|
|
||
State of Ohio Mathematics StandardsData Analysis and Probability |
||
| Grade: K Data Analysis and Probabilty Standard Data Collection Standard Number: 1 Gather and sort data in response to questions posed by teacher and students; e.g., how many sisters and brothers, what color shoes Standard Number: 2 Arrange objects in a floor or table graph according to attributes, such as use, size, color, or shape Statistical Methods Standard Number: 3 Select the category or categories that have the most or fewest objects in a floor or table graph Grade: Gr. 1 Data Analysis and Probabilty Standard Data Collection Standard Number: 1 Identify multiple categories for sorting data Standard Number: 2 Collect and organize data into charts using tally marks Standard Number: 3 Display data in picture graphs with units of 1 and bar graphs with intervals of 1 Standard Number: 4 Read and interpret charts, picture graphs and bar graphs as sources of information to identify main ideas, draw conclusions, and make predictions Standard Number: 5 Construct a question that can be answered by using information from a graph Probability Standard Number: 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 Statistical Methods Standard Number: 6 Arrange five objects by an attribute, such as size or weight, and identify the ordinal position of each object Standard Number: 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 Grade: Gr. 2 Data Analysis and Probabilty Standard Data Collection Standard Number: 1 Pose questions, use observations, interviews and surveys to collect data, and organize data in charts, picture graphs and bar graphs Standard Number: 2 Read, interpret and make comparisons and predictions from data represented in charts, line plots, picture graphs and bar graphs Standard Number: 3 Read and construct simple timelines to sequence events Probability Standard Number: 7 List some of the possible outcomes of a simple experiment, and predict whether given outcomes are more, less or equally likely to occur Standard Number: 8 Use physical models and pictures to represent possible arrangements of 2 or 3 objects Statistical Methods Standard Number: 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 Standard Number: 5 Identify untrue or inappropriate statements about a given set of data Standard Number: 6 Recognize that data may vary from one population to another; e.g., favorite TV shows of students and of parents Grade: Gr. 3 Data Analysis and Probabilty Standard Data Collection Standard Number: 1 Collect and organize data from an experiment, such as recording and classifying observations or measurements, in response to a question posed Standard Number: 2 Draw and interpret picture graphs in which a symbol or picture represents more than one object Standard Number: 3 Read, interpret and construct bar graphs with intervals greater than one Standard Number: 4 Support a conclusion or prediction orally and in writing, using information in a table or graph Standard Number: 5 Match a set of data with a graphical representation of the data. Standard Number: 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 Standard Number: 7 Analyze and interpret information represented on a timeline Probability Standard Number: 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 Standard Number: 10 Use physical models, pictures, diagrams and lists to solve problems involving possible arrangements or combinations of two to four objects Statistical Methods Standard Number: 8 Identify the mode of a data set and describe the information it gives about a data set Grade: Gr. 4 Data Analysis and Probabilty Standard Data Collection Standard Number: 1 Create a plan for collecting data for a specific purpose Standard Number: 2 Represent and interpret data using tables, bar graphs, line plots and line graphs Standard Number: 3 Interpret and construct Venn diagrams to sort and describe data Standard Number: 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 Standard Number: 5 Propose and explain interpretations and predictions based on data displayed in tables, charts and graphs Probability Standard Number: 9 Conduct simple probability experiments and draw conclusions from the results; e.g., rolling number cubes or drawing marbles from a bag Standard Number: 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 Standard Number: 11 Relate the concepts of impossible and certain-to-happen events to the numerical values of 0 (impossible) and 1 (certain). Standard Number: 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 Standard Number: 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 Statistical Methods Standard Number: 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 Standard Number: 7 Identify the median of a set of data and describe what it indicates about the data Standard Number: 8 Use range, median and mode to make comparisons among related sets of data Grade: Gr. 5 Data Analysis and Probabilty Standard Data Collection Standard Number: 1 Read, construct and interpret frequency tables, circle graphs and line graphs. Standard Number: 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 Standard Number: 3 Read and interpret increasingly complex displays of data, such as double bar graphs Standard Number: 4 Determine appropriate data to be collected to answer questions posed by students or teacher, collect and display data, and clearly communicate findings Standard Number: 5 Modify initial conclusions, propose and justify new interpretations and predictions as additional data are collected Probability Standard Number: 7 List and explain all possible outcomes in a given situation. Standard Number: 8 Identify the probability of events within a simple experiment, such as three chances out of eight Standard Number: 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 Standard Number: 10 Compare what should happen (theoretical/expected results) with what did happen (experimental/actual results) in a simple experiment Standard Number: 11 Make predictions based on experimental and theoretical probabilities Statistical Methods Standard Number: 6 Determine and use the range, mean, median and mode, and explain what each does and does not indicate about the set of data Grade: Gr. 6 Data Analysis and Probabilty Standard Data Collection Standard Number: 1 Read, construct and interpret line graphs, circle graphs and histograms. Standard Number: 2 Select, create and use graphical representations that are appropriate for the type of data collected Standard Number: 3 Compare representations of the same data in different types of graphs, such as a bar graph and circle graph. Probability Standard Number: 7 Design an experiment to test a theoretical probability and explain how the results may vary Statistical Methods Standard Number: 4 Understand the different information provided by measures of center (mean, mode and median) and measures of spread (range). Standard Number: 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. Standard Number: 6 Make logical inferences from statistical data Grade: Gr. 7 Data Analysis and Probabilty Standard Data Collection Standard Number: 1 Read, create and interpret box-and-whisker plots, stem-and-leaf plots, and other types of graphs, when appropriate Standard Number: 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 Probability Standard Number: 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 Standard Number: 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 Statistical Methods Standard Number: 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. Standard Number: 4 Construct opposing arguments based on analysis of the same data, using different graphical representations. Standard Number: 5 Compare data from two or more samples to determine how sample selection can influence results Standard Number: 6 Identify misuses of statistical data in articles, advertisements, and other media Grade: Gr. 8 Data Analysis and Probabilty Standard Data Collection Standard Number: 1 Use, create and interpret scatterplots and other types of graphs as appropriate Standard Number: 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 Standard Number: 3 Differentiate between discrete and continuous data and appropriate ways to represent each. Probability Standard Number: 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 Standard Number: 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 Statistical Methods Standard Number: 4 Compare two sets of data using measures of center (mean, mode, median) and measures of spread (range, quartiles, interquartile range, percentiles). Standard Number: 5 Explain the mean’s sensitivity to extremes and its use in comparison with the median and mode Standard Number: 6 Make conjectures about possible relationship in a scatterplot and approximate line of best fit Standard Number: 7 Identify different ways of selecting samples, such as survey response, random sample, representative sample and convenience sample Standard Number: 8 Describe how the relative size of a sample compared to the target population affects the validity of predictions Standard Number: 9 Construct convincing arguments based on analysis of data and interpretation of graphs Grade: Gr. 9 Data Analysis and Probabilty Standard Data Collection Standard Number: 1 Classify data as univariate (single variable) or bivariate (two variables) and as quantitative (measurement) or qualitative (categorical) data Standard Number: 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 Probability Standard Number: 7 Use counting techniques and the Fundamental Counting principle to determine the total number of possible outcomes for mathematical situations Standard Number: 8 Describe, create and analyze a sample space and use it to calculate probability Standard Number: 9 Identify situations involving independent and dependent events, and explain differences between and common misconceptions about probabilities associated with those events Standard Number: 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 Statistical Methods Standard Number: 3 Analyze and interpret frequency distributions based on spread, symmetry, skewness, clusters and outliers. Standard Number: 4 Describe and compare various types of studies (survey, observation, experiment), and identify possible misuses of statistical data Standard Number: 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 Standard Number: 6 Make inferences about relationships in bivariate data, and recognize the difference between evidence of relationship (correlation) and causation Grade: Gr. 10 Data Analysis and Probabilty Standard Data Collection Standard Number: 1 Describe measures of center and the range verbally, graphically and algebraically Standard Number: 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 Standard Number: 3 Display bivariate data where at least one variable is categorical Standard Number: 4 Identify outliers on a data display; e.g., use the interquartile range to identify outliers on a box-and-whisker plot. Probability Standard Number: 7 Model problems dealing with uncertainty with area models (geometric probability) Standard Number: 8 Differentiate and explain the relationships between the probability of an event and the odds of an event, and compute one given the other. Statistical Methods Standard Number: 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 Standard Number: 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 Grade: Gr. 11 Data Analysis and Probabilty Standard Data Collection Standard Number: 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 Standard Number: 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 Probability Standard Number: 10 Understand and use the concept of random variable, and compute and interpret the expected value for a random variable in simple cases Standard Number: 11 Examine statements and decisions involving risk; e.g., insurance rates and medical decisions. Statistical Methods Standard Number: 3 Describe how a linear transformation of univariate data affects range, mean, mode, and median. Standard Number: 4 Create a scatterplot of bivariate data, identify trends, and find a function to model the data. Standard Number: 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. Standard Number: 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 Standard Number: 7 Describe the standard normal curve and its general properties, and answer questions dealing with data assumed to be normal. Standard Number: 8 Analyze and interpret univariate and bivariate data to identify patterns, note trends, draw conclusions, and make predictions. Standard Number: 9 Evaluate validity of results of a study based on characteristics of the study design, including sampling method, summary statistics and data analysis techniques Grade: Gr. 12 Data Analysis and Probabilty Standard Data Collection Standard Number: 1 Identify and use various sampling methods (voluntary response, convenience sample, random sample, stratified random sample, census) in a study. Probability Standard Number: 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 Statistical Methods Standard Number: 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 Standard Number: 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 Standard Number: 4 Apply the concept of a random variable to generate and interpret probability distributions, including binomial, normal and uniform Standard Number: 5 Use sampling distributions as the basis for informal inference |
||
