ILLUSTRATING
INTEGERS
July 28, 2017
Adapted by Mr. Michael Broskowski
from
The University of Texas at Dallas
INTEGERS REVIEW
Integers are positive and negative numbers.
…, -6, -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, +6, …
Each negative number is paired with a positive
number the same distance from 0 on a number
line.
-3 -2 -1
0
1 2
3
INTEGERS REVIEW
We can represent integers using red and
yellow counters.
Red tiles will represent negative integers,
and yellow tiles will represent positive
integers.
A zero pair is a red & a yellow counter.
They are opposites so together they equal
zero.
Negative integer
Positive integer
Zero Pair
INTEGERS REVIEW
The diagrams below show 2 ways to
represent -3.
ZERO PAIRS
-3
Represent -3 in 2 more ways.
-3
INTEGERS REVIEW
Tell which integer each group of tiles represents.
-2
+2
+1
INTEGERS REVIEW
If there are the same number of red tiles
as yellow tiles, what number is
represented?
It represents
0.
ADDITION AND
SUBTRACTION
of
INTEGERS
ADDING INTEGERS
We can model integer addition with the
colored tiles.
Represent -2 with the fewest number of
tiles.
Represent +5 with the fewest number of
tiles.
ADDING INTEGERS
What number is represented by combining
the 2 groups of tiles?
X X
X X
+3
Write the number sentence that is
illustrated.
-2 + +5 = +3
ADDING INTEGERS
Use red and yellow tiles to find each sum.
-2 + -3 = ?
= -5
+
-2
+ -3 = -5
ADDING INTEGERS
-6
+
=
+ X X
X X
-3
+2
?
= -4
- 6 + +2 = - 4
+
X X
+
X
+4
X X
X
-3
=
?
=
+1
+ +4 = +1
SUBTRACTING INTEGERS
We often think of subtraction as a “take away”
operation.
Which diagram could be used to compute +3 - +5 = ?
We can’t take away 5
yellow tiles from this
diagram. There are
not enough tiles to
take away!!
X X
X
X X
This
also
+3 diagram
- +5 = -2
represents +3 but we
can take away +5.
SUBTRACTING INTEGERS
Use red and yellow tiles to model this
subtraction problem.
-2
- -4 = ?
SUBTRACTING INTEGERS
X
X X X
This representation
of -2 doesn’t have
enough tiles to take
away -4.
-2
- -4 = +2
If we add 2 ‘zero pairs’ we
would have 4 red tiles and
the tiles still represent -2.
Now we can
take away 4 red
tiles.
2 yellow tiles are
left, so the
answer is…
ADDING & SUBTRACTING
INTEGERS
Use the tiles to solve these problems.
......
..
........
.....
........
..
1. 6 + -2
4
...
....
...
......
.....
2. -3 + -4 -7
3. 8 + 5
3
4. 3 - 9
5. 6 - -2
8
6. -3 - -4
6
1