# Big Ideas, Goals & Content for 4 th grade Data Collection & Analysis Unit

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1 Big Ideas, Goals & Content for 4 th grade Data Collection & Analysis Unit Big Ideas Graphs are a way of organizing data and they appear in newspapers, magazines, on the Internet and other places in everyday life. Graphs need to be interpreted in order for them to have meaning. Graphs can be used to compare related data. It is important to look at the shape of the data on a graph to make general statements about its meaning. There are also specific ways to interpret data and summarize what it represents, such as how spread out the data is (range) and what the center of the data looks like (median, average, mode). Anyone can collect data, and this is often done by counting, measuring or conducting experiments. Once data is collected, it needs to be sorted and classified. Many objects can be classified in different ways, and a single object can belong to more than one group. Once data is sorted, it can be used to make a graph. It is possible, and often helpful, to represent the same data in different ways. Statistics is when data is represented in a numerical way. Statistics can be used to make predictions about a population from data collected on a sample of the population. The greater the sample size, the more likely its data will be representative of the whole population. Goals GLCEs from given data Order a given set of data, find the median, and specify the range of values Solve problems using data presented in tables and bar graphs NCTM Content Standards Recognize the differences in representing categorical and numerical data Formulate a survey question and collect data for this question Describe the shape and important features of a set of data and compare related data sets, with an emphasis on how the data are distributed; Compare different representations of the same data and evaluate how well each representation shows important aspects of the data. Propose and justify conclusions and predictions that are based on data NCTM Process Standards Communicate mathematical thinking coherently and clearly to peers, teachers, and others Given a chart or graph, find range, mode, median, average, and any outliers for the data

2 Select, apply, and translate among mathematical representations to solve problems Use representations to model and interpret physical, social, and mathematical phenomena Content In this unit I will address how data can be collected, sorted, visually represented and interpreted. I will also address how to use tables, charts and graphs to solve problems and gather information. The unit will begin by introducing the idea of statistics, data collection, data organization, line plots and making observations about data. Students will become comfortable with collecting data, organizing it into categories and visually representing the data in the form of a table, bar graph, line plot or other form, including 3-D representations. Students will work toward mastery of constructing line from data, interpreting the shape of the data, and finding range, median, mode, average and outliers from an ordered data set. One recurring theme for the unit will be how data can be collected, sorted, and represented in multiple ways. These different ways can be compared and critiqued for effectiveness. Another theme will be the need for active interpretation of data and graphs. The data does not have meaning until it is interpreted. Students should also see a strong connection between what they are learning and doing in math class to the data, graphs, and statistics used in the world around them. A third theme will be the idea that statistics for a sample set of data can be used to make predictions about larger populations. Students will need to become comfortable making interpretations and predictions based on data. They will need to justify their conclusions and communicate their ideas effectively to the rest of the class. Students will work toward mastery of using mathematical representations, (namely charts and graphs) to solve problems, by gleaning specific information from them. They will also work toward mastery of creating their own mathematical representations to model and interpret phenomena of the world around them. Assessment Final Project: Each student will choose a survey question, survey 4 th graders during a special free-for-all survey time, organize their data, create a table, a bar graph, and then use the computer to create another type of graph. They will find the median, mode, average, range and any outliers for their data, then give a short presentation about their findings to the class. Classmates will be able to ask questions and make comments about the data and graphs. The table, graphs, mean, median, mode, range and outliers will be displayed on a piece of colored to be used as a visual during the presentation.

6 6 7 Graphs can be used to make predictions. Median can only be found if data is ordered, or graphed. The median is the very middle number if the data set contains an odd number of items. The median is the point exactly between the two middle values in an even numbered data set. Looking at Mystery Data. Investigations Grade 4 Statistics, p. 45. Students looks at graphs of unknown data to describe the data and guess what it represents. HW: Mystery Data C Finding the Median. Investigations Grade 4 Statistics, p. 51. Students line up in height order and sit down 2 at a time (1 at one end, 1 at the other) to act out finding the median. Talk about median as a way of determining "typical", talk about what median is good for and find median for other data sets. Mystery Data A, B, C handouts NBA All-Star cards, previously collected height, raisin and family size data. Describe the shape of data, including range, outliers and mode. Compare data to related data set in order to draw conclusions and make predictions. Propose and justify conclusions and predictions that are based on data Order a given set of data, find the median, and specify the range of values. 8 The median is not always the best indicator for what's typical of data. The median can be used to compare two data sets. Using Landmarks in Data. Investigations Grade 4 Statistics, p. 57. Discuss if median is a good indicator of "typical" in the case of the Cat Data. Use the median of the Cat data and Lion Data to compare the two data sets Cat Data handout, Lion Data handout. Order a given set of data, find the median. Use the median to compare two data sets. 9 Average is another way of determining what's typical of a data set. Cat and Lion Data continued. Investigations Grade 4 Statistics, p. 57. Students find range, outliers, and mode of both sets. Afterward, the idea of average is introduced as another way of talking about what's typical of a data set. Cat Data handout, Lion Data handout. Describe the shape of data, including range, outlier and mode.

9 Once data is sorted, it can be used to make a graph. It is possible, and often helpful, to represent the same data in different ways. Once data is sorted, it can be used to make a graph. It is possible, and often helpful, to represent the same data in different ways. Once data is sorted, it can be used to make a graph. It is possible, and often helpful, to represent the same data in different ways. Data collection and analysis can be used to provide helpful information about a group of people. Students use the "Create a Graph" program at nces.ed.gov/nceskids/index.asp?flash=true to create a circle graph of their data. Students finish their poster, adding the computer-generated graph and gluing everything in place. They practice what they will say for their presentation. Extra time can be used to work on one of the "extra" projects or worksheets. Presentations. Students present their poster with the two graphs, data table, question and writing about data to teacher and classmates. Posters are collected for grading. computers, Create a Graph website extra project worksheets, 11x17 colored hand and computergenereated graphs, data table Survey Project posters Create a graph using computer software. Communicate mathematical thinking coherently and clearly to peers, teachers, and others Communicate mathematical thinking coherently and clearly to peers, teachers, and others 21 Once data is collected, it needs to be organized and interpreted to have meaning and be used for solving problems. Field Trip Assessment. Students use data presented in three different ways to solve a problem about where 4th graders will go for their field trip. They also determine cost of the trip per student. Field Trip packet Solve problems using data presented in tables and bar graphs. Create a graph using given data. 22 Continuation of Day 21. Students who finish early may work on an "extra" assignment

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