectives: Using theoretical probability, predict frequencies of outcomes and determine the probability of compound events, using organized lists, tables, tree diagrams, and simulations.

Task Analysis Vocabulary Create lists, tables, and tree diagrams to

represent sample spaces for compound events.

Identify the correct method for representing sample space for a given compound event.

Identify the outcomes in the sample space, which compose the event.

Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.


InstructTheoretical and experimental probabilityTree diagramsFrequency tables PermutationsCombinationsFavorable outcomes





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critique the reasoning of others.4. Model with mathematics.


Grade Specific Standard: 7.SP.8 Investigate chance processes and develop, use, and evaluate probability models. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.c. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?Information Technology Standard: 7.TT.1 Use technology and other resources for assigned tasks.Clarifying Objectives: Using theoretical probability, predict frequencies of outcomes and determine the probability of compound events using simulations.Task Analysis Vocabulary Design a simulation to generate frequencies

for compound events. Determine appropriate method for recording

sample space. Conduct simulation to generate frequencies

for compound event. Analyze simulation and determine real world

applications based on outcomes. Design and use a simulation to generate

frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?


InstructTheoretical and experimental probabilityTree diagramsFrequency tables PermutationsCombinationsFavorable outcomesPercentListSimple eventsSimulation





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