A Method of Front-End Arithmetic

Eddie Newton                   Carver Area High School
4800 S. Lake Shore Drive       l3l00 S. Doty Avenue
Chicago IL 606l5               Chicago IL 60627
                               312-535-5250

Objectives:

Grades 3-l2

     Upon completion of the Front-End Mathematics lesson, students will be able 
to:

     a. Transfer computational fatigue from the most significant to the 
least significant columns.

     b. Eliminate carry-overs and their errors.

     c. Use one or more of the fundamental laws of commutation, association and 
distribution, and the concepts of place value and regrouping.

Multicultural Aspects:

     Many peoples contributed to the development of the modern system of 
numerals.  Any society that uses Arabic numerals can use the Front-End Method of 
Arithmetic for calculating. 

Materials Needed:

     Notebook Paper for a class of 20 students.
     Pencils for the class.
     Twenty store receipts from supermarkets.

Strategy:

     Students will be given four shopping lists and asked to estimate the  
number of $20 bills needed to purchase the items on each list.  Calculators are 
not allowed. 
 
     Students will be asked to add the figures on the list to obtain the exact 
totals.

     Students will be taught the Front-End Method of Arithmetic.

     Students will recalculate the shopping lists using front-end arithmetic 
without calculators.


     Example of front-end addition:

                          $37.55
                           63.86
                           97.23
                            8.98
                          l8
                           25.
                            2.4
                             .22
                          l-7.62
                          l0     
                          207.62

     The numbers are lined up as usual in their proper vertical columns.  The 
first column is totalled and the subtotal, 3+6+9=18, written in its proper  
place under the line.  At this stage we already know that the final sum will 
exceed $l80.  The second column is summed, its subtotal, 7+3+7+8=25, is  written 
in its proper place under the line.  The first two subtotals add up to $205, a 
second approximation to the final answer.  The third column subtotal, 24, is 
again written in its proper place under the line.  The first three subtotals 
give the partial sum $207.4, a third approximation to the final answer.  The 
fourth column subtotal, 22, is again written in its proper place under the line.  
Added to the previous partial sum, it yields the final answer $207.62. 

Performance Assessment:

     Students will be given a post-test consisting of ten front-end addition 
problems using supermarket receipts.  Students will be expected to use this new 
method to compute the problems with l00% accuracy. 

Conclusions:

     Front-end arithmetic provides an interesting variation for and supplement 
to, the classical rear-end approach.  Students are able to add columns of 
figures without carrying.  This method has real-world application to consumer 
mathematics. 

Reference:

     DeBethune, Andre J. A Method of Front-End Arithmetic, in Enrichment
for the Grades, The National Council of Teachers of Mathematics, Inc.
Washington, D.C., l963.