GraphingGraphing

Independent vs. DependentIndependent vs. Dependent

In an experiment, the variable that YOU In an experiment, the variable that YOU change is the Independent Variablechange is the Independent Variable

The variable that you measure is the The variable that you measure is the Dependent variableDependent variable

EX: We are going to grow bean plants EX: We are going to grow bean plants over the next few weeks.over the next few weeks.

Quantitative vs. QualitativeQuantitative vs. Qualitative

Quantitative – something you Quantitative – something you observe or measure using numbers – observe or measure using numbers –

EX: he is 6 ft tallEX: he is 6 ft tall

Qualitative – something you observe Qualitative – something you observe or measure using descriptions only – or measure using descriptions only –

Ex:he is tallEx:he is tall

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 Qualitative vs. QuantitativeQualitative vs. Quantitative

Line Graph Line Graph Quantitative vs. QuantitativeQuantitative vs. Quantitative

Circle Graph Circle Graph PercentagesPercentages

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

TAILSTAILS

T itleT itleA xisA xis I ntervalsI ntervalsL abelsL abelsS caleS cale

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)

Start a New Page…Start a New Page…BARBIE BARBIE

BUNGEE JUMP!!BUNGEE JUMP!!

PurposePurpose: To use : To use EXTRAPOLATIONEXTRAPOLATION to provide to provide

a a THRILLINGTHRILLING, yet , yet SAFESAFE, jump from the top of the , jump from the top of the bleachers (4.6 m). Note: “Thrilling” is .5 m or bleachers (4.6 m). Note: “Thrilling” is .5 m or less than from the ground!! less than from the ground!!

ProblemProblem: What is the: What is the relationshiprelationshipbetween the drop distance and the numberbetween the drop distance and the numberof rubber bands used to make the bungeeof rubber bands used to make the bungeecord?cord?

Identify independent, dependent and Identify independent, dependent and controlled variables.controlled variables.

HypothesisHypothesis: (An “If… then...” statement): (An “If… then...” statement)

MaterialsMaterials: Barbie, meter stick, rubber bands: Barbie, meter stick, rubber bands

ProcedureProcedure::1.1. Use one rubber band to secure Barbie’s Use one rubber band to secure Barbie’s

ankles together and to serve as a point of ankles together and to serve as a point of attachment. Use another rubber band to attachment. Use another rubber band to secure hair and arms secure hair and arms

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

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

4.4. Drop Barbie 3 times and record Drop Barbie 3 times and record measurementmeasurement

5.5. Add 1 rubber band to your attached bungee Add 1 rubber band to your attached bungee cord. Drop Barbie three times and record the cord. Drop Barbie three times and record the data.data.

6.6. Repeat step 4 and 5 until you have a total of Repeat step 4 and 5 until you have a total of 6 rubber bands. Record data each time.6 rubber bands. Record data each time.

7.7. Calculate the average and round to the Calculate the average and round to the nearest .01 m. Record in the data table.nearest .01 m. Record in the data table.

# 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

Fill in the following on your lab:Fill in the following on your lab: IVIV DVDV ConstantsConstants Hypothesis: If/Then…..Hypothesis: If/Then….. Draw the Axes on your graphDraw the Axes on your graph

Turn in your graphing packet!!! Turn in your graphing packet!!! Double check to make sure everything is Double check to make sure everything is

therethere Analysis:Analysis:

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

2.2. Use your line of best fit and predict how Use your line of best fit and predict how many rubber bands would be needed to many rubber bands would be needed to allow Barbie a successful, yet thrilling, jump allow Barbie a successful, yet thrilling, jump from the top of the bleachers (5.4 meters). – from the top of the bleachers (5.4 meters). – write this in your lab!!write this in your lab!!• Prediction: ________________Prediction: ________________• Result: ___________________Result: ___________________

Monday, September 13Monday, September 13Answer the following in your Answer the following in your

notebook:notebook: Conclusion:Conclusion:

1.1.How did you use your graph to make the How did you use your graph to make the prediction of the number of rubber bands for a prediction of the number of rubber bands for a jump from the bleachers?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 Why do you think the results turned out the way

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

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

Glue in your hand drawn graph. Make sure Glue in your hand drawn graph. Make sure it has labels and a title!!it has labels and a title!!

Graphing TestGraphing Test

You have a graphing test You have a graphing test Wednesday. You will be asked to Wednesday. You will be asked to create two data tables and to graph create two data tables and to graph the data on those tables. You may the data on those tables. You may use your science notebook. Make use your science notebook. Make sure it is ready to go!! Do not forget sure it is ready to go!! Do not forget to bring it to class. to bring it to class.

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.