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I first encountered Napiers Bones back in Mrs. Hutnicks 4th grade EL math class. We had a build day

of sorts in which we made our own Napiers Bones, and at the time I thought they were really cool. Now,

a bunch of years later, I still think theyre really cool--theyre very simple to make and to use, they aredurable, and they can be personalized in any way you see fit.

My old pair is quite sloppy (though not bad for a 10-year-old, Id say. Good job, former me), so I decided

to make a new and improved set--documented here on Instructables.

Now for the important part: what Napiers Bones are. They are a multiplication tool/math toy that allows

you to multiply 0-9 with large numbers extremely quickly with only slabs of wood. As long as you add

small numbers and read correctly, you will get the correct solution every time.

Step 1: How They Work

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About This Instructable

Posted:

Aug 4, 2008

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r's Bones: Quickly Multiply, Wooden Style http://www.instructables.com/id/Napiers-Bones-Quickly-Multiply-Wood..

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Watch the video below while relaxing to the smooth tunes in the background:

Step 2: Materials

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Before you cut the wood, you want to decide how many pieces you want in your set. A set of two bones

would be the minimum: you would be able to multiply some two digit numbers. I chose to make a set of

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four free bones, which covers every two digit number*, most three digit numbers, and about half of the

possible combinations that entail four digit numbers. Also consider the size of your set: too many bones

will no longer make your set portable and easy to use.

*NOTE: This numbering system does not include 1s and 0s in them--this is because 1s and 0s are not

very interesting mathematically here, or not interesting enough to warrant more bones, in my opinion. If

you want to include these numbers, you'll have to renumber some bones or make more.

For a set of four free free bones, you need to cut:

Five9" pieces of your 1"x1" or 3/4" x 3/4" pole of wood

One3.5" piece of the pole of wood

You need one more than the number of free bones because one bone needs to be fixed. The other

piece is the base, so the length is dependent on how many bones you will make. (More bones, longerpiece.)

I used a chop saw and a ruler to make the cuts, then sanded down anything not smooth.

You also need to cut the hardboard: measure out a size that is the width of one large piece and the

length of the small piece added together, and then cut. I used the circular saw again, flipping it to cut the

whole thing.

Step 4: Pencil in the Lines

I tend to make mistakes when I do stuff. To avoid this, I draw everything in pencil first. I recommend this

method.

On the small 3.5" piece, do not draw anything.

On one of the 9" pieces, draw horizontal lines at 1" intervals along oneside.

For the other four 9" pieces, draw horizontal lines every 1" down the rod on eachside. To do this most

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effectively, measure and make a small mark at each 1" interval on all of the sides; then, using scrap

wood or other pieces as right angles, draw lines at each mark. Make sure your measurements are

careful--you want the lines on each side to line up with each other!

You should now have 9 boxes on each side of these four bones (formed by lines and edges). Draw a

diagonal line from the upper right-hand corner of each box to the lower-left hand corner of that same

box. Dont draw a diagonal in the uppermost box for all pieces and all sides!

Step 5: Sharpie Round 1(/files/deriv/FMN/R6B4/FJBP07X4/FMNR6B4FJBP07X4.LARGE.jpg)

(http://cdn.instructables.com/FY0/ISPJ/FJD5CBK2/FY0ISPJFJD5CBK2.LARGE.jpg)

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Go over all of the lines you just drew with a sharpie or equivalent artistic drawing device. Ask your inner

artist how you want the bones to look, and color/decorate accordingly.

If you are using a sharpie, be careful: the marker lines will bleed a li ttle on the wood.

Step 6: Pencil in the Numbers

Now its time to enter the numbers.

Dont draw any numbers on the 3.5" small piece. This piece will remain unmarked.

On the 9" piece with only horizontal lines on one side, write the numbers 2 through 0 (2,3,4.....,9,0), one

in each box, in that order.

Take one of the remaining 9" pieces and draw the number 2 in the top box on one side. Turn the piece90 degrees and draw the number 3 in the top box on that side. Repeat with 4 and 5 and the remaining

two sides.

Repeat these exact steps with another 9" piece.

(http://cdn.instructables.com/FHY/3VZ2/FJD5CBKZ/FHY3VZ2FJD5CBKZ.LARGE.jpg)

(http://cdn.instructables.com/F1R/45RG/FJD5CBL9/F1R45RGFJD5CBL9.LARGE.jpg)

(http://cdn.instructables.com/F8W/LADW/FJD5CBLD/F8WLADWFJD5CBLD.LARGE.jpg)

(http://cdn.instructables.com/F9C/6B44/FJD5CBL3/F9C6B44FJD5CBL3.LARGE.jpg)

(/files/deriv/FBP/66UX/FJD5CBO5/FBP66UXFJD5CBO5.LARGE.jpg)

(http://cdn.instructables.com/FY1/ZCU9/FJD5CBL7/FY1ZCU9FJD5CBL7.LARGE.jpg)

Show All 7 Images


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Go over the numbers in sharpie or equivalent artistic drawing device. I consulted my inner artist and

decided to use a different color than I used for the lines, and so the numbers are red and the lines black

on my set.

For the smaller numbers, I found it easier to use a fine point sharpie as opposed to a regular tip.

Step 8: Glue Fixed Bones

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The piece with just horizontal lines and one side of numbers is the fixed vertical piece. Using wood glue,

glue it down on the left side of the hardboard. The bottom of the piece should be flush with the bottom of

the hardboard, but there should be space at the top. Clamp and let sit according to directions on the

glue.

Glue the small piece perpendicular to the vertical fixed piece and flush with the bottom of the hardboard.

Follow directions again!

Step 9: Practice and Impress Your Friends!

Your set of Napiers Bones is now complete--all you need to do is practice! The free bones should align

with the fixed numbers, and you read across left to right, adding inside the parallelograms (see step 2

for full use instructions).

Remember that not all numbers will work with the numbers of bones that youve made. With four bones,

you cannot multiply the number 9999 because you only have two 9 digits. A number like 9471 will workperfectly, though.

Once you know how to use them, they are fun to try and to show people, especially if youve made them

yourself. Everyone (all ages and backgrounds) I show the bones to thinks they are really cool and

interesting. A "whats that sitting over there on your messy desk?" usually leads to an "oooh" or a "wow."

Plus, you can challenge people to multiplication games: you, with the bones versus your arch-nemesis,

armed with only pen and paper and his/her/its measly little brain.

This can be a great project for kids, too, if you cut the wood first and let them insert the numbers

themselves, decorate, and glue. They will have their own set of Napiers Bones, just like I did back in 4th

grade that I have kept for nearly a decade.

Mathtastically,

joshf

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Feb 12, 2009. 6:34 AM Reply (CV7JG00FR122Y5M)

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Cinders2001 (/member/Cinders2001/)says:

Very well put together.....I just need to learn how to use them!! Probably easier than I thinkt....but im

hick!! Thanks.

bkind2all (/member/bkind2all/)in reply to Cinders2001

as noted below, wikipedia

explains.

bruno13069 (/member/bruno13069/)says:

Sometimes Ill draw a "Napiers grid" to do multiplication instead of trying to line-up all of the columns

vertically. The first time I did this, I got weird looks from some friends, but I was doing (6 figure * 6

figure) multiplications faster than the rest of them.

frkohler (/member/frkohler/)says:

Muito legal!!! Muito mais fcil de usar que o baco! Congratulaes!

hammer9876 (/member/hammer9876/)says:

I love this! Im thinking of building a couple of sets for my puzzle loving nephews. They should get a

kick out of it. OK. It isnt a puzzle, I realize that, but because they like puzzles, we have the material

because we keep making stuff for them. I am thinking though, that it would be great if the wood could

be finished.

mattdonahoe (/member/mattdonahoe/)says:Mrs. Hutnick? Nice. By the time they let me in her EL math class, it was the end of fifth grade and we

were playing with platonic solids.

capricorn (/member/capricorn/)says:

I love that :) Will do as soon i find the wood ;)

hornbadoing (/member/hornbadoing/)says:

my new fevered Instructable

Doctor What (/member/Doctor+What/)says:

I had to watch the video twice, but I get it. This is a really neat project!

Doctor What (/member/Doctor+What/)in reply to Doctor What

And I like your instructions. They are

really thorough!


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Aug 4, 2008. 11:46 PM Reply (CG32G67FJHGBWMY)

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Tinker83 (/member/Tinker83/)says:

his is the method that was taught when my dad was in school. i dont recall him saying anything

about using a tool like this, but the thought process was the same. its disgusting how he can spout off

a number before i can even get it written down.

Rob K (/member/Rob+K/)says:

Neat way to do math.

=SMART= (/member/%3DSMART%3D/)says:

I think i get it, ill have to make it and test it out

:P Very nice way to work math out though : 5

*

jessyratfink (/member/jessyratfink/)says:

Im really happy you posted this. I now

understand how to use them! I was at a bit

of loss while you were working on them. :P

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