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Elementary-Level Pi Day Ideas?

March 10, 2008
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Many bloggers are asking for or writing about Pi Day ideas. And I’ve been reading with a rather casual interest, since I am not in charge of such things. Until I realized that I am. I am going to be teaching the upper-elementary math group on Friday, Pi Day! And my pi-obsessed youngest son is in the group, so it’d be perilous not to commemorate it. This is about a 3rd – 5th grade level group, so they don’t really know much about pi. Any good ideas?

I thought about having them measure the circumference and diameter of some round things, and then do the division (they are just now working on long division) and talk about why the answers we get are close to pi, but not exact, and not all exactly the same.

I’m not sure about using technology to bring in some of the YouTube videos of Pi songs, but I could bring in some poetry. Or maybe we should make Pi Necklaces.

Any other thoughts?

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21 Comments leave one →
  1. Joshua Zucker permalink
    March 10, 2008 5:12 pm

    I show them some joke pictures, like “pumpkin pi”.

    I also put a digit on each of a bunch of signs and have a parade around the circle (my school is built around a circular lawn rather than a quad, so this is especially easy for me!).

    Then we pace around the circle, and pace across the diameter, and discover that “pi” is about 3.28 … when we take the average of everyone’s values … so maybe we walk differently around than across? Or maybe the circle isn’t as round as it looks? I leave it to them to figure out ways of trying to answer that question. (And with older kids, talk about constant-diameter non-circular shapes).

    Eating pie is always good of course.

    http://www.exploratorium.edu/pi/ is a great source of fun pi-day things as well. I took the trip up there one year when it was on a weekend and that was loads of fun.

    And to the tune of 867-5309, which some of us may remember from the 80s:
    http://facstaff.bloomu.edu/kferland/Pi_Songs/PiSong.mp3

    But Poe, E., Near a Raven, is surely the best (I see you have the link to it in your poem links)

  2. March 10, 2008 5:48 pm

    I just completed the first of our Pi Day celebrations. In my most recent blog posting, I uploaded several documents that might help you out. I definitely think your students would love to sing the silly Pi songs.

    They would also be completely capable of using string to measure diameters and circumferences of different sizes of cylinders. In fact, our 6th graders loved bringing in the containers. The only thing we had to make sure was that we used duct tape whereever the edge was too sharp.

    You could also use a chalk board protractor and trace 3 concentric circles with different diameters. The you put masking tape across the diameter…repeat 3+ times. Once you have shown them that those pieces are a diameter’s length long, you put them around the circumference. You’ll always go a full three times with a little more leftover. I think it’s a huge demo that gives very concrete experience with understanding the ratio…and for my 6th graders the emphasis was getting the concept of pi as a RATIO and that it was a bit more than 3x.

    I think all of these give meaning to 3.14159 which they seem to easily memorize but have no understanding of.

    Hope this helps and keep in touch. Exchanging ideas is the best between likeminded teachers.

  3. March 10, 2008 9:52 pm

    Thanks for the ideas, Joshua and Marsha.

    And don’t forget these Pi Jokes :-D

  4. Efrique permalink
    March 10, 2008 10:05 pm

    Here’s something that you might find interesting – getting them to demonstrate (in a way that at least suggests a formal proof) that pi must lie between 3 and 4, and then discuss how it relates to Archimedes’ approach of inscribed and circumscribed polygons to bound pi by using the ratio of their perimeters to the circle’s radius.

    Step 1: Draw a square which has been divided into 4 equal squares. If the side length is 1, compute the perimeter of the square (4).

    Inscribe a circle in the square.

    We see immediately that the circle has the same diameter as the height of the square (it’s already marked in!)

    The perimeter of the square (4) is longer than the perimeter of the circle.

    (If that’s not instantly obvious, it may help to imagine two people, one walking around the circle, and the other walking around the square, in order to see that the circle is smaller.)

    Step 2: Now draw a regular hexagon. Divide it into 6 equilateral triangles. Call the distance from one corner of the hexagon to the opposite corner 1, so a triangle has side 1/2. Note that the perimeter of the hexagon is therefore 6 x 1/2 = 3.

    /Circumscribe/ a circle. Note that the circle has diameter 1, and its perimeter is longer than the hexagon (you may like to point to the six lens-shaped pieces of the circular disc external to the hexagon and note that the curved part is longer than the straight side).

    Step 3 (consolidation). Draw a square with an inscribed circle and inside that inscribe a hexagon, oriented with top and bottom sides of the square and hexagon horizontal and parallel, and a horizontal “diameter” of 1 common to all three figures.

    As we have seen, this drawing shows us that 3<pi<4.

    They presumably don’t have enough geometry to do further calculations themselves, but a brief discussion of the basic idea of using other figures may still be interesting, in the context of Archimedes’ approach to approximation of pi.

    For example, inscribed and circumscribed squares gives
    2.828…< pi < 4 (they have computed the 4 for themselves), while hexagons gives 3 < pi < 3.464… (ditto for the 3).

    By using an approach to finding those bounding values after doubling the number of sides of both polygons, Archimedes built up from hexagons to the equivalent of 96-sided polygons, getting fairly good bounds on pi.

    (There’s a little on this at the wikipedia page on pi).

    It at least gives some of the flavor of a more rigorous approach to approximations for pu.

  5. Efrique permalink
    March 10, 2008 10:09 pm

    http://www.math.utah.edu/~alfeld/Archimedes/Archimedes.html

    has a nifty applet that would be useful to play with after that, if you have computer access in the room.

  6. March 10, 2008 10:21 pm

    Thanks Effrique, that is really nice!

    These elementary kids don’t know what pi is at all, other than that it has a decimal expression that never ends. They don’t know that pi is equal to the circumference divided by the diameter of a circle. So they wouldn’t appreciate that proving something about the circumference of a circle with diameter 1 said anything about pi, so we’d have to start with establishing that first!

    So, I might send this one to the middle school teacher instead. I think she’d enjoy doing it with that group, and they’d be more likely to appreciate it.

  7. March 11, 2008 9:38 am

    I am thinking of having my elementary students compare the circumference of cylinders to their heights (assorted soup/veggie cans + string), and then introducing pi. Maybe we will graph the relationships: circum to height should be random, but circum to diameter would be relatively straight, depending on their measurement skills. If that doesn’t fill out the hour, we may try a circle-drawing contest or something.

    For the older group, I haven’t decided yet. We may try the Egyptian value for pi, a bit of Archimedes, or maybe throw in Eratosthenes and the circumference of the Earth (which could lead to the “belt around the earth” puzzle). Also, MathCounts did a Pi Day set for their problems of the week a few years back. Way too many options for an hour’s class!

    Of course, the kids would love to do the frozen hot-dog toss, but I’m not sure the church that hosts our co-op would appreciate that one, especially in a carpeted classroom.

  8. March 11, 2008 9:49 am

    All good ideas, Denise.

    Indeed, MathCounts has another Pi Day set up this week, so those are a possibility if you want to do some practice with circle geometry, but I think your other ideas are “cooler” for a special day.

    I pulled out Sir Cumference and the Dragon of Pi, and it’s a cute introduction to the idea of dividing the circumference by the diameter to get pi, so I think we’ll read that.

    I’ll probably first ask them what they know about pi, and list it on the board, then read the book, then I think move to a measurement activity like the soup cans or something similar. Either that or the pi necklace/bracelet idea, but I think that reinforcing the meaning of pi is more valuable at this stage than reinforcing the randomness of its digits.

    Thanks to everyone for the ideas so far, and keep them coming! And come on back and report how things worked after you do them, so we’ll have a list of tried-and-true ideas for next year!

  9. March 13, 2008 12:05 pm

    “I think that reinforcing the meaning of pi is more valuable at this stage than reinforcing the randomness of its digits.”

    Definitely! Too many of the online lessons I’ve seen focus on the digits. Pi chains, pi quilts, memory contests… Until a student understands how pi is defined and how to use it (ratios and proportions), and until he has some understanding of rational vs. irrational numbers (long division!), I don’t see any point in spending time on that sort of thing.

    Well, perhaps there is a little bit of cultural literacy value.

    Now I’m off to the library to look for Sir Cumference…

  10. March 13, 2008 12:25 pm

    The main thing I don’t like about Sir Cumference and the Dragon of Pi is that it suggests that 3 1/7 is the exact value of pi, and doesn’t tell you that it’s only an approximation until the last page that gives some details after the story ends. (The plot is that Sir Cumference’s son, Radius, must discover the value of pi and give that much antidote to his father to save him.)

  11. March 14, 2008 11:52 pm

    So here’s what we did:

    1) We talked about what the kids already knew about pi. It was more than I expected. They all knew that it was related to circles, and at least a couple knew that it represented a relationship between the circle’s circumference and diameter. We reviewed the vocabulary “circumference” “diameter” “radius” and “perimeter”. We looked at the “fact triangle” related to C = pi x d.

    2) I read the story Sir Cumference and the Dragon of Pi to them. They loved the bad puns. ;-) When Radius was trying different fractional pieces for the part higher than 3, we figured out the decimal equivalents to see how close they were getting to the 3.14 figure the kids were familiar with

    3) I had them go in groups of 2-3 to find something round in the building and measure its circumference and diameter. We made a chart of all the items on the board and computed an approximation of pi for each of them. We talked about whey their answers were not exactly pi, and they were very clear on the ideas of measurement error, and they also suggested that the items may not have been precisely round. The only thing I wish I had pointed out was that the accuracy of the estimate of pi was best for the largest circle, and worst for the smallest one. It would have been interesting to see if they would have appreciated why a smaller item might magnify the impact of the measurement error.

    I had about 5 minutes left (of a 45-minute class) left at that point, so I went around and let them all recite as much of pi as they knew, which was mostly about 5 digits worth. ;-) We also admired the pi banner that my youngest son had made as one of his independent activities earlier in the school year — he had copied the first 1000 digits of pi onto a cash register tape, drawing each number in a different color than the one before it, and decorating them in various ways, making it into a geeky work of art. ;-)

    Oh, and my son and I wore our Rainbow Pi T-Shirts. :-D

  12. John Phillips permalink
    March 14, 2009 5:25 pm

    we do this at my school we have to do a project were we dress up as mathematiceans and are statues and we have a can for money and when someone puts in money you come to life and tell about your person its pretty cool and the money goes to the missions. its great and alot of fun Happy Pi day!!!!!!!!!!!

    if you have any quetions leave a comment

  13. March 14, 2009 5:28 pm

    Sounds like a great project, John!

  14. September 16, 2010 6:24 am

    My math teacher use to have Pi written all across the room. I think that a fun activity for Pi day would be creating the Pi banner that surrounds the room. Another idea would be to see who can remember the most digits.

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