Collecting and Displaying Data
Collecting and Displaying Data
Objectives
Students will develop a general understanding of how to display, interpret, and analyze data from a graph, chart, or probability outcome. Students will:
- investigate solutions to problems and determine answers to questions related to data from a graph or table.
- display data using a line plot.
- perform computations on rational data displayed in a line plot.
- display data using a variety of methods such as tables, charts, and graphs.
Essential Questions
How can data be organized and represented to provide insight into the relationship between quantities?
How can probability and data analysis be used to make predictions?
How does the type of data influence the choice of display?
In what ways are the mathematical attributes of objects or processes measured, calculated and/or interpreted?
What does it mean to estimate or analyze numerical quantities?
What makes a tool and/or strategy appropriate for a given task?
- What does it mean to estimate or analyze numerical quantities?
- What makes a tool and/or strategy appropriate for a given task?
- How can data be organized and represented to provide insight into the relationship between quantities?
- How does the type of data influence the choice of display?
- How can probability and data analysis be used to make predictions?
Related Unit and Lesson Plans
Related Materials & Resources
The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.
- Data Sources
http://www.cityrating.com/averagetemperature.asp
http://www.usatoday.com/news/snapshot.htm
- Create a Graph
http://nces.ed.gov/nceskids/createagraph/
http://www.fiu.edu/~graphing/misleadmain.htm
- Interchangeable Graphs
http://www.fiu.edu/~graphing/interchangmain.htm
http://www.ixl.com/math/practice/grade-5-choose-the-best-type-of-graph
- How to Make a Line Plot
http://ellerbruch.nmu.edu/classes/cs255w03/cs255students/nsovey/p5/p5.html
- How to Make a Line Plot
http://www.ehow.com/how_2121853_make-line-plot.html
- Components of an Exemplary Line Plot
http://mdk12.org/instruction/curriculum/mathematics/graph_line_plot.html
- Create a Circle Graph
http://www.ixl.com/math/practice/grade-5-circle-graphs
- Create a Bar Graph
http://nces.ed.gov/nceskids/graphing/classic/bar.asp
http://www.ixl.com/math/practice/grade-5-bar-graphs
- Make Your Own Pictograph
http://www.softschools.com/math/data_analysis/pictograph/make_your_own_pictograph/
http://www.ixl.com/math/practice/grade-5-pictographs
- Making Line Graphs
http://www.basic-mathematics.com/making-line-graphs.html
http://www.mathgoodies.com/lessons/graphs/line.html
http://www.ixl.com/math/practice/grade-5-line-graphs.
Formative Assessment
-
View
Multiple-Choice Items:
- Which data-gathering method would be an effective way to collect data to make a graph of the number of hours fifth graders spend on homework each week night?
A
experiment
B
observation
C
Simulation
D
Survey
- Which data-gathering method would be an effective way to collect data to make a graph of the number of times a four-colored spinner lands on each color for 25 trials?
A
observation
B
research
C
simulation
D
survey
- Which title could represent the data in the following table?
A
Number of Flavors of Ice Cream
B
Number of Ice Cream Sundaes Made Each Day
C
Best-Selling Ice Cream Flavors Each Day
D
Different Types of Sundaes
Use the line plot shown below to answer questions 4–6.
4. How many seedlings in total are represented by the line plot shown above?
A
2
B
7
C
10
D
13
5. How many seedlings are taller than 1 inch but shorter than 2 inches?
A
2
B
3
C
5
D
9
6. What is the difference in height between the tallest plant and the shortest plant?
A
inchB
inchesC
inchesD
inchesUse the following bar graph to answer questions 7 and 8.
7. What is the total number of cans collected for the food drive on Tuesday, Wednesday, and Thursday?
A
9
B
20
C
28
D
36
8. Kelly makes a pictograph to display the same data that is represented in the bar graph. She uses the key shown below:
How many pictures of cans should Kelly use to represent the number of cans collected on Friday?
A
10
B
18
C
20
D
40
9. Use the following graph to answer question 9.
Based on the graph, what is the best estimate of the temperature at 4:30 PM?
A
55°F
B
57°F
C
60°F
D
70°F
Multiple-Choice Key:
1. D
2. C
3. B
4. D
5. B
6. C
7. D
8. A
9. B
Short-Answer Items:
10. Use the following graph to answer the questions.
- Which data-gathering method was most likely used to collect this data? How do you know?
- What is one observation you can make from this graph?
- What is one question that can be answered using this graph that is different from the observation you made?
11. The line plot below shows the length of commercials shown on television.
The total length of all the commercials represented in the line plot is
minutes. Hannah adds three more commercials to the line plot with times of 
minutes, 
minutes, and 2 minutes.A. Add Xs to the line plot to represent the three commercials Hannah is adding.
B. What is the total time of all the commercials represented in the line plot after including the three commercials Hannah added?
12. The line graph below shows the number of text messages Holly has sent in the month of March.
A. Between which two dates shown on the horizontal axis did Holly send the most text messages? Explain how you know.
B. Based on the graph, how many text messages did Holly send from the beginning of the month until March 4th? Explain how you know.
Short-Answer Key and Scoring Rubrics:
10. Use the graph to answer the questions below.
- Which data-gathering method was most likely used to collect this data? How do you know?
The data-gathering method that was most likely used was a survey. Fifth graders had to be asked this question for the data to be collected.
- What is one observation you can make from this graph?
One observation that can be made from the graph is that this group of fifth graders likes spring most. Winter is the least favorite season for this group of fifth graders. (Answers will vary for observations.)
- What is one question that can be answered using this graph that is different from the observation you made?
Possible questions may include the following: How many more students like spring than like summer? How many students were surveyed in all?
Points
Description
2
- Mathematical thinking is correct.
- Written explanation is complete and detailed.
- Thorough understanding of gathering and interpreting data is shown.
1
- Mathematical thinking is correct but does not have a clear or complete written explanation. OR
- Mathematical thinking has errors but a written explanation is given.
- Some understanding of gathering and interpreting data is shown.
0
- Mathematical thinking is incorrect or contains many errors.
- Written explanation is missing or erroneous.
- No understanding of gathering and interpreting data is shown.
11. The line plot below shows the length of commercials shown on television.
The total length of all the commercials represented in the line plot is
minutes. Hannah adds three more commercials to the line plot with times of 
minutes, 
minutes, and 2 minutes.A. Add Xs to the line plot to represent the three commercials Hannah is adding.
B. What is the total time of all the commercials represented in the line plot after including the three commercials Hannah is adding?
The total length of time of all the commercials is
minutes.Points
Description
2
- The student correctly places the Xs to represent the three new data values.
- The student correctly determines the total length of time of all the commercials.
1
- The student correctly places the Xs to represent the three new data values. OR
- The student correctly determines the total length of time of all the commercials.
0
- The student does not correctly place the Xs to represent the three new data values.
- The student does not correctly determine the total length of time of all the commercials.
12. The line graph below shows the number of text messages Holly has sent in the month of March by date.
A. Between which two dates shown on the horizontal axis did Holly send the most text messages? Explain how you know.
The week with the greatest number of text messages sent was the week between March 8th
and March 15th because the line connecting the two points is the steepest.
B. Based on the graph, how many text messages had Holly sent from the beginning of the month until March 4th? Explain how you know.
An estimate for March 4th is about 20 text messages. March 4th is about halfway between the 1st and the 8th, and it looks like the line is at about 20 halfway between the 1st and the 8th.
Points
Description
2
The student correctly answers the question and gives an accurate and precise explanation of the process.
1
The student correctly answers the question or completely and accurately explains how to obtain the answer.
0
The student does not correctly answer the question, and the explanation is missing or inaccurate.
Performance Assessment:
Students should choose a topic and then collect data from classmates, friends, and/or family members. They will prepare a presentation based on their work showing the results. Their presentation should include information about how they collected their data (e.g., survey, observation, etc.). They should explain how they decided on the topic and discuss any difficulties they had in collecting the data (e.g., finding enough respondents, getting unanticipated answers, etc.).
Each student’s presentation should include at least two different data displays, one of which must be a bar graph, line plot, line graph, or pictograph. Students should explain the relationship between the two data displays, pointing out similarities and differences in the data displays. They should also justify their choices for the particular data displays chosen.
Performance Assessment Scoring Rubric:
Points
Description
4
- The student collects data and provides information about how s/he collected it.
- The student outlines any difficulties s/he had in collecting the data.
- The student creates two different data displays, at least one of which is a bar graph, line plot, line graph, or pictograph.
- The student explains the relationship between and justifies the choice of the two data displays.
- The student demonstrates an advanced understanding of organizing, displaying, and interpreting data.
3
- The student correctly completes 3 of the 4 tasks outlined above.
- The student demonstrates a strong understanding of organizing, displaying, and interpreting data.
2
- The student correctly completes 2 of the 4 tasks outlined above.
- The student demonstrates a limited understanding of organizing, displaying, and interpreting data.
1
- The student correctly completes 1 of the 4 tasks outlined above.
- The student demonstrates a very limited understanding of organizing, displaying, and interpreting data.
0
- The student does not correctly complete any of the tasks outlined above.
- The student demonstrates no understanding of organizing, displaying, and interpreting data.
Final 05/03/2013
