Return to Mathematics IndexAdding 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 theadding 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 anadding 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.