Students will learn about various data collection methods and how to show data in a variety of displays. Students will:
- answer questions based on a variety of displays.
- identify the various data-collecting methods and their purposes.
- create a graph with a title, proper scale, and labels.
- How may data be organized and represented to reveal the relationship between quantities?
- How can probability and data analysis be used to make predictions?
- How does the type of data effect the display method?
- What does it mean to analyze and estimate numerical quantities?
- What makes a tool and/or strategy suitable for a certain task?
- Pictograph: A way of representing statistical data using symbols to match the frequencies of different kinds of data.
- chart paper
- index cards
- copies of Collecting Data Four Square (M-5-4-1_Collecting Data Four Square)
- copies of Data Table (M-5-4-1_Data Table)
- copies of Graph Paper (M-5-4-1_Graph Paper)
- copies of Graphs (M-5-4-1_Graphs)
- copies of Misleading Graphs (M-5-4-1_Misleading Graphs and KEY)
- Monitoring student responses throughout the carousel walk activity will help establish a baseline for graph comprehension.
- Student responses throughout the Four Square Activity will be used to assess how well students understand how to collect information for graphing purposes.
- The Data Table activity can be used to assess how well students transfer data into different kinds of graphical displays.
Scaffolding, Active Engagement, Modeling, and Explicit Instruction.
W: Display graphs around the classroom and encourage students to walk around the room to observe and report observations that differ from previous groups.
H: Engage students in the lesson by discussing the similarities and differences between graphs. Build a list of for gathering data that will be used to create graphs.
E: Discuss the limitations of collecting data. Because you won't be able to allow all responses, you may need to limit the options accessible in order to provide a comparable graph.
R: Have students works in pairs with onw creating a bar graph and one, a line graph using the same data from the Data Table in the Resources. Check that they have included all of the relevant graph components (e.g., labels, title) and are using the correct scale.
E: Discuss with students the graphs they created, their conclusions, who can benefit from the information, and the best type of graph to represent the data.
T: Extra activities that can be used to reinforce this lesson, students can interpret graphs from current news sites or identify misleading graphs and explain how the data can be misinterpreted.
O: This lesson teaches students how to represent data using various graphs.
Before the lesson, print and hang the graphs (M-5-4-1_Graphs) on chart paper around the classroom. "I've displayed various graphs around the room. You will be assigned to a small group and as a group will take a carousel walk around the room, viewing each graph and recording as many different observations as possible for each graph within the time restriction." (A carousel walk is a physical activity in which students rotate around the room in a clockwise direction. Students should have at least two minutes at each station. If several responses are recorded on the chart paper, students may need additional time.) "Be sure to read previous student responses before recording any new ones. Make sure all of your observations are relevant to the graph or can be answered by the data in the graph. Each group will be given a different colored marker to record responses." While students are recording their observations at each station, keep an eye on their responses and group interactions to determine their level of graph interpretation. When students have finished, share one response from each chart to demonstrate the range of information that may be obtained from a graph.
"After reviewing the various graphs, what do you believe they all have in common? How do you detect that they differ?" Create a chart on the board similar to the one shown below. Allow students time to think-pair-share, and then ask for volunteers to add one idea to the chart.
Refer to the graphs by creating an overhead transparency or pointing to them while asking, "How did the person creating each graph collect the data required to construct the graph?" Allow students time to think-pair-share. Elicit responses from students and guide student understanding of the following ways to collect data:
Research: accessing materials such as books with statistics or exploring the Internet (M-5-4-1_Graphs).
Survey or Interview: ask people a question orally or in writing (number of pets our class owns graph, in M-5-4-1_Graphs).
Experiment or Simulation: Perform a technique to examine the outcomes of various factors (Number Cube Results graph in M-5-4-1_Graphs).
Observation: record what is seen at a certain time and place.
Give each student two index cards. Students should write one of the four ways to collect data (previous bullets) on one side of an index card, then turn it over and write another category on the back. Have students use the second card to record the last two categories. Sample cards are provided below.
Use a list like the one below to get students thinking about how data can be collected. Ask, "If we wanted to make a graph of the following data, which method do you think would be the best way to collect the data for that graph?" Tell students to hold up the side of the index card that they believe is the best way to collect data for each data set. Discuss student responses; sample responses are provided, but certain data sets may have multiple appropriate ways to collect data.
number of students that ride their bike to school each week (observation)
number of points scored by a team in each game of a football season (research)
number of times each marble color gets pulled from a bag of marbles in 50 trials (experiment/simulation)
class's favorite ice cream flavors (survey)
number of each color of M&Ms in a snack-sized package (experiment)
number of electoral votes that went to the Democratic Party's nominee for president in the previous 10 elections (research)
vehicle manufacturers parked in the teacher parking lot at school (observation)
average monthly temperature in your city (research)
number of siblings per classmate (survey)
amount of food donated by each classroom to the food drive (observation or survey)
types of trees found on the school lot (observation)
Distribute Collecting Data Four Square (M-5-4-1_Collecting Data Four Square) to all students. Allow them around five minutes to generate as many different responses as possible for each category. Collect their responses. Scanning the responses can provide formative feedback on whether extra instruction or clarification is required.
"Suppose we wanted to collect data on the types of books that students enjoy reading. What are some possible responses that students could give?" (Responses could include fantasy, nonfiction, biography, science fiction, mystery, realistic fiction, folklore, and fables.) "Sometimes the responses we receive overlap, do not fit into a single category, or leave us with too many categories to graph. One method for controlling replies is to provide students with a list of options. In this way, we avoid some of the problems that may arise when using open-ended responses. What if we asked everyone of our fifth graders what their favorite sports team was? What kind of replies might we get? What problems may arise if we try to graph this data? What can we do to achieve better results? Please share your thoughts with the students sitting near you. I'll ask volunteers to give their ideas in a few minutes." After students have had time to talk and volunteers have shared their opinions, bring student thinking to the realization that questions asked must be well-structured. Also, explain to students that providing options might help them control the data required to create a graph. Make sure students understand that the method used to collect data can influence the outcomes.
Provide students with the Data Table (M-5-4-1_Data Table). Have students work in pairs. One student will produce a bar graph, while the other will create a line graph. Students can make a graph with paper and pencil (M-5-4-1_Graph Paper), a program like Microsoft Excel, or an interactive Web site such as http://nces.ed.gov/nceskids/createagraph/. Remind students of the essential components of a graph: title, axis labels, a suitable and consistent scale, and data. After creating the graphs, students can answer the questions on the Data Table sheet. Monitor student performance and clarify understanding as needed.
While students are finishing their graphs, hold mini-conferences with them and pose questions similar to those below.
What's the title of your graph?
What scale did you choose for the vertical axis? Why?
What conclusions can you draw after reading your graph?
Who would benefit from reading this graph?
Is the data affected when used to create two different types of graphs?
What graph do you believe represents this data, and why?
Students that complete early can design a new graph using data from the following two websites: http://www.cityrating.com/averagetemperature.asp or http://factfinder2.census.gov/faces/nav/jsf/pages/index.xhtml. Students can also design a survey question and collect data in the classroom to create a graph.
Additional questions to assess learning (that can be used as journal prompts) follow.
Where do we find graphs? (Newspapers, magazines, books, television, etc.)
Why do we present data in graphs? (Visualizing data often makes it easier to understand.)
What are the different methods for gathering data to create a graph? (Line graph, bar graph, circle graph, tally chart, pictogram, etc.)
Can the same data be represented in two different types of graphs while still conveying the same information? Explain. (Yes . . .)
Extension:
Use the ideas and activities below to satisfy your students' needs during the lesson and throughout the year.
Routine: Gather graphs from the internet, magazines, or newspapers. Students can help collect samples, then create a graph and interpret the data. Possible questions to ask are:
What type of graph is this?
What is the graph's title?
How do you think the data was collected?
What conclusion can you take from this graph?
What question might this graph help to answer?
These websites provide a few graphs that might be used for this activity:
http://nces.ed.gov/nceskids/createagraph/ (click on the EXAMPLES tab)
http://www.mathgoodies.com/lessons/graphs/line.html
http://www.usatoday.com/news/snapshot.htm (current data is displayed in various graphic forms, not necessarily traditional graphs.)
Small Groups: For students who may require a review in graphing, this Web site displays line graphs, and students answer questions using data from the graphs: http://www.ixl.com/math/practice/grade-5-line-graphs.
This website can be used to review bar graphs: http://www.ixl.com/math/practice/grade-5-bar-graphs
This website can be used to review pictographs: http://www.ixl.com/math/practice/grade-5-pictographs
This website can be used to review circle graphs: http://www.ixl.com/math/practice/grade-5-circle-graphs
This website can be used to determine which graph would best represent a given data set: http://www.ixl.com/math/practice/grade-5-choose-the-best-type-of-graph
Expansion: Data might be misinterpreted in graphs sometimes. Have students examine graphs that may include misleading data. As an introduction, students can visit the following website, which demonstrates how graphs can be misleading: http://www.fiu.edu/~graphing/misleadmain.htm. Students can then be assigned Misleading Graphs (M-5-4-1_Misleading Graphs and KEY) to complete. If time permits, students can use one of the graphs from earlier in the lesson to make a "misleading" graph.
This lesson shows students how data can be represented in several types of graphs. Students learn that there are various approaches for gathering and presenting data. After viewing many types of graphs, students design a graph based on a data table. The graph has the following features: title, appropriate scale, and labels. Students interpret and answer questions based on the data.
