Transcript Let`s Do Algebra Tiles

Let’s Do
Algebra Tiles
Algebra Tiles
Manipulatives used to enhance
student understanding of subject
traditionally taught at symbolic level.
 Provide access to symbol
manipulation for students with weak
number sense.
 Provide geometric interpretation of
symbol manipulation.

Algebra Tiles
Support cooperative learning, improve
discourse in classroom by giving
students objects to think with and talk
about.
 When I listen, I hear.
 When I see, I remember.
 But when I do, I understand.

Algebra Tiles
Algebra tiles can be used to model
operations involving integers.
 Let the small green square represent
+1 and the small red square (the flipside) represent -1.

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The green and red squares are additive
inverses of each other.
Zero Pairs
Called zero pairs because they are
additive inverses of each other.
 When put together, they cancel each
other out to model zero.

Addition of Integers
Addition can be viewed as
“combining”.
 Combining involves the forming and
removing of all zero pairs.
 For each of the given examples, use
algebra tiles to model the addition.
 Draw pictorial diagrams which show
the modeling.

Addition of Integers
(+3) + (1) =
3
+ 1
=
(6) + (+6) =
6
+6
12
(-2) + (-1) =
-2 + (-1) = -3
4
Addition of Integers
(-3) + (-1) =
-3
+ (-1) = -4
(-4) + (-5) =
-4
+(-5)
-9
(-6) + (-6) =
-6+ (-6) = -12
Addition of Integers
(+3) + (-1) =
3
+ (-1) =
2
(+4) + (-4) =
4
+
0
+
5=
(-2) + 5 =
(-2)
3
(-4) =
So, what are the rules for
addition of integers

When adding two positive integers, the answer
is always positive.

When adding two negative integers, the
answer is always negative.

When adding two integers of opposite sign, you
subtract the numbers & the answer is the sign
of the bigger number.
Subtraction of Integers
Subtraction can be interpreted as
“take-away.”
 Subtraction can also be thought of as
“adding the opposite.”
 For each of the given examples, use
algebra tiles to model the subtraction.
 Draw pictorial diagrams which show
the modeling process.

Subtraction of Integers
(+5) – (+2) =
Remove or take away +2 of the tiles:
So,….What’s left?
(+1) – (+1) =
(-4) – (-3) =
(-7) – (-2) =
Subtracting Integers
(+3) – (-5) =
+3 “remove” -5, but you do not have any
negatives to remove.
Add zero pairs!
Subtracting Integers
Zero pair
(+3) – (-5) =
Now you can remove -5
And, your left with……
Now, try: (-4) – (+1) =
Subtracting Integers
Zero pair
(-4) – (+1) =
Add a zero pair.
Now you can remove +1
And, your left with……
Now, try these:
(+3) – (-3) =
(-8) – (+3) =
4 – (-7) =
-6 – (+9) =
So, what are the rules for
subtracting integers?
Look at the second number to see if you can
remove that many from what you have.
 If not, add zero pairs.
 Remove the tiles you need to remove.
 Count tiles left.


Your end result will be to simply add the
opposite of whatever the sign is.
Multiplication of Integers

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Integer multiplication builds on whole
number multiplication.
Use concept that the multiplier serves as
the “counter” of sets needed.
For the given examples, use the algebra
tiles to model the multiplication. Identify the
multiplier or counter.
Draw pictorial diagrams which model the
multiplication process.
Multiplication of Integers

The counter indicates how many rows to make.
It has this meaning if it is positive.
(+2)(+3) =
or, 2 rows of +3 =
(+3)(-4) =
or, 3 rows of -4 =
Multiplication of Integers
If the counter is negative it will mean “take the
opposite of.” (flip-over)
(-2)(+3)
means to take 2 sets of 3….
…but, because the counter is
Negative, you must flip them over.

Try These:
(-3)(-1)
(-4)(+3)
(3)(-1)
(-4)(-3)
(-5)(-3)
(5) (3)
(2)(-6)
(-2)(6)
(-1)(5)
(-1)(-5)
Rules for Multiplication of
Integers

If the two signs are both negative or both
positive the answer will be positive.
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If the two signs are both different, the answer will
be negative.
Division of Integers
Like multiplication, division relies on the concept
of a counter.
 Divisor serves as counter since it indicates the
number of rows to create.
 For the given examples, use algebra tiles to
model the division. Identify the divisor or
counter. Draw pictorial diagrams which model
the process.

Division of Integers
(+6)/(+2) =
Then split it into 2 groups
So, how many in each group?
So, how about this one:
(-8)/(+2) =
Split it into 2 groups:
And, how many in each group here?
Division of Integers
A negative divisor will mean “take the opposite
of.” (flip-over)
(+10)/(-2) =
First, split:
Then flip:
Third, Answer:

Division of Integers
(-12)/(-3) =
First, split:
Then flip:
Third, Answer:
Now, try these:
(12)/(-3) (-8)/4
(8)/(-2)
-12/(-6)
(+6)/(+3)
Rules for Division of Integers

If the two signs are both negative or both
positive the answer will be positive.

If the two signs are both different, the answer will
be negative.