Learning Lincoln On-line


Frontier Education-- Ciphering with Abe, 1819

       While with the Lincoln family, you will do some math practice.  Abe has been showed how to do ciphering to the rule of three.  Here's how you can learn how to do it too.

       Abraham Lincoln stated in his 1859 autobiography,". . . Of course when I came of age I did not know much. Still somehow, I could read, write, and cipher to the Rule of Three."   By ciphering (cipher'n) Abraham learned to "work with numbers." 
His learned math skills centered on the math processes of PROPORTION.  He could cipher numbers to the RULE OF THREE. 

       To cipher to the rule of three for 3, 9, and 2 is to complete the phrase "3 is to 9 as 2 is to __," with the answer being the quantity 6. In other words, ciphering to the rule of three is to solve a proportion such as 3/9 = 2/x, where x=6.

Cipher the rule of three for 4, 6, and 3.

Cipher the rule of three
for a, b, and c. 

Go here for more explanation of the Rule of Three. 

The rule of three can include the processes of addition, subtraction, multiplication and even division.  It also shares algebraic procedures and the working with fractions and decimals.  The Rule of Three can be the basis for understand numbers and mathematical processes. 

Abe would like for you to work these ciphering problems with him, "under the shade of the old oak tree."  Mr. Lincoln has allowed Abe to do some school work for the afternoon.

A Starter to understand proportions and then the RULE of THREE
Proportions (also called RATIOS in modern math)

Example:is to  4  as 10 is to  ___ or  3 : 4 :: 10:___        the answer is 11. 
The way to do a simple addition ratio is to figure out the relationship of the first number to the second.  In this problem,   3 is 1 less than 4, therefore in figuring the ratio (unknown) on the right side, you add 1.     

How does this apply to the Rule of Three?  

The problem has three known elements:  the 3, the 10 and the 4.   The unknown is the answer, in this problem is 11.

Example: is to 16 as 5 is to ___ or 4 : 16 :: 5 :___         the answer is 20.  

The way to do this multiplication ratio is to see the relationship of 4 to 16.   16 is 4 times greater than 4. 

Therefore, the ratio for the right side will be 4 times 5, or 20.   How does this apply to the Rule of Three?  

The problem has three known elements: the 4, the 16 and the 5. The unknown is the answer, in this problem is 20.

Example: 24 is to 8 as 36 is to ___ or 24 : 8 :: 36:___          the answer is 12.  

The way to do this division ratio is to see the relationship of 24 to 8.  8 is 1/3rd  of 24, therefore the right side of the ratio would be figured by dividing 36 by 3.  The answer is 12.     

It could be written in the form of fractions (algebraically)  

       24 : 36 :: 8 : __

Here are some actual problems for the Cipher'n Student to tackle.  Have fun!

#1 (with numbers)   48 : 12 ::  8 : ___    Answer:______

#2 (with shapes)   %%% : ************ :: &&&& : ___     Answer:______

#3 (using objects)   15 eggs : 3 eggs :: 45 hogs : ___ hogs   Answer:______

#4 (using fractions)  1/4 : 3/4 :: 1/3 : __/__    

Answer: _______

#5 (using number groups) 000000 : 00  ::  18 : ___    

Answer:  _______  

Young Abraham Lincoln learned to do
long multiplication and division
very well and accurately.   Write these problems with division brackets and work them.  You need to know your multiplication facts to do these. 

#6   4,340  divided by 2 =     answer:

#7   5,555 divided by 250 =    answer:

#8   3,670  times 4,678 =      answer:

#9   2250  times 9,021=        answer:

You can make up your own problems.  To be a little more
modern, use a calculator to check your answer.

To see if you can write your "long multiplication or division"
problems as neatly and correctly as Abraham Lincoln.

Lincoln's Sum Papers

Learning Like Lincoln Learning Home Page

16th President Topics List