Algebra with Crazy Symbols

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Children do not get exposed to algebra early enough so when they are introduced to these abstract concepts in 6^th and 7^th grade, they often resist.

Algebra is a branch of mathematics that uses letters instead of numbers to make computations.

For example, if we say “a + b = c” and we say that a=4 and b=6, then we can conclude that c=10.

We are used to operations such as (+ - x ÷) to mean sum, difference, product and quotient.

Sometimes it is fun to use crazy symbols to introduce algebra. I try to get the children to see this like a set of instructions for a puzzle. First define the “function,” then substitute the given values to solve the puzzle.

Notice how the letter “a” is to the left of the crazy symbol and the letter “b” is to the right of the crazy symbol. When we look at the given number to the left of the same crazy symbol, we know that “a” is being substituted by that number (in the examples below, a=4). When we look at the given number to the right of the same crazy symbol, we know that “b” is being substituted by that number (in the examples below, b=6).

Level 1 (grades K-1):

         Function                               Example                       Answer

aøb = a + b                           4ø6 = 4 + 6                  =       10    

a∧b = b - a                            4∧6 = 6 – 4                           =       2

aÅb = (a + b) + (b – a)        4Å6 = (4 + 6) + (6 – 4)

                                                             =    10   +    2       =       12

a◊b = a + b + b + b              4◊6 = 4 + 6 + 6 + 6     =       22

ab = (a + b)(b - a)               46 = (4 + 6)(6 – 4)    

                                                      =   10  x    2                  =       20

a♥b = (a + 1)(b + 1)              4♥6 = (4 + 1)(6 + 1)    

                                                     =    5   x   7           =       35

Level 2 (grades 2-5):   For children in grades 2-5, we introduced more difficult algebraic functions (see below). If they complete the first 7 pages of the attached worksheet, they should try the last page, which includes combining algebraic symbols. This is very challenging and should only be first attempted with a parent.

For example, if two functions are defined as follows:

ab = (a + b)(b - a)

a♥b = (a + 1)(b + 1)

(26)♥5= 196

First, we solve, (26) which is (2 + 6) (6 – 2) = 8 X 4 = 32,

Then, we solve 32♥5 which is (32 + 1)(5 + 1) = 33 x 6 = 196

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