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)

20 + 12

32

4(14) = 4(10 + 4) = 40 +16

= 56

2(16) = 2(10 + 6)

2(19) = 2(20 – 1)

= 40 – 2 = 38

Distributive PropertyThis 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 Property3(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 EquationsNow, 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.

After that, divide the sides into even groups of x’s & #’s

Therefore: x = 2

Two Step EquationsHow 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.

After that, divide the sides into even groups of x’s & #’s

Therefore: x = 5