Patterns & Inquiry Skills Unit Packet – STEM Physics

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Patterns & Inquiry Skills Unit Packet – STEM Physics

Name: _________________________________ Period: __________ Date: __________________

Learning Targets:

ALT 1 – I can find patterns in nature and use them to predict future results or understand past events.

1.1 I can conduct an investigation to find and communicate the relationship between an independent and dependent variable, a relevant mathematical pattern in the collected data, and a correct prediction an additional data point.

1.4 I can represent the patterns: linear, quadratic, and inverse graphically, mathematically, in data tables, and in words.

1.5 I can make a high school level graph (labeled axis, scale, data points with error bars, applicable best-fit), explain its meaning (pattern and slope), and use the graph to make an accurate prediction.

1.6 I can identify, compare, and contrast patterns, specifically including the concept of rate of change (slope).

1.7 I can communicate the value of finding patterns and explain the reasoning behind making data- informed decisions based on them.

1.8 I can use computational reasoning with the patterns to extend my understanding of and to make predictions about the behavior of objects (for example, finding and using patterns in constant velocity and constant accelerated to understand and make predictions for about the motion of an accelerating object with an initial speed).

ALT 8 – I can utilize and communicate a variety of problem solving techniques to make correct predictions about how the world changes.

8.1 Formulate the question - Based on observations and science principles, I can formulate a question or hypothesis that can be investigated through the collection and analysis of relevant information.

8.2 Design the Investigation - I can design and conduct a controlled experiment, field study, or other investigation to make systematic observations about the natural world, including the collection of sufficient and appropriate data.

8.3 Collect and Present Data - I can collect, organize, and display sufficient and appropriate data to facilitate scientific analysis and interpretation.

8.4 Analyze and Interpret Results - I can summarize and analyze data to draw a valid and supported conclusion to communicate the findings of an investigation, and identify uncertainties.

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Vocabulary (words to know):

***Using the resources available to you (your prior knowledge, textbook, instructor, etc.) define the following terms in the context of this unit.

Science Pattern Relationship Hypothesis Conversion Slope Extrapolate Ratio

Proportional reasoning

Note: Although much of the content in this unit is “not in the textbook,” the principle of finding and using patterns in nature to understand the past and predict the future is helpful in understanding why science approaches problems the way it does. As we move on to more ‘typical’ physics topics in future units, your understanding of ‘patterns’ will prove very helpful. Concerning your textbook (Conceptual Physics), you may find it interesting to read Chapter 1 ‘About Science’ (pgs. 1-9) during this unit – this section also discusses to how science sees the world.

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Inquiry Cube

1. a. What qualities do scientists have? b. What are scientists like?

2. Draw what a scientist looks like 

3. a. How do scientists do their work?

b. How would they describe a scientific investigation?

4. What are questions we can investigate about this cube?

5. What is science? (How is it different than asking your friend or looking something up on Wikipedia?)

NOTES: (Science is…)

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2

^nd

Inquiry cube:

6. First hypothesis (wild guess)  Confidence (circle one): Low Medium High

(what is on the bottom of the cube?)

7. Data:

(make notes of exactly what you see on each visible side)

8. What patterns do you observe?

a. b. c.

 Research groups, plan to publicly share your explanations!!!

9. What is the benefit of hearing other research groups’ ideas?

Scientists use patterns in data to make predictions and then design an experiment to assess the accuracy of their prediction. This process can also produce additional data.

10. What number do you predict? Were you correct? Yes____ No ___

(in the top right corner of bottom face of the cube)

11. Final Hypothesis: Confidence: Low Medium High

12. Describe how your confidence changed from first hypothesis and final hypothesis and why?

13. How is this activity like real science?

14. What about science does this activity not capture?

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Inquiry Skills - Finding relationships to investigate:

While watching skateboarders drop into half-pipes of different heights, you notice two things: (1) that different skateboarders on the same half-pipe can reach different speeds by the bottom (flat portion) using different drop-in technique and (2) that the same skateboarder reaches faster speeds on half-pipes with higher walls. Being a scientist, you decide to investigate "How does the height of a half-pipe affect the speed a skateboarder reaches at the bottom (flat portion) of the half- pipe?"

1. What is the independent variable? _____________________

2. What is the dependent variable? ______________________

3. What are the controlled variables? (i.e. what must you keep constant?)

While sliding your physics textbook across the table, you realize it becomes much more difficult when your English and Math book are stacked on top. So you create the focused research question

"How does the force of friction between the surface of the bottom of your physics textbook and the table top surface depend on how much the weight of the books is pressing the surfaces together?"

4. What is the independent variable? ______________________

Answer the questions about the following research questions…

"How does the height of a crater formed by a falling rock depend on the height from which the rock was dropped?"

"How does the breaking strength of a column of cement depend on its diameter?"

"How does the thickness of rope affect the max tension it can withstand before breaking?"

Create Your Own Scenario:

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Data Sets Practice

Find the average and uncertainty for the following data sets:

1. Five students time a bowling ball travelling from point A to point B. They record the following times:

2.45s 2.49s 2.58s 2.55s 2.51s Average with uncertainty ____________ +/- _____ _s__

2. Seven students independently measure the length of a car. They record the following lengths:

4.5 m 4.7 m 4.4 m 4.6 m Average with uncertainty ____________ +/- _____ _m__

4.5m 4.6m 4.8m

3. Three students independently measure the volume of a small metal cube. They record the following volumes:

18 mL 20 mL 20 mL Average with uncertainty ____________ +/- _____ _mL__

4. Three students as in case 3 above also independently measure the volume of a small metal cube.

They record the following volumes:

22 mL 22 mL 19mL Average with uncertainty ____________ +/- _____ ___

5. Three students independently measure the mass of an egg. They record the following masses:

47 g 32 g 37 g Average with uncertainty ____________ +/- _____ ___

6. Circle the data set that appears to be the most trustworthy.

7. Draw a box around the data set that appears to be the least trustworthy.

8. Write a single sentence that explains what it is about the circled data set that indicates it was measured more carefully than the boxed data set?

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Measurement Activity

1. Find the volume of one of the density cubes by measuring each side in centimeters and using the formula: volume = length x width x height. Be sure to write down all of your raw data, and then show the calculation you completed to find your answer.

Raw Data: Length = Show Calculation:

Width = Answer: ______ _cm³___

Height =

2. Find the volume of the same density cube used in question #1 using the fluid displacement method. Be sure to record all of your raw data and show the calculation you completed to find the volume. After completing the calculation answer the question below:

Initial Volume = Show Calculation:

Answer: ______ _mL___

Final Volume =

3. How the measurements from questions 1 and 2 to compare?

4. Based on this imperfect information how many cm³ equals 1 mL? ______ cm³ = 1 mL

5. With your group, take a ball and drop it from the ceiling. Have three of your teammates time how long it takes to fall to the ground. Find the average time to fall with its uncertainty.

Raw Data: Time 1 Time 2 Time 3

Answer: ______ ____

6. Qualitative remarks on data taking (Write a sentence about the quality of your data taking into account your uncertainty):

7. Find the mass of 3 different objects (not too heavy though so we don’t break the electronic balance – see instructor for details). Be sure to describe the objects qualitatively and then record their mass to the correct digit (also include uncertainty).

object 1: __________________________________________________________________________ ______ ___

object 2: __________________________________________________________________________ ______ ___

object 3: __________________________________________________________________________ ______ ___

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Reading Instruments Practice – Before digital balances, scientists used to use triple beam balances (see picture) to determine masses by balancing known masses with an unknown mass.

Read the scales below and record all answers in grams.

Answer __________ Answer __________

Graduated Cylinders - be sure to first establish what increments are used on the cylinder then read the instrument accordingly.

Answer _________ Answer _________

5 0.0 0.1

4

90 100

0.0 10.0

9 0.5 7

0.4

2000 0.2

0.1 1000

5 100

50 0

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Introduction to LoggerPro

– Show your instructor your graph for each scenario before you move on to the next!!!

Time

s Distance Travelled by Car m

0.0 0

1.0 5

2.0 10

3.0 15

4.0 20

5.0 25

Scenario A: Plot the following data set collected from a car traveling at a constant speed of 5 m/s.

1. Write the equation for the best-fit line of this graph:

2. Use the graph (by changing the scale of the axes) to determine the distance the car would travel in 16 s?

3. Use the equation for the best-fit line to determine the distance the car would travel in 200 s?

Time

s (± 0.2) Distance Ball fell from Cliff m (±0.5)

0.0 0.0

1.0 5.0

2.0 20.0

3.0 45.0

4.0 80.0

5.0 125.0

Scenario B: Plot the following data gathered as a ball was dropped from rest from a cliff.

5. Use the equation for the best-fit line to determine the distance the ball will fall in 9 s? d = _____

6. Use the equation for the best-fit line to determine the time it would take the ball to fall 200 m? t = _____

7. Use the graph (by changing the scale of the axes) to determine the time it would take the ball to fall 200 m? t =____

8. Explain which method (equation or graph) was easier to determine the time it would take the ball to fall 200m?

Scenario C: Plot the following data for a car that was moving at 30 m/s and then suddenly hit the brakes.

Average Time

(s)

Uncertainty in Average Time (s)

Speed of Car (m/s)

Uncertainty in Speed of Car

(m/s)

0.0 0.2 30.0 0.2

1.0 0.3 25.0 0.4

2.0 0.1 20.0 0.6

3.0 0.3 15.0 0.5

4.0 0.5 10.0 0.7

10. When will the car stop? t = _____

11. How did you determine this?

12. Why is the y-intercept 30 m/s?

13. Determine when the car is going 23 m/s? t = _____

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Title: _____________________________________________

Name: ____________________

Period: ___________________

Date: _____________________

Wild Guess:

Research Question:

Hypothesis:

Graph form:

In words:

Variables:

Independent variable (IV):

Dependent variable (DV):

Controls (C):

Method: Experimental Set-up

(Diagram):

o Note how IV is measured and what values of the IV you measured.

o Note DV and how you measure it?

o Note how you controlled your controls and the value of the controls.

o Check that another scientist could reproduce your test based only on the information below.

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Data:

Brief description/comments on carrying out experiment:

Values of Controlled variables:

Graph of Data:

Conclusion:

Research Extension Question:

= ___________

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***Do you notice anything strange here?

Data Tables, Graphs, and Drawing Conclusions Homework #1 A construction company gathers data for the following question:

"How does the compression strength of a concrete column depend on the diameter of the column?"

Diameter of Column m (+/- 0.3)

Compression Strength lbs. (±5) Trial #1

Average Compression

Strength (lbs.)

Compression Strength Uncertainty

(lbs.)

0.5 2620 2510 2370

1.0 4750 5025 5225 5000 200

1.5 7100 7825 7575

2.0 9400 10275 10225 400

2.5 11900 12475 13125 600

1. Fill out the average and uncertainty columns in the data table.

2. Graph this data on the table below.

3. What does the slope signify?

It tells us that the compression strength of the column increases by ___ pounds for every 1 meter increase in the diameter of column.

4. What kind of conclusion can be drawn from the graph?

Since the best-fit line is ________,

I conclude that there is a ________ relationship between _____________ and ______________.

This can be modeled mathematically as ________ = 5000 * __________. So I predict with _______

confidence based on my data that when the 1.8 m column is compressed with a 8000 lb. load it will hold/break, because the best- fit line hits near the ____ of most of the data points and the prediction is within my data range.

A freshman basketball player gathers data for the following question.

"How is the rebound height of a basketball dropped from 6 m high affected by the air pressure inside of the ball?"

Pressure PSI (± 0.5)

Rebound Height cm (± 3)

Trial #1

Rebound Height cm (± 3)

Trial #2

Rebound Height cm (± 3) Trial #3

Average Rebound Height

(cm)

Uncertainty in Average Rebound

Height (cm)

0.1 0 0 0 0

5.0 102 99 99 2

7.1 203 198 204 202

11.3 511 503 514 6

6. Using the Logger Pro program create a graph of rebound height vs. pressure.

7. What kind of relationship is this? ___________

8. Using the data and the graph, what conclusions can be drawn?

Since the best-fit line is __________, I conclude that there is a __________ relationship between

______________ and ________________. This can be modeled mathematically as ________ = 4 * ______. So I predict with _____ confidence based on my data that when the ball is pressurized to 14.0 psi and dropped from 6 m high the ball will rebound to _____ __ high, because the best-fit line hits near the ____ of most of the data points and the prediction is ______ my data range.

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"How does the max tension of a rope depend on the diameter of the rope?"

Diameter of rope cm (+/- 0.05)

Max Tension lbs. (±5) Trial #1

Average Max Tension

(lbs.)

Max Tension Uncertainty

(lbs.)

1.00 99 102 99 100 2

2.00 197 206 197

3.00 280 310 310 20

4.00 375 425 400 400

5.00 530 470 500

2. Graph this data on the table below.

3. What does the slope signify?

4. What kind of conclusion can be drawn from the graph?

Since the best-fit line is ________,

I conclude that there is a ________ relationship

between _____________ and ______________.This can be modeled mathematically as ________ = 100 * _______. So I predict with _____ confidence based

on my _____ that when the 25 cm rope is brought

under 3000 lbs of tension it will hold, because the best-fit line hits near the _________ of all the data point and the prediction is far outside my data range.

Data for the following question is gathered while you are playing on a seesaw with an old childhood friend.

"How does the distance from the pivot point on the seesaw affect the force needed to support your 600 N friend?"

Distance

m (+/- 0.1) Force Needed N (± 6) Trial #1

Force Needed N (± 6) Trial #2

Force Needed N (± 6) Trial #3

Average Force

(N) Uncertainty in Force

(N)

0.1 6010 6030 5930 5990

0.5 1222 1183 1207

1.0 611 606 588

1.3 462 470 455

1.7 347 366 350 10

6. Using the Logger Pro program create a graph of Force Needed vs. Distance.

7. What kind of relationship is this? ______________

8. Using the data and the graph, what conclusions and predictions can be made about the force needed to balance your 600 N friend when she is sitting 1.8 m away from the pivot point?

Since the best-fit line is ________, I conclude that there is a ________ relationship between _____________ and ______________. This can be modeled mathematically as ________ = ____________. So I predict with _____

confidence based on my _____ that when the _______________________________, because the best-fit line hits near the _________ of all the data point and the prediction is _____________ my data range.

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"How does the resistance to twisting of a concrete column depend on the diameter of the column?"

Diameter of Column

m (+/- 0.01)

Breaking Twisting Strength lbs. (±5) Trial #1

Average Breaking Twisting Strength

(lbs.)

Breaking Twisting Strength Uncertainty

(lbs.)

0.50 252 251 247

1.00 980 990 1030 30

1.50 1775 1715 1760

2.00 4040 3800 4160 200

2.50 6300 6260 6190 6250

2. Graph this data on the grid  3. What kind of relationship is this?

4. Using the data and the LoggerPro graph what

conclusions and predictions can be made for a 8.0 m column subjected to 65,000 pounds of twisting force?

While blowing bubbles with little cousin, you notice that the bigger the bubbles you make the more bubble solution you use. So you wonder, ‘How does the radius of a bubble affect how many bubbles you can make out of a 100 mL bottle of bubble solution?’ and take the following data:

Radius of Bubble cm (+/- .3)

Number of Bubbles Trial #1

Average Number of

Bubbles

Uncertainty Number of Bubbles

0.5 444 457 451 7

1.0 119 119 122

2.0 31 31 30 31

4.0 8 7 8

8.0 2 2 2 2 0

6. Use the Logger Pro program to create a graph of number of bubbles vs. radius of bubble.

7. What kind of relationship is this?

8. Using the data and the graph, what conclusions and predictions can be made for the number of bubbles made if each one has a 6.0 cm radius?

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x y x y

x y

Patterns Review

Graphically:

Linear Quadratic Inverse Inverse-square

Mathematically:

y = y = y = y =

Data Table: (Using the equations you wrote above, write in 3 values for x below and then calculate the corresponding values for y. Assume a = 1)

Visually (a.k.a. proportional reasoning)

x ->

x

x ->

x

x ->

x

x ->

x

y -> y -> y -> y ->

In words: (“If x doubles, then y…”):

1. At a high school level clearly explain why in science we prefer a data-informed decision over a wild-guess:

2. At a high school level clearly explain why is it useful for people to find patterns in nature?

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3. What does it mean to use evidence-based reasoning?

Comparing Patterns:

Find two significant similarities between linear and quadratic:

1.

2.

Find two significant differences between linear and quadratic:

3.

4.

Find two significant differences between linear and inverse:

5.

6.

Find two significant differences between inverse and inverse-square:

7.

8.

Proportional reasoning: For each pattern use proportional reasoning to complete the relationship. For each of the questions below, assume a=1.

9. Linear relationship: 10. Quadratic relationship

if x becomes 2x then y _____________ if x becomes 2x then y _______

X ->

x

(doubles) then Y -> _____________ X ->

x

(doubles) then Y -> _____________

y -> y(quarters) then x must have -> y -> y(quarters) then x must have ->

if x becomes 4x, then y _____________ if x quadruples, then y ________

11. Inverse relationship: 12. Inverse Square relationship:

if x becomes 2x then y ___________ if x becomes 2x then y __________

X ->

x

(doubles) then Y -> _____________ X ->

x

(doubles) then Y -> ___________

y -> y(quarters) then x must have -> _____________ y -> y(quarters) then x must have -> _______

if x becomes 4x, then y _____________ if x quadruples, then y ________

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13. Rank the four patterns from easiest to reason about to most difficult to reason about:

Patterns & Inquiry Skills Unit Packet – STEM Physics