Napier's Bones

bones / strips / stick
multiples of a number
take a square root
big paper
smaller paper

Read Vocabulary First

      You must know Napier's Bones vocabulary and multiples.

      Read: Vocabulary


Multiply Any Numbers
1st:Think pencil & paper multiplication. The rows on the bones provide the rows of the multiplication problem.
2nd:Arrange bones for one number to the right of the index bone.
3rd:Identify a row for each digit of the multiplier.
    Write the sum of the digits in each diagonal in the row, one digit per diagonal.   Carry as needed. This is the product of the 1-digit number by the multi-digit number.
4th:Lay out the problem as in a pencil and paper multiplication.
    Let each row product serve as the corresponding row of the multiplication.
    Remember to shift, indent, to the left to line up the correct place.
5th:The sum of the shifted rows is the final product.
Click on graphic to enlarge.

Instructions & Manipulatives

Instructions on the Operations
root extraction
Napier's Bones Digital Manipulatives
Napier's Bones big paper version
Napier's Bones small paper version
digital manipulatives

      Many other manipulatives on many different topics are found at: MathTokens.Com.

Azzolino, Agnes "algorithm"
© 2005 at
(last modified 2005), visited 10 April 2009.
Azzolino, Agnes "Multiplication & Division"
© 2008 at
visited 10 April 2009.
Azzolino, Agnes "multiple"
© 2005 at
visited 10 April 2009.
Wikipedia®', Wikimedia Foundation, Inc.,
"Napier's bones - From Wikipedia, the free encyclopedia"
GNU Free Documentation License at
(last modified 16 March 2009, at 20:42 (UTC) ), visited 10 April 2009.

© 2009, October 2010, A. Azzolino
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