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CURRICULUM MAP Content Area: Grade Level: Duration: (30-35 days) *Accelerated (25-30 days) Essential Question/Understandings: Standards for Mathematical Practice: Focus Area: Date: 1) Use random sampling to draw inferences about a population. (supporting) 2) Draw informal comparative inferences about two populations. (additional) 3) Investigate chance processes and develop, use, and evaluate probability models. (supporting) 4) Investigate patterns of association in bivariate data.* (supporting) * Accelerated 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and 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. Unit 4: Statistics and Probability (7.SP) Common Core Standard Performance Indicator 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 a representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. 7.SP.1 Students recognize that is difficult to gather statistics on an entire population. Instead a random sample can be representative of the total population and will generate valid results. Students use this information to draw inferences from data. A random sample must be used in conjunction with the population to get accuracy. For example, a random sample of elementary students cannot be used to give a survey about the prom. Vocabulary Biased Convenience Sample Inference Invalid Population Sample Simple Random Sample Systematic Random Sample Valid Voluntary Sample Assessments 5 Week Tests (Including Midterm and Final Exams) Quizzes/Buddy Quizzes Homework Checks for Understanding Tickets Out The Door Problems of the Week Journals Group Work Resources Common Core Modules Glencoe Course 2/Course 3 Textbook Series Teacher Created /Workshop Materials Page 1 of 6 Edited by: lvs 4/30/2017 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 a 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.2 Students collect and use multiple samples of data to answer question(s) about a population. Issues of variation in the samples should be addressed. 7.SP.3 This is the student’s first experience with comparing two data sets. Students build on their understanding of graphs, mean, median, Mean Absolute Deviation, and interquartile range from 6th grade. Students understand that 1. A full understanding of the data requires consideration of the measures of variability as well as mean or median. 2. Variability is responsible for the overlap of the two data sets and that an increase in variability can increase the overlap. 3. Median is paired with the interquartile range and mean is paired with the mean absolute deviation. Compound Event Dependent Event Event Independent Event Probability Probability Model Random Sample Sample Space Simulation Uniform Probability Model Bivariate Box-Plot (Boxand-Whisker Plot) Clustering Data Set Dot Plot Histogram Interquartile Range Median Mode Range Scatter Plot Shape Skew Spread Statistics Page 2 of 6 Edited by: lvs 4/30/2017 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 even that is neither unlikely nor likely, and a probability near 1 indicated a likely event. Mean Mean Absolute Deviation (MAD) Measures of Variability (Central Tendency) Median Mode Observation Quantitative 7.SP. 5 This is students’s first formal introduction to probability. Students recognize that all probabilities are between 0 and 1, inclusive, the sum of all possible outcomes is 1. For example, there are three choices of jellybeans – grape, cherry, and orange. If the probability of getting grape is 3/10 and the probability of getting cherry is 1/5, what is the probability of getting oranges? The probability of any single event can be recognized as a fraction. The closer the fraction is to 1, the greater the probability the event will occur. Larger numbers indicate greater likelihood. For example, if you have 10 oranges and 3 apples, you have a greater likelihood of getting an orange. Page 3 of 6 Edited by: lvs 4/30/2017 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.6 Students collect data from a probability experiment, recognizing that as the number of trials increase, the experimental probability approaches the theoretical probability. The focus of this standard is relative frequency—The relative frequency is the observed number of successful events for a finite sample of trials. Relative frequency is the observed proportion of successful events. Relative Frequency 7.SP. 7 Develop a probability model and use it to find probabilities of event. 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 examples, is a student is selected at random from a class, find the probability that Jane will be selected 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? Page 4 of 6 Edited by: lvs 4/30/2017 7.SP.8 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. b. Represent 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 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? Linear Association Positive and Negative Correlation 7.SP.8 Students use tree diagrams, frequency tables, and organized lists, and simulations to determine the probability of compounding events. Probabilities are useful for predicting what will happen over the long run. Using theoretical probability, students predict frequencies of outcomes. Students recognize an appropriate design to conduct an experiment with simple probability events, understanding that the experimental data give realistic estimates of the probability of an event but are affected by sample size. Independent Probability Tree Diagram Dependent Probability Dot Plots Histograms Accelerated 8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. 8.SP.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter Page 5 of 6 Edited by: lvs 4/30/2017 plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. 8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. 8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. Page 6 of 6 Edited by: lvs 4/30/2017