Thanks, everyone for being patient and persistent as some technical bugs were worked out, etc. It was a great day for the presenters and I hope you got a lot out of the great discussions, labs, activities, etc.
FOR HOMEWORK: Please post your impressions, questions, answers to the lab questions and your comments. You could divide each portion of the day into separate paragraphs, if you'd like.
Dr. Koppang would like you to work up your data for the density lab.
Dr. Ezrailson would like you to discuss your results for the light lab -- especially about your data -- what went as you expected and what surprised you. Discuss, also what you would change in your method/techniques if you should do this experiment, again.
We look forward to reading your posts and to tomorrow's activities.
Have a great evening.
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I was trying to wait to post because I wanted to see how someone else did theirs! I will give it a try...regardless!
ReplyDeleteImpressions, questions, answers to the lab questions and my comments:
To me the density lab was applicable to me because it made me realize the usefulness of using Excel for data collection and creating graphs. My middle school students really struggle with using, interpreting and creating graphs. This application would give them some time to utilize technology AND incorporate more graphing into my class. As I was looking at the data from our different samples, it made me think about how important the number of samples is. By using the Excel graphing I can show the students the difference between using just a few sets of data with the best fit line and multiple sets of data with a best fit line.
My answers to the lab questions are:
Solid Sample Mean: 8.8g/mL Standard of Deviation is 0.36
Confidence Interval at 95% is 7.9-9.7g/mL
The number of significant figures used should be two. Reason being, the equipment only was capable of accurately measuring to the hundredth. Since the graduated cylinder went to the tenth, it was necessary to go one more significant figure with estimation.
Liquid Sample: Density is 0.99999g/ml (using a best fit line)
For the Light Brightness and Distance Lab- I have never conducted an investigation using probe ware. The light sensor was useful in accurately recording the data from the various distances. Prior to starting the lab, my group was discussing how the light intensity would exponentially decrease. Our prediction was correct, and the first set of data collected proved that. We conducted the experiment again, reducing the amount of ambient light affecting the system AND using measurements that started from the middle of the light box (which is actually where the light is located). This second trial created data that was much closer to the natural log of 2 (1.8355), whereas our first trial was not (1.5059). If I were to conduct this experiment a 3rd time, I would use a dark atmosphere to hopefully get results closer to 2.
My impression of today is that portions were applicable (the labs, use of equipment/probe ware, explanations of the meaning of our data). There were other parts of today that were really difficult for me (the math!). I know this course is supposed to assist ME with my background knowledge in Math to help me be able to apply it to my class. My 7th graders are not going to be calculating the standard deviation or confidence interval, yet I still need to stay one step ahead of them. I did appreciate the professional discussion about applicability to my classroom and the informational sessions to help build my background knowledge.
Hope everybody had a better data collection day than my group had. Of the three sets, the water density was what I would consider the best. The calculations were spot on.
ReplyDeleteWe had some interesting figures for the metals density. The calculations gave us a range starting in the mid 6's going as high as a little over 11 g/ml. With this range of data we had a STD of 2.4. I was wondering if any other group had some interesting data with the metal that looked like copper? Just want to see if the instuctors tried to pull a quick one.
The light intensity lab went OK once we got the Vernier device to work. With the time we spent getting the device to work, I wish we would have thought through the factors that influence the results. It think it would have given better data if we would have shielded the probe from the room lights. I don't think you'all wanted us to turn off the lights.
After all was done, I enjoyed the day.
I know some people are not able to post due to computer issues (no login and/or internet access).
ReplyDeleteDensity: This would be a great activity to work in conjunction with our science, computer teacher and myself. Science can do the collection, computer generating and in math we can do the interpretations, predictions and different scenarios (more samples, less samples, etc.). At my level standard deviations don't come into play. We could however in algebra discuss the linear relationship.
ReplyDeleteAs for the light intensity one...I was a bit overwhelmed. I understand the jist of it, but am looking for the other posts to solidify it in my brain! Our data and the inverse square were close because our slope and power were the same. As far as getting the -2 like we should have, we had quite a variation. This was probably due to the overhead lighting, not having the light centered where it should have been or other human error. The negative correlation was a result of the intensity decreasing as the distance increased.
The only question I have at this time is about whether or not our equation agrees with the model of light intensity using the concentric spheres. I'm unsure what this is saying.
Todd,
ReplyDeleteWe had the one that looked like possibly copper (C) and our results ranged from 7.7 to 10.3 at the 90% with a SD of .7. I think that one worked fairly well for our group.
Impression, Questions and Answers-
ReplyDeleteDensity Determinations for Liquid and Solid Samples: I really enjoyed this lab even though my middle school students do not have a lab like this. I do believe I can 'tweak' it to their level and apply the graphing w/ Excel which I really liked. It is something my middle school students can do quite easily- I hope! Our 6th grade Science book briefly touches density but I will add this experiment this year. Standard deviation may be a bit much but I'll give it a try.
Light, Brightness and Distance
This lab went really well for our group. We had no major issues w/ the equipment but we re-did the experiment and covered the top to allow no extra light in and we had a better, more accurate graph. I will have to check with our high school science teachers to see if we have the equipment available. I was wondering if the equipment has the ability to have my TI-83 plus attached right away to do the graphing.
It was a good first day-my brain just had to bet back to classroom mode:)
Our group has our labs typed in a document and I think we are to hand in a paper copy or would you like it attached to this?
First of all: The Density Lab
ReplyDeleteI agree with Nicole's comment that this lab does a good job of showing the usefulness of Excel when it comes to data collection and creating graphs. I already do some activities in my classes where we gather data, create a scatter plot, and then find the line of best fit. We also find the correlation factor. However, we do it all on a graphing calculator, we don't use the Excel program. It was fun to see another way of approaching those activities.
Anyways, when we found the mean of the values that we found experimentally for the density of the solid, it came out to be 10.1 grams/ml. Our standard deviation was 1.49. The confidence interval at the 95% confidence level was between 6.40 and 13.80.
When Dr. Kopang first gave us the bottle containing the unknown solid, my lab group said that it looked like either zinc or lead. As it turned out, we were pretty much right on the nose, because it turned out to be lead.
Next, we created a volume vs. mass graph for the unknown liquid in the second part of the Density lab. Using the trend-line from our graph we found the density of the liquid to be 0.988 g/ml. We also found the value of r squared to be 0.883.
Next: The lab over Light Intensity
The data that we collected in this lab was not nearly as good as the data we collected in the density lab. When we created a ln(I) vs. ln(r) graph for our data, our value of n came out to be -0.969. Which is obviously not very close the -2 which was the correct answer. Our value of r sqaured was 0.883, which also shows a lot of room for improvement.
If I was going to do this lab over again, I would find ways to cut down on the amount of excess light in the room. There was a lot of light being produced by the overhead flourescent lights in the room, and a lot of sunlight coming in through the windows in the back of the room. My lab group was working in the back of the room, so the sunlight probably had a huge impact on our data. In retrospect, we should have covered the windows or pulled the shades, and we should have also turned off the overhead lights.
However, as Todd said above, when all was done, I enjoyed the day.
I have enjoyed reading all of your posts and thank you for a great day! The light lab can be frustrating but I think it is an important lab to try and do with your kids as it is a great example of an inverse square law. I actually do it in my physical science class during our discussion on gravity since both follow the inverse square law. You can also show this just using an overhead projector on a white wall. Lori, you can use this with TI-83/84 but you will need a CBL unit. Those of you that use CBL's should check out the EASY LINK from Vernier. It is great as it is relatively cheap, small, doesn't require batteries and eliminates those constant link errors! Thanks again for your great effort and attitudes today! Keep the questions coming!
ReplyDeleteDensity Determination for Liquid and Solid Samples: I really liked doing this lab. I do something similar but this gives a different tweek to using Excel and graphing data. I would have to get some different metal samples to use because we do not have any samples like these in our lab. I was wondering where you got the different metal samples?? Also, how many different metal samples would you recommend to use in a Middle School Lab setting? For middle school, I do like the repetition of the data collecting---3 samples---this allows them the chance to make sure they are collecting their data correctly. I also use the water displacement method in labs for volume. This would be more practice for them. I would have them record the mass, volume and density because this is something I already do in labs. I don't know if I would go into the Standard Deviation----it would depend on the level of the students that I have in a particular class and if they could handle the math calculations at this age.
ReplyDeleteLight, Brightness and Distance: In this lab our calculations fit what we expected to happen except at the very end we did have a different reading due to getting closer to a outside light source that was affecting the data. I have used some of the Vernier products before so was familiar with the basic set up. We did have to change our first Lab Quest because it wouldn't collect the data---possibly due to a low battery charge. Once we got it working the lab went fine. I think I could use this lab in Earth Science when I talk about stars and Absolute and Apparent Magnitude. It would be useful in comparing the intensity of stars and how distance affects the light we see from earth.
This 1st day was enlightening--teaching an old dog new tricks!! The math was a new challenge because I haven't used some of the calculator options before. That is why I have friends in the math department!!!! Keep crunching those numbers!! LSuess
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ReplyDeleteDensity Lab: I really enjoyed the variation in this lab. I do something quite similar in my chemistry classes but with it I incorporate the types of error associated with determining density. As for the calculations, I would see this being very appropriate for my AP Chemistry class. I use excel later in the year for graphing data, but this would be very appropriate to start off the school year. I have not incorporated confidence level into a particular lab and am anxious to bring out this concept.
ReplyDeleteLight Intensity Lab: I have not spent very much time working with probes. I think this would be a very beneficial lab for our physics teacher. This was an excellent lab for collecting data concerning the inverse square law. We say that as the distance increased, out intensity decreased. Based on our data, we got a slope of -1 as compared to the accepted being -2. Our liner and power graphs looked great with the error involved. I think some of our problems were based on the lighting in the room. Also, our light source was at an angle. I can see myself using the excel program to make graphs to demonstrate the inverse square law. In my chemistry classes, however, I would try to integrate this technique when discussing radioactive decay or radiation intensity.
Overall, this was a good day.
Darwin Daugaard
ReplyDeleteLab: Activity “Density for Liquid and Solid Samples
Part I: Density of a Solid
First of all I do start my courses by doing a density activity. It is a great review of measurements, conversions and calculations along with a discussion and implementation of “precision and accuracy” and scientific notation. I like the different angle of finding the density of a unique shaped solid. It will definitely lend to a more inquisitive setup for the students to ponder. I have taught all the sciences from 7th through 12th grade at some point and I feel this lab is relevant to all the levels. The extent at which it is carried through can be based on the educational readiness of the individual groups or classes involved. This activity will definitely meets some of the standards in any of these levels.
Portion Mass Volume Density
1st 1/3 38.12 g 5.00 mL 7.62 g/cm3
2nd 1/3 23.40 g 2.55 mL 9.18 g/cm3
3rd 1/3 27.79 g 3.65 mL 7.61 g/cm3
Average = 8.14 g/cm3
n = 3 trials
s = standard deviation of .9
t at 90% confidence (n-1)=2 is 2.920
t at 95% confidence (n-1)=2 is 4.303
at 90% is 6.62 to 9.66
at 95% is 4.27 to 12.01
As the confidence level increases the interval widens and allows more measurements to meet the conditions because the interval becomes more broad and less on target.
We used 3 significant digits based on our graduated cylinder. It is incremented in units of 0.5 mL with an estimate being made between these increments.
Our precision was based on our graduated cylinder because it was the least precise instrument between the balance of 4 digits and the cylinder of only 3 digits.
Part II: Density of a Liquid
Mass Volume Density
5.069g 5.04 mL 1.01 g/mL
9.75 g 9.800 mL 0.995 g/ml
15.05 g 15.05 mL 1.00 g/mL
20.00 g 19.98 mL 1.00 g/mL
24.95 g 24.94 mL 1.00 g/mL
We got a linear relationship. Used best fit to get a line.
Density= 1.0007 g/mL
Deviation=.0084
Correlation factor = 1
Standard deviation = 0.00547
Light lab response.
ReplyDeleteI do a similar lab comparing 2 different light bulbs. Not all 100 watts bulbs are created equal. Some students see this clearly and other are a little foggy or frosted as I say. Ha!. We even use colored bulbs from the drama department. What a good way to value the judgment of a color blind student if there is one to be had. Now we even have fluorecent bulbs to green up our results.
OK.
Preliminary Questions
1. a.The power passing through the inner sphere and reaching the outer sphere is the same. It will be more spread out at the 2nd sphere and even more as it moves out. The same amount of light is required to light up more area. As you move out the area lit increases in size both by width and length. Length times width gives us square units which gives us an idea what might happen.
b.The surface area of the second sphere is 4 times as much as the first. If you double the distance from the source then you double both the width and length. If you triple the distance you triple both the width and length then you get 3 squared when you find the area lit.
c.The intensity varies as 1 over the square of the different in the change of distance.
2. There will be some error in the actually intensity depending on the direction of the filament.
Procedure
1. As you double the distance the intensity becomes ¼ as bright. Triple becomes 1/9 as bright and so on. 1/x2.
Analysis
1. Yes. The line of best fit looks pretty close based on 1/ x2.
2. It matches pretty good with the first 4 points then we had some experimental error. Our equation does come close but I am sure we could repeat it and come closer. The equation does agree to a certain point.
3. I blame the surrounds, extra light and the steadiness of the probe.
Overall I felt today was a great example of why accuracy and precision are important. It also gave us great examples of how to show students how to use them.
ReplyDeleteDensity lab:
I typically start out my year in chemistry talking about units of measure and derived units. Along with this we also talk about accuracy and precision. We discuss how they are related and what kinds of information that we can take from interpreting them. The density lab that we did today gives me another great tool for teaching this in a hands on setting. We typically do an exploration and an application lab regarding density every year in Chemistry and Physics and show the relationships between the variables. We also discuss how taking accurate measurements and being precise in our procedures can affect the outcome. Having the students calculate the standard deviation and then figure the confidence intervals will give them a better understanding of how to use this data for identification of substances. From this they can then come up with other ways that this can be used in the real world. Using Excel not only makes the process faster but allows the you to analyze the data more thoroughly.
Our average density of our solid was 10.1 g/mL with a standard deviation of 1.49. Our confidence interval for 95% was from 6.40-13.80
Our average density for our liquid was .95 g/mL with a standard deviation of .35. Our confidence interval for 95% was from .52 - 1.38
The light intensity lab was a great way to show the relationship between light intensity and distance. This lab can be applied in so many ways. Some of which include the brightness of stars and other luminous objects in the sky. When we graphed our ln r vs ln I we got an n value of -.969. The value of n should be 2. This also showed when our r value ended up being .883. This shows that we were off by a bit. I feel the light pollution from the fluorescent lights as well as the light coming through the windows caused much of this error. Eliminating as much outside light as possible should help the results. Excel again gave us a very powerful tool for analyzing this data.
As others have said, I feel today was a good day.
I learned a lot today in this lab, not sure what it all means. But I think we should have turned off the lights in this lab to get more accurate readings. I have never done any of these labs. I enjoyed the math lesson in natural logs. Do remember some of it from 25 years ago. The questions in the analysis are way over my head. This is the first time I have heard of the power regression.
ReplyDeleteHi from Betsy Koenig
ReplyDeleteSolid and Liquid Density Lab
I was glad to do this lab, I do something very similar in my eighth grade science class. Students really need practice with balance beams and volume measurement. My students have actually never done anything with balance beams and graduated cylinders, when they enter the seventh grade.
I forced myself last night to read my calculator's manual and I actually figured out how to input a string of data in TI-30 calculator! I then figured out how to get the mean and the sample standard deviation! I will use this knowledge with my seventh grade PreAlgebra class and teach them how to use the calculators in this way! Thank you for making us learn this!
Light Lab
I really enjoyed the light lab. It has been a lot of years and I forgot (or quite possibly never understood!) what logorithms were. What a practical application with the light lab, very interesting too.
Our data got quite messed up. I must not have moved the probe when I thought I did and the first two data points were way too close together.
It really taught me a lot to see the logorithms turn a very complex relationship into a straight line. Our school does not have light meters, but this is something I could maybe show the Calculus teacher as an application so the students could understand what a logorithm does.
DENSITY LAB
ReplyDeleteI thought the density lab was very interesting. I definitely think it is a true lesson learned on how simple it is to have error in an experiment. We really need to keep that in mind when doing experiments with our students and help them develop the thinking and reasoning to see where the errors may have come from or what they could be credited to. I also LOVE the connection of the slope of our graph to density when mass is plotted vs. volume in the second part of the lab. It is great for students to see that the slope of a line has excellent connections.
For the density lab our unknown sample had an average density of 8.8 g/mL. Our measure of standard deviation was .36. When calculating our 90% Confidence Interval, our data would fall between 8.2 – 9.4 g/mL. In our 95% Confidence Interval, the data would fall between 7.9 – 9.7 g/mL. We thought this was pretty good because from our list of different metals only two metal densities fell in this range. From there we could use color to rule out one of the choices. We determined our data could have 2 significant digits. It was restricted by the precision of our measurement of density. The cylinder was the limiting factor being that it could only measure to the hundredth.
For our liquid sample we found the density to be 0.99999 g/ml using the best fit line and looking at its slope.
LIGHT, BRIGHTNESS, AND DISTANCE LAB
I thought is lab was very interesting. It was fun using this equipment to form different types of mathematical graphs. Our pre-lab discussion was very interesting. It was fascinating by applying the natural log laws we could turn our exponential graph into a linear graph and in turn find the value of the power in the exponential function by the slope of the linear function. WOW taking such heavy mathematical laws and “showing” them through a scientific experiment.
Upon coming into the lab I had a feeling that the ambient lighting would have a great affect on the results of our lab. Also upon doing the experiment a first time, we noticed that the light actually sat in the middle of the box instead of the front (where we had been measuring from).
Our first experiment we found the value of n (our power) to be -1.509. We knew theoretically it should have been -2, so we began to question what would have made that difference in our data (discussed in the paragraph above). Then, just for fun we decided to conduct the experiment again. This time we measured the distance from our light source from the middle of our box and we also laid a sheet of paper above the equipment to try to block out some of the light of the room. For our second trial our results were much better. We found the value of n to -1.855.
Because we made the changes together in one trial, I had to wonder which had the most affect on our data or if they both had a large affect. If I were to do the experiment again I would like to test the data again one time adjusting the distance while measuring the light and a second time testing the affect from the ambient light source.
Again, I just love the mathematical connection!