SECTION 210:15-3-59. Standard Four: Data and Probability

(a)   Statement of the standard. Students will have an increased emphasis on understanding data and probability to enable all students to formulate questions that can be addressed by appropriate statistical methods. Students will analyze data, develop and evaluate inferences and predictions that are based on data, and understand and apply basic concepts of probability. Students will have an opportunity to apply the basic skills of computing with number and being an educated consumer of information providing application and use of fractions in daily life.

(b)   Standard Four objectives for Pre-Kindergarten. The following objectives apply for students in Pre-Kindergarten:

(1)   Collect and organize categorical data.

(A)   Objective 1. Collect and organize information about objects and events in the environment.

(B)   Objective 2. Use categorical data to create real-object graphs.

(c)   Standard Four objectives for Kindergarten. The following objectives apply for students in Kindergarten:

(1)   Collect, organize, and interpret categorical data.

(A)   Objective 1. Collect and sort information about objects and events in the environment.

(B)   Objective 2. Use categorical data to create real-object and picture graphs.

(C)   Objective 3. Draw conclusions from real-object and picture graphs.

(d)   Standard Four objectives for Grade 1. The following objectives apply for students in Grade 1:

(1)   Collect, organize, and interpret categorical and numerical data.

(A)   Objective 1. Collect, sort, and organize data in up to three categories using representations (e.g. tally marks, tables, Venn diagrams).

(B)   Objective 2. Use data to create picture and bar-type graphs to demonstrate one-to-one correspondence.

(C)   Objective 3. Draw conclusions from picture and bar-type graphs.

(e)   Standard Four objectives for Grade 2. The following objectives apply for students in Grade 2:

(1)   Collect, organize, and interpret data.

(A)   Objective 1. Explain that the length of a bar in a bar graph or the number of objects in a picture graph represents the number of data points for a given category.

(B)   Objective 2. Organize a collection of data with up to four categories using pictographs and bar graphs with intervals of 1s, 2s, 5s, or 10s.

(C)   Objective 3. Write and solve one-step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of one.

(D)   Objective 4. Draw conclusions and make predictions from information in a graph.

(f)   Standard Four objectives for Grade 3. The following objectives apply for students in Grade 3:

(1)   Summarize, construct, and analyze data.

(A)   Objective 1. Summarize and construct a data set with multiple categories using a frequency table, line plot, pictograph, and/or bar graph with scaled intervals.

(B)   Objective 2. Solve one- and two-step word problems using categorical data represented with a frequency table, pictograph, or bar graph with scaled intervals.

(g)   Standard Four objectives for Grade 4. The following objectives apply for students in Grade 4:

(1)   Collect, organize, and analyze data.

(A)   Objective 1. Represent data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units.

(B)   Objective 2. Use tables, bar graphs, timelines, and Venn diagrams to display data sets. The data may include benchmark fractions or decimals (1/4, 1/3, 1/2, 2/3, 3/4, 0.25, 0.50, 0.75).

(C)   Objective 3. Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table and line plot.

(h)   Standard Four objectives for Grade 5. The following objectives apply for students in Grade 5:

(1)   Display and analyze data to find the range and measures of central tendency (mean, median, and mode).

(A)   Objective 1. Find the measures of central tendency (mean, median, or mode) and range of a set of data. Understand that the mean is a "leveling out" or central balance point of the data.

(B)   Objective 2. Create and analyze line and double-bar graphs with whole numbers, fractions, and decimals increments.

(i)   Standard Four objectives for Grade 6. The following objectives apply for students in Grade 6:

(1)   Display and analyze data.

(A)   Objective 1. Calculate the mean, median, or mode for a set of real-world data.

(B)   Objective 2. Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.

(C)   Objective 3. Create and analyze box and whicker plots observing how each segment contains one quarter of the data.

(2)   Use probability to solve real-world and mathematical problems; represent probabilities using fractions and decimals.

(A)   Objective 1. Represent possible outcomes using a probability continuum from impossible to certain.

(B)   Objective 2. Determine the sample space for a given experiment and determine which members of the sample space are related to certain events. Sample space may be determined by the use of tree diagrams, tables, or pictorial representations.

(C)   Objective 3. Demonstrate simple experiments in which the probabilities are known and compare the resulting relative frequencies with the known probabilities, recognizing that there may be differences between the two results.

(j)   Standard Four objectives for Grade 7. The following objectives apply for students in Grade 7:

(1)   Display and analyze data in a variety of ways.

(A)   Objective 1. Design simple experiments, collect data and calculate measures of central tendency (mean, median, or mode) and spread (range). Use these quantities to draw conclusions about the data collected and make predictions.

(B)   Objective 2. Use reasoning with proportions to display and interpret data in circle graphs (pie charts) and histograms. Choose the appropriate data display and know how to create the display using a spreadsheet or other graphing technology.

(2)   Calculate probabilities and reason about probabilities using proportions to solve real-world and mathematical problems.

(A)   Objective 1. Determine the theoretical probability of an event using the ratio between the size of the vent and the size of the sample space; represent probabilities as percents, fractions, and decimals between 0 and 1.

(B)   Objective 2. Calculate probability as fraction of same space or as a fraction of area. Express probabilities as percents, decimals, and fractions.

(C)   Objective 3. Use proportional reasoning to draw conclusions about and predict relative frequencies of outcomes based on probabilities.

(k)   Standard Four objectives for Pre-Algebra. The following objectives apply for students in Pre-Algebra:

(1)   Display and interpret data in a variety of ways, including using scatterplots and approximate lines of best fit. Use line of best fit and average rate of change to make predictions and draw conclusions about data.

(A)   Objective 1. Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Know how to create data displays using a spreadsheet and use a calculator to examine this impact.

(B)   Objective 2. Explain how outliers affect measures of central tendency.

(C)   Objective 3. Collect, display, and interpret data using scatterplots. Use the shape of the scatterplot to informally estimate a line of best fit, make statements about average rate of change, and make predictions about values not in the original data set. Use appropriate titles, labels, and units.

(2)   Calculate experimental probabilities and reason about probabilities to solve real-world and mathematical problems.

(A)   Objective 1. Calculate experimental probabilities and represent them as percents, fractions, and decimals between 0 and 1 inclusive. Use experimental probabilities to make predictions when actual probabilities are unknown.

(B)   Objective 2. Determine how samples are chosen (random, limited, biased) to draw and support conclusions about generalizing a sample to a population.

(C)   Objective 3. Compare and contrast dependent and independent events.

(l)   Standard Four objectives for Algebra 1. The following objectives apply for students in Algebra 1:

(1)   Display, describe, and compare data. For linear relationships, make predictions and assess the reliability of those predictions.

(A)   Objective 1. Describe a data set using data displays, describe and compare data sets using summary statistics, including measures of central tendency, location, and spread. Know how to use calculators, spreadsheets, or other appropriate technology to display data and calculate summary statistics.

(B)   Objective 2. Collect data and use scatterplots to analyze patterns and describe linear relationships between two variables. Using graphing technology, determine regression lines and correlation coefficients; use regression lines to make predictions and correlation coefficients to assess the reliability of those predictions.

(C)   Objective 3. Interpret graphs as being discrete or continuous.

(2)   Calculate probabilities and apply probability concepts.

(A)   Objective 1. Select and apply counting procedures, such as the multiplication and addition principles and tree diagrams, to determine the size of a sample space (the number of possible outcomes) and to calculate probabilities.

(B)   Objective 2. Describe the concepts of intersections, unions, and complements using Venn diagrams to evaluate probabilities. Understand the relationships between these concepts and the words AND, OR, and NOT.

(C)   Objective 3. Calculate experimental probabilities by performing simulations or experiments involving a probability model and using relative frequencies of outcomes.

(D)   Objective 4. Apply probability concepts to real-world situations to make informed decisions.

(m)   Standard Four objectives for Algebra 2. The following objectives apply for students in Algebra 2:

(1)   Display, describe, and compare data. For linear and nonlinear relationships, make predictions and assess the reliability of those predictions.

(A)   Objective 1. Use the mean and standard deviation of a data set to fit it to a normal distribution (bell-shaped curve).

(B)   Objective 2. Collect data and use scatterplots to analyze patterns and describe linear, exponential, or quadratic relationships between two variables. Using graphing calculators or other appropriate technology, determine regression equation and correlation coefficients; use regression equations to make predictions and correlation coefficients to assess the reliability of those predictions.

(C)   Objective 3. Based upon a real-world context, recognize whether a discrete or continuous graphical representation is appropriate and then create the graph.

(2)   Analyze statistical thinking to draw inferences, make predictions, and justify conclusions.

(A)   Objective 1. Evaluate reports based on data published in the media by identifying the source of the data, the design of the study, and the way the data are analyzed and displayed. Given spreadsheets, tables, or graphs, recognize and analyze distortions in data displays. Show how graphs and data can be distorted to support different points of view.

(B)   Objective 2. Identify and explain misleading uses of data. Recognize when arguments based on data confuse correlation and causation.

[Source: Added at 33 Ok Reg 1324, eff 9-11-16]