principles of graphing lab- teacher version

8/6/2019 Principles of Graphing Lab- Teacher Version

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Principles of Graphing Teacher Version

Key Concepts:

Understand the three components of a completed graph: (1) main title, (2) x and y-axis

titles, and (3) using correct units of measurement.

Distinguish between data representing independentand dependent variables.

Choose the most appropriate graph to useline, bar, orpiegiven different sets of data.

Analyzing and interpreting data that may be difficult to appreciate in a table format.

Introduction:

As data is gathered during a laboratory investigation or experiment, it is often helpful to not only

generate data tables, but graph the data for further analysis, comparison, and interpretation.

Graphs help to show relationships between sets of data that may be difficult to appreciate in a

table format only. These data are called variables.Independent variables can be changed,

altered, or modified by the scientist running the experiment.Dependent variables rely on the

conditions of the investigation. Dependent variables are dependent on the independent variables

and can be thought of as the outcomes of an investigation or experiment. Three types of graphs

will be used in this activity: line graphs, bar graphs, and pie graphs.Line graphs generally show

relationships between two sets of data in which the independent variable is continuous.Bar

graphs are used when there is no continuity from one piece of data to the next.Pie graphs, also

called pie charts, are particularly useful when parts or pieces of data will be compared to thewhole. Pie graphs normally include a key or legend describing the data each piece represents.

Example of a Line Graph


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http://www.galeschools.com/research_tools/images/src/LineGraph.gif

Example of a Bar Graph

http://www.mathworksheetscenter.com/mathtips/bar2.gif

Example of a Pie Graph


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http://www.swiftchart.com/pie_ex1.png

Materials:

Graph paper (several sheets per student)

Unlined, white computer paper (several sheets per student)

Protractors (at least one per student group)

Metric rulers (at least one per student group)

Calculators (or use of the calculating function on any cell phone)

Pencils and/or pens

Part 1: Pre-lab Questions

Answer the following pre-lab questions in the space provided.

1. What are variables and how do they affect scientific investigations?

Variables can be thought of as factors or items (data) scientists test in order to determinepotential cause and effect relationships in nature. Variables are part of the investigative

process and can be modified, altered, or controlled by scientists (independent variables) to

produce expected or unexpected outcome (dependent variables). In general, scientists

choose to keep all variables constant (controlled for) during an experiment except one,

which will be to focal point of the investigation.


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2. Describe the difference(s) between independent and dependent variables.

A variable is independent when the scientist and not the events of the investigation control

it. Another common name for an independent variable is the manipulative variable, because

it is under direct control of the scientist. A variable is dependent because it depends on the

conditions of the investigation. Dependent variables are also referred to as respondervariables because they change in response to the manipulative, or independent, variables.

3. What are the three things that all graphs need to be complete?

a. Main title that briefly explains what the graph illustrates

b. X and Y-axis titles

c. Proper units of measurement for the X and Y-axis

Part 2: Making GraphsFor each of the following groups of data, make the appropriate kind of graph on a separate sheet

of paper. Be sure to include the three components that complete a graph. Line and bar graphs

should be drawn on graph paper, whereas pie graphs can be drawn on unlined paper if available.

1. Relationship of Water Temperature to the Heart Rate of Northwest Pacific Salmon

Advanced and Basic

Temperature in Degrees Celsius Heartbeats/Minute

10C 0/min

11C 8/min

13C 12/min

15C 16/min

21C 19/min

29C 23/min

31C 23/min

34C 20/min

38C 0/min


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Water Temperature vs. Heart Rate of Northwest Pacific Salmon

0

3

6

9

12

1518

21

24

0 11 10 11 13 15 21 29 31 34 38

Temperature in Degrees Celsius

Heartbeats/Minute

2. U.S. Energy Expended in the Production of Wheat for 1975 and 2005 - Advanced

Input 1975 2005

Labor 3.0 kcal/m2 1.1 kcal/m2

Machinery 44.3 kcal/m2 103.9 kcal/m2

Gasoline 134.2 kcal/m2 196.4 kcal/m2

Nitrogen 14.2 kcal/m2 232.4 kcal/m2

Phosphorus 2.2 kcal/m2 11.2 kcal/m2


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Potassium 1.2 kcal/m2 16.4 kcal/m2

Seeds 8.4 kcal/m2 15.3 kcal/m2

Irrigation 4.2 kcal/m2 8.2 kcal/m2

Insecticides 0.0 kcal/m2 2.5 kcal/m2

Herbicides 0.0 kcal/m2 2.5 kcal/m2

Other 15.1 kcal/m2 123.8 kcal/m2


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U.S. Expended Energy to Produce Wheat in

1975 and 2005

0

20

40

60

80

100120

140

160

180

200

220

240

Labor

Machin

ery

Gasoline

Nitro

gen

Phosph

orus

Potas

sium Seeds

Irriga

tion

Insecticides

Herbicides

Other

Input

kcal/m

2

1975

2005


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2. U.S. Expended Energy in the Production of Wheat for 2005 -Basic

Input 2005

Labor 1.1 kcal/m2

Machinery 103.9 kcal/m2

Gasoline 196.4 kcal/m2

Nitrogen 232.4 kcal/m2

Phosphorus 11.2 kcal/m2

Potassium 16.4 kcal/m2

Seeds 15.3 kcal/m

2

Irrigation 8.2 kcal/m2

Insecticides 2.5 kcal/m2

Herbicides 2.5 kcal/m2

Other 123.8 kcal/m2


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U.S. Expended Energy to Produce

Wheat in 2005

0

20

40

60

80

100

120

140

160

180

200

220

240

Labor

Machin

ery

Gasoline

Nitro

gen

Phosph

orus

Potas

sium

Seeds

Irriga

tion

Insecticide

s

Herbicide

sOther

Input

kcal/m

2


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3. Distribution of Butterfly Species in North America Advanced (graphed in degrees)

Species Name Number of

each Species

Fraction of Total

Students to fill in

Percent (%) of Total

Students to fill in

Degrees

Students to fill in

Tiger

Swallowtail

4,200 0.0046 0.46% 1.66

Black

Swallowtail

9,200 0.010 1.00% 3.60

Giant

Swallowtail

6,000 0.0066 0.66% 2.36

Pine White 12,500 0.0137 1.37% 4.93

Cabbage

White

70,000 0.0766 7.66% 27.59

Orange

Sulphur

6,500 0.0071 0.71% 2.56

Harvester 750,000 0.8211 82.11% 295.60

Blue Copper 5,000 0.0055 0.55% 1.97

Great Purple

Hairstreak

46,000 0.0504 5.04% 18.13

Silver-

Spotted

Skipper

4,000 0.0044 0.44% 1.58

Totals 913,400 ~ 1.0 ~ 100% ~ 360 degrees

** Fraction of Total = Number of each Species/Total # of all Species (decimal)

** Percent of Total = Number of each Species/Total # of all Species x 100

** Degrees = Number of each Species/Total # of all Species x 360


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Distributions of Butterfly Species in North America

1.66o1.58o18.1o

1.9o

3.6o2.36o

4.93o 27.59o2.56o

295.6o

Tiger Swallowtail Black Swallowtail

Giant Swallowtail Pine White

Cabbage White Orange SulphurHarvester Blue Copper

Great Purple Hairstreak Silver-Spotted Skipper

** Note: Due to the small size of several of the pie pieces, the teacher may suggest that

students combine these pieces together to make graphing more effective. Students should


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give a new name to this combined piece (e.g. other), add this new piece to their key or

legend, as well as list the name of each species of butterfly that make up the new piece.


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3. Distribution of Butterfly Species in North America Basic (graphed in percents)

Species Name Number of each

Species

Fraction of Total

Students to fill in

Percent (%) of Total

Students to fill in

Tiger

Swallowtail

4,200 0.0046 0.46%

Black

Swallowtail

9,200 0.010 1.00%

Giant

Swallowtail

6,000 0.0066 0.66%

Pine White 12,500 0.0137 1.37%

Cabbage White 70,000 0.0766 7.66%

Orange Sulphur 6,500 0.0071 0.71%

Harvester 750,000 0.8211 82.11%

Blue Copper 5,000 0.0055 0.55%

Great Purple

Hairstreak

46,000 0.0504 5.04%

Silver-Spotted

Skipper

4,000 0.0044 0.44%

Totals 913,400 ~ 1.0 ~ 100%

** Fraction of Total = Number of each Species/Total # of all Species (report in

decimal form)

** Percent of Total = Number of each Species/Total # of all Species x 100


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Distribution of Butterfly Species in North America

82%

1%

1%

1%0%0%5%1%

1%8%

Tiger Swallowtail Black Swallowtail

Giant Swallowtail Pine White

Cabbage White Orange Sulphur

Harvester Blue Copper

Great Purple Hairstreak Silver-Spotted Skipper

** Note: Due to the small size of several of the pie pieces, the teacher may suggest that

students combine these pieces together to make graphing more effective. Students should

give a new name to this combined piece (e.g. other), add this new piece to their key or

legend, as well as list the name of each species of butterfly that make up the new piece.


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Part 3: Post-Lab Questions - Advanced

1. What is the independent variable for question number one?

The primary independent variable for question number 1 is the temperature of the water

as this can be controlled (either increased or decreased) by the scientist. Secondary

independent variables include: (1) number of fish, (2) species of fish, (3) age of fish, (4) sex

of fish, and (5) salt concentration of the water.

1a. The independent variable should be graphed on the X-axis.

1b. Line graphs show the relationship between two kinds of data in which the

independent variable is continuous.

2. Explain your selection of graph type for the data presented in question number two. In

other words, why did you select the type of graph and why does it illustrate the data given

the best?

In general, a bar graph is indicated for this set of data because the data is finite in nature

and there is no continuity from one piece of data to the next. Specifically, a double bar

graph is indicated because the question and data table indicate a comparison between two

years worth of information; 1975 and 2005.

2a. Bar graphs are used when there is no continuity or continuation from one piece

of data to the next.

3. Look at the data given in question number three. What would be an effective way tocheck your math calculations for percents, fractions, and degrees to make sure your graph

is correct? In other words, what should your totals add up to? (Hint: For degrees, think

about the shape your graph should be in).

A good way to check to see if calculations are done correctly is to individually add up all

the data from the three columnsFraction of Total, Percent (%) of Total, and

Degreesin the data table. If student calculations are within a few significant digits of

the expected totals for each category1.0, 100%, and 360 degrees respectivelythen

calculations were done correctly.

3a. Give a logical, reasonable explanation as to why your calculations for fractions,

percent, and degrees may not add up to exactly what you might have expected.

Normally, if student calculations are considerably off what is expected, a manual

error in using the calculator is to blame. If student calculations are only off by a few

significant digits (e.g. 360.76 degrees total instead of 360.0 degrees), generally these


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types of errors are due to rounding variation. Students may round to the nearest

tenth, hundredth, or thousandth place which can affect the total slightly.

Part 3: Post-Lab Questions Basic

1. What is the independent variable for question number one?

Students should answer similarly to advanced lab answer given above.

1a. The independent variable should be graphed on the X-axis.

1b. Line graphs show the relationship between two kinds of data in which the

independent variable is continuous.

2. Why do you think individual bars on a bar graph are not connected to each other as data

points are in a line graph?

Bar graphs are used when there is no continuity or connection from one piece of data to the

next. Points on a line graph are generally connected because there is some kind of

relationship between the dependent variable and the independent variable which is

continuous in nature.

2a. Bar graphs are used when there is no continuity or continuation from one piece

of data to the next.

3. Look at the data given in question number three. What would be an effective way to

check your math calculations for percents and fractions to make sure your graph is

correct? In other words, what should your totals add up to?

Students should be able to offer suggestions similar to the projected answers of advanced

students listed above. Overall, basic students should understand that rounding errors may

slightly alter final calculations, but not enough to make their answers incorrect.

3a. Can you think of any other units of measurement pie charts can be graphed in

other than percentages? (Hint: Think about the shape of a pie graph).

Pie charts are graphed using the shape of a circle, which is comprised of 360

degrees. Thus, pie charts can also be graphed in degrees instead of percents which

are more commonly seen.

References:

Activity adapted from Making Graphs by MacMillan Publishing Co., Inc.

principles of graphing lab- teacher version

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