Ohio's Academic Content Standards in Mathematics
Grade Level Indicators
Data Analysis and Probability StandardStudents pose questions and collect, organize, represent, interpret and analyze data to answer those questions. Students develop and evaluate inferences, predictions and arguments that are based on data.
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| PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
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| Prekindergarten |
| 1. | Gather, sort and compare objects by similarities and differences in the context of daily activities and play. (ORC Resources) | | 2. | Place information or objects in a floor or table graph according to one attribute (e.g., size, color, shape or quantity). (ORC Resources) | | 3. | Select the category or categories that have the most or fewest objects in a floor or table graph. (ORC Resources) |
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| PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
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| Kindergarten |
| 1. | Gather and sort data in response to questions posed by teacher and students; e.g., how many sisters and brothers, what color shoes. (ORC Resources) | | 2. | Arrange objects in a floor or table graph according to attributes, such as use, size, color, or shape. (ORC Resources) | | 3. | Select the category or categories that have the most or fewest objects in a floor or table graph. (ORC Resources) |
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| PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
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| Grade 1 |
| 1. | Identify multiple categories for sorting data. (ORC Resources) | | 2. | Collect and organize data into charts using tally marks. (ORC Resources) | | 3. | Display data in picture graphs with units of 1 and bar graphs with intervals of 1. (ORC Resources) | | 4. | Read and interpret charts, picture graphs and bar graphs as sources of information to identify main ideas, draw conclusions, and make predictions. (ORC Resources) | | 5. | Construct a question that can be answered by using information from a graph. (ORC Resources) | | 6. | Arrange five objects by an attribute, such as size or weight, and identify the ordinal position of each object. (ORC Resources) | | 7. | Answer questions about the number of objects represented in a picture graph, bar graph or table graph; e.g., category with most, how many more in a category compared to another, how many altogether in two categories. (ORC Resources) | | 8. | Describe the likelihood of simple events as possible/impossible and more likely/less likely; e.g., when using spinners or number cubes in classroom activities. (ORC Resources) |
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| PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
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| Grade 2 |
| 1. | Pose questions, use observations, interviews and surveys to collect data, and organize data in charts, picture graphs and bar graphs. (ORC Resources) | | 2. | Read, interpret and make comparisons and predictions from data represented in charts, line plots, picture graphs and bar graphs. (ORC Resources) | | 3. | Read and construct simple timelines to sequence events. (ORC Resources) | | 4. | Write a few sentences to describe and compare categories of data represented in a chart or graph, and make statements about the data as a whole. (ORC Resources) | | 5. | Identify untrue or inappropriate statements about a given set of data. (ORC Resources) | | 6. | Recognize that data may vary from one population to another; e.g., favorite TV shows of students and of parents. (ORC Resources) | | 7. | List some of the possible outcomes of a simple experiment, and predict whether given outcomes are more, less or equally likely to occur. (ORC Resources) | | 8. | Use physical models and pictures to represent possible arrangements of 2 or 3 objects. (ORC Resources) |
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| PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
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| Grade 3 |
| 1. | Collect and organize data from an experiment, such as recording and classifying observations or measurements, in response to a question posed. (ORC Resources) | | 2. | Draw and interpret picture graphs in which a symbol or picture represents more than one object. (ORC Resources) | | 3. | Read, interpret and construct bar graphs with intervals greater than one. (ORC Resources) | | 4. | Support a conclusion or prediction orally and in writing, using information in a table or graph. (ORC Resources) | | 5. | Match a set of data with a graphical representation of the data. (ORC Resources) | | 6. | Translate information freely among charts, tables, line plots, picture graphs and bar graphs; e.g., create a bar graph from the information in a chart. (ORC Resources) | | 7. | Analyze and interpret information represented on a timeline. (ORC Resources) | | 8. | Identify the mode of a data set and describe the information it gives about a data set. (ORC Resources) | | 9. | Conduct a simple experiment or simulation of a simple event, record the results in a chart, table or graph, and use the results to draw conclusions about the likelihood of possible outcomes. (ORC Resources) | | 10. | Use physical models, pictures, diagrams and lists to solve problems involving possible arrangements or combinations of two to four objects. (ORC Resources) |
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| PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
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| Grade 4 |
| 1. | Create a plan for collecting data for a specific purpose. (ORC Resources) | | 2. | Represent and interpret data using tables, bar graphs, line plots and line graphs. (ORC Resources) | | 3. | Interpret and construct Venn diagrams to sort and describe data. (ORC Resources) | | 4. | Compare different representations of the same data to evaluate how well each representation shows important aspects of the data, and identify appropriate ways to display the data. (ORC Resources) | | 5. | Propose and explain interpretations and predictions based on data displayed in tables, charts and graphs. (ORC Resources) | | 6. | Describe the characteristics of a set of data based on a graphical representation, such as range of the data, clumps of data, and holes in the data. (ORC Resources) | | 7. | Identify the median of a set of data and describe what it indicates about the data. (ORC Resources) | | 8. | Use range, median and mode to make comparisons among related sets of data. (ORC Resources) | | 9. | Conduct simple probability experiments and draw conclusions from the results; e.g., rolling number cubes or drawing marbles from a bag. (ORC Resources) | | 10. | Represent the likelihood of possible outcomes for chance situations; e.g., probability of selecting a red marble from a bag containing 3 red and 5 white marbles. (ORC Resources) | | 11. | Relate the concepts of impossible and certain-to-happen events to the numerical values of 0 (impossible) and 1 (certain). (ORC Resources) | | 12. | Place events in order of likelihood and use a diagram or appropriate language to compare the chance of each event occurring; e.g. impossible, unlikely, equal, likely, certain. (ORC Resources) | | 13. | List and count all possible combinations using one member from each of several sets, each containing 2 or 3 members; e.g., the number of possible outfits from 3 shirts, 2 shorts and 2 pair of shoes. (ORC Resources) |
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| PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
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| Grade 5 |
| 1. | Read, construct and interpret frequency tables, circle graphs and line graphs. (ORC Resources) | | 2. | Select and use a graph that is appropriate for the type of data to be displayed; e.g., numerical vs. categorical data, discrete vs. continuous data. (ORC Resources) | | 3. | Read and interpret increasingly complex displays of data, such as double bar graphs. (ORC Resources) | | 4. | Determine appropriate data to be collected to answer questions posed by students or teacher, collect and display data, and clearly communicate findings. (ORC Resources) | | 5. | Modify initial conclusions, propose and justify new interpretations and predictions as additional data are collected. (ORC Resources) | | 6. | Determine and use the range, mean, median and mode, and explain what each does and does not indicate about the set of data. (ORC Resources) | | 7. | List and explain all possible outcomes in a given situation. (ORC Resources) | | 8. | Identify the probability of events within a simple experiment, such as three chances out of eight. (ORC Resources) | | 9. | Use 0,1 and ratios between 0 and 1 to represent the probability of outcomes for an event, and associate the ratio with the likelihood of the outcome. (ORC Resources) | | 10. | Compare what should happen (theoretical/expected results) with what did happen (experimental/actual results) in a simple experiment. (ORC Resources) | | 11. | Make predictions based on experimental and theoretical probabilities. (ORC Resources) |
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| PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
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| Grade 6 |
| 1. | Read, construct and interpret line graphs, circle graphs and histograms. (ORC Resources) | | 2. | Select, create and use graphical representations that are appropriate for the type of data collected. (ORC Resources) | | 3. | Compare representations of the same data in different types of graphs, such as a bar graph and circle graph. (ORC Resources) | | 4. | Understand the different information provided by measures of center (mean, mode and median) and measures of spread (range). (ORC Resources) | | 5. | Describe the frequency distribution of a set of data, as shown in a histogram or frequency table, by general appearance or shape; e.g., number of modes, middle of data and level of symmetry, outliers. (ORC Resources) | | 6. | Make logical inferences from statistical data. (ORC Resources) | | 7. | Design an experiment to test a theoretical probability and explain how the results may vary. (ORC Resources) |
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| PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
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| Grade 7 |
| 1. | Read, create and interpret box-and-whisker plots, stem-and-leaf plots, and other types of graphs, when appropriate. (ORC Resources) | | 2. | Analyze how decisions about graphing affect the graphical representation; e.g., scale, size of classes in a histogram, number of categories in a circle graph. (ORC Resources) | | 3. | Analyze a set of data by using and comparing combinations of measures of center (mean, mode, median) and measures of spread (range, quartile, interquartile range), and describe how the inclusion or exclusion of outliers affects those measures. (ORC Resources) | | 4. | Construct opposing arguments based on analysis of the same data, using different graphical representations. (ORC Resources) | | 5. | Compare data from two or more samples to determine how sample selection can influence results. (ORC Resources) | | 6. | Identify misuses of statistical data in articles, advertisements, and other media. (ORC Resources) | | 7. | Compute probabilities of compound events; e.g., multiple coin tosses or multiple rolls of number cubes, using such methods as organized lists, tree diagrams and area models. (ORC Resources) | | 8. | Make predictions based on theoretical probabilities, design and conduct an experiment to test the predictions, compare actual results to predicted results, and explain differences. (ORC Resources) |
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| PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
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| Grade 8 |
| 1. | Use, create and interpret scatterplots and other types of graphs as appropriate. (ORC Resources) | | 2. | Evaluate different graphical representations of the same data to determine which is the most appropriate representation for an identified purpose; e.g., line graph for change over time, circle graph for part-to-whole comparison, scatterplot for relationship between two variants. (ORC Resources) | | 3. | Differentiate between discrete and continuous data and appropriate ways to represent each. (ORC Resources) | | 4. | Compare two sets of data using measures of center (mean, mode, median) and measures of spread (range, quartiles, interquartile range, percentiles). (ORC Resources) | | 5. | Explain the mean's sensitivity to extremes and its use in comparison with the median and mode. (ORC Resources) | | 6. | Make conjectures about possible relationship in a scatterplot and approximate line of best fit. (ORC Resources) | | 7. | Identify different ways of selecting samples, such as survey response, random sample, representative sample and convenience sample. (ORC Resources) | | 8. | Describe how the relative size of a sample compared to the target population affects the validity of predictions. (ORC Resources) | | 9. | Construct convincing arguments based on analysis of data and interpretation of graphs. (ORC Resources) | | 10. | Calculate the number of possible outcomes for a situation, recognizing and accounting for when items may occur more than once or when order is important. (ORC Resources) | | 11. | Demonstrate an understanding that the probability of either of two disjoint events occurring can be found by adding the probabilities for each and that the probability of one independent event following another can be found by multiplying the probabilities. (ORC Resources) |
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| PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
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| Grade 9 |
| 1. | Classify data as univariate (single variable) or bivariate (two variables) and as quantitative (measurement) or qualitative (categorical) data. (ORC Resources) | | 2. | Create a scatterplot for a set of bivariate data, sketch the line of best fit, and interpret the slope of the line of best fit. (ORC Resources) | | 3. | Analyze and interpret frequency distributions based on spread, symmetry, skewness, clusters and outliers. (ORC Resources) | | 4. | Describe and compare various types of studies (survey, observation, experiment), and identify possible misuses of statistical data. (ORC Resources) | | 5. | Describe characteristics and limitations of sampling methods, and analyze the effects of random versus biased sampling; e.g., determine and justify whether the sample is likely to be representative of the population. (ORC Resources) | | 6. | Make inferences about relationships in bivariate data, and recognize the difference between evidence of relationship (correlation) and causation. (ORC Resources) | | 7. | Use counting techniques and the Fundamental Counting principle to determine the total number of possible outcomes for mathematical situations. (ORC Resources) | | 8. | Describe, create and analyze a sample space and use it to calculate probability. (ORC Resources) | | 9. | Identify situations involving independent and dependent events, and explain differences between and common misconceptions about probabilities associated with those events. (ORC Resources) | | 10. | Use theoretical and experimental probability, including simulations or random numbers, to estimate probabilities and to solve problems dealing with uncertainty; e.g., compound events, independent events, simple dependent events. (ORC Resources) |
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| PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
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| Grade 10 |
| 1. | Describe measures of center and the range verbally, graphically and algebraically. (ORC Resources) | | 2. | Represent and analyze bivariate data using appropriate graphical displays (scatterplots, parallel box-and-whisker plots, histograms with more than one set of data, tables, charts, spreadsheets) with and without technology. (ORC Resources) | | 3. | Display bivariate data where at least one variable is categorical. (ORC Resources) | | 4. | Identify outliers on a data display; e.g., use the interquartile range to identify outliers on a box-and-whisker plot. (ORC Resources) | | 5. | Provide examples and explain how a statistic may or may not be an attribute of the entire population; e.g., intentional or unintentional bias may be present. (ORC Resources) | | 6. | Interpret the relationship between two variables using multiple graphical displays and statistical measures; e.g., scatterplots, parallel box-and-whisker plots, and measures of center and spread. (ORC Resources) | | 7. | Model problems dealing with uncertainty with area models (geometric probability). (ORC Resources) | | 8. | Differentiate and explain the relationships between the probability of an event and the odds of an event, and compute one given the other. (ORC Resources) |
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| PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
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| Grade 11 |
| 1. | Design a statistical experiment, survey or study for a problem; collect data for the problem; and interpret the data with appropriate graphical displays, descriptive statistics, concepts of variability, causation, correlation and standard deviation. (ORC Resources) | | 2. | Describe the role of randomization in a well-designed study, especially as compared to a convenience sample, and the generalization of results from each. (ORC Resources) | | 3. | Describe how a linear transformation of univariate data affects range, mean, mode, and median. (ORC Resources) | | 4. | Create a scatterplot of bivariate data, identify trends, and find a function to model the data. (ORC Resources) | | 5. | Use technology to find the Least Squares Regression Line, the regression coefficient, and the correlation coefficient for bivariate data with a linear trend, and interpret each of these statistics in the context of the problem situation. (ORC Resources) | | 6. | Use technology to compute the standard deviation for a set of data, and interpret standard deviation in relation to the context or problem situation. (ORC Resources) | | 7. | Describe the standard normal curve and its general properties, and answer questions dealing with data assumed to be normal. (ORC Resources) | | 8. | Analyze and interpret univariate and bivariate data to identify patterns, note trends, draw conclusions, and make predictions. (ORC Resources) | | 9. | Evaluate validity of results of a study based on characteristics of the study design, including sampling method, summary statistics and data analysis techniques. (ORC Resources) | | 10. | Understand and use the concept of random variable, and compute and interpret the expected value for a random variable in simple cases. (ORC Resources) | | 11. | Examine statements and decisions involving risk; e.g., insurance rates and medical decisions. (ORC Resources) |
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| PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
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| Grade 12 |
| 1. | Identify and use various sampling methods (voluntary response, convenience sample, random sample, stratified random sample, census) in a study. (ORC Resources) | | 2. | Transform bivariate data so it can be modeled by a function; e.g., use logarithms to allow nonlinear relationship to be modeled by linear function. (ORC Resources) | | 3. | Describe the shape and find all summary statistics for a set of univariate data, and describe how a linear transformation affects shape, center and spread. (ORC Resources) | | 4. | Apply the concept of a random variable to generate and interpret probability distributions, including binomial, normal and uniform. (ORC Resources) | | 5. | Use sampling distributions as the basis for informal inference. (ORC Resources) | | 6. | Use theoretical or experimental probability, including simulations, to determine probabilities in real-world problem situations involving uncertainty, such as mutually exclusive events, complementary events and conditional probability. (ORC Resources) |
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