Symbolic Exploration Day 3 (Module 15) Level IX of IX Distribution Warm Up Find the Number Guided...

Symbolic ExplorationDay 3

(Module 15)

Level IX of IX

Distribution

Warm UpFind the Number

Guided PracticeDistributing the Negative Sign

Distributing a CoefficientDistributing a Fraction

Anything New

Find the Number (Warm up)

x = 4

Use combining like terms to solve the following problems.

1) –2x – 3 + 6x – 4 +2 = 6 – 2x + 4x – 3

2n+1

n

2) What are the measurements of the rectangle below if the perimeter is 20 cm?

Since n=3, then the length is 3 cm and the width is 7 cm.

Distributing the Negative Sign (Tiles)

–

Distribution(Guided Practice)

Notice there is a negative sign outside the parentheses.What do you think it means?

The negative sign means “OPPOSITE”.

1

–(– x + 2) = – 6-

x – 2 = – 6

x – 2 + 2 = – 6 + 2

x = – 4

Distributing the Negative Sign (Tiles and Abstract)


1

– (– x + 3) = 2

x – 3 = 2

x – 3 + 3 = 2 + 3

x = 5

Distributing the Negative Sign (Abstract)


2

3


Distributing a Coefficient (Tiles)

Notice there is a coefficient of 3 outside the parentheses.What do you think it means?

Every tile inside the parenthesis is going to increase by a factor of 3.

3

3(2x+4) = – 63

+ 12 = –6

6x + 12 – 12 = –6 – 126x = –18

x = –3

6x


Distributing a Coefficient (Tiles and Abstract)

3

3(x + 2) = x + 2

3x + 6 = x + 2

3x – x + 6 = x – x + 2

2x + 6 = 2

2x + 6 – 6 = 2 – 6

2x = –4

x = –2


Distributing a Coefficient (Abstract)

4

–2


Distributing a Negative Coefficient (Tiles)

Notice there is a coefficient of –2 outside the parentheses.What do you think it means?

Every tile inside the parentheses is going to increase by a factor of 2. Then you will flip the tiles to represent the “opposite”.

5

–12 = –2(– 2x + 4)

– 2

– 12 = 4x – 8

– 12 + 8 = 4x – 8 + 8

– 4 = 4x

– 1 = x


Distributing a Negative Coefficient (Tiles and

Abstract)

6


Distributing a Negative Coefficient (Abstract)

–2(x + 3) = 2(x + 1)

–2x – 6 = 2x + 2

–2x – 6 + 2x = 2x + 2 + 2x

–6 = 4x + 2

–6 – 2 = 4x + 2 – 2

–8 = 4x

–2 = x

7

1_2


Distributing a Fraction (Tiles)

Notice there is a coefficient of ½ outside the parentheses.What do you think it means?

You will have to decrease the number of tiles by a factor of ½ .

8

–12 = (– 2x + 4)

–

– 12 = 1x – 2

– 12 + 2 = x – 2 + 2

– 10 = x

1_2

2

1


Distributing a Fraction (Tiles and Abstract)

9

1_2


Distributing a Fraction (Tiles)

Again, notice there is a coefficient of ½ outside the parentheses.

Is it easier to solve equations with fractional coefficients abstractly or with tiles? Let’s see…

It’s easier to manipulate these type of equations abstractly.

10


Distributing a Fraction (Abstract)

11 ½(x + 4) = 8

½(x) + ½(4) = 8

½x + 2 = 8

½x + 2 – 2 = 8 – 2

½x = 6

2(½x) = 2(6)

x = 12

6

?

12


Anything New?

THE END

Symbolic Exploration Day 3 (Module 15) Level IX of IX Distribution Warm Up Find the Number Guided...

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