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I want to teach "measurement" to grade schoolers

  1. Apr 12, 2015 #1
    I have a family member in a private grade school and I am organizing a teaching plan for those grades. I was struck by how measurements are integral to the learning and understanding of so many facets of physical science and math.

    I got good feedback from an initial try by teaching distance measurements. I did not start with standards but used a relative measurement approach using a "story stick" to take measurements and compare them to another distance and establish a relationship. I asked them to measure a bookcase and then identify all books that would (or not) fit. As distances increase, materials change and one must pass through standards, conversion factors, geometry, trigonometry, light refraction and relativity physics.

    My plan is to have students build all of their own measurement instruments to keep. I have found simple methods for almost all possible measurements using easily acquired materials and occasional battery operated parts.

    I hope to get ideas from the forum members that will fill out parts of the program.

  2. jcsd
  3. Apr 12, 2015 #2


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    Welcome to the PF, Bob.

    Any educator who can bring Relativity into sizing a bookcase is okay in my book! :smile:

    One thought would be to introduce the relationship between circumference and linear distance by building a wheel with a comfortable extension handle and a clicker on one of the spokes. And maybe add a count of the spokes with respect to the total number of spokes to let the student measure longer distances to an accuracy of one spoke circumference separation....
  4. Apr 12, 2015 #3


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    I seem to recall in the dim, dark past of my schooling we were supposed to supply our own measuring instruments, like rulers, protractors, and such for school. :smile:

    My only concern is if you spend a lot of time trying to construct your own measuring instruments, there will be less time available to actually use and understand them, which IMO, is the important thing. After all, we don't make our own paper or craft our own pencils for school; it's much more important to use these tools to capture and understand ideas. :wink:
  5. Apr 12, 2015 #4
    I understand and agree. I started with a strip of poster board that each student had to cut out and use to mark measurements. The measuring took more time to perform and report. Done once, the students can then translate the non-standard lengths to either inch/feet or metric then convert to the opposite. I asked them to do that because the exercise could have been to tell a foreign manufacturer the desired measurements of a bookcase in Metric values instead of the U.S. customary standard.

    Light measurement takes only two light sources, a strip of poster board to set the distance from the source and a stack of copier paper sheets to measure which source is stronger and how many sheets the light can penetrate. One can then calculate the calibrated value of each sheet by using the number of thicknesses and the claimed lumen value of each source. Done enough times with different sources, one can plot the consistency of radiation claims on the packaging materials.
  6. Apr 12, 2015 #5
    Yes it does sound fantastic. The reference was a class I taught for distance measurement. Taken to the most distant, a student would have to next measure the distance across a street or body of water without crossing using stakes, a rope and a right triangle. Next level gets into geometry and trig. to use stakes, rope a protractor and the formulas to calculate the longest side opposite the hypotenuse. One cannot send all students to an observatory to get the parallax data from astronomical observations (maybe we can!) but we can teach it. Then referring to relativity physics, we can teach how Hubble came to the conclusion that we are experiencing universal expansion. I know that these lessons must span several grades, but isn't that the mission a teacher assumes when teaching?

    I have ideas to connect several class lessons to fun things like buying flags or maybe bandannas from a vendor that charges for materials by the square yard or foot. I have plans to ask students to specify carton dimensions for packaging jars for their products. It requires measuring diameter and height then adding a few steps to specify material thickness and external dimensions of the carton then figure out how much the materials cost. Now the challenge is to get them to fill the jars with the right amount of peanut butter, jelly or whatever by measuring the dimensions and calculating the volume of product and cost per whatever u/m the vendor likes.

    I know the lessons must be planned for several grade levels and revisit the same topic each year. I assume that to be the case to keep focus on the same types of problems but taking a more detailed approach each year.
  7. Apr 12, 2015 #6
    OK I'm recording this. How many ways can one calculate PI? Good idea with the spokes. Some unborn student may get the benefit of that some day.
  8. Apr 13, 2015 #7
    Go to the Pi Day sites from 3/14/15 celebrations and there are tons of ideas.
  9. Apr 13, 2015 #8

    Andy Resnick

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    What grade level?
  10. Apr 13, 2015 #9
    Starting in 3rd. More advanced work could be as late as 6th or 7th. The 2nd graders picked up on the practical measurements easily. That included using the story stick, fingers, hands and outstretched arms for various units, measuring items like books, tables, doorways, recording them and making comparisons. Some of them took the idea home and measured things there.
  11. Apr 13, 2015 #10
    Do the kids a big favor and get to the metrics ASAP. Have them use meter sticks and metric tape so they naturally think in meters, liters, and grams. All the units are interchangeable and multiples are x 0, x 100, and x 1000. Paper clips and small metal nuts or nails will approximate the units of mass, and water droppers are easily calibrated for ml and cm3. Forget conversions to the English system, they will not need to use it in science. Use liter pop and bottled water containers as a cheap source for measurement.
  12. Apr 13, 2015 #11
    Thanks for the reminder. I had notices from my FB friends that day.
  13. Apr 13, 2015 #12
    Good idea. I am familiar with metric and its benefits. I retired from Siemens. When I work on carpentry or structural maintenance, it drives me crazy to not easily add the widths and thicknesses of panels and trim or to decide on proportions by dividing fractions in my head. I got spoiled at work.
  14. Apr 13, 2015 #13
    By the way (recent translation of BTW). I had a good teaching experience during Dinosaur Week at the school. My wife and I were assisting the Kindergarten teacher. My station was the dig site. The students were to examine the site of buried bones (a chocolate chip cookie) and record their estimates of the number of bones they suspected were buried. The excavating was done with toothpicks until they had extracted all of the bones, cleaned them and counted them. They completed their dig by recording the count and stating a conclusion that their estimate was either the same, higher or lower than the actual number discovered. There were about twelve students. Some of them stumbled over the wording of the conclusion (two even read it!) but they all understood it and stated theirs accurately. I don't know what is a good starting age level for teaching science, but it is fun thinking of ways to make it interesting.
  15. Apr 13, 2015 #14

    Andy Resnick

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    How about activities based on measuring angle, mass or time? You can have the students build 'instruments' that measure angle pretty easily, and for measuring time, a simple pendulum clock could work. Measuring mass may be too complicated, but weight can be measured with a spring (and ruler).
  16. Apr 13, 2015 #15
    As far as I am concerned, the sooner you get kids doing science and physics, the better.

    That seems doable. I am not sure that I would have had the attention span for something like that when I was in grade school, though. But I like to think that most grade school children can listen to their teacher for more than three seconds.
  17. Apr 15, 2015 #16
    My experience with the kindergarten exercise leads me to agree that any age could be appropriate as long as the ideas are framed in a way that teaches the material and also keeps their attention. Fun projects work the best. Our third/fourth grade class recently worked on "Sound". Instruments could be anything simple as long as it made a type of sound, a certain way and was described by the student. The fun in my family was my child's shoe box stringed instrument and washtub bass. The shoe box instrument was like a kalimba or harp. The engineering took much longer than the science behind it but after three days and two experiments, the learning was complete.
  18. Apr 15, 2015 #17
    A coathanger balance scale is the quickest way I know of to weigh small items.
  19. Apr 19, 2015 #18


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    A small-scale version for measuring pi is to use a piece of string pinned at one point to measure a radius,
    then another piece of string laid out to measure the circumference. On a plane, the ratio is a constant, independent of the radius.
    Certainly, the accuracy is better for a large circle using the spoked-wheel odometer.
    However, circles on the surface of a basketball, it's easy to see that this ratio is not 2*pi and is not constant.
    This ties together the definition of pi with a circle on a plane... and a hint of the sphere as a non-euclidean geometry.

    I think students need a better appreciation of area.
    Many college students incorrectly convert ##1 m^2## to ##100 cm^2## rather than ##1 (10^2 cm)^2=10^4 cm^2##,
    probably relying too much on (misunderstood) symbolic notation ("cm^2" isn't "c(m^2)" but "(cm)^2")
    and not understanding what "1 square-meter" and "1 square-centimeter" look like.
    So, it may be good to get younger students to appreciate area by having them
    measure area by counting the number of "1 square-centimeter" squares,
    plus some estimates for the irregular sections, needed to fill a region.
    In "nice cases", this can then be "simplfied" to base-times-height.
    Last edited: Apr 19, 2015
  20. Apr 19, 2015 #19
    Try Googling:

    "Making a Microbalance/Nuffield Foundation"

    Using easily available bits and pieces youngsters can make a balance that can weigh a grain of sand.
  21. Apr 19, 2015 #20
    Some of the stuff at this site might be interesting to you.
    http://scitoys.com/ [Broken]
    Last edited by a moderator: May 7, 2017
  22. Apr 19, 2015 #21


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  23. Jun 28, 2015 #22
    Dadface @ 19: thanks for the microbalance pointer!

    Some printable paper rulers http://www.vendian.org/mncharity/dir3/paper_rulers/ (disclaimer: own work)
    Being paper
    , they can be taped to things, drawn on, used disposably, etc.

    I'm currently-ish working on some "use body as ruler" content. The core idea is: arms-sized (like a door), hand-sized (like a cup), fingernail-sized (pencil width), "tiny"-sized (pencil point?, coin width?, better name than "tiny"?). 1000, 100, 10, 1 mm. For calibration: use a meter-stick or doorway to learn how wide to hold your arms. With "standard" non-accessible doors, you hit the jams, which seems nice for periodic refreshes of "this is a meter". Fold paper in half, for a ~100 mm reference, and depending on your hand size, find some direction across it [1] that's close. Similarly, use pencil width ~9mm to choose a fingernail. And for tiny... I don't yet have a good story. Nail lunula, measured by ruler or coin thickness? Hold fingers up to eye and pinch? One can then do a back-and-forth game ("this big!"->"that's like 200 millimeters"; "500 millimeters"->"um, that's like this big"; "1. 10. 1000. 100. book. chair.", etc). If anyone is interested in collaborating...
    [1] eg, https://en.wikipedia.org/wiki/File:Hand_Units_of_Measurement.PNG from https://en.wikipedia.org/wiki/Palm_(unit)
  24. Jun 28, 2015 #23
    It will be very helpful for us if you start to teach about measurement. Its very indeed for us to know. Thank you very much for taking a nice step. Carry on.
  25. Jul 1, 2015 #24
    Measurement without error estimates is meaningless. You might find it helpful to introduce the kids to some rudimentary form of error estimate and error propagation. In this respect, you can find some inspiring examples in the first chapters of Taylor's wonderful book "An Introduction to Error Analysis". Most of the book, albeit introductory, might be beyond the scope of your course, but showing how the error in length results in an error in a computed area, or how to measure the thickness of a sheet of paper with a meter stick (dividing the thickness of a 500 sheet stack by 500 will result in an error reduced by the same factor), might be well within your boundaries.

    Actually, realizing you can make measurement with an error of a few microns by using a meter stick can be quite a discovery for a kid.

    Oh dear.
    I necroed a thread.
  26. Jul 12, 2015 #25
    I have been concerned about how to keep things simple. The objective is to teach the idea of measuring things. Your spring/ruler suggestion is perfectly valid. It is simple and can be used to teach the idea of measuring.
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