GraphingGraphing

Data TablesData TablesTimeTime

(seconds(seconds))

DistanceDistance

(meters)(meters)

Straight lines drawn with a ruler

Independent

Variable

Dependent

Variable

Units

Or like this….Or like this….

TimeTime

(seconds)(seconds)

Distance Distance (meters)(meters)

Straight lines drawn with a ruler

Independent

Variable

Dependent

Variable

Units

Types of GraphsTypes of Graphs

Bar Graph Bar Graph ComparisonComparison

Line Graph Line Graph Trend over timeTrend over time

Circle Graph Circle Graph Parts of a wholeParts of a whole

Rules for GraphingRules for Graphing

You MUST use graph paper and a You MUST use graph paper and a ruler!!!ruler!!!

The independent variable is on the X-The independent variable is on the X-axisaxis

The dependent variable is on the y-axisThe dependent variable is on the y-axis DRY MIXDRY MIX

DRY – Dependent, Responding, Y-axisDRY – Dependent, Responding, Y-axis MIX – Manipulated, Independent, X-axisMIX – Manipulated, Independent, X-axis

The axes should be labeled with the measured quantity and the unit in which it was measured. Use Both!!!

0

0.1

Density (g/ mL)

Temperature (oC)

Scales on the axes should be appropriate for the data, spread out as much as possible, and the axis must be divided evenly giving each square the same value.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Density (g/ mL)

5 10 15 20

Temperature (oC)

Title should be in Y-axis vs. X-axis format

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Density (g/ mL)

5 10 15 20

Temperature (oC)

Density of water vs. Temperature of water

Is there a relationship between thumb Is there a relationship between thumb length and number of wins?length and number of wins?

Independent Independent Variable?Variable? Thumb lengthThumb length

Dependent Dependent Variable?Variable? Number of winsNumber of wins

Thumb Length (mm)

Number of Wins

Is there a relationship between Is there a relationship between thumb length and number of wins?thumb length and number of wins?

0

2

4

6

8

10

12

14

16

0-15 16-30 31-45 46-60

Thumb length Thumb length (mm)(mm)

Number of Number of WinsWins

0-150-15

16-3016-30

31-4531-45

46-6046-60

Thumb Length (mm)

# of wins

# of wins vs. thumb length

** Use this if we are comparing the number of wins

Is there a relationship between Is there a relationship between thumb length and number of wins?thumb length and number of wins?

0

2

4

6

8

10

12

14

16

18

0-15 16-30 31-45 46-60

Thumb length Thumb length (mm)(mm)

Number of Number of WinsWins

0-150-15

16-3016-30

31-4531-45

46-6046-60

Thumb Length (mm)

# of wins

# of wins vs. thumb length

** Use this if we are looking for a trend in the number of wins

Extrapolation:Extrapolation:

Extrapo – huh??Extrapo – huh?? Extrapolation – using a graph to Extrapolation – using a graph to

make an estimation outside the make an estimation outside the known range.known range.

Example please….Example please….

Physical science students poured liquid into a Physical science students poured liquid into a graduated cylinder and measured the mass of graduated cylinder and measured the mass of several pre-determined volumes. Use your graph to several pre-determined volumes. Use your graph to predict the mass of 23 mL of liquidpredict the mass of 23 mL of liquid

1.1. Draw a line of best fit: a Draw a line of best fit: a straight line that encompasses straight line that encompasses as many points as possible.as many points as possible.

2.2. Draw a line up from 23 until it Draw a line up from 23 until it reaches the line of best fit.reaches the line of best fit.

3.3. Draw a line over to the y-axis Draw a line over to the y-axis and read the measurement.and read the measurement.

4.4. The mass of 23mL of water is The mass of 23mL of water is approximately 79.0 grams.approximately 79.0 grams.

5.5. Why doesn’t the line of best fit Why doesn’t the line of best fit go through the origin?go through the origin?

1.1. The container that holds the The container that holds the liquid has massliquid has mass

Mass vs. Volume

0

20

40

60

80

0 10 20 30

Volume (mL)

Mass

(g)

InterpolateInterpolate

So the opposite of extrapolate is….So the opposite of extrapolate is….

INTERPOLATE!INTERPOLATE!

using a graph to make an estimation within using a graph to make an estimation within the known rangethe known range

This process is very similar to extrapolating.This process is very similar to extrapolating.

Physical science students poured liquid into a Physical science students poured liquid into a graduated cylinder and measured the mass of graduated cylinder and measured the mass of several pre-determined volumes. Use your graph to several pre-determined volumes. Use your graph to predict the mass of 10 mL of liquidpredict the mass of 10 mL of liquid

1.1. Draw a line of best fit:Draw a line of best fit:

2.2. Draw a line up from 10 until Draw a line up from 10 until it reaches the line of best fit.it reaches the line of best fit.

3.3. Draw a line over to the y-axis Draw a line over to the y-axis and read the measurement.and read the measurement.

4.4. The mass of 10mL of water is The mass of 10mL of water is approximately 61.0 grams.approximately 61.0 grams.

Mass vs. Volume

0

20

40

60

80

0 10 20 30

Volume (mL)

Mass

(g)

Table of Contents:Table of Contents:09/07/07 Juiced Up Lab page: 09/07/07 Juiced Up Lab page:

10&1110&11

Purpose: To Purpose: To practice practice extrapolating data extrapolating data from graphs.from graphs.

Place graph on Place graph on page 11page 11

Height Height of Water of Water (cm)(cm)

Mass of Mass of Water Water (g)(g)

22

44

66

Barbie Bungee Jump – Part 1Barbie Bungee Jump – Part 1 Purpose:Purpose: To ensure a safe and thrilling jump, you will determine the To ensure a safe and thrilling jump, you will determine the

relationship between the drop distance and the number of rubber bands relationship between the drop distance and the number of rubber bands to make the bungee cord.to make the bungee cord.

Materials:Materials: Barbie, meter stick, rubber bands Barbie, meter stick, rubber bands

Procedure:Procedure:1.1. Use one rubber band to secure Barbie’s ankles together and to serve Use one rubber band to secure Barbie’s ankles together and to serve

as a point of attachment. Use another rubber band to secure hair as a point of attachment. Use another rubber band to secure hair and arms (see teacher demonstration).and arms (see teacher demonstration).

2.2. Construct a bungee cord composed of 2 rubber bands and attach to Construct a bungee cord composed of 2 rubber bands and attach to Barbie’s ankles. Barbie’s ankles.

3.3. Barbie will fall freely from a standing position, plunging head first. Barbie will fall freely from a standing position, plunging head first. Test drop Barbie 3 times to practice taking measurements.Test drop Barbie 3 times to practice taking measurements.

4.4. Drop Barbie 3 times and record measurementDrop Barbie 3 times and record measurement5.5. Add a rubber band to your attached bungee cord. Drop Barbie three Add a rubber band to your attached bungee cord. Drop Barbie three

times and record the data.times and record the data.6.6. Repeat step 4 until you have a total of 6 rubber bands. Record data Repeat step 4 until you have a total of 6 rubber bands. Record data

each time.each time.7.7. Calculate the average of the data and record.Calculate the average of the data and record.

# of # of rubber rubber bandsbands

Length Length of of bungee bungee (meters)(meters)

Drop Drop distance distance trial 1 trial 1 (meters)(meters)

Drop Drop distance distance trial 2 trial 2 (meters)(meters)

Drop Drop distance distance trial 3 trial 3 (meters)(meters)

AverageAverage

(meters)(meters)

22

33

44

55

66

Table of Contents:

09/11/07 Barbie Bungee Jump Page 12 & 13

Barbie Bungee Jump – Part 2Barbie Bungee Jump – Part 2 Analysis:Analysis:

1.1. Graph your Graph your average drop heightaverage drop height vs. vs. number of number of rubber bandsrubber bands

2.2. Use your line of best fit and predict how many rubber Use your line of best fit and predict how many rubber bands would be needed to allow Barbie a successful, yet bands would be needed to allow Barbie a successful, yet thrilling, jump from the top of the bleachers (4.6 meters).thrilling, jump from the top of the bleachers (4.6 meters).

• Prediction: ________________Prediction: ________________• Result: ___________________Result: ___________________

Conclusion:Conclusion:1.1. How did you use your graph to make the prediction of the How did you use your graph to make the prediction of the

number of rubber bands for a jump from the bleachers?number of rubber bands for a jump from the bleachers?2.2. How did your result compare to your prediction?How did your result compare to your prediction?3.3. Why do you think the results turned out the way they Why do you think the results turned out the way they

did?did?4.4. Is the origin (0,0) a valid point (meaning will the line go Is the origin (0,0) a valid point (meaning will the line go

through it)? Why/why not?through it)? Why/why not?