Integer Tiles
SCMP September 2008
Introduction to Integer Operations
using Integer Tiles
The number 4 can be represented by
++++
or
+++++++
or
+++++++++++
The number 0 can be represented by the same number of
positive and negative tiles. An equal number of positive and
negative tiles is called a neutral field or zero pair.
+++
or
+++++
or
++++
The number ( −1) can be represented in many ways: Here are
a few possible models:
−
or
−+++
or
++++−
1. Use a minimum number of tiles to represent the following
integers. Build each model and then sketch it on your paper.
a) 3
b) -5
c)
0
d) -2
Use at least 10 tiles to represent each of the following integers.
Sketch each model after you have built it.
a) 5
b) -3
c) 0
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d) 3
Integer Tiles
SCMP September 2008
2. Represent each of the statements below using tiles. Sketch
each model, show the addition or subtraction, and write your
simplified solution below each drawing.
a) -7 + (-2)
b) -1 + 5
e) -7 – (-8)
f)
-2 – 5
c) 3 + (-4)
g)
3–5
d) 4 – (-2)
h)
3 – (-2)
3. Represent each of the products with integer tiles and sketch
the model below the problem. If a positive integer is
multiplying another integer, you add that many groups of the
integer. If a negative integer is multiplying another integer,
you remove that many groups of the integer. Write your
solution below each drawing.
a) 2 x −3
b) 4 x −2
c) −3 x 2
d) −4 x 2
e) −3 x −3
f) −2 x −3
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Integer Tiles
SCMP September 2008
4. Build an integer tile model to represent each of the
quotients below. Draw a sketch below each problem and show
the division as the inverse of multiplication. You will find how
many groups of the divisor must be “added” to create the
dividend. Write a short explanation for each step of the
process.
a) 6 ÷ 3
b) −6 ÷ −3
c) −6 ÷ 3
d) 6 ÷ −3
e) 8 ÷ −4
f) −8 ÷ 4
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