7TH GRADE PACING GUIDEMATH INNOVATIONS UNIT 5: DRIVEN BY DATA

April-MayStandards: 7.SP.1 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. Understand that random sampling tends to produce representative samples and support valid inferences. 7.SP.2 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. 7.SP.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, 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.7.SP.4 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. 7.SP.5 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 ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. 7.SP.6 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.7.SP.7ab 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. 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? 7.SP.abc Find probabilities of compound events using organized lists, tables, tree diagrams, and simulations. 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. 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. 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?

Standard/Target Section/Lesson # Days Formative AssessmentSection 1: Counting Strategies ACT #53

7.SP.7ab Knowledge Target: Recognize uniform (equally 1.1: Outcomes 2 PARCC #6

Lewis County Middle School

Standard/Target Section/Lesson # Days Formative Assessmentlikely) probability. Knowledge Target: Use models to determine the probability of events. Reasoning Target: Develop a uniform probability model and use it to determine the probability of each outcome/event. Reasoning Target: Analyze a probability model and justify why it is uniform or explain the discrepancy if it is not.

*Add: Develop a uniform probability model and use it to determine the probability of each outcome/event.

1.2: Counting 2 ACT #49, 88, 80, 115; PARCC #4Study Guide 1

Percent Proficiency: Quiz 1Section 2: Probability

7.SP.5 Knowledge Target: Know that probability is expressed as a number between 0 and 1. Knowledge Target: Know that a random event with a probability of ½ is equally likely to happen. Knowledge Target: Know that as probability moves closer to 1 it is increasingly likely to happen. Knowledge Target: Know that as probability moves closer to 0 it is decreasingly likely to happen.7.SP.6 Knowledge Target: Determine relative frequency (experimental probability) is the number of times an outcome occurs divided by the total number of times the experiment is completed.7.SP.7ab Reasoning Target: Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

2.1: Experimental Probability*Add: Know that probability is expressed as a number between 0 and 1.*Add: Know that a random event with a probability of ½ is equally likely to happen.*Add: Know that as probability moves closer to 1 it is increasingly likely to happen.*Add: Know that as probability moves closer to 0 it is decreasingly likely to happen.

3 PARCC #18

2.2: Probability and Outcomes 27.SP.5 Reasoning Target: Draw conclusions to determine that a greater likelihood occurs as the number of favorable outcomes approaches the total number of outcomes.7.SP.6 Reasoning Target: Determine the relationship between experimental and theoretical probabilities by using the Law of Large Numbers. Reasoning Target: Predict the relative frequency (experimental probability) of an event based on the (theoretical) probability.

2.3: Theoretical Probability 2 ACT #60, 16, 78, 116; PARCC #16, 1

7.SP.8abc Knowledge Target: Define and describe a compound event. Knowledge Target: Know that the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. Knowledge Target: Define simulation. Reasoning Target: Find probabilities of compound events using organized lists, tables, tree diagrams, etc. and analyze the outcomes. Reasoning Target: Choose the appropriate method such as

2.4: Multistage Experiments*Add: Define and describe a compound event.*Add: Know that the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.*Add: Define simulation.

2

Lewis County Middle School

Standard/Target Section/Lesson # Days Formative Assessmentorganized lists, tables and tree diagrams to represent sample spaces for compound events. Reasoning Target: Design and use a simulation to generate frequencies for compound events.

*Add: Design and use a simulation to generate frequencies for compound events.

Study Guide 1Percent Proficiency: Quiz 1

Section 3: Organizing, Representing and Analyzing Data

7.SP.3 Knowledge Target: Identify measures of central tendency (mean, median, and mode) in a data distribution. Knowledge Target: Identify measures of variation including upper quartile, lower quartile, upper extreme—maximum, lower extreme—minimum, range, interquartile range, and mean absolute deviation (i.e. box-and-whisker plots, line plot, dot plots, etc.).

3.1: Data, Data Everywhere*Add: Identify measures of central tendency (mean, median, and mode) in a data distribution.*Add: Identify measures of variation including upper quartile, lower quartile, upper extreme—maximum, lower extreme—minimum, range, interquartile range, and mean absolute deviation (i.e. box-and-whisker plots, line plot, dot plots, etc.).

2 ACT #109, 63, 61, 26, 39, 73, 17; PARCC #6

7.SP.3 Reasoning Target: Compare two numerical data distributions on a graph by visually comparing data displays, and assessing the degree of visual overlap. Reasoning Target: Compare the differences in the measure of central tendency in two numerical data distributions by measuring the difference between the centers and expressing it as a multiple of a measure of variability.

3.2: Double Bar Graphs*Add: Compare the differences in the measure of central tendency in two numerical data distributions by measuring the difference between the centers and expressing it as a multiple of a measure of variability.

1 PARCC #22

7.SP.4 Knowledge Target: Find measures of central tendency (mean, median, and mode) and measures of variability (range, quartile, etc.). Reasoning Targets: Analyze and interpret data using measures of central tendency and variability. Reasoning Target: Draw informal comparative inferences about two populations from random samples.

3.3: Histograms*Add: Find measures of central tendency (mean, median, and mode) and measures of variability (range, quartile, etc.).*Add: Draw informal comparative inferences about two populations from random samples.

1

3.4: Circle Graphs 1 ACT #1207.SP.1 Knowledge Target: Know statistics terms such as population, sample, sample size, random sampling, generalizations, valid, biased and unbiased. Knowledge Target: Recognize sampling techniques such as convenience, random, systematic, and voluntary. Knowledge Target: Know that generalizations about a population from a sample are valid only if the sample is representative of that

3.5: Sampling Populations*Add: Statistics terms—sample size, generalizations, valid.*Add: Recognize sampling techniques such as convenience, random, systematic, and voluntary.*Add: Know that generalizations about a

1 PARCC #32

Lewis County Middle School

Standard/Target Section/Lesson # Days Formative Assessmentpopulation. Reasoning Target: Apply statistics to gain information about a population from a sample of the population. Reasoning Target: Generalize that random sampling tends to produce representative samples and support valid inferences.7.SP.2 Knowledge Target: Define random sample. Knowledge Target: Identify an appropriate sample size. Reasoning Target: Analyze and interpret data from a random sample to draw inferences about a population with an unknown characteristic of interest. Reasoning Target: Generate multiple samples (or simulated samples) of the same size to determine the variation in estimates or predictions by comparing and contrasting the samples.

population from a sample are valid only if the sample is representative of that population.*Add: Identify an appropriate sample size.*Add: Analyze and interpret data from a random sample to draw inferences about a population with an unknown characteristic of interest.*Add: Generate multiple samples (or simulated samples) of the same size to determine the variation in estimates or predictions by comparing and contrasting the samples.

Study Guide 1Percent Proficiency: Quiz 1

Study Guide 1Percent Proficiency: Unit Exam 1

Lewis County Middle School

Lewis County Middle School

Lewis County Middle School

Lewis County Middle School

Lewis County Middle School

Lewis County Middle School

Lewis County Middle School

Lewis County Middle School

Lewis County Middle School

Lewis County Middle School