## Cut-and-Paste Pi: Pi Post #3

### January 17, 2014

Here’s a hands-on, cut-n-paste paper project that, hopefully, puts pi in your hands. This post is 19 photographs long, so, in deference to anyone to whom seeing that circumference divided by diameter equals 3.14 is inconsequential, I have hidden the bulk of this post under the MORE tag button in this post. If you want to see the whole project, please click the more button, and I will see you on the other side….

You will want to have a pencil, a ruler, a sheet of lined paper, four crayons, a circular cylinder that fits on the paper, and some tape or glue. My circular object here is a roll of silver tape.

1. Here I’m laying my big roll of silver tape on a line of the paper and marking the lowermost point.

2. Next, the top of circle gets marked. It so happens that this mark lands on a line, but this won’t always be the case!

3. Use the ruler to make lines across the paper to show the distance between the points. The lower point, which was on a line to start with, will be easy to draw. If the top point didn’t land on a line, lay the ruler on the point and eyeball the ruler so that it is parallel to the lines of the paper. This is easier than it sounds. You’ve now delineated across the page length of the diameter of the circle.

4. Crayon in four strips of color between the drawn lines.

5. Cut out the strips. They can be different *widths *but the heights should be* exactly** *the same as the diameter measurement.

6. Use paste or scotch tape to attach the first strip to the circular cylinder.

7. Paste or tape the second strip on to the cylinder, making sure that it is *right next to* the end of the first strip.

8. Paste or tape the third strip onto the cylinder, again making sure that this strip is* exactly lined u*p with the end of the previous strip.

9. After gluing down the three strips around the cylinder, notice that there is a small gap between the first and last strips. This is a .14, or 14%, length of the diameter that we started with. Now, get ready to make .14 of the original diameter:

10. Note that the full length of the strip is 100% of the diameter.

11. Fold it in half, and you have .50 of the diameter.

12. Fold in half again and you’ve got .25 of the diameter.

13. Here I’ve cut off the .25 diameter piece so its easier to work with. Fold this in half and….

…and this half equals between ..12 and .13 of the diameter. But I need a piece that is

. 14, so,…

I will cut this piece just a bit bigger than half!

The piece I’ve just cut is acceptably close to .14 of the diameter, which I can prove by fitting it into the space between the strips that are already glued on to my cylinder.

And there it is! it took 3.14 diameters to surround the cylinder.

If you have made it all the way to the end of this post, please let me know what you think. Thank you!!

January 17, 2014 at 4:03 pm

[…] the way that the image above visually explains the Pi relationship that I’ve put together a hands-on cut-and-paste activity to really drive the point home. It’s 19 photographs long. I think it will be a few days […]

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January 17, 2014 at 6:48 pm

This is the kind of thing that young children should be doing in the classroom! How will they know for themselves that the diameter of a circle is the value of pi? Or even know what pi really means for mathematics? Great post, thank you for sharing! Wonderful pictures as well! (I have a younger sister that I will be doing this with! She is 11 years old. :))

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January 18, 2014 at 12:53 pm

Thanks for you enthusiasm…when I finally figured out a way to cut and paste pi, I have to tell you I got really excited. I hope it goes well with your sister. Let me know!

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January 18, 2014 at 12:55 pm

Certainly! 🙂 She doesn’t like math very much, but hopefully an activity like this will show her that it does make sense and that it isn’t as useless as she thinks haha. 🙂

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January 27, 2014 at 9:17 pm

Wow! I understand this better than I ever did before! What a fun and very clear way to show this relationship! I love the easy practicality of getting to your .14 measurement at the end. Go, Paula!

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March 13, 2015 at 7:52 am

I just found a new unique project that hasn’t been done in our building. I am totally going to share it.

Love the 4 diameters at the beginning.

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March 13, 2015 at 8:37 am

I’m so pleased you like this. I hope it clicks with your students!

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December 27, 2016 at 12:49 pm

[…] Pi Post #3 : A hands-on, cut and paste pi project […]

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