Adding Integers

Thomas, John Charles                  N. F. Simeon Voc. H. S.
                                      962-2800
                           

Objectives:

1. The students will be able to add integers.
2. The students will be able to subtract integers.
3. The students will be able to define:
      A. Additive inverse
      B. Identity element of addition
      C. Associative property of addition
      D. Addend
      E. Sum
      F. Magnitude
4. The student will be able to follow oral directions.
5. The student will be able to add and subtract integers
   without using the adding machine.
6. The students will be able to write a definition for adding
   integers and one for subtracting integers.

Apparatus Needed:

1. Poster board. (11" x 14")
2. Cut strips of paper from the poster board of a pre-determined 
   length and width.
3. A ruler or a straightedge.
4. Pencils.
5. Felt tip pens to write the numerals on the adding machine.


Recommended Strategy:

     I will tell each class that we are going to make an adding 
machine.  We will make a machine out of paper.  This machine will add 
certain combinations of integers.  (Note: The extent of the 
combinations depends on the length of the scales on the "Addend" 
number lines.)  Let's get the show on the road.  I will give each 
student a strip of paper and a ruler.  The paper has three lines on 
one side.  Turn that side face up.  We are going to divide each line 
into two equal parts.  (Note: Give oral instructions as well as visual 
instructions for dividing the line into two equal parts.)  Ask the 
students to put a tick mark," - ", at the midpoint of each line.  Tell 
students to put a zero besides each tick mark on the lines.  (Note: 
Turn rulers to the metric side.)  Put a tick mark one cm (centimeter) 
apart on the line in the middle.  Put a tick mark two cm apart for 
each of the other two lines.  (Note: Check the students' papers for 
accuracy.)  We are ready to write the numerals on the adding machine. 
Count upward using positive integers for each tick mark.  Count 
downward using negative integers for each tick mark.  (Note: Check 
papers for errors.)
     Now, let's label the lines.  Write the word, "SUM," over the line 
in the middle.  Write the word, "ADDEND," over each of the other two 
lines.  You have just made an adding machine. 
     Write "ADDEND + ADDEND = SUM" on the board or overhead projector 
to explain adding two integers.  Write any combination similar to the 
one below. 
                            +6 + (+4) = +10
                            +6 + (-4) = +2
                            -6 + (+4) = -2
                            -6 + (-4) = -10
     Ask the students to connect the "ADDENDS" with their ruler or 
straightedge to verify the answers.  (Note: If the same combinations 
are used, the students will, hopefully, intuitively determine a 
definition for adding or subtracting integers.) 
     Write "SUM - ADDEND = ADDEND" on the board to explain 
subtraction.  Write several combinations similar to the one below. 
                            +8 - (+5) = +3
                            +8 - (-5) = +13
                            -8 - (+5) = -13
                            -8 - (-5) = -3
     The students can verify the answers by connecting the "SUM" and 
the "ADDEND" with a straightedge. 
     This approach has worked for me in the past.