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.
3 This assessment matches the goals of formulating a survey question, collecting data, organizing data, and representing data graphically in different ways. Students will be representing social phenomena with a model and communicating mathematical ideas to their classmates and teacher. Students are constructing bar graphs and tables. They will not need to solve a problem using data presented in tables and bar graphs, but this goal is assessed in the Field Trip assessment. Children need to know about what kind of question will work best for the survey. We will have a discussion in class about how to word a survey question and how it can be helpful to offer answer choices for the question. They will need to know how to organize data into a table and a bar graph. They will also need to know how to use Excel or another graph-creating program to make a graph from their data. They will need to know how to find range, median, average, mode and outliers for a set of data. I expect some initial difficulty with students deciding on a survey question. Hopefully the discussion about picking a question will help with this. I foresee some students having difficulty with making a computer-generated graph because they tend to have trouble during computer assignments, and I do not know how much experience students have with this sort of task. Finding the average and median may be difficult for some, along with remembering the difference between the two. Computer skills are not a specific part of this unit, and this could hinder some students when they prepare their computer-generated graph. I will still be able to see their graph-making, data organizing and data analysis skills demonstrated in the noncomputer part of the assignment. I also found a website with a Create a Graph program that is more straightforward than using Excel. I may offer students the choice of which program to use or have everyone use the easier one. Some students may have difficulty sharing their ideas in front of the class. One of the unit goals is being able to effectively communicate mathematical ideas, though. Hopefully after looking at many graphs and talking a lot about data in whole group and small group discussions, students will be comfortable with this kind of talk. This assessment emphasizes visual representations of ideas, as well as verbal representation of ideas. There is a kinesthetic aspect in that students will get to move around the classroom as they conduct their survey. That part of the assessment is also social, as students are interacting with one another to complete the task. The assessment appeals to the logical learning style because it deals with organization. For those who are less logic and more creative, I will emphasize the choice students have for making their computer graph. Creativity can also be used in thinking up a unique survey question. Field Trip Problem: The fourth grade classes at Sunset Elementary School are going on a field trip together. They have a choice of three places to go (Discovery World, Modern Art Museum, or SeaTown). The students in each class took a vote to see which place most of them wanted to go. They agreed that they would go to the place that got the most votes. Here are the voting results from the three classes. Students are given the results of the three classes voting: They are all in different table/chart forms. The students have to figure out which destination got the most votes by using the information from the tables to make a graph or table that shows how many fourth graders voted to go to each place. They also have to figure out how much the trip
4 (to the winning destination) will cost for each student by using the information given about student/adult admission and bus fees. This assessment will meet the goal of solving problems using data in tables and graphs, as well as organizing data, and constructing tables and graphs. The students will need to know how to read tables and charts, organize the data and create their own table or graph. The assessment does not meet all learning goals because the others are addressed with the final project. The main focus of this assessment is problem solving with tables and graphs. Multiplication and division are skills needed for this assessment. These skills are not an explicit part of this unit, but were covered earlier in the year, and it will be good to see what students have retained of these skills. I expect the students to have the most difficulty with figuring out the cost for each student because there are several steps. They must first figure out which destination the 4 th graders are going on, locate the information for that destination and then interpret the chart. The price of all the children needs to calculated, as well as the price for adults and buses. Students have to pay attention to the fact that each class must have 2 adult chaperones, but these people are not helping pay the student or bus cost, so should not be factored in when dividing up these costs. I anticipate some students being overwhelmed by all the steps in the problem, so I will explicitly break down the assessment into steps to lessen anxiety. Careful reading of the problem is necessary. Reading is not an explicit skill of the unit, so I will read the problem with the whole class and clear up any questions before the students work on their own. This assessment emphasizes problem solving, visual representation and computation. I will collect all work students do to solve the problem so I can see their thinking. If some students need to write out what is going on, use labels, or breakdown computations into smaller parts, that s fine. This will show me more about their learning styles and problem solving styles. This also shows me that their incorrect answer came from a computation mistake, not a misunderstanding of the problem. Overall Plan at a Glance Day Big Idea Activity Materials 1 Data can be collected by counting. Once data is collected and organized into a graph, it is helpful to talk about the shape of the data. A graph helps us make predictions. How Many Raisins in a Box? Investigations Grade 4 Statistics, p. 16. Each student counts the number of raisins in their box. The teacher collects data from students. In groups, students sketch quick graphs and write 3 things they can say about the data boxes of raisins, unlined paper GLCE/Teaching Objective from given data; Describe the shape and important features of a set of data, including range and outliers
5 It's important to define data collection. Graphs can be used to think about what's typical. Data can be collected by measuring. It's important to define data collection. Graphs can be used to think about what's typical. Graphs can be used to make predictions. How do we define what's typical? How do we use "what's typical" to compare to related data sets? How many people in a family? Investigations Grade 4 Statistics, p. 25. Data about students' family size is collected and students represent data in 2 different ways, and disucss how to determine typical family size. During Kindergarten Buddy time, 4th graders will measure their K bud, and K buds will help 4th graders measure selves. How Many People in a family (cont.) Investigations Grade 4 Statistics, p. 28. Go over homework where students graphed "How Many Brothers/Sisters?" data. Finish up discussion from previous day. How Tall are Fourth Graders? Investigations Grade 4 Statistics, p. 34. Previously collected height data of class is represented, shape of data, range, outliers, mode are discussed. Data is compared to other 4th grade classes' data. unlined cubes, Homework Sheet--How Many Brothers & Sisters? Measuring tapes taped to wall, recording sheet Completed homework sheets, student graphs from previous day Previously collected data, Other 4th grade classes' height graphs handout from given data; Describe the shape and important features of a set of data, Compare different representations of the same data and evaluate how well each representation shows important aspects of the data, including range and outliers Collect data by measuring. from given data. Describe the shape of data. Compare different representations of the same data, propose and justify conclusions and predictions that are based on data from given data. Describe the shape and important features of data. Compare related data sets, with an emphasis on how the data are distributed. 5 Graphs can be used to compare two related data sets and draw conclusions about the represented populations. Compare Kindergarten & 4th Graders-- How Much Taller? Investigations Grade 4 Statistics, p. 40. In groups, students decide on a way to compare height data from Kindergarteners and own class, and publish findings as a graph or chart. Previously collected data, colored markers, graph paper from given data. Compare related data sets. Communicate mathematical thinking coherently and clearly to peers and teachers.
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.
7 10 Median and average are two different measures of what's typical. They each have different uses and are found using different methods. Data collection through experiments and activites (self-created). Students go to different stations, perform a task, and collect data. Their data is recorded on a big chart on the board. Once data is collected, class calculates and discusses average and median. Homework: Compare data sets, find average and median. Materials to support station activites. Collect data by experiments. Order a given set of data, find the median and the average When working in a group, it's important to clearly explain your thoughts to others, and listen to group members' ideas. More can be accomplished when people work together. Range, mode, median, average and outliers can be found from a data set. Groupworthy Task--Using Build It! Task from "Get it Together", groups work to build figures from clue cards. Overflow day. This day can be used to review/reteach concepts that students are still having trouble with. Students who do not need reteaching will have an independent task related to graphing to work on. task cards, build it! Cards in envelopes, isometric graph role cards data to practice with, worksheets for independent task Practice working successfully with a group to accomplish a math task. from given data; Describe the shape and important features of a set of data, including range, mode, median, average and outliers 13 What happens when new data is added to an existing data set? Cavity Data handout from Investigations p. 58. Students find range, median, mode, outliers and average. Then they tell which of these would be affected if two new data pieces were added to the data set. Students who finish early can write a story about the class from which the data came. Cavity Data handout, calculators (for average) Describe the important features of a data set, including range, mode, median, average, and outlier. Recognize when and why these features would change with the addition of new data pieces.
8 14 It's important to word a survey question carefully to get the results you are after. It is helpful to offer choices for the answer, so data can be easily classified. Students receive the guidelines from the Survey Project assignment. Teacher goes over guidelines and how to choose a survey question. Students use discussion about "What makes a good survey question?" to choose their survey question and come up with answer options if appropriate. Survey Project guidelines handout, scrap paper Think of a survey question that can be used to collect data, which will be graphed and analyzed. 15 Range, median and mode can be found given a set of data organized into a line plot. Exploring Range, Median, and Mode Assessment. Addison-Wesley Problem Solving p. 10. Independently students find range, median, mode of data, explain how line plot helps them find these and explains how range, mode and median are affected with the addition of new data. Finding average is optional (on back) Exploring Range, Median and Mode handout. Describe important features of a data set, including range, median and mode. Communicate mathematical thinking coherently and clearly through writing Data can be collected by conducting a survey. All three fourth grades get together in the team room to conduct their surveys. Students must get at least fifteen pieces of data. Data collection sheet Collect data using a survey. 17 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). Using the data from their survey question, students make a table and bar graph. They find the range, mode, mean, median and any outliers, as well as write a few sentences about their data and how it could be useful. 18 continuation of day 17 1cm graph colored 11x17 markers Organize data in a table and graph it; find important features of data including range, mode, median, average and outlier (if applicable to data set). Propose and justify conclusions that are based on data
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
10 Extra There are many ways to organize and graph data. circle graph, letter tallying and horizontal/vertical bar graph worksheets. These can all be completed independently by following directions on the worksheets. circle graph, letter tallying and horizontal/ vertical bar graph worksheets Solving problems using data presented in tables and bar graphs. Organizing data. Graphing data. Extra Anyone can collect data, and this is sometimes done with the help of surveys. Data collection can be used to help people make decisions. You have just inherited a lot of money and want to start your own amusement park. You want to attract as many people as possible to your park, so you need to create a survey to find out what people like. Design a survey of at least 8 questions to find out how you should design your park. assignment sheet, lined paper Formulate survey questions. Extra To analyze data, one should know about line plots, median, mode, range, outlier and average. Of course you now know a lot about collecting, graphing and analyzing data, but 3rd graders do not. Create a book, cards or a poster that shows and explains line plots, mode, median, range, outlier, average and anything else you think is important that 4th graders next year would find helpful when learning about these things. unlined markers, graph colored pencils Communicate mathematical thinking coherently and clearly to peers, teachers, and others Extra There are many ways to organize and graph data. Sometimes it is helpful to represent data in more than one way. Is there a type of graphing that we haven't done in class that you'd like to try? Line graph, pictograph, graphs with more than one data set on them? You can either use data we've already worked with or create your own data set and try a new form of graphing. past data sets, graph unlined paper Graph data from a given data set. Extra Graphs can be used to make predictions. 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. Mystery Data D Handout 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