Author 
Post 


I am looking for a fun and easy way to teach dimensional analysis




I will need to look for the lesson, but I had one that was kind of fun for the kids. It had to do with an island, where there were certain ratios in play, like 4 people per house, 8 trees per house, etc. It related a bunch of unrelated things as equivalences on trading cards. The students draw a beginning unit (like people) and an ending unit (dogs) and then must match them up with other equivalences to find out how many of the ending units they have. It's a little like matching dominoes, and wouldn't be too hard to make with a little downloaded clip art and creativity.




This has been a huge problem with me this year...along with sig figs. I don't get what the aversion to "conversions" is with the kids, but they hate it and don't get it. I had a girl ask me the other day if we were done with conversions...and I was like 'oh honey, this is chemistry, they never go away." Any ideas to make dimensional analysis less painful would be appreciated. I don't really push sig figs, do other chemistry teachers really emphasize the importance of significant figures in science. I had a math teacher in my room for awhile, while I was teaching them and he was flabbergasted. "How can you say zeroes aren't important, we tell kids zeroes always matter in math!"




Thanks
sounds fun , is it possible to get a lesson plan




Thanks
I am looking forward to teaching it.




I found the comments on sig fig enlighted. I thought I was the only one with the problem. I teach Physics and Chemistry so often enough I heard :how many decimals do you want? I tried to explain the kids about sig dig but I have not been succesful. I think it is important to enphasize that we are dealing with measurements of teh natural world versus mathematical abastraction (which are OK) since my students tend to "believe" the Math teacher (although we have some not so good). In relation to dimensional analysis I quit teaching it as a unit in my measurement and address as needed when solving problems or doing a lab activity. This way seems to be more palatable to teh students.




Maybe you could use the measurement of the classroom or a hallway with many classrooms? Then you can tell them they can choose to any thing as a measurement tool like books, chairs or anything they can move. Once they measure a classroom they could figure out how many classrooms in a hallway and convert classrooms to hallways. (Sorry, I just came up with this on the fly)
I have also used this equations (I did not make them up. I got them from a fellow teacher):
8. From the poem Jabberwocky by Lewis Carroll:
There are 20 tumtum trees in the tulgey wood.
In each tulgey wood is one frumious Bandersnatch.
There are 5 slithy toves in 2 borogoves.
There are 2 mome raths per Jabberwock.
There are 2 Jubjub birds in 200 tumtum trees.
There are 200 mome raths in each borogove.
There are 5 Jubjub birds per slithy tove.
If there are 5 frumious Bandersnatches, how many Jabberwocks are there?
How many seconds old are you? (Express with 2 sig figs in scientific notation.)
1. There are 4 red balls for every 9 blue balls. There are 7 blues for every 8 greens and 3 greens for every 1 white
balls. How many white balls are there if you had 49 red balls?
2. You have come down with a bad case of the geebies, but fortunately your grandmother has a sure cure. She gives
you an eyedropper bottle labeled:
Take 1 drop per 15 lb of body weight per dose four times a day until the geebies are gone.
You weigh 128 lb, and the 4oz bottle is halffull. You test the eyedropper and find there are actually 64 drops in
a teaspoon. You already know that it takes 3 teaspoons to equal a tablespoon and 2 tablespoons make up an
ounce. You are going on a threeweek trip and are deeply concerned that you might run out of granny's geebie
tonic. Do you need to see her before leaving to get a refill? Hint: write down "days/bottle" as the units you want
in your answer
3. At the pizza party you and two friends decide to go to Mexico City from El Paso, TX where y'all live. You
volunteer your car if everyone chips in for gas. Someone asks how much the gas will cost per person on a round
trip. Your first step is to call your smarter brother to see if he'll figure it out for you. Naturally he's too busy to
bother, but he does tell you that it is 2015 km to Mexico City, there's 11 cents to the peso, and gas costs 5.8 pesos
per liter in Mexico. You know your car gets 21 miles to the gallon (hah, obviously not a Prius), but you still don't
have a clue as to how much the trip is going to cost (in dollars) each person in gas ($/person). But one of your
friends recalls that there is 39.37 inches in a meter and the other is sure that there is 4.9 ml in a teaspoon, and
5,280 feet to the mile. Then you call your mom (of course). She knows that there are 3 teaspoons in a
tablespoon, 16 tablespoons in a cup, 2 cups in a pint, 2 pints in a quart, and 4 quarts in a gallon. Figure out how
much each person is going to have to “donate” to your Mexicotrip fund.




TraciAnn,
Appreciate the Jabberwocky 'brainteaser' and other exercises you shared! Giving students practical, handson activities which guide them to problem solve initially without a formal label is effective to get them grounded in thinking outside of the box, so to speak. I've had success having students make measurements of the classroom, themselves, and other objects in the class (they choose) using US system and then proceed with conversions. This was notably effective with students with special needs students and students that had lower academic i386performance levels. These activities engaged them and it easy to transition into more rigorous applications.
I've never used the term dimensional analysis prior to taking students through this content as some noted previously. The term seems to generate the 'glazed' eyes and responses similar to a 'deer in the headlights'. Some students seem to become psychologically paralyzed before they even begin. Students also need more introductory foundation prior to the Sig. Figures lesson. They have difficulty understanding the importance of this concept. I try to introduce accuracy and precision in measurement prior to Sig. Figs.




Wow! Such great comments!
A trick I learned is to tell my kids that I'm going to show them how to make math easy. They're always looking for a way to get a leg up in math class. So, I show them my "magic grid" and we go through their math homework a bit (usually, I've timed it for when the math teacher on my team is doing ratios or proportions). By that point, they usually want to learn more about how the 'magic grid' works. Then, I give them some problems about feet and meters, etc and we go from there.
I think I'm going to try some of your resources this year, though.




TraciAnn
I really love your ideas. Thank you. I see in this the opportunity to teach students to "think" mathematically while converting your sentences to ratios. I often get students in my class who, although having past algebra, do not think mathematically.




Chris
This story illustrating the importance of sig figs may help you
The science teachers at a Baltimore County middle school wished to acquire a steel cube, one cubic centimeter in size to use as a visual aid to teach the metric system. The machine shop they contacted sent them a work order with instructions to draw the cube and specify its dimensions. On the work order, the science supervisor drew a cube and specified each side to be 1.000 cm. When the machine shop received this job request, they contacted the supervisor to double check that each side was to be one centimeter to four significant figures. The science supervisor, not thinking about the "logistics", verified four significant figures. When the finished cube arrived approximately one month later, it appeared to be a work of art. The sides were mirror smooth and the edges razor sharp. When they looked at the "bottom line", they were shocked to see the cost of the cube to be $500! Thinking an error was made in billing, they contacted the machine shop to ask if the bill was really $5.00, and not $500. At this time, the machine shop verified that the cube was to be made to four significant figure specifications. It was explained to the school, that in order to make a cube of such a high degree of certainty, in addition to using an expensive alloy with a low coefficient of expansion, many manhours were needed to make the cube. The cube had to be ground down, and measured with calipers to within a certain tolerance. This process was repeated until three sides of the cube were successfully completed. So, "parts and labor" to prepare the cube cost $500. The science budget for the school was wiped out for the entire year. This school now has a steel cube worth its weight in gold, because it is a very certain cubic centimeter in size.




Holy smokes, Pamela! Is that story true?! I can't even imagine their shock! Stories like that would really get students' attention, though. After reading your anecdote, I started to wonder if there are other reallife stories about the dramatic impact of sig figs and unit conversions. I seam to remember there was some snafu or other that occurred over in NASA with a Mars lander or probe? Either way, these stories can give real evidence for the importance of what students are learning in class and, even more importantly, numbers have meaning.




There was a discussion in the science dep meetings about teaching sig figs with most teachers thinking that it was irrelevant. The cube story is great! The problem with the Mars mission in 1999 was that one of the engineers read the metric units as English units, inches instead of centimeters and the probe end inside a crater.
When I was teaching in the bilingual program one story the students enjoyed hearing was temp conversion, baking in Farenheit ovens thinking in Celsius




Maria
In learning that you have bilingual student I thought that you might find the ACS Spanish language resources useful
http://208.77.250.174/portal/acs/corg/content?_nfpb=true&_pageLabel=PP_TRANSITIONMAIN&node_id=1974&use_sec=false&sec_url_var=region1&__uuid=228f61b18e0545249298fa4f1cafa61b




Thank you, all resources are always useful.




This is my first year teaching physical science. I learned from my mentor to set up dimensional analysis problems using "parenthesis" (xunits/yunits)(yunits/zunits)(zunits/finalunits), then cross cancelling the units. The students with neat handwriting got it with this method. Then my student teacher showed me her method using a lined 2row grid rather than parenthesis (sorry I don't know how to use the keyboard to get that), and then putting the units in the same order. This made such a difference for the students with large or messy handwriting.




Jennifer,
I have struggled with the choice of presenting dimensional analysis as a series of multiplicative ratios explicitly using the "parentheses" representation of the "railroad track representation such that the multiplication by fractions equal to one is obfuscated.
In the end I have opted for using a representation that makes the multiplication my fractions equal to one explicit. I find that If I do not do this my students learn the process but not the concept behind the process. Later when we use dimensional analysis in stoichiometry is is much easier for those students who understood the concept rather than simply understood the process of the units on the top need to then appear on the bottom for the units to "cancel".
One of the "revelations" I had that students were not understanding the concept was when they asked questions including (1) how can you multiply by different numbers on the top and bottom and say they are a ratio equal to one? (2)So you mean all I have to do is plug in the right units and then multiply everything on the top and divide by everything on the bottom?
Physical science concepts build on each other and it is easier to make sure students understand concepts at each stage as we build the framework. It is much harder when we learn later that something has gone wrong and need to conduct an education forensics inquiry into the source of the misunderstanding.




All
Maybe some of you would enjoy this song on the factor label method aka dimensional analysis
FactorLabel It, Baby!  Dave Haas
http://www.youtube.com/watch?v=dxJUDUULaeA




I love your questions  great introduction to conversions. I've used ones about so many so many cans in a case, cases on a pallot, etc., but yours are so much more fun!




Pam, I am curious to know a bit more about your method. What exactly do you do to make it explicitly clear which fractions are equal to one?




I taught my kids how to calculate their age in hours. Then we used these playing cards where the kids had to calculate the number of turtles on this island. They had to cancel the pictures out. It helped. Constantly reinforcing and lots of practice helps too.




Eric,
Check this out http://www.wwnorton.com/college/chemistry/gilbert2/contents/ch01/studyplan.asp
I think this makes equivalency to one is made obvious in the animated tutorial




In reading my latest copy of Chem 13 news I came across a suggested resource for unit conversions put together by Theodore Wildi a professor at Laval University in Canada
http://www.wilditheo.com/index.php?p=SI_Charts




I am teaching a summer class and it is time for DA. Never being completely satisfied with my lessons I am working on this yet again. I especially like this video clip as it clearly reviews the necessary math
http://educationportal.com/academy/lesson/unitconversionanddimensionalanalysis.html




Thanks Pam,
I loved the dominoes analogy in this video. I think it would really help some of my struggling students.
I have found that many math phobic students do well initially with some type of manipulative. If one can express the dimensional analysis as an images or images then it makes more sense to students. I also think it is important to start with units in which students are familiar before moving to less familiar units.




Significant figures....ugh!
So I thought I would do a play on the "give them numbers and only let certain numbers in the door" concept that I've heard discussed...but I changed it a little bit.
I gave them the rules the other day...and tomorrow to review I'm going to give everyone a number or a decimal point and they have to make the following numbers...
A 2 digit number with 1 sig fig
A 2 digit number with 2 sig figs
A 3 digit number with 1 sig fig
A 3 digit number with 3 sig fig
A 4 digit number with 2 sig figs
A 6 digit number with 4 sig figs
A 10 digit number with 6 sig figs
I figure that this will make them really think about what it means for a number to be significant...especially with the 10 digit number. I will have spare numbers available if they want to swap out numbers. I was just wondering some thoughts on the activity...any suggestions?
Also my kids are really struggling with the adding/subtracting and multiplying/dividing concept with sig figs....how do you guys make that more understandable??




I just came across this approach to teaching DA. I love the connection to math
http://blog.mathed.net/2011/08/modelingdimensionalanalysis.html
and the creation of various number lines on each axis  very clever




Pamela,
I still see the problem there that you have to know the path from miles to meters...which is the struggle that most kids have. If the kids cant figure out...milesfeetinchescmmeters...than that method doesn't help either.
I'm amazed at how poorly my kids know the metric system....when is it going to become a consistent priority that they learn it in the elementary grades?




Chris,
Getting a "feel" for a different measurement system is actually a complex cognitive task. I know that when I moved to the states, temperature complete befuddled me for quite a while. The voice on the TV said 40, it was fall and 40 is HOT! This is not merely as issue of number there are strong memory associations that take you down the wrong path.




That was kind of my point...why aren't we teaching them both systems of measurement from a young age? Eventually we will have to switch to metrics...start teaching it to the elementary kids, hit them with it every year so by the time they are grownups they feel comfortable with both systems.




Chris,
Whether or not the US every goes metric, I wander if NOT learning the metric system disadvantages US students. Learning a system that is based on powers of 10 might make exponents and logs easier later on. I pokes about and actually found a bit of relevant research on this. I thought that you might appreciate it too




While searching for some fun activities to do with my freshman on dimensional analysis, I came across this discussion. I have plenty of reallife example worksheets, but was hoping someone had a more handson activity and would love to hear ideas.
I wanted to comment on the significant figures conversation. I do have my chemistry students learn and use them, and it seems an odd concept to them. I show them the "7minutes of terror video" http://www.youtube.com/watch?v=h2I8AoB1xgU so that they can see how precise you need to be in engineering.
We then do a lab where the students have to use length and width measurements (to the hundredth of a centimeter) of four 10x10 aluminum foil squares to find the area, the mass and density to find volume and then the volume/area to get the thickness. We had 2 groups accidentally use a scale that only measured to the tenth instead of hundredth, and they ended up with a thickness of 0.001 instead of the 0.0017 cm that almost every other group gets. It ended up driving home the point of why precise measurements are needed plus it shows how rounding to too few figures could wipe out important info. Leaving too many wouldn't give the consistency the 0.0017 or occasionally 0.0016 does. I may purposefully give groups instructions that have them measure to different units places next year just to compare results and show why it makes a difference.




Shawn
Thank you for this video. I love it! Do you have a write up of the aluminum foil activity that you would be willing to post
Thanks
Pam




Pam,
with our honors chem students we do an activity similar to this. They find the thickness of normal aluminum foil and then heavy duty aluminum foil and then they have to do a cost/benefit analysis of whether the "heavy duty" foil is worth the extra money. You always get kids arguing both ways, so it is interesting. I don't have that handout on my home computer, but can attach it when I return to school.

