Number Juggler Math Ideas

     1 + 1 = 2             3 - 2 = 1          5 x 5 = 25         9 ÷ 3 = 3

Those four math statements are equations. The famous RULE of EQUATIONStells you why:

�Equations are true number statements.  They tell you that the amount on the left side of the equal sign is equivalent to the amount on the right side.  If the two amounts are not equal to each other, the statement is not an equation.
 

�You can have more than one number on either side of an equation.  For example:  4 x 2 = 7 + 1.

                                4  x  2  =  7 +1
                                    8      =    8
 

The illustration on this page was drawn by Deborah Zemke for the book
Number Jugglers Math Game Book by Ruth Bell Alexander (Workman Publishing).
 

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The Order of Operations

     The language of mathematics is like any other language; it has some rules for proper communication.  One of the most important rules is called the "order of operations."  It tells us how to read an equation properly.

     Operation symbols tell us what to do with the numbers in the equation.  According to the order of operations, there is a certain order in which these operations are to be performed:  reading from left to right, we do multiplication and division before addition and subtraction.

     Naturally there are exceptions to every rule, and the two exceptions to this rule are:

1. The order of operations tells us we must perform operations within parentheses before we perform any operations outside the parentheses.  In this electronic Number Ladder Game, the computer will perform multiplication and division sequences before addition and subtraction unless you use parentheses to tell the computer otherwise.

2.  An exponent (the little number or letter that sits above and to the right of a particular number or letter) tells us how many times to multiply that number by itself.
     If an exponent is directly associated with a particular number, we perform that function before performing other operations associated with that number.  (This electronic version of the Number Ladder Game doesn't recognize exponents, so you won't be able to use exponents in this game.)
 
 
 

Parentheses    (pah-REN-theh-sees)

Parentheses (  )  are very important math tools. You use them to designate a number.  Parentheses tell which math operations to perform first to give you the number that makes your equation true.  For example, what does this number expression equal?  1 + 3  x  2 = ?
 

If you add 1 + 3 first:    (1 + 3) x 2  = 8
                                     4      x 2  = 8
 

BUT if you multiply 3 x 2 first:   1 + (3 x 2) = 7
                                                1 +     6     = 7
 

�Parentheses can make a BIG difference!  In your Number Ladder equation, if you want 1 + 3 * 2 to equal 8, be sure to put the parentheses around (1 + 3) to make it 4 * 2.  If you want 1 + 3 * 2 to equal 7, be sure to put your parentheses around (3 * 2) to make it 1 + 6. To make sure the computer reads your equation accurately, put parentheses around any part of your equation that might be confusing.  (1 + 3) * 2 = 8.

�When you are playing, if you need more than one set of parentheses in a given expression, you may use them:

NOTE:  Usually in math equations, to put parentheses around some number expression that is already in parentheses, you use brackets [ ], not another set of parentheses.  But in the electronic Number Ladder Game, the computer will not always read brackets correctly, so you must use double parentheses.
 
 
 
 

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