Students know how to identify and critically evaluate information in data, tables, and graphs. E/S
Have you ever tried to read a science book or website without looking at any tables or graphs? It would be like trying to make hot chocolate without using any chocolate.
Science often uses tables and graphs to illustrate the important facts and relationships surrounding a concept. However, the ability to read, gather, and interpret information is not always a part of the students’ skill set. These skills need to be taught and practiced often in science so that students can learn to express the data from their experiments through tables and graphs. These skills are also essential if we are to expect students to interpret graphs and data from other sources.
Making Inferences
Data interpretation problems usually require two basic steps. First, you have to read a chart or graph in order to obtain certain information (interpolate). Then you have to apply or manipulate the information in order to obtain an answer. Occasionally students will be expected to extrapolate beyond the bounds of the graph or recorded data and predict what may occur if the data values were to continue to that point. Or interpolate, look inside the data bounds, at what the data value would likely be that was not collected.
In articles or textbooks you are likely to find graphs and tables. In science, data tables are often used as part of experiments as a way to organize information. Frequently, one quantity depends on the other and a relationship can be seen. Tables are used in labs to record information and to synthesize conclusions. For example, Figure 1 “Pulse Rate Table” below shows the relationship between a person’s pulse rate and time. This format allows students to see information organized in ways that aide in gathering information and making comparisons easier.
Comparison of Pulse Rates During a 20 Minute Period
Time (minutes) 
Mabel’s Pulse Rate
(Beats per minute) 
Albert’s Pulse Rate
(Beats per minute) 
0 
60 
80 
5 
78 
84 
10 
144 
118 
15 
93 
112 
20 
80 
62 
Figure 1 Pulse Rate Table
As an additional step, this table can be turned into a graph to illustrate the relationship visually. This line graph helps students make observations and inferences visually.
Figure 2. Graph comparing the pulse rate to the amount of time spent exercising.
(From http://www.twingroves.district96.k12.il
.us/ScienceInternet/ChartsGraphs.html)
From both the table and the graph, students can be asked to gather information as well as interpret the information using higher level thinking skills. For example, they can be asked to compare the difference between Mabel and Albert at a particular time, or they can be asked to compare the total change in pulse rate between the two people or for each person. By asking the students to compare, they are now interpreting the data, rather than just finding an answer to a question like, “What is Mabel’s pulse rate at 5 minutes?”
Students also need practice seeing the overall relationship in the graph, rather than just individual points. Below is a graph showing the relationship between the mileage of a car and its value. By making conclusions about the entire graph, students can begin to see that there is an overall relationship. As the mileage of the car increases, the value of the car decreases.
Car’s Value in Relation to Mileage
Figure 3. Line graph of the car’s value in relation to its mileage.
(From http://www.mathleague.com/help/data/data.htm)
Motion graphs need to be part of interpreting graphs as well. There are two types of motion graphs students should be familiar with in middle school. The first is a distance versus time graph.
Distance versus Time Graph
Figure 4 Distance versus time graph.
(From http://www.mste.uiuc.edu/courses
/summer99/300tcd_1/mickley/Graphmatching.htm)
On this graph, the horizontal line of the graph represents the time that the object is not moving. For example, a person walked to the store and this portion of the line shows their time inside the store. Then as the line starts down, the person is moving back towards their original location, but they stop again somewhere else. If the line was to go back to 1.0, they would have returned to their original location. This is a difficult concept because students often expect the lines to meet again to show that the person returned as if their path was being drawn on a map, rather than being graphed as a relationship of their distance over time.
Velocity over time is another motion graph students need to be able to interpret.
Figure 5 Velocity versus time graph.
(From http://www.glenbrook.k12.il.us/
gbssci/phys/Class/1DKin/U1L4c.html)
In figure 5, the horizontal line, Section A, the object is moving at a constant speed. Then they slow down during Section B, and then returns to a constant, but slower, speed during Section C. This graph does not show the relationship of the object relative to its location. Instead it shows its velocity over time. Both figures 4 and 5 can then be used for discussion and interpretation of what may be occurring during the graphed periods. For example, students can be asked to explain what happened to cause Section B and C. One possible answer would be that the person got tired, so they slowed down to a lower speed.
Identifying and Organizing Information from an Experiment
In addition to interpreting tables and graphs, students should be able to organize the data gathered from an experiment into a data table and plot the data on a graph. This includes knowing what information to collect and how to create tables and graphs using accepted conventions. The basic requirements for a data table include a title, column headings, and the data needed to complete the table.
For more details on widely accepted conventions, go to HS TIPS Benchmark N.12.A.1
Students need to be able to create data tables so they can use them to collect information as a lab is being conducted. Then they need to be able to organize the information into graphs for their conclusion. For example, if a student is studying the effects of sunlight on plant growth, they need to have these headings as part of their data table so they have a place to write down their observations.
Data Table of Plant Height Results
Date 
Time 
Amount of sunlight (hours) 
Amount of water (mL) 
Plant height (cm) 
3/25 
10:00am 
1.0 
50mL 
3cm 
3/27 
10:00am 
2.0 
50mL 
4cm 
3/29 
10:00am 
3.0 
50mL 
5cm 
3/31 
10:00am 
4.0 
50mL 
7cm 
4/2 
10:00am 
5.0 
50mL 
9cm 
Figure 6 Plant Height Table
Not all the collected data may be graphed, so students need to realize which variables should be used in the graph and which variable are simply extra information. In the case above, the student should use amount of sunlight as the independent (what they controlled) and the plant height as the dependent (what changed as a result). The independent variable, sunlight, belongs on the Xaxis while the dependent variable, plant height, goes on the Yaxis. This graph can now help the student to more easily see the relationship between the two variables and utilize this information in developing a conclusion based on authentic data.
Figure 7 Plant Height Graph
Making Predictions
Making predictions using graphed data is a great way to test higher level thinking skills because it requires the student to be able to read and interpret the graph as well as use their background knowledge and experience to support their predictions. A student can be asked to predict (extrapolate) where the next 3 data points might be located and justify their thinking based on the data available and their experiences.
Figure 8 Plant Height Graph
For example, if we use the plant height graph, a student might predict the next 3 points to be 11cm, 13 cm, and 15 cm stating that as the sunlight increased, the plant grew at a rate of 2 cm per hour of sunlight provided, because plants need sunlight for photosynthesis. However, another student might predict 11cm, 12cm, and 13 cm saying that too much sunlight could slow the growth rate of the plant because it may dry out. In both situations, the students are using the graph to make predictions supported by their background knowledge and experience with plant growth.
Figure 9 Graph comparing the pulse rate to the amount of time spent exercising.
(From http://www.twingroves.district96.k12.il.us/ScienceInternet/ChartsGraphs.html)
Another example would be to have a student predict what might happen if one of the variables was changed. For instance, looking at the pulse rate graph from above, a student could be asked to predict what might happen if the office worker were required to exercise for a longer period of time, or if the college athlete were to be required to do more strenuous exercises. Both of these questions require students to make predictions based on the graph as well as their knowledge about age and health, but one focuses on age as a factor while the other focuses on the physical condition on athletes.
Precision, Accuracy, and Estimation
In science, precision and accuracy are not the same thing.
Precision refers to the ability of a measurement to be consistently reproduced. This is important to scientists because an experiment must be able to be reproduced with similar outcomes in order for the results to be considered valid.
However, accuracy refers to the truthfulness, or correctness of the results which means that if an experiment produces incorrect results consistently, those results are precise, but not accurate.
Here is a visual comparison of precision and accuracy using targets.

These marks on the target are not precise or accurate. They are not all in the same area (precise) and they are not in the center (accurate). 

These marks are precise (repeatedly in the same location), but not accurate because they are not in the center of the target. 

These marks are accurate because of their average proximity near the center. However, they are not precise because they are not all in one particular area. 

These marks are both accurate (in the center) and precise (all in one location). 
Figures 1013 Graphs of accuracy and precision.
(From http://honolulu.hawaii.edu/distance/sci122/SciLab/L5/accprec.html)
Here's another example of precision and accuracy using time. The sports announcer says that the race will take between 3 to 6 hours to complete. The actual time it takes the race to be completed is 5 hours. This means that the announcer was accurate, but not very precise. The announcer provided a true statement but without enough detail for us to make timely plans after the race. A different station has an announcer that says the race will be exactly 3 hours and 15 minutes long. This statement was very precise, but completely inaccurate.
Is it useful to have accuracy without precision, or precision without accuracy? Not really. Being accurate without being able to repeat it is not useful in science because no one can reproduce your results. However, being precise is not useful either if you are constantly getting incorrect results. By being both precise and accurate, scientists can get the best, most reliable results from their experiments.
To learn more about precision and accuracy in science, go to
http://www.theweatherprediction.com/habyhints/246/
Estimation
Occasionally, scientists make rough estimates so they can create a hypothesis or plan possible experiments. The accuracy of estimates depends on reference materials available about the content, time dedicated to them, and experience by that scientist with similar problems.
Estimation is used in the classroom to help students design quality experiments and to help them predict possible outcomes. Often times in the classroom, the time and supplies may not be available to use to recreate a particular circumstance. In this case, students can collect data from textbooks and the internet to use as a basis for an experiment. They can take that information and estimate the causes and effects of certain actions and then use that information during their own lab experiments. For example, they can analyze the amount of trash in Nevada and then estimate the consequences of renewable and nonrenewable sources.
To learn more about estimation, go to
http://72.14.253.104/custom?q=cache:J6Ue2arHaPkJ:online.
physics.uiuc.edu/courses/Phys496/Spring08/Lectures/
EstimatesResearch_Sp08.ppt+making+estimates+in
+science&hl=en&ct=clnk&cd=2&gl=us&client=
pub0300676182177506
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Performance Benchmark N.8.A.1
Students know how to identify and critically evaluate information in data, tables, and graphs. E/S
Common misconceptions associated with this benchmark
1. Students inaccurately assume that precision and accuracy mean the same thing.
We often use the words interchangeably in daily conversation. However, accuracy is the ability to reach the correct answer. Precision is the ability to produce similar results again regardless of how correct the outcome is.
For a website tutorial that explains and illustrates the difference between precision and accuracy visit
http://phoenix.phys.clemson.edu/
tutorials/ap/index.html
A website tutorial that explains the difference and includes worksheets and online quizzes is found at
http://www.fordhamprep.org/gcurran/
sho/sho/lessons/lesson22.htm
2. Students have difficulty treating a graph as a continuously changing situation rather than a series of points.
Students are able to recognize and read points on the graph, but often struggle to see the overall relationship between the variables. For example, they don’t realize that the length of the rubber band is directly related to the number of paperclips on it. Or they don’t see the inverse relationship between the mileage of the car and its value.
A review of how to create a graph including practice problems for interpreting graphs can be accessed at
http://staff.tuhsd.k12.az.us/gfoster/standard/bgraph2.htm
3. Students have difficulty relating real world motions to a graph and viceversa.
Students often confuse distance/time graphs with velocity/time graphs. On a distance/time graph, a horizontal line means the object is not moving, while on a velocity/time graph a horizontal line means that the object’s velocity is the same, either constant motion or at rest.
For an example of a motion graph done correctly visit
http://www.physics.montana.edu/physed/
misconceptions/graphs/realworld/discover.html
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Performance Benchmark N.8.A.1
Students know how to identify and critically evaluate information in data, tables, and graphs. E/S
Sample Test Questions
1st Item Specification: Make inferences using information from data tables, charts, and graphs.
Depth of Knowledge Level 1
 Use the following graph to answer the question below.
(From: http://hyperphysics.phyastr.gsu.edu/hbase/tables/elabund.html)
Which elements make up approximately onethird of the Earth’s crust?
 Aluminum, Iron, and Other
 Aluminum, Iron, and Sodium
 Calcium, Sodium, and Other
 Silicon, Calcium, and Sodium
 Use the following graph to answer the question below.
(From http://www.twingroves.district96.k12.il.us/
ScienceInternet/ChartsGraphs.html)
Which of the following brands of fertilizer had the least effect on the plant’s height?
 Granny’s Bloomers
 Jobe’s House Plant Spikes
 Miracle Gro
 K Mart Fertilize
Depth of Knowledge Level 2
 Use the following graph to answer the question below.
(Create on http://nces.ed.gov/nceskids/graphing
/classic/bar_pie_data.asp?ChartType=bar)
Which statement describes the relationship between the number of paper clips and the length of the rubber band?
 As the number of paper clips increase, the length of the rubber band stays the same.
 As the number of paper clips increase, the length of the rubber band increases.
 As the number of paper clips decrease, the length of the rubber band stays the same.
 As the number of paper clips decrease, the length of the rubber band increases.
 The following data table shows the number of deaths caused by influenza and pneumonia from 19171918, during the time of the 1918 influenza pandemic.
U.S. Deaths per 100,000 Attributed to Influenza and Pneumonia, 19171918
Age 
1917 
1918 
<1 
2,944.5 
4,540.9 
14 
422.7 
1,436.2 
514 
47.9 
352.7 
1524 
78 
1,175.7 
2534 
117.7 
1,998.0 
3544 
193.2 
1,097.6 
4554 
292.3 
686.8 
Adapted from Agespecific death rates (per 100,000), Influenza & Pneumonia, USA (Noymer, 2007)
According to the data table, which age group shows the GREATEST INCREASE in death rates caused by influenza and pneumonia from 1917 to 1918?
 <1
 14
 1524
 2534
 Use the following graph to answer the question below.
Car’s Value in Relation to Mileage
(From http://www.mathleague.com/help/data/data.htm)
In what mileage range does the car’s value decrease the QUICKEST?
 020,000
 20,00040,000
 40,00060,000
 60,00080,000
2nd Item Specification: Identify meaningful data from an experiment and then organize the information into appropriate graphs, tables, or charts.
Depth of Knowledge Level 1
 Use the following data table to answer the question below.
HOW MANY COLDS A YEAR DO PEOPLE HAVE?
# of Colds per Year 
# of People 
0 
3 
1 
5 
2 
8 
3 
5 
4 
4 
5 
3 
6 
1 
(From http://www.qacps.k12.md.us/cms/sci/tools/MATHTBX.HTM#Percentage)
Which of the following graphs would be BEST to represent the data above?
 Bar graph
 Line graph
 Pictograph
 Histogram
 Below are data tables of observations made by a group of students during a chemistry lab. They keep track of what color the mystery substance became once the indicator solution was added. Use tables #14 to answer the question below.
Table 1
Letter of Mystery Substance 
Color After Indicator Solution 
Z 
yellowishgreen 
U 
light purple 
B 
dark red 
X 
forest green 
Y 
bright yellow 
C 
pale pink 
D 
light magenta 
I 
sky blue 
O 
eggplant 
Table 2
Letter of Mystery Substance 
Color After Indicator Solution 
B 
dark red 
C 
pale pink 
D 
light magenta 
I 
sky blue 
O 
eggplant 
U 
light purple 
X 
forest green 
Y 
bright yellow 
Z 
yellowishgreen 
Table 3
Letter of Mystery
Substance 
B 
C 
D 
I 
O 
U 
X 
Y 
Z 
Color After
Indicator Solution 
dark red 
pale
pink 
light
magenta 
sky
blue 
egg
plant 
light
purple 
forest
green 
bright
yellow 
yellowish
green 
Table 4
Letter of
Mystery Substance 
X 
I 
B 
O 
D 
U 
C 
Y 
Z 
Color After Indicator Solution 
forest
green

sky
blue 
dark
red 
eggplant 
light
magenta 
light
purple 
pale
pink 
bright
yellow 
yellowish
green 
Which of the following tables is the BEST choice to represent the data?
 Table 1
 Table 2
 Table 3
 Table 4
Depth of Knowledge Level 2
 Use the following table to answer the question below.
% of Animals Eaten by a Fox
Prey 
Number Eaten 
Percentage of Diet 
Rabbits 
3 
7.5% 
Birds 
6 
15% 
Mice 
27 
67.5% 
Rats 
4 
10% 
Total 
40 
100% 

(From http://www.qacps.k12.md.us/cms/sci/tools/MATHTBX.HTM#Percentage)
Which of the following types of graphs would be the BEST choice to represent the data above and why?
 A bar graph because it would compare the animals side by side.
 A boxwhisker plot because it shows the whole range of numbers.
 A line graph because it would show a comparison over time.
 A pie graph because it would show the percentages out of the total
 During a physics lab, students were asked to test the start height of a ramp versus the final distance of where their cart stopped. Use tables #14 to answer the question below.
Table 1
Start Height 
Run Distance 
10 cm 

20 cm 

30 cm 

40 cm 

50 cm 


Table 2
Run Distance 
Start Height 

10 cm 

20 cm 

30 cm 

40 cm 

50 cm 

Table 3
Start Height 
Run Distance 
10 cm 

40 cm 

30 cm 

20 cm 

50 cm 


Table 4
Run Distance 
Start Height 

10 cm 

40 cm 

30 cm 

20 cm 

50 cm 

Which data table represents the best way for them to organize their information?
 Table 1
 Table 2
 Table 3
 Table 4
 The following data table shows the percentage of elements found in the human body.
Elements of the Human Body
Element 
Percentage 
Oxygen 
65% 
Carbon 
18% 
Hydrogen 
10% 
Nitrogen 
3% 
Calcium 
1.5% 
Phosphorus 
1% 
Trace Elements 
1% 
Which of the graphs is the best representation of this data?
 Graph 1
 Graph 2
 Graph 3
 Graph 4
3rd Item Specification: Given data set (table, graph, or chart) make prediction based on information presented.
Depth of Knowledge Level 1
 The graph below shows a car traveling at a steady speed.
Distance (miles) traveled over time (hours)
(From http://www.studyzone.org/testprep/math4/k/trendsp.cfm)
After how many hours will the car be at a distance of 420 miles?
 13 hours
 14 hours
 15 hours
 16 hours
Depth of Knowledge Level 2
 The table below shows the growth on a Pacific Giant Kelp plant.
Height of Pacific Giant Kelp
Week 
Height (cm) 
1 
3.3 
2 
5.3 
3 
7.8 
4 
10.3 
5 
13.3 
6 
16.3 
7 
19.8 
8 

9 

10 

Based upon the information in the table, predict the height of the plant at Week 10.
 23.3cm
 27.3cm
 31.3cm
 35.8cm
 The following chart shows the times of moonrise and moonset in Las Vegas during December 1stDecember 6th.
Moonrise and Moonset Chart
Date 
Moonrise 
Moonset 
Dec 1 
9:52am 
7:51pm 
Dec 2 
10:26am 
8:51pm 
Dec 3 
10:55am 
9:51pm 
Dec 4 
11:22am 
10:51pm 
Dec 5 
11:47am 
11:52pm 
Dec 6 
12:13pm 
12:52am 
Dec 7 


Dec 8 


Dec 9 


Based upon this data, predict the moonrise and moonset times for December 9th.
 Moonrise 12:48pm, Moonset 1:52am
 Moonrise 1:23pm, Moonset 2:52am
 Moonrise 1:38pm, Moonset 3:53am
 Moonrise 2:33pm, Moonset 4:53am
 Use graphs #14 to answer the question below.
(From http://www.scienceclass.net/NOS/data_graphs.htm)
Which of the following distance/time graphs best shows a person who starts walking and then begins to jog as they warm up?
 Graph 1
 Graph 2
 Graph 3
 Graph 4
 Use graphs #14 to answer the question below.
World Carbon Dioxide Emissions by Region
(Million Metric Tons of Carbon Equivalent)
(From http://www.eia.doe.gov/oiaf/1605/ggccebro/chapter1.html)
Which of the following is an accurate prediction of the amount of carbon dioxide emitted by the total world in 2025?
 4,000  6,000 Metric Tons
 6,000  8,000 Metric Tons
 8,000  10,000 Metric Tons
 10,000  12,000 Metric Tons
 Use the graph to answer the question below.
Which of the following stories best match the graph above?
 A person walked to a store, shopped for awhile, and then went to a friend’s house.
 A person walked to a store, shopped for awhile, and then returned home.
 A person walked up a steep hill, paused at the top, and then walked back down.
 A person went to the store, then to a friend’s house, and then returned home.
4th Item Specification: Recognize the differences between precision, accuracy, and estimation.
Depth of Knowledge Level 1
 Use diagrams #14 to answer the question below.
Which of the diagrams represents a target hit by someone who is very precise, but not accurate?
 Diagram 1
 Diagram 2
 Diagram 3
 Diagram 4
 Use diagrams #14 to answer the question below.
Which of the diagrams represents a target hit by someone who is neither precise nor accurate?
 Diagram 1
 Diagram 2
 Diagram 3
 Diagram 4
Depth of Knowledge Level 2
 Students were asked to measure a string. The actual length of the string was 8.25 cm long. Which of the following shows the measurements from the MOST accurate group and why?
 7.25cm, 7.75cm, 8.25cm, because these were the closest to the actual length.
 7.2cm, 7.25cm, 7.3cm, because these had the most agreement between lengths.
 8.25cm, 8.75cm, 9.25cm, because these had the most agreement between lengths.
 8.2cm, 8.25cm, 8.9cm, because these were the closest to the actual length.
 Students were asked to measure a string. The actual length of the string was 8.25 cm long. Which of the following shows the measurements from the MOST precise group and why?
 7.25cm, 7.75cm, 8.25cm because these were the closest to the actual length.
 7.2cm, 7.25cm, 7.3cm, because these had the most agreement between lengths.
 8.25cm, 8.75cm, 9.25cm, because these had the most agreement between lengths.
 8.2cm, 8.25cm, 8.9cm, because these were the closest to the actual length.
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Performance Benchmark N.8.A.1
Answers to Sample Test Questions
 D, DOK Level 1
 C, DOK Level 1
 B, DOK Level 2
 C, DOK Level 2
 B, DOK Level 2
 A, DOK Level 1
 B, DOK Level 1
 D, DOK Level 2
 A, DOK Level 2
 B, DOK Level 2
 B, DOK Level 1
 C, DOK Level 2
 C, DOK Level 2
 D, DOK Level 2
 D, DOK Level 2
 A, DOK Level 2
 A, DOK Level 1
 B, DOK Level 1
 D, DOK Level 2
 B, DOK Level 2
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Performance Benchmark N.8.A.1
Students know how to identify and critically evaluate information in data, tables, and graphs. E/S
Intervention Strategies and Resources
The following is a list of intervention strategies and resources that will facilitate student understanding of this benchmark.
1. On line Practice Tests
Practice questions are great ways for students to see what they know and give them practice answering questions. It also allows the student to see what areas in which they still need further practice.
For distancetime graphs that provide a quick tutorial of how to read graphs and then gives students a chance to take a practice test go to http://www.bbc.co.uk/schools/gcsebitesize/
physics/forces/speedvelocityaccelerationfhrev2.shtml
For an awesome site on interpreting graphs that also gives feedback on the answer choice selected visit
http://www.tv411.org/lessons/cfm/
reading.cfm?str=reading&num=10&act=2&que=1
2. Sample Graphs
Examples of different types of graphs and practice worksheets allow students to practice their interpretation skills with graphs and tables. This site shows graphs used in real life and also offers lessons to use in the classroom on each type of graph.
To access this great website which includes multiple graphs and worksheets visit http://www.eslflow.com/describinggraphstables.html
3. Interactive Activities
Interactive websites are great for the students to explore and practice concepts. This site allows students to choose a type of graph and then walks them through the steps of creating a graph. They enter their own data and then have the option of saving and printing out the final product.
This link allows students to create different types of graphs using their own data
http://nces.ed.gov/nceskids/createagraph/default.aspx
4. Tutorials
On line tutorials with diagrams can help students by reteaching ideas in a different way. They tell stories about motion and velocity and then illustrate with graphs. They also introduce and review vocabulary needed, including slope and variables.
For a tutorial that teaches distance/time graphs see
http://www.glenbrook.k12.il.us/gbssci/phys/Class/1DKin/U1L3a.html
How to create graphs from experiments tutorial is found at
http://www.sciencebuddies.org/mentoring/project_data_analysis.shtml
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