Fifth Grade
Data Analysis and Probability
Standard 5-6: The student will demonstrate through the mathematical processes an understanding of investigation design, the effect of data-collection methods on a data set, the interpretation and application of the measures of central tendency, and the application of basic concepts of probability.
The indicators for this standard are grouped
by the following major concepts:
The indicators that support each of those major concepts and an explanation of the essential learning for each major concept follows.
5-6.1 Design a mathematical investigation to address a question.
5-6.2 Analyze how data-collection methods affect the nature of the data set.
In third grade students compared the benefits of using different forms of data representation. In fourth grade students compared how data collection methods impact survey results. Now in fifth grade students should design a mathematical investigation to address a question and analyze how data collection methods affect the nature of the data set.
Frequent investigations with brief surveys should be used to acquaint students with collecting, representing, summarizing, comparing, and interpreting data while more extensive projects can allow students to analyze data—formulate, questions, collect and represent data, and consider whether the data gave them the information they needed to answer their question.
When designing the investigation students should decide whether data will be collected through observation, survey, or experiment. Students should compare data sets collected in different ways and determine how the methods used affect the data sets. Aspects of data collection to consider are: (a) how to word questions, (b) whom to ask, (c) what and when to observe, (d) what and how to measure, and (e) how to record data.
5-6.3 Apply procedures to calculate the measures of central tendency (mean, median, and mode).
5-6.4 Interpret the meaning and application of the measures of central tendency.
In third grade students applied a
procedure to find the range of a data set. Now in fifth grade students should
apply procedures to calculate the measures of central tendency (mean, median,
and mode). Not only should students be
able to calculate the measure of center but most importantly they should be
able to interpret the meaning and application of the measures of center. In
other words, fifth grade students should have clear knowledge about the
relationship of the measures of central tendency to the data set. They should
begin to see a set of data as a whole, describe its shape, and describe the
features of data sets including measures of central tendency. Mean, median and
mode provide a numeric picture of the shape of the data. While each of these
measures represents a specific average, mean is computed by adding all of the
values in the data set and dividing the sum by the number of data pieces added.
Mode describes the value that occurs most frequently in the set and median
describes the value in the center of the data when arranged in numeric order. The
emphasis in fifth grade is on interpreting the relationship between the data
set and the measures of central tendency and on knowing what the measures say
about the data set. Students in sixth grade will progress to analyzing when one
measure is more appropriate for a given situation than another.
5-6.5 Represent the probability of a single-stage event in words and fractions.
5-6.6 Conclude why the sum of the probabilities of the outcomes of an experiment must equal 1.
Fourth grades students analyzed the possible outcomes for a simple event. Fifth grade students build on that to represent the probability of a single-stage event in words and fractions. (Fractions were introduced in third grade.) In grade 5, students should explore probability through experiments that have only a few outcomes. They should use common fractions to represent the probability of single stage.
In third grade students gained an understanding as to when the probability of an event is either 0 or 1. Now in fifth grade students should engage in learning experiences that that will enable them to come to the conclusion that the sum of the probabilities of the outcomes of a a single-stage event must equal 1.
Given information from a problem situation, students should be able to create a problem statement involving probability based on that situation. In other words, students should be comfortable enough with probability to take a problem situation like “the chance of landing on red is more likely” and translate that to a probability situation. In that case, students might create a spinner where the largest portion is red and be able to explain why the spinner matches the problem situation. Through experiences, students should realize that although they cannot determine an individual outcome, they can predict the frequency of different outcomes. Students should be able to write the probability of an event as a fraction and use vocabulary such as likely, unlikely impossible, certain and equally likely.