Bernice E. Holloway            Bellwood School District #88
                               1801 N. 36th Avenue
                               Stone Park, IL 60165

     -to use grouping symbols and the standard order of operations to
      simplify numerical expressions.
     -to use the order of operations to evaluate variable expressions.
     -to use the calculator and computer to solve numerical expressions.


     -calculators(generic brand)
     -banners(computer printouts)

     A.  To bring out the comparison of punctuation marks in a sentence with
         grouping symbols in a numerical expression (signs with the expressions 
         Robin Lee Travis and I love computers;Slow Children Playing;Save
         Rags and Waste Paper.), ask if students can explain why the banners are
         Without commas, the sentence Robin Lee Travis and I love computers,
         implies that two people love computers. Depending on where commas are
         inserted, the sentence can state that three or four people love 
         Sample Activities:
         1) ask students to simplify 10+2*3-1 to get as many different
            answers as they can (use calculators and computers to compare 
         2) discuss the need for a standard order of performing operations
            so that there is no ambiguity about the value of such
         3) discuss the steps of the standard order of operations and show
            how they would be used to simplify the expression above.
                                 10+6-1    multiplication
                                  16-1     addition (from left to right)
                                   15      subtraction (from left to right)
         4) show how parentheses could be used to give different meanings 
            to the same expression.

                       (10+2)x3-1       (10+2)x(3-1)
                          12 x3-1          12 x 2
                            36 -1            24
         In expressions with more than one operation, grouping symbols such 
         as parentheses or division bars are often used to indicate the
         order in which to do the operations. These grouping symbols can 
         change the meaning of an expression, just as commas or other
         punctuation marks can change the meaning of a sentence. Whenever
         the order of operation is not indicated by grouping symbols, there
         is a standard order of operations to be followed.(Do exponents,
         multiplication/division, addition/subtraction from left to right.)

         In mathematics, more than in some other forms of written 
         expression, ambiguity must be eliminated. Otherwise, different
         people may assign different meanings to the same symbols, and 
         communication is faulty. Ambiguity is eliminated using grouping
         symbols and the order of operations rule.

         In examples #1 and #2, the expressions do not have grouping
         symbols, the standard order of operations is used.
                  #1    13-4x2-3        #2   2x3^2-4
                        13-4x2-3             2x3^2-4
                        13- 8 -3             2x 9 -4
                           5-3                18-4
                            2                   14

         In examples #3 and #4, notice that the two expressions have the
         same numbers and the same operations, but the results are 
         different because of grouping symbols.(Do operations within
         parentheses, exponents, multiplication/division, addition or
         subtraction from left to right.)
                  #3   (8+5)x3          #4  8+(5x3)
                       (8+5)x3              8+(5x3)
                        13x3                8+15
                         39                   23

     B.  To give additional practice using the correct order of
         operations, have students:
         1) replace the variable in each row or column to make a true
            equation in puzzle #1 (see handout).
         2) write the operations sign (+,-,x,/) in each row or column to 
            make a true equation in puzzle #2 (see handout).

     C.  To check progress of students have them complete the Grouping 
         Symbols-Review (see handout and below).

     The use of the calculator is so common to us that we tend to take
     certain things for granted...only with the wide use of personal 
     computers are we being forced to reevaluate the function, the
     appropriate use, and the correct method(s) of teaching students  
     certain mathematical concepts using both machines.
     It should be pointed out to students that people communicate with
     computers by using programs. Programs tell the computer what to do.
     However, it is not always necessary for a person to be able to write
     a program in order to use a computer. Programs can be written in such
     a way that an operator can use them by answering a series of questions
     that are written into the program. Nevertheless, the best way to learn
     what a computer can and cannot do is to learn a little about

     To program arithmetic calculations in BASIC, you use the following 
                +       addition
                -       subtraction
                *       multiplication
                /       division
               ( )      parentheses
                ^       raised to a power(exponent)
     BASIC follows the order of operations. Sample BASIC program:
     10 PRINT 21*34+35/7
     20 END
     719 (answer)

                        Grouping Symbol-Review
Select each answer from the choices in parentheses. Write the answer in the 
1) ab  means  a______________b. (plus, divided by, times)
2) _   means  a______________b. (plus, divided by, times)
3) a____________b means a is not equal to b. (=,<>,.)

4) Parentheses are an example of a ______________.(grouping symbol, value,

Simplify each expression with the calculator. Translate each expression into 
BASIC. Use the computer to check answers.(Remember to type PRINT before the 
numerical expression.) 

5) 7+(12-3)_____________________  6) (18-3) ____________
7) (7x3)-(5x4)__________________  8) 10-(3+4)___________ 

9) 24- (63/(6+3))_______________ 10) 36/12+6____________ 
11) 15-5x2+8/4__________________ 12) 20(12-8)-30/(10+5)___________

Simplify the expression on each side of the ----?----.
Make a true statement by replacing the ? with the symbol = or <>. Check your 
answers using the computer.(If the computer prints 1, your answer is true; if your 
answer is false, the computer will print 0.) Remember the numerical expressions 
must be in BASIC. 

13) 16+3   ?   9+3 _______         14) (8-3x2)   ?   (8-3)x2_________
    8+4        4-1

15) 3(5+2)  ?  3x5+2 ______               16+4    ?   8+4x3____________
          -----                    16) 1+ ----  -----  ----
                                          3+2         8-2-2

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