Teaching the ADDITION & SUBTRACTION of Integers
1. Using Counters
• 2 colours, one for positive and the other for negative
• based on the “zero principle” – adding “opposite” integers gives zero
Example: (+1) + (-1) = 0
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Addition – relatively straight forward, upon understanding of zero principle
Subtraction – more involved, often requires the “addition of zero” before
subtraction can take place
Example: (+5) – (+7) cannot be performed using only 5 red chips, thus we need
to add 2 red and 2 blue chips (“zero principle”) and then subtract the 7 red chips,
leaving 2 blue chips remaining … thus (+5) – (+7) = (-2).
2. Using Number Lines
<----------|----|----|----|----|----|----|---------->
-3 -2 -1 0 1 2 3
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Use arrows above a number line to illustrate addition and subtraction
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Addition – e.g. (-5) + (-2) – find the first number on the number line, then draw
an arrow from that number going LEFT # units if adding a NEGATIVE number
(thus becoming less positive) or RIGHT if adding a POSITIVE numbers (becoming
more positive), where # units is “2” in this example
Subraction – e.g. (-5) – (-2) – now what?? What does it mean to SUBTRACT a
NEGATIVE number? … the number is becoming less negative and thus move to
the RIGHT ☺
Example: (-5) – (+2) – here you move LEFT because you are subtracting a positive
number and thus becoming less positive.
•
3. Using “Rules” (without manipulatives)
• Once addition of integers is understood, you could teach subtraction of integers as
a rule:
• “To subract an integer, add its opposite”
Example: (+5) – (+7) = (+5) + (-7) = (-2)
Questions to think about:
• Which method is best?
• Should all methods be taught?
• What does it mean to understand addition/subtraction of integers?
• Can students understand the model and yet, not be able to do the arithmetic?
• How much practice is required?
• What about “5 - 7”? Does the "-" sign mean “take away” or is it tied to the
number 7, as (-7)?
Addition & Subtraction Using Number Lines
A. Illustrate the following additions:
1. (+5) + (+2) =
<---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|--->
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
2. (-3) + (+7) =
<---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|--->
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
3. (+8) + (-7) =
<---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|--->
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
4. (-6) + (-4) =
<---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|--->
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
B. Illustrate the following subtractions:
1. (+5) - (+2) =
<---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|--->
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
2. (+5) - (+10) =
<---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|--->
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
3. (+5) - (-2) =
<---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|--->
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
4. Additional Examples:
<---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|--->
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
<---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|--->
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10