Getting Started with the HP Mobile Calculating Lab · 2012. 1. 5. · Getting Started with the HP...

Getting Started with the HP Mobile

Calculating Lab

G.T. Springer © 2009

Getting Started with the HP MCL Version 1.0

1: Getting Started with the HP Mobile Calculating Lab (HP MCL) This series of short articles is designed to help you learn about the HP MCL in a few, short, simple exercises. We hope you enjoy them! In this Volume #1, we offer you two Try This activities. The first one can be done alone, or you can do both together. Try This #1 1. Connect the Streamsmart 400 to your HP graphing calculator using the serial port (on the top left side as you hold the calculator facing you). Then connect the light intensity sensor to the StreamSmart 400 using the mini-DIN cable. Aim the sensor at a florescent light source. Make sure the switch on the sensor is set to C: 0 – 600 lux. 2. Press the APLET key on the HP 39/40gs (or the APPS key on the HP 50g) and scroll down to select the StreamSmart application. Press the START menu key to see Figure 1. Your data stream may be lower than that shown. Move the sensor around and you will see the readings vary. Imagine giving your students the direct experience of variable as something that actually varies! Figure 1 Then press the STOP menu key. You have now collected your first data set! Before we go on, let’s describe what we are seeing. The plot window of the display shows a number of items, as described in the table below.

Item Description Ch1 Channel 1 has a light sensor, measuring lux Win The display width (window) represents 5.0 seconds X, Y At time x=3.304 sec, the sensor measured the light intensity as y=531.3 lux Graph A horizontal time graph indicates the light intensity seems constant In addition, there are a number of menu functions as described below. These are activated by pressing the corresponding key in the top row of keys on the calculator.

Menu Function Description PAN Toggles between PAN (scroll) and ZOOM to dynamically adjust

the data stream PAN When active, uses the cursor keys to translate the stream ZOOM When active, uses the cursor keys to zoom in/out, horizontally or

vertically, on the stream SCOPE Enters oscilloscope mode STOP Ends data streaming

Copyright 2009 by HP Calculators May 4, 2009 [email protected] Page 1


3. Use the PAN function to center the data stream in the display, if needed. Press the PAN key to activate panning; a small square appears to indicate activation. Use the down-cursor key to translate the stream and center it in the display, as in Figure 2. Note two new menu functions: Trace and Export. 4. We will now zoom in horizontally on our data. In effect, we will be decreasing the time interval represented by the width of the display. Press the PAN menu key to toggle to zooming. Then press the right-cursor key to start zooming in. Keep the key depressed and zooming will continue smoothly. At around Win: 0.5 s, you will start to notice the fluctuations in the light intensity, as shown in Figure 3. Once you have zoomed all the way in (Figure 4), use the up-cursor key to zoom in vertically on the graph until it fills most of the display (Figure 5). You may have to pan again to get the graph just as you want it. 5. You can now see that the light intensity fluctuates in such as way as to produce almost 3 cycles in 0.022 seconds. This is consistent with 120 cycles per second, which would be expected from AC electricity at 60 cycles per second. 6. Now here is your first surprise! Press the START menu key and you should see these same waves in REAL TIME! The HP MCL collects data in real time at rates over 5,000 samples per second. 7. In fact, you can zoom and pan as you did in Steps 3 and 4 while data streaming is occurring. Try it now and get comfortable with tailoring the data stream to your needs and expectations. 8. EXTRA: Press the SCOPE menu key to enter oscilloscope mode. Nothing much changes, except that two dotted lines appear (Figure 6). Use the direction keys to move these cross-hairs with the TRG (trigger) function active. You can get just the standing wave you want! Congratulations! You now know how to stream data from sensors using the HP MCL!

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7



Try This #2 We continue with our previous example. 1. Use the ZOOM and move the trigger until you see 4 or 5 of the standing waves, as in Figure 8. Then press the STOP menu key. Just as an estimate, Figure 8 shows roughly 4 cycles in 0.033 seconds. This gives us a frequency of 4/0.033 = 121.21… cycles per second. 2. To get another estimate, press the menu key to see the second page of menu functions, as in Figure 9. Use the cursor keys to move the tracer to the maximum of one of the cycles. Then press the MRK (Mark) menu key to leave a mark at that location. Now move the tracer to the maximum of an adjacent cycle, as in Figure 10. Now we see that cycle took 0.008 seconds to complete for another frequency estimate of 1/0.008 = 125 cycles per second. 3. To obtain better estimates, we will need to download the data to the Statistics Aplet. Press the

menu key to return to the first page of menu functions and press the EXPRT (Export) menu key to export data to the Statistics Aplet. The upper right corner indicates you currently have 131 data points to export. We will use the cropping tools to select just the data we want. In Figure 11, the left-crop tool ( [ ) is active. With it active, use the left- and right-cursor keys to crop data from the left. Similarly, use the right-crop tool to crop data from the right. In Figure 12, the cropping tools have been used to select three cycles of the data. You can thin the data set further; simply go back to the second page of menu options and use the + and – menu keys to add or subtract points from the data set. 4. Once the final data set has been identified, it is ready for export to the Statistics Aplet. Press the

menu key and the OK menu key to see Figure 13. Here you can set what columns in the Statistics Aplet are the destinations for the time and sensor data from the experiment.

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13



Copyright 2009 by HP Calculators May 4, 2009 [email protected]

5. As shown in Figure 13, by default the time values will be saved in column C1 of the Statistics Aplet. After that, the data from sensors in Channel 1, 2, 3, and 4 will be saved in column C2, C3, C4, and C5. Press the OK menu key to accept these default settings.

Figure 13

6. After a message screen telling you the data has been transferred and all other data has been deleted, you will be directed to the Statistics Aplet, as in Figure 14. Notice that Row 1 has t=14.1796 and the light intensity is at a relative maximum. In Figure 15, we scroll down to Row 43, where t=14.1874 and light intensity is again at a maximum. This time we can estimate the frequency

as ...205.1281796.141874.14

1=

− cycles per

second.

Figure 14

Page 4

7. As a final exercise, we fit a sinusoidal model to

the data and use the model parameters to estimate the frequency. Notice in Figure 15, that the 2Var menu key is active. This key toggles between 1-Var and 2-Var. With 2-Var active, press the VIEWS key and select the Autoscale option to see a graph similar to that shown in Figure 16.

Figure 15

Figure 16 8. Press the Shift of the SYMB (Symbolic) key and

use the cursor keys to highlight the S1fit field. By default, this field is set to a linear fit, which we want to change to sinusoidal. Press the CHOOS menu key to choose Trigfit, as in Figure 17.

9. Return to the graph by pressing the PLOT key. Press the MENU key to see the menu functions and press the FIT menu key to generate and graph the fit. This will take a few moments.

Figure 17

10. Once the fit has been generated, press the SYMB key and highlight the Fit1 field. Press the SHOW menu key to see the entire equation. Figure 18 shows the coefficient of x in our model is 783.69…. Our last estimate of the frequency is

...2.1252

69.786=

π. You have now experienced the

HP MCL used as a data streamer! Congratulations!

Figure 18


2: Activities with the Pressure Sensor This series of articles is designed to help you learn about the HP MCL in a few, short, simple exercises. In this Volume #2, we offer you two more Try This! activities. For Try This #3!, you will need to borrow a common 20 ml syringe from your Science Department. Each activity should take 10 minutes or less to complete. You can do the first one by itself or both together. Try This #3 1. Connect the Streamsmart 400 to your HP graphing calculator using the serial port (on the top left side as you hold the calculator facing you). Then connect the gas pressure sensor to Channel 1 of the StreamSmart 400 using the mini-DIN cable. Set the syringe plunger to maximum capacity and thread the gas pressure sensor onto the end of the syringe. We will assume a 20 ml syringe; if your syringe is larger, adjust the volumes accordingly. 2. Press the APLET key on the HP 39/40gs (or the APPS key on the HP 50g) and scroll down to select the StreamSmart application. Press the START menu key and move the plunger in and out. Your data stream will have a different shape but will appear similar to Figure 1. As in the Try This #1! exercise, imagine giving your students the direct experience of variable as something that actually varies!

Figure 1 Figure 2 Now press the NUM key to see Figure 2 (your reading may vary from that shown). In this Numeric View, you get a meter read-out of the sensor data. Before we go on, let’s describe what we are seeing. The meter window of the display in Figure 2 shows that Channel 1 is active, with a pressure sensor that is measuring kilopascals, and that the current reading is 90.26 kpa. In addition, there are a number of menu functions as described below. These are activated by pressing the corresponding key in the top row of keys on the calculator. Menu Function Description ADD Add the current sensor reading to the Statistics Aplet SETUP Set up which columns in the Statistics Aplet get the data from each

sensor, as well as whether or not to add an entry to each data point PROBE If StreamSmart does not ID the probe correctly, manually choose the

probe type UNIT Change the units of measurement of a sensor (if available) STAT Go to the Statistics Aplet to analyze the collected data




We will take pressure readings when the volume of air in the syringe is 20, 15, and 10 ml.

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1. We will set up StreamSmart so that it will prompt us for the volume of the syringe every time we take a pressure reading. Press the SETUP menu key to see Figure 3. By default, the data in Ch1 (the pressure readings) will go to column C2 in the Statistics Aplet. There is a field named ENTRY and its data will go to column C1 in the Statistics Aplet. These are the volume readings we will enter manually during the experiment. Use the cursor keys to highlight the EVENT METHOD field (now set to Auto Number as in Figure 3). Press the CHOOS menu key and select the With Entry option, as in Figure 4. Then press the OK menu key to return to the meter read-out in the Numeric view.

Figure 3

Figure 4

2. Set the syringe plunger at 20 ml.

3. Press the ADD menu key to record the pressure when the syringe volume is 20 ml. You will be prompted to provide an entry. Enter 20 (as in Figure 5) and press the OK menu key. StreamSmart will flash a message saying “Adding Event #1” and then return to monitoring the pressure.

Figure 5

4. Move the syringe plunger to 15 ml, let the readings stabilize, and repeat the process in Step 3 to add this 2nd volume-pressure pair to the data (Figure 6).

Figure 6 5. Repeat Step 4 with the plunger set at 10 ml.

6. Press the STAT menu key to see your data, as in Figure 7. Your data may vary from that shown. Remember that column C1 contains the volume readings while column C2 contains the corresponding pressure readings.

Figure 7 7. Note that the product of the volume and pressure readings in each row is close to constant (eg. 10x175.193≈1752). Since the product of the volume and pressure readings yields a constant, this data can be modeled using an inverse variation.

You have now collected your first data set point by point using the HP MCL!

In the next Try This! activity, we derive a mathematical model from this experimental data.


Try This #4 Our inverse variation is V*P=C, or Volume times Pressure = a Constant. We want to estimate the value of this constant. In the last activity, we estimated the value of this constant as 1752, so our estimate is likely to be in this neighborhood. We will use the HP 39gs to make these calculations quickly and show us the average. 1. Press the HOME key and enter C1*C2 and store the result in C3, as in Figure 8. STO is the first menu key in the Home screen. You can use the ALPHA shift to type the letter C. 2. Now press the NUM key to return to our data table. Figure 9 shows the new column C3. To see the average of C3, press the 2Var menu key; you will see it toggle to read 1Var. Now press the SYMB key and set H1 to use C3, as in Figure 10. Press the NUM key to return to the table and then press the STATS menu key. The mean is shown in Figure 11. 3. If we use the mean of C3 as our constant, our new model for the data is V*P=1774. Press the OK menu key to return to the table when you are done. 4. Press the 1Var menu key to toggle it back to 2Var, then press the shift of the SYMB key to enter our new model to our data set. Highlight the S1FIT field and press the CHOOS menu key to select the User Defined option, as in Figure 12. Now press the SYMB key, highlight the SIFIT field, and enter the model expression. In V*P=1774, we substitute V=X and P=Y and solve for Y: X*Y=1774 or Y=1774/X. Figure 13 shows the result. 5. To see the scatter plot of your data, press the VIEWS menu key and select the Auto Scale option. Figure 14 shows the data from Figure 7. The data points are connected by default, so you can easily see the points do not line up.

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

Figure 14




6. To turn the auto-connect feature off, press the Shift of the PLOT key and press the menu key. Highlight the CONNECT field and press the menu key to de-select the option, as in Figure 15. Press the PLOT key again to return to the graph (see Figure 16).

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7. Press the MENU key and then the FIT key to see the model plotted over the data (Figure 17). Now we can use our model to predict the pressure for any volume in the syringe!

8. The tracer is currently on the scatter plot. Press the up- or down-cursor key to move to the model and then trace along the curve. Press the MENU key until you see the tracer read-out. Figure 18 shows the pressure is predicted to be about 136 kpa when the volume is approximately 13 ml. Of course, the HP 39gs can use regression techniques to fit a power curve to this data instead of using our user-defined function.

9. Return to Step 10 and choose the Power option instead of the User Defined option (Figure 19). The simply press the PLOT key to return to the graph and see the new model (Figure 19). For the data shown in Figure 7, the HP 39gs reported a power fit of approximately

. This is not too far from our own rough model of .

958.01587 −= xy11774 −= xy

10. To see your model, press the SYMB key, highlight the S1FIT field, and press the SHOW menu key. In Figure 20, the tracer is on the point that corresponds to that shown in Figure 17 in order to compare the two models. In this activity, you developed your own simple model for the experimental data and saw both model and data plotted on the same axes. You then used the HP 39gs to quickly develop a more accurate power model. Both models allowed you to make predictions about the physical phenomenon. With the HP 39gs, the choice is always yours!

Figure 15

Figure 16

Figure 17

Figure 18

Figure 19

Figure 20


3: The StreamSmart Applet and the Virtual Calculator This is the last of our three-part series designed to help you learn about your new HP MCL. In this last volume, we offer a set of tips and tricks for both the DataStreamer Aplet and the HP Virtual Calculator application. Tip #1: Using the Fourier Distance Sensor When the Fourier Distance sensor is connected to the HP MCL, the DataStreamer Aplet sets the streaming window to 18 seconds by default. Thus, each pixel represents approximately 0.14 seconds (see Figure 1). You can zoom in until the window shows 13 seconds, at which point each pixel represents 0.1 seconds. If you zoom in much further than that, StreamSmart may request data faster than the sensor can provide it, resulting in duplicate data points.

To avoid zooming in past the sensor’s effective sampling rates, you can also use the Experiment feature to manually set the sampling rate and duration for your data stream. Here’s how:

1. Start a data stream with the Fourier Distance sensor so that StreamSmart can identify the sensor.

2. Once the Distance sensor is identified, press the VIEWS key, scroll down to the Experiment option, and press the OK menu key. Figure 2 shows the Experiment Menu. By default, the duration is set to 10 seconds and the number of samples is set to 100.

3. Suppose you want to do a typical “match my graph” experiment for 4 seconds. Set LENGTH to 4 seconds and SAMPLES to 40. Keep the sampling rate at or less than 10 samples per second. Press the OK menu key and StreamSmart will start a 4-second data stream with 40 samples.

4. Figure 3 shows the result. Export:40 means there are 40 data points to export. You may want to crop out the first and last few samples. Figure 4 shows the final data; notice that StreamSmart will still export 40 data points. Figure 5 shows the data actually exported, showing the total of 40 samples.

If you want to repeat this experiment, return to the Experiment option under VIEWS and press the OK menu key.

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Copyright 2009 by HP Calculators June 2, 2009 [email protected] Page 9


Tip #2: Using the VIEWS menu! Let’s look at the other options in the Views menu. HP Aplets use the VIEWS key to define any custom views that the Aplet may have, and the StreamSmart Aplet is no exception. Press the VIEWS key to see Figure 6. The first two options, Plot and Multimeter (not shown in Figure 6), correspond to the PLOT and NUM views that are the major StreamSmart views. The other views are described in the table below.

Figure 6

View Name What it looks like What you can do Plot Setup

• XRNG: set the window width manually • PLOT DISPLAY: choose Stack or

Overlap for multiple data streams • DISPLAY FILTER: plot the Average

of readings within a pixel, or choose Max, Min, First, etc.

• EXPORT FILTER: when exporting data values, use the same filter as display, or choose another method

Sensor Setup

If StreamSmart incorrectly identifies a Fourier sensor, use this option to correct the identification. Either press the CHOOS menu key and select the correct sensor, or press the first letter of the sensor type (eg P for pressure) repeatedly until the sensor you want appears.

Unit Setup

Use this option to change measurement units for a selected Fourier sensor. Press the CHOOS menu key and select from the list of available units.

Calibrate

This option allows you to perform custom 1-point or 2-point calibrations of any Fourier sensor.

Experiment

This option lets you use your data streamer as a data logger. Simply set the length of the experiment in seconds as well as the number of samples you wish to collect. When you press the OK menu key, data logging will commence.



The Virtual HP Calculators This section provides some tips about using the HP Virtual Calculators. Tip #1: Try Out a New Skin The HP Virtual Calculators launch with 1024x768 skins by default. Most PCs are capable of rendering the higher quality 1280x960 skins. To switch to a higher resolution skin, look at the menu bar and locate the Skin menu. Click on Skin to open the Skin menu (Note, by the way, the Full Screen option available here). Click on Skin again and choose the 1280x960 option. The current application will close and there will be a pause before the new application opens. The new skin appears as in Figure 7. Although it seems as though the menu has disappeared, it hasn’t really. Click on the HP logo to open the menu! Tip #2: As You Like It If you are doing presentations with the virtual HP 39/40gs, you can set up all your data, in multiple Aplets, and save it under a name you give it. This is called saving the calculator state. You can save multiple calculator states in order to have different HP 39/40gs machines set up for different presentations. To save state, click on the HP logo to open the menu, select Calculator, and choose Save As…. Then give the state a name. The next time you use the virtual calculator, you can go to Calculator/Open, and choose your state. The Calculator menu also has the Capture Screen option to help you write activities using the virtual calculator. Just use this option and then paste into your favorite application.

Figure 7



Tip #3: Macros! The HP Virtual Calculators let you capture your steps, keystroke by keystroke, and play them back at any time. Open the menu, click on Macros, and select the Record… option. Figure 8 shows the controls available while recording your macros. Click on the Record button to begin recording your macro. Type a name into the input box at the bottom of the menu and click on the Save button. Close this control panel when you are done with macros. Now you can go back to the menu, click on Macro/Replay. You will see a list of your macros from which to choose. Tip #4: Help and More Help You can access both the calculator User Guide and the Virtual Calculator Help from within the virtual calculator. Simply open the menu and click on Help. You will see the following options:

• Emulator Help • Calculator Manual

Click on Emulator Help to open the online Help tool or click on Calculator Manual to open the Calculator User’s Guide.

Figure 8

We hope you have enjoyed the three volumes in this series of articles, and we hope they have been helpful in showing you some of the features of the HP MCL. As a final tip, remember that you can plug the HP StreamSmart 400 into your PC using the mini-USB to USB cable. When you launch your virtual HP graphing calculator, it will automatically recognize the StreamSmart 400. You can run the StreamSmart Aplet and project the display for your class to see!


HP 39gs Graphing Calculator Grades 6-12 Mathematics Materials Using Technology to Enhance Mathematical Understanding Version 1.0

G.T. Springer ([email protected]) October 26, 2009 Copyright 2009 HP Calculators Page 13

4: Using Technology to Enhance Mathematical Understanding

Two fundamental concepts in school mathematics are variable and function. In this paper, we

look at ways to strengthen student understanding of these concepts by the appropriate use of

technology. We will be using the HP Mobile Calculating Lab (MCL). The HP MCL consists of

the HP 39gs graphing calculator and the HP StreamSmart 400 data streamer, used to stream

incoming data from one or more Fourier sensors to the graphing calculator display. Figure 1

shows our initial setup, with the HP 39gs graphing calculator on the right, the HP StreamSmart

400 data streamer on the left, and a Fourier gas pressure sensor in the middle.

Figure 1

We start the StreamSmart Aplet on the HP 39gs and for our

first activity, we do nothing. Figure 2 shows the result.

The sensor is automatically recognized, the display is set to

show 10 seconds of data, and the incoming data shows time

varying from 0 to 10, but the pressure remains constant at

95.61 kPa. The graph has the appearance of a constant

function.

Figure 2



The pressure that the Fourier sensor is monitoring is simply

the barometric pressure, which remains relatively constant

over short periods of time.

We attach a valve to the end of the pressure sensor tubing

and close it off. Then we restart the data streamer while

pinching and releasing the tubing. Figure 3 shows the

result. We expected to see variation in the stream, but the

graph still looks constant. There is a good lesson here, for

graphs that look constant on one scale may reveal variation

on another scale. Can we zoom in on our data stream just

as we zoom in on a graph of a function? Yes we can and

Figure 4 shows the result. The pressure did indeed vary

slightly and we can see the variation once we zoom in

vertically on the data stream. Again, the perception is that

the stream of data represents a function; this time, a

function that varies. We re-run this second activity at the

new scale so the student can see the variation occurring in

real time. Such a simple activity can focus student

attention on the basic concept of variable. The gas pressure

measured by the sensor is a quantity that can vary.

One can use a wide variety of sensors to repeat the

activities above and obtain similar results. A light intensity

sensor can be moved about the room (Figure 5) or a

temperature sensor can be held in the hand (Figure 6). All

of these activities give students the experience of

measuring a quantity that can vary, which is the basis of the

concept of variable.

Figure 3

Figure 4

Figure 5

Figure 6

Pressure of a gas, light intensity in a room, and temperature of a hand are all quantities that vary

and so they can be represented mathematically as variables. Students must understand this and

technology can help make this notion part of their personal experience.

The concept of variable as a quantity that can vary is also bound up in our conception of relations

between two variables and function. My everyday experience is that the temperature at a point

on my hand or the light intensity at a point in the room has exactly one value at any point in time.

The technology samples these physical quantities discreetly in the same way that the graphing

calculator takes numerical samples to make a representation of a graph of a function.



The pixels in the calculator display represent regions rather

than points, which is essential to understanding the

graphing calculator representation of function. Thus,

zooming in and out on the graph becomes an important

activity when using technology to represent functions

graphically. Figure 7 shows the data stream from a light

intensity sensor monitoring a florescent light. The light

intensity appears constant, which would match our

expectations for a sensor held a constant distance from a

light source. However, florescent lights flicker on and off

at a rate controlled by the frequency of the alternating

current that powers them. In the US, AC frequency is set a

60 cycles per second. That means the florescent light

should flicker on and off 120 times each second, far too fast

for our eyes to discern. In Figures 8 and 9, we zoom in live

on the data stream, only to see the flicker appear. As we

zoom in horizontally by a factor of approximately 10 (from

5 seconds of data to 0.49 seconds), we see the uniform

oscillations appear. In Figure 9, we have zoomed

horizontally in all the way (over 200x) and we also zoomed

in vertically to see more of the character of the oscillations.

The point of this exercise is not to study trigonometric

functions or create mathematical models. We simply want

students to have the experience of seeing two quantities

vary in a way that makes them related to each other.

Figure 7

Figure 8

Figure 9

Figure 10

We want them to understand that the intensity of a florescent light varies in a way that is not

discernable to the naked eye, that this variation is regular with respect to time, and that we would

represent the relationship between time and light intensity as a function because the sensor will

report exactly one value for light intensity at any given time. We would represent all of the

graphs depicted in Figures 3-6 with functions for similar reasons. We want the students to have

these experiences BEFORE we launch into the study of any particular function family! We also

want the student to appreciate that the shape of the graph of a function depends in part on the

scale from which you view it. What appeared as a constant function in Figure 7 was really a

trigonometric function, as shown in Figure 9. Similarly, the graph of y=cos(20x) will appear

(and trace) as the horizontal line y=1 on any graphing calculator where the tracer steps by 0.1.

Simply zooming in horizontally will show that each pixel contained 1 full cycle of the curve with

the center of the pixel containing the maximum at y=1 (see Figure 10). In short, the HP MCL

technology can enhance the student’s understanding of variable and function because it treats

data collection in a way that is consistent with how the graphing calculator treats functions.



An accelerometer is strapped to a ruler with a rubber band.

One end of the ruler is clamped to a table top and the other

end is flexed and released to set the ruler in motion. This is

done several times over a 5-second period. The result is

shown in Figure 11, where two of the events can be seen as

small peaks.

Zooming in on one of the peaks reveals the detail shown in

Figure 12. What looked like just a bump or two is actually

a clearly-defined set of dampened oscillations. Also, what

looked like events that lasted far less than second actually

turn out to have a greater duration than Figure 11

suggested. As with the oscillation of the florescent light,

students are intrigued by familiar phenomena which have

surprising twists. The simple ruler can behave in a way

that is both complex and simple – beautiful!

Using the StreamSmart Aplet, I can trace to each peak and

add the point to a data set manually. Figure 13 shows the

final data set graphically. Students can see that the

oscillations are fairly regular; that is, the “peaks” are evenly

spaced even though the amplitude decreases over time.

Connecting phenomena of growth and decay to exponential

models is natural here. Figure 14 shows an exponential fit

for the data set.

Figure 11

Figure 12

Figure 13

Figure 14

The progression illustrated in this paper runs from getting students to notice a quantity that can

(and does) vary to noticing 2 quantities that vary together in recognizable ways. Along the way,

students are intrigued by the un-noticed complexity and beauty of their everyday world as it is

revealed to them by data streaming from scientific sensors. Affordable technology opens up new

opportunities for teaching and learning mathematics and science!

Getting Started with the HP Mobile Calculating Lab · 2012. 1. 5. · Getting Started with the HP...

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