Ask /r/math: Introducing Pi to 2nd graders.

highwind · 1 year

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.

chicomathmom · 1 year

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.

hbweb500 · 1 year

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

Adjal · 1 year

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 · 1 year

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!

benitohoover · 1 year

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 · 1 year

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

whatgoodisaroad · 1 year

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 year

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

anonemouse2010 · 1 year

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.

Ph4g3 · 1 year

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.

caks · 1 year

3.1415... :)

ac3raven · 1 year

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.

highwind · 1 year

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kcirtsew · 1 year

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 year

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.

efrique · 1 year

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.

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