Download Let`s Do Algebra Tiles

Distributive Property
Use the same concept that was
applied with multiplication of integers,
think of the first factor as the counter.
 The same rules apply.
3(12) You can split this up into
manageable parts: 3(10 + 2)
 Three is the counter, so we need
three rows of (10 + 2)

Distributive Property

3(10 + 2)
30

+ 6
36
Now try these

2(16)
4(14)
2(19)
2(16) = 2(10 + 6)
20
+
32
12
4(14) = 4(10 + 4)
= 40 +16
= 56
2(19) = 2(20 – 1)
=
– 2
40
= 38
Distributive Property
This also works with a
variable in the parentheses.
3(X + 2)
3x + 6

Now try these:
3(x + 4)
2(x – 2)
4(x – 3)
Distributive Property
3(x + 4)
2(x – 2)
2x – 4
3x + 12
4(x – 3)
4x – 12
Solving Equations



Algebra tiles can be used to explain and
justify the equation solving process. The
development of the equation solving model
is based on two ideas.
Variables can be isolated by using zero
pairs.
Equations are unchanged if equivalent
amounts are added to each side of the
equation.
Solving Equations

Use the green rectangle as X and the
red rectangle (flip-side) as –X (the
opposite of X).
X+2=3
Solving Addition Equations
X+2=3
Therefore:
X
= 1
Now try these: x + 3 = 8
5 + x = 12
Solving Addition Equations
X+3=8
Therefore:
X
= 5
Solving Addition Equations
5 + x = 12
Therefore:
X
= 7
Solving Addition Equations
9=x+4
Therefore:
5
= x
Now try these: 8 = x + 6
14 = 10 + x
Solving Addition Equations
8=x+6
Therefore:
2
= x
Solving Addition Equations
14 = 10 + x
Therefore:
4
= x
Solving Subtraction Equations
X–2=3
Therefore:
X
= 5
Now try these: x – 3 = 8
5 – x = 12
Solving Subtraction Equations
X–3=8
Therefore:
X
= 11
Solving Subtraction Equations
5 – x = 12
Then flip all to make the x positive
Therefore:
X
= -7
Solving Subtraction Equations
9=x–4
Therefore:
13
= x
Now try these: 8 = x – 6
14 = 10 – x
Solving Subtraction Equations
8=x–6
Therefore:
14
= x
Solving Subtraction Equations
14 = 10 – x
Then flip the sides to make the x positive
Therefore:
-4
= x
Multiplication Equations
2X = 6
Then split the two sides into 2 even groups.
Therefore:
x = 3
Now, try these: 4x = 8
3x = 15
Multiplication Equations
4X = 8
Then split the two sides into 4 even groups.
Therefore:
x = 2
Multiplication Equations
3x = 15
Then split the two sides into 3 even groups.
Therefore:
x = 5
Multiplication Equations
4x = -16
Then split the two sides into 4 even groups.
Therefore:
x = -4
Now, try these: -10 = 2x
-2x = -10
Multiplication Equations
-10 = 2x
Then split the two sides into 2 even groups.
Therefore:
x = -5
Multiplication Equations
-10 = -2x
Then split the two sides into 2 even groups.
But to make the x’s positive, you have to flip
both sides.
Therefore:
x = 5
Division Equations
=6
We can’t split or cut the x into 2 parts here.
So let’s manipulate the two sides to fit the whole
x. It takes 2 groups of the 6 to make the whole
x. So make enough of the number side to
make the whole x—make another group of 6.
Therefore:
x = 12
Division Equations
=9
We can’t split or cut the x into 3 parts here.
So let’s manipulate the two sides to fit the whole
x. It takes 3 groups of the 9 to make the whole
x. So make enough of the number side to make
the whole x—make two other groups of 9.
Therefore:
x = 27
Division Equations
=3
We can’t split or cut the x into 5 parts here.
So let’s manipulate the two sides to fit the whole
x. It takes 5 groups of the 3 to make the whole
x. So make enough of the number side to make
the whole x—make 4 other groups of 3.
Therefore:
x = 15
Division Equations
2=
We can’t split or cut the x into 6 parts here.
So let’s manipulate the two sides to fit the whole
x. It takes 6 groups of the 2 to make the whole
x. So make enough of the number side to make
the whole x—make 5 other groups of 2.
Therefore:
x = 12
Division Equations
-2 =
We can’t split or cut the x into 6 parts here.
So let’s manipulate the two sides to fit the whole
x. It takes 6 groups of the -2 to make the whole
x. So make enough of the number side to make
the whole x—make 5 other groups of -2.
Therefore:
x = -12
Division Equations
= -3
We can’t split or cut the x into 5 parts here.
So let’s manipulate the two sides to fit the whole
x. It takes 5 groups of the -3 to make the whole
x. So make enough of the number side to make
the whole x—make 4 other groups of -3.
Therefore:
x = -15
Division Equations
= -9
We can’t split or cut the x into -3 parts here.
So let’s manipulate the two sides to fit the whole
x. It takes -3 groups of the -9 to make the whole
x. So make enough of the number side to make
the whole x—make two other groups of -9.
Only this time, the x is negative, so we have to flip
everything in order to make it positive.
Two Step Equations
2X + 4 = 6
The first thing is to get the x’s by themselves. Do this by
subtracting 4 from both sides of the equation.
Then, get rid of zero pairs.
Now, split the two sides into equal parts.
Therefore:
x = 1
Two Step Equations
Now, try this:
4x + 2 = 10
First, make your
equation with
algebra tiles
Next, add/subtract
#’s to get the x’s by
themselves.
And get rid of the
zero pairs.
Therefore: x = 2
After that, divide
the sides into even
groups of x’s & #’s
Two Step Equations
How about this one:
3x – 2 = 13
First, make your
equation with
algebra tiles
Next, add/subtract
#’s to get the x’s by
themselves.
And get rid of the
zero pairs.
Therefore: x = 5
After that, divide
the sides into even
groups of x’s & #’s