Also Assesses or Assessed by MACC.912.S-CP.1.2 Item Types This benchmark will be assessed using MC items. Content Limits Limit to real world contexts and age appropriate situations. Benchmark Clarification Students will determine probable outcomes of events using the addition rule. Stimulus Attributes Test items may include illustrations of the following: tables, lists, tree diagrams, and other forms. Response Attributes Responses may be in decimal or reduced fraction form. Sample Item If P(A) = 0.24 and P(B) = 0.52 and A and B are independent, what is P(A or B)? (a) 0.1248 (b) 0.28 * (c) 0.6352 (d) 0.76 (e) The answer cannot be determined from the information given. Solution: 0.24 + 0.52 – (0.24)(0.52) Benchmark MACC.912.S-CP.2.8 Reporting Category Statistics and Probability Domain Conditional Probability & the Rules of Probability Benchmark Number MACC.912.S-CP.2.8
Reporting Category Statistics and Probability Standard Conditional Probability & the Rules of Probability Benchmark Number MACC.912.S-CP.1.5 Benchmark Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. Also Assesses or Assessed by MACC.912.S-CP.1.3 & MACC.912.S-CP.1.4 Item Types This benchmark will be assessed using MC and FR items. Content Limits Limit to real world contexts and age appropriate situations. Benchmark Clarification Students will determine probable outcomes of events using the multiplication rule. Stimulus Attributes Test items may include illustrations of the following: tables, lists, tree diagrams, and other forms. Response Attributes Responses may be in decimal or reduced fraction form. Sample Item Researchers are interested in the relationship between cigarette smoking and lung cancer. Suppose an adult male is randomly selected from a particular population. Assume that the following table shows some probabilities involving the compound event that the individual does or does not smoke and the person is or is not diagnosed with cancer: Event Probability smokes and gets cancer 0.08 smokes and does not get cancer 0.17 does not smoke and gets cancer 0.04 does not smoke and does not get cancer 0.71 Suppose further that the probability that the randomly selected individual is a smoker is 0.25. (a) Find the probability that the individual gets cancer, given that he is a smoker. Answer : 0.08/0.25 = 0.32
Benchmark MACC.912.S-IC.1.1 Reporting Category Probability and Statistics Standard Making Inferences & Justifying Conclusions Benchmark Number MACC.912.S-IC.1.1 Benchmark Understand statistics as a process for making inferences about population parameters based on a random sample from that population. Benchmark Clarification Students will calculate, summarize, and interpret data using measures of center including mean and median and measures of spread including range, standard deviation, and variance. Students will use these measures to make comparisons and draw conclusions about data sets. Also Assesses or Assessed by MACC.K12.MP.5.1, MACC.K12.MP.6.1 Item Types This benchmark will be assessed using FR, GR, and MC items. Content Limits Items may include calculations for mean, median, variance, and standard deviation. Items may include the choice of which measure of center is the best representation of a data set. Benchmark Clarification Students will calculate, summarize, and interpret data using measures of center and spread. Stimulus Attributes Items must be set in mathematical or real-world context. Response Attributes Responses will be rational numbers. Sample Items Sample Item 1 MC The average grade point average (GPA) for 25 top-ranked students at a local college is listed below. (Use the rounding rule for the mean). 3.80 3.77 3.70 3.74 3.70 3.86 3.76 3.68 3.67 3.57 3.83 3.70 3.80 3.73 3.67 3.78 3.75 3.73 3.65 3.66 3.75 3.64 3.78 3.73 3.64 Find the mean of the GPAs. Sample Response 1 A. 3.7236 B. 3.764 *C. 3.724
1. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. b. Informally assess the fit of a function by plotting and analyzing residuals. c. Fit a linear function for a scatter plot that suggests a linear association. MACC.912.S-ID.3.7 2. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Also Asses MACC.K12.MP.4.1, MACC.K12.MP.5.1, MACC.K12.MP.8.1 Item Types This benchmark will be assessed using MC and FR items. Benchmark Clarification Students will graph data on a scatter plot, describe the association, and interpret the slope. Content Limits Data points limited to one, two, or three digits Stimulus Attributes Tables and charts may be used. Items may be set in either real-world or mathematical contexts. Response Attributes Equations may be presented in standard or slope-intercept form. * Teacher may assess in the classroom. SAMPLE ITEM Mrs. Santiago would like to know how well her Algebra students will perform on the state’s End-of-Course Assessment. She has decided to gather some data from the previous year in