Math Forum | Urban Systemic Initiative

Exploring Data - All Levels || Student Center || Teachers' Place

### 1989 NCTM Standards: Statistics and Probability

In grades K-4, the mathematics curriculum should include experiences with data analysis and probability so that students can -

• collect, organize, and describe data;
• construct, read, and interpret displays of data;
• formulate and solve problems that involve collecting and analyzing data;
• explore concepts of chance.

Focus: Collecting, organizing, describing, displaying, and interpreting data, as well as making decisions and predictions on the basis of that information, are skills that are increasingly important in a society based on technology and communication. These processes are particularly appropriate for young children because they can be used to solve problems that often are inherently interesting, represent significant, applications of mathematics to practical questions, and offer rich opportunities for mathematical inquiry. The study of statistics and probability highlights the importance of questioning, conjecturing, and searching for relationships when formulating and solving real-world problems.

Read more about the 1989 NCTM Standards by logging in to my.nctm.org
Read the current NCTM Data Analysis and Probability Standard

### California Draft Standards: Statistics, Data Analysis, Probability

Kindergarten
Students collect information about objects and events in their environment, posing information questions, collecting data, and recording the results using objects, pictures, and picture graphs. Sample task: Place your sticker on our classroom graph to show which of these five books is your favorite.

Read California's final Kindergarten Mathematics Content Standards

Students collect, organize, represent and compare categorical data on simple graphs and charts, 1) sorting objects and data by common attributes and describing the groups formed using categorical labels; and 2) collecting and comparing data using pictures, bar graphs, tally charts, and picture graphs, explaining how the data were organized and represented. Sample tasks: Given a question such as "What is your favorite ice cream flavor," ask each member of your group of 10 to record the answers in an organized way, and report on the results to the class.

Students collect, record, organize, display and interpret numerical data on bar graphs and other representations, 1) collecting numerical data in systematic ways, keeping track of what/who has been counted; 2) representing the same data set in more than one way (e.g., charts with tallies and bar graphs; 3) identifying features of data sets (range and mode); 4) asking and answering simple questions related to data representations. Sample tasks: Generate survey questions that can be answered with a number (e.g., number of people in your class). Predict the survey results, carry out the survey, graph the data and write true statements about the data.

Students collect data and conduct simple probability experiments, determine the number of possible outcomes, and make simple predictions, 1) identifying whether common events are certain, likely, unlikely, or impossible; 2) recording the possible outcomes for a simple event (e.g., tossing a coin), and systematically keeping track of the outcomes when the event is repeated many times; and 3) summarizing and displaying the results of probability experiments in a clear and organized way and using the results to make predictions about future events, recognizing that the predictions include a degree of uncertainty. Sample task: Make a cube from construction paper so that three of the sides have a picture of a dog, two of the sides have a picture of a cat, and one of the sides has a picture of a bird. Before you roll the cube 20 times, predict which animal will come up most and give a reason why.

Students collect, organize, represent and interpret numerical and categorical data, and clearly communicate their findings, 1) formulating survey questions and systematically collecting data to answer them; 2) representing data on a number line, coordinating graphs, tables, and charts; 3) identifying the mode(s) for sets of categorical data, and the mode(s) median, and any apparent outliers for numerical data sets; and 4) interpreting one- and two-variable data graphs to answer questions about a situation. They make predictions for simple probability situations, 1) representing all possible outcomes for a simple probability situation in an organized way (e.g. tables, grids, tree diagrams; and 2) expressing outcomes of experimental probability situations verbally and numerically (e.g. 3 out of 4 3/4).

Solve problems by interpreting data and predicting outcomes; make decisions based on the information collected, and clearly communicate the reasoning used to obtain the results.

BENCHMARKS: Grade-appropriate knowledge, skills and concepts ALL students achieve:

1. Collect data by observing, measuring, surveying, and counting. Determine the most effective way to organize data for a display.
2. Interpret data by making inferences and convincing arguments that are based on data analysis.
3. Predict and determine why some outcomes are more likely, less likely, or equally likely.
4. Recognize the concepts of "fair" and "unfair" as applied to simple games.
5. Solve problems using various strategies for making combinations.
6. Demonstrate a variety of techniques for representing and organizing data such as physical objects, tallies, pictographs, and bar graphs.
7. Interpret data using the concepts of largest, smallest, most often, and middle.

PERFORMANCE EXAMPLES: The students may do ONE or MORE of the following as an example of a task that incorporates the benchmarks:

• Generate a survey questionnaire comparing healthy foods vs. "junk" foods. Distribute, collect, and analyze data in a cooperative learning group. Present and defend the findings.
• Generate a chart, spreadsheet and/or graph of statistical information (e.g., using the survey above or charting weather day by day for a period of time).
• Determine, when given a fixed number of teams, the number of games that would need to be played in a round-robin tournament.
• Use number cubes, coins, spinners, or sets of objects to determine if outcomes have an equal probability of occurring.
• Determine the absorbency of different brands of paper towels. Compare and evaluate the results.