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[–][deleted] 21 points22 points ago* 

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That sounds like everything a second-grader should know about pi. I think you should start off with a circle of 1 unit diameter first. You should definitely draw the circle on the chalkboard using a piece of string of 1 unit length, folded in half.

[edit]

Perhaps you should start by drawing a square with a 1 unit length side, and asking what's the length of all the sides together. All the kids should be able to figure out it's 4 on their own. Then draw an equilateral triangle. Then drop the bomb.

[–]highwind[S] 5 points6 points ago

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Thanks for the tip! I'll try to add that into the presentation.

[–]sidek 1 point2 points ago

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Sadly ,the thing he described doing is seventh grade level in the Albertan(and other provinces) curriculum :(

[–]bomber991 -5 points-4 points ago

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Jeeze, 3rd year engineering major here and I didn't realize Pi was meant as a relationship between circumference and diameter.

[–]kops 8 points9 points ago

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You're kidding, right? What context did you know it in?

[–]bomber991 0 points1 point ago

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Well I remember back in trig they showed us how they came up with Pi. Then after that, it's just remember "2pi = radians around a circle, standard period for sine, cosine, and tangent."

I was aware that there was a relationship between the circumference and the diameter of a circle, I had just forgotten that it was pi. I guess the relationship was something like 22/7, and that's how they came up with the 3.14~~~ for pi.

Also, this is the first I've ever heard of 'Pi day'.

[–]kton 3 points4 points ago

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what's a radian to you? :)

[–]chellomere 1 point2 points ago

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uh, 22/7 is just an approximation, slightly better than 3.14, but still not very good.

[–][deleted] 4 points5 points ago

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where do you go to school?

[–]chicomathmom 18 points19 points ago

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I do this measurement activity with my college students, who are training to become high school teachers :)

Beware that your measurements will be all over the place--we typically get between 2.9 and about 3.5 so it may not be obvious that C/D is the "same" for all circles. You'll get better results if the things you measure have thickness--like the lids of peanut butter jars, rather than around CDs, because flat things are hard to measure. Also, be sure they measure the diameter to the outside of the circle, since that is where they will be measuring the circumference.

There are other things you can discuss with this activity. Have some kids measure with inches, and others with centimeters. Pi is the same, regardless of the units you use.

You will typically get better results with big circles (I use a hula hoop, but be sure you have a long tape for this, and probably use several people to hold the tape in place, because it will want to slip) (A bike wheel is goo, too) than with little circles (like the lids of 2 liter bottles or film canisters) It is worth discussing why-- that a "little" measurement error is relatively larger when measuring a small circle.

[–]highwind[S] 4 points5 points ago

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Thanks for the tip of using big things. I'll keep that in mind.

[–]hbweb500 17 points18 points ago

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You should definitely add in how the root of pi is the Gaussian integral. Blow their minds.

[–]Scalawag 3 points4 points ago

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This is funny, but I think it raises a good point concerning the lack of mind-blow in college students. By the time we learn what a Gaussian integral is, pi is just "some number". No one considers "so... the area under the curve e-x2 multiplied by itself is the ratio of the circumference of a circle to its diameter?". And this is without considering what, exactly, e is. It's things like this that make math fascinating to me. Where's the connection? How are these things possibly related?

[–][deleted] 0 points1 point ago

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It's almost kind of sad how complex analysis turns that "mystical" connection into "well yeah, duh". All the sudden the "weird" connections between e and pi are obvious and somehow less exciting ;)

[–]Scalawag 0 points1 point ago

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WHAT!? And here I've been on the brim of complex analysis while still going "gee, what's with all these relationships between pi and e". I would go get a complex analysis book but I find it hard to learn math books on my own. Perhaps I'll go check out what wikipedia has to say on the matter.

[–]Adjal 7 points8 points ago* 

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One additional thing I would have them try after making their estimates is to tell them the diameter of a circular object, and have them cut a length of string that should fit around it exactly. Maybe one each or in groups or however fits the setting. Then see who's gets closest. Then give examples of how this has been needed in the past and present and... segue straight into Pi.

[–]highwind[S] 2 points3 points ago

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That's actually really good idea. Thanks!

[–]highwind[S] 8 points9 points ago

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It was a success! Kids had a blast measuring things and guessing the value of Pi. They learned the term Ratio and Constant, and most importantly the meaning of Pi in terms of circle.

Thanks everyone for the input!

[–]caks 1 point2 points ago

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Glad to hear! I thought the approach of measuring things was really neat, kids love that. Congratulations!

On another note, you should probably make an edit in the post, instead of commenting.

[–]cowinabadplace 0 points1 point ago

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Congratulations! Good stuff. Something that demonstrates that pi shows up in unexpected places would be a Buffon's-needle-like experiment. It would be a little too hard to teach little kids the reason behind it, but if you've got some time to kill at the end of class, it might be something worth simplying doing without proof.

[–]highwind[S] 0 points1 point ago

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Forgot about editing. Thanks.

[–]benitohoover 6 points7 points ago

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If you can have them understand this gif then I think you've done your job.

I think your pot and pan idea should get it done. Maybe also build a unit circle (in whatever unit it is kids in your schools work in) and roll it out so they don't have to deal with ratios.

[–]spacecataz 3 points4 points ago

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use oranges cut into cylindrical slices they can measure the diameter of a slice, then cut the slice in half and measure the sides, or calculate the area as if it was a rectangle

then they can eat the oranges

[–]highwind[S] 0 points1 point ago

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Hahahaha, that's awesome! I don't think they learned the concept of area yet.

[–]spacecataz 1 point2 points ago

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even without area, cutting the orange slice again allows them to measure straight lines instead of curves

[–]vanostran 4 points5 points ago

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Or even as last resort, just feed them some oranges.

[–]rm999 0 points1 point ago

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"How many M&Ms can you fit on this plate?" could work, but I agree that squaring the radius and then multiplying by PI is probably too much for them.

[–]whatgoodisaroad 1 point2 points ago

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That's a totally cool idea! I wish I had this experience when I was in elementary school. Ganbatte!

I don't think I ever really fully grasped the concept of Pi until I was in precalculus.

[–]thetallestpaul 1 point2 points ago

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I just wanna say I did this in elementary school and I remember the class getting values like to 3.4 so be ready for a little confusion. Perhaps you can do this more effectively with paper strips and tape? We used yarn and markers

[–]highwind[S] 1 point2 points ago

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The conclusion will that it appears to be little more than 3 and less than 4 and remind kids that experiments are for science, not math.

[–]anonemouse2010 1 point2 points ago* 

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That's what I'd do with a grade 7/8 class. But... typical 2nd graders don't relate fractions with division but as separate objects... that's if they've been introduced to them at all, which typically they havn't.

Oh... in the future there is a book called... sir cumference and the dragon of pi, or sir cumference and the first round table

You could read it to them.

[–]highwind[S] 2 points3 points ago

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Thanks for the input. The 2nd graders had a great time understanding the concept of Pi. It wasn't hard for them at all.

2 important thing that they learned:

  • Concept of ratio
  • How the ratio, pi, remains constant

2nd graders, I believe, are more than capable to learn those concepts.

[–]anonemouse2010 0 points1 point ago

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I think you need to go back and see how well they actually understood it.

Did you do any assessment? If not how can you give any objective method of determining what they learned?

I'm sorry but I'm a teacher, and I guarantee you that a good portion is lost right after the lesson.

[–]highwind[S] 1 point2 points ago

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You are right. I can't give you a objective metric that can prove to you that they understood the material. All I have is their verbal communication at the end of the session. Which gave me the confidence to say that it was a success. I can't say every single one of the students got every single concept that I taught, but I believe I can safely say that lot of, if not most, understood the fundamental concepts that I want to expose them to. Now, without reinforcement I'm sure not many will retain those information. But this session was to expose them to interesting topics in Mathematics not to make them memorize what Pi is.

You don't need to be sorry for being a teacher. I'm a teacher too. But since I'm not a elementary teacher maybe you can give me better tips in having these kind of special sessions.

Thanks again for your input.

[–]anonemouse2010 0 points1 point ago

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I would imagine you did well, but little kids need more than auditory feedback to retain the material. They need to do something. Generally kids that age havn't got to the cognative development point where they can work in abstractions, so you need to make it as concrete as possible and in a way that they can make the connection.

But this session was to expose them to interesting topics in Mathematics not to make them memorize what Pi is.

Then if that's your goal no doubt you succeeded.

[–]meanruse 0 points1 point ago

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If that's the case, it's still best to get to them early with an interactive description of pi so that they can begin recognizing fractions as division as soon as possible. Waiting until they are in 8th grade to do this elementary activity because everyone said it was too hard for anyone but 8th graders has got to be one of the reasons 8th graders don't know what fractions are...

[–]Adjal 0 points1 point ago* 

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Obligatory.

Edit: Not that I think it's a bad idea; just struck me as a funny counterpoint.

[–]Ph4g3 4 points5 points ago

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If I were in your place I would begin by having them understand real numbers, as opposed to integers or quotients. By that I mean I would ask them what is between 1 and 2, 1 and 1.5 etc, and ensure that they understand that it goes on infinitesmally. Then I would go on to explain the irrationality of Pi.

It seems to me, however, that "elementary" school children would already grasp the concept of infinite. I know I toyed with the idea when I was their age.

  • Pardon me, I'm a tad drunk.

[–]Scalawag 2 points3 points ago

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I think introducing the idea of an "infinitely long" number is a great idea. It'll get them doing the "hold on... what?" thing that makes us all interested in these things.

[–]acetv 0 points1 point ago

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Upvoted for drunkenness.

[–]whatgoodisaroad 0 points1 point ago

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That reminds me of this article. A truly wonderful blog, that.

However, even though kids might be able to understand infinity, irrational numbers might be asking a little much. Plus, irrationality isn't necessarily integral to the "meaning" of Pi.

[–]caks 2 points3 points ago

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3.1415... :)

[–]christianjb -1 points0 points ago

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3.1416 is closer.

[–]rickiibeta 7 points8 points ago

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false. he said "3.1415...", not "3.1415". his is more accurate and closer.

[–]rickiibeta -5 points-4 points ago

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false. he said "3.1415..." not "3.1416". there is a difference, his is closer.

[–]ac3raven 0 points1 point ago

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that's a great demonstration, it shows an easily understood relationship between properties of a circle, and I think that is what will fascinate kids more than anything. Perhaps mention sine waves and other patterns related to Pi. This way, it extends beyond the mathematical relevance.

[–][deleted] ago

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[deleted]

[–]highwind[S] 0 points1 point ago

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Yeah. I changed my presentation to talk about ratio first.

[–]kcirtsew -1 points0 points ago

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First Kings chapter 7 verse 23 says that pi is equal to exactly 3. This should be much simpler for second graders to understand.

[–]bombadil77 -1 points0 points ago

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To communicate that pi is irrational, start by drawing a triangle inside a circle. Then a square, pentagon, hexagon and so on, but show how no matter how close you get, there is always space left over.

[–]rm999 1 point2 points ago

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Irrational? I learned what fractions were in third grade.

Also, drawing the conclusion from that proof is not really obvious, you first need to show that the area leftover from the polygon is irrational.

[–]anonemouse2010 0 points1 point ago

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That doesn't prove that pi is irrational. I could do the same thing with squares in squares and have each side be rational say... sn = 1-1/2n. Clearly the limit area is rational.

Furthermore you seem to have a complete lack of understanding of what a typical 2nd grader can do or can understand. Most kids this age havn't learned their shapes past a rectangle nevermind formulas concerning area for them. In many cases they even have just a vague understanding of area.

[–]efrique -1 points0 points ago

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You could show an argument that pi is between 3 and 4 by inscribing a hexagon dividied into equilateral triangles and circumscribing a square divided into 4 squares.

However, I am not sure this will be worth the effort, since they'll already be measuring a ratio that's better and may not see why the derivation matters.

Maybe Buffon's needle (using the thin kind of toothpicks), perhaps? Again, perhaps not worthwhile given the effort with young ones.