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Published byPresley Shreve Modified over 2 years ago

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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)

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Distributive Property 3(10 + 2) 30 + 6 36 Now try these 2(16)4(14)2(19)

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20 + 12 32 4(14) = 4(10 + 4) = 40 +16 = 56 2(16) = 2(10 + 6)

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2(19) = 2(20 – 1) =40– 2 = 38

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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)

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Distributive Property 3(x + 4) 2(x – 2) 2x – 4 3x + 12 4(x – 3) 4x – 12

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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.

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Solving Equations Use the green rectangle as X and the red rectangle (flip-side) as –X (the opposite of X). X + 2 = 3

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Solving Addition Equations X + 2 = 3 Therefore: X = 1 Now try these: x + 3 = 8 5 + x = 12

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X + 3 = 8 Therefore: X = 5

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5 + x = 12 Therefore: X = 7

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9 = x + 4 Therefore: 5 = x Now try these: 8 = x + 6 14 = 10 + x

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8 = x + 6 Therefore: 2 = x

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14 = 10 + x Therefore: 4 = x

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Solving Subtraction Equations X – 2 = 3 Therefore: X = 5 Now try these: x – 3 = 8 5 – x = 12

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X – 3 = 8 Therefore: X = 11

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5 – x = 12 Then flip all to make the x positive Therefore: X = -7

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9 = x – 4 Therefore: 13 = x Now try these: 8 = x – 6 14 = 10 – x

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8 = x – 6 Therefore: 14 = x

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14 = 10 – x Then flip the sides to make the x positive Therefore: -4 = x

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Multiplication Equations 2X = 6 Then split the two sides into 2 even groups. Therefore: x = 3 Now, try these:4x = 8 3x = 15

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Multiplication Equations 4X = 8 Then split the two sides into 4 even groups. Therefore: x = 2

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Multiplication Equations 3x = 15 Then split the two sides into 3 even groups. Therefore: x = 5

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Multiplication Equations 4x = -16 Then split the two sides into 4 even groups. Therefore: x = -4 Now, try these:-10 = 2x-2x = -10

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Multiplication Equations -10 = 2x Then split the two sides into 2 even groups. Therefore: x = -5

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Multiplication Equations -10 = -2x Then split the two sides into 2 even groups. But to make the xs positive, you have to flip both sides. Therefore: x = 5

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Division Equations = 6 We cant split or cut the x into 2 parts here. So lets 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 xmake another group of 6. Therefore: x = 12

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Division Equations = 9 We cant split or cut the x into 3 parts here. So lets 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 xmake two other groups of 9. Therefore: x = 27

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Division Equations = 3 We cant split or cut the x into 5 parts here. So lets 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 xmake 4 other groups of 3. Therefore: x = 15

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Division Equations 2 = We cant split or cut the x into 6 parts here. So lets 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 xmake 5 other groups of 2. Therefore: x = 12

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Division Equations -2 = We cant split or cut the x into 6 parts here. So lets 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 xmake 5 other groups of -2. Therefore: x = -12

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Division Equations = -3 We cant split or cut the x into 5 parts here. So lets 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 xmake 4 other groups of -3. Therefore: x = -15

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Division Equations = -9 We cant split or cut the x into -3 parts here. So lets 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 xmake two other groups of -9. Only this time, the x is negative, so we have to flip everything in order to make it positive.

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Two Step Equations 2X + 4 = 6 The first thing is to get the xs 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

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Two Step Equations Now, try this: 4x + 2 = 10 First, make your equation with algebra tiles Next, add/subtract #s to get the xs by themselves. And get rid of the zero pairs. After that, divide the sides into even groups of xs & #s Therefore: x = 2

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Two Step Equations How about this one: 3x – 2 = 13 First, make your equation with algebra tiles Next, add/subtract #s to get the xs by themselves. And get rid of the zero pairs. After that, divide the sides into even groups of xs & #s Therefore: x = 5

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