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Location: I am located in Phoenix Arizona, where i fully recognize the Public School resistance
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Understanding How to Create Napier's Rods

03/16/2013 3:47 PM

Napier, a Scotsman invented a way to create a manual computer for Multiplication. Even 1st graders can create and grow vastly the concept of Multiplication and successive addition - Here's how to create the least expensive calculator:

1. Go to any store that sells paint. Fast talk the salesman to give you a dozen paint paddles for a good cause.

2. Have your student lay one of the paddles across the bottom of another paddle at a "right Angle - this creates a square when you draw a line across the top.

3. continue this until you are at the curve near the handle - this should be the ninth square,

4. Draw diagonals from the lower left to the upper right - to the lower right will be the single digit numerals, and to the upper left will be the "carry" when needed.

5. the 1st handle will be X1 shown on the handle. In the top square will be "1" in the 1st digit area below the diagonal - there is no "carry" so the upper left will be blank. (This will be true for all nine numerals).

6. Count to add the next numeral in the square below - 1,2,3,4,5,6,7,8 & 9. this completes the X1 Rod.

7. The 2nd Rod will have the title X2. This rod will have the single digits from top to bottom: 2,4, 6, 8, 0, 2, 4, 6, 8 & 0 in the one's digits.

8. At 8 and 2 more, there is a carry to the upper left of 0. ( the ones will continue 0n to the single digit 8 which will be opposite 9 on the x1 paddle. (9 x 2 = 18, 1 in the upper left and 8 at the lower right which is read as 10 + 8 = 18.

9. the next paddle has the title of X3 and has the single digits of: 3, 6, 9, 2, 5, 8, 1, 4, & 7. This will be the real challenge for a 3rd grader when placed to the right of the X1 paddle. (9 x 3 = 27, 2in the upper left became "1" at 9 & 3 more and became "2" at 18 & 3 more - 3 x 6 = 18; 3 x 9 = 27.

10. The times five paddle is unique due to 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5. (5 x 9 = 45).

11. watch for more Napier's rods at "the Second Five"

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#1

Re: Understanding how to Create Napier's Rods

03/16/2013 9:22 PM

My eyes are spinning in opposite directions!

Picture worth a thousand words.

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#2
In reply to #1

Re: Understanding how to Create Napier's Rods

03/16/2013 11:42 PM

From Wikipedia:

The abacus consists of a board with a rim; the user places Napier's rods in the rim to conduct multiplication or division. The board's left edge is divided into 9 squares, holding the numbers 1 to 9. The Napier's rods consist of strips of wood, metal or heavy cardboard. Napier's bones are three dimensional, square in cross section, with four different rods engraved on each one. A set of such bones might be enclosed in a convenient carrying case.

A rod's surface comprises 9 squares, and each square, except for the top one, comprises two halves divided by a diagonal line. The first square of each rod holds a single digit, and the other squares hold this number's double, triple, quadruple, quintuple, and so on until the last square contains nine times the number in the top square. The digits of each product are written one to each side of the diagonal; numbers less than 10 occupy the lower triangle, with a zero in the top half.

A set consists of 10 rods corresponding to digits 0 to 9. The rod 0, although it may look unnecessary, is needed for multipliers or multiplicands having 0 in them.

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#3
In reply to #2

Re: Understanding how to Create Napier's Rods

03/17/2013 4:04 PM

Thanks for the Wikipedia article! What I was trying to accomplish was the conceptual understanding was to have the student actually create the concept. I have used it on two of my Great Grand Kids. The older at the time, was that you get the same answers when counting by two's both horizontal and vertical

Mr. Larry

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#7
In reply to #2

Re: Understanding how to Create Napier's Rods

03/27/2013 6:24 PM

Thanks for discovering a commercial version of Napier's Rods. I find that third graders learn much while creating Napiers Rods. What would the Public Schools call the Numerals in the "upper left corner and how would it be used?

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#4

Re: Understanding How to Create Napier's Rods

03/17/2013 6:10 PM

My old primary school (5-10) maths teacher used to make us say the tables direct.
i.e. 7 14 21 28 35 etc... (with no 1 x 7 =.. 2 x 7 = .. etc.) He would drop on us,
especially if he thought we were not paying attention, and say e.g "nine times table!"
and if you couldn't say... 9 18 27 36 45 54 63 ... like a machine gun! Look out!

I used to like the nines, because they're easy, add one and delete one.. 45 54 63 etc..
It's 70 years since I did this! (trip down memory lane..) But, all credit due to him,
I am still great with numbers to this day. They don't teach them like this any more.

jt

Whoever said the Irish grow their rice in paddy fields is taking the mickey.

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#5
In reply to #4

Re: Understanding How to Create Napier's Rods

03/17/2013 9:10 PM

Thanks for your trip down memory lane! Unfortunately you are right about not finding teaching like that today. "Did you know" that what you say abut nines, is true of eights eacept you need to use two instead of one: 2x8 = 16 & 2x1= 2+6 = 8;

8x8 = 64, 2 x 6 = 12 + 4 = 16 & 2x1=2+6 =8

Try seven with three and six with four

Mr. Larry

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#6
In reply to #5

Re: Understanding How to Create Napier's Rods

03/18/2013 6:38 AM

I couldn't trust myself to calc. those on the fly, so I had to learn them. (bite the bullet).

The downside of my being "brain washed" into the numbers was never did I get
to explore Napier or Abacus etc... ah well, all over now.

jt.

A man goes to the doctor and says, 'doctor, I get so depressed when

I do the crossword'. The doctor replied 'well, try not to get two down.'

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