Symbolic Exploration Day 3 (Module 15) Level IX of IX Distribution Warm Up Find the Number Guided...
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Transcript of Symbolic Exploration Day 3 (Module 15) Level IX of IX Distribution Warm Up Find the Number Guided...
![Page 1: Symbolic Exploration Day 3 (Module 15) Level IX of IX Distribution Warm Up Find the Number Guided Practice Distributing the Negative Sign Distributing.](https://reader036.fdocuments.in/reader036/viewer/2022081515/56649f4a5503460f94c6c062/html5/thumbnails/1.jpg)
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
![Page 2: Symbolic Exploration Day 3 (Module 15) Level IX of IX Distribution Warm Up Find the Number Guided Practice Distributing the Negative Sign Distributing.](https://reader036.fdocuments.in/reader036/viewer/2022081515/56649f4a5503460f94c6c062/html5/thumbnails/2.jpg)
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.
![Page 3: Symbolic Exploration Day 3 (Module 15) Level IX of IX Distribution Warm Up Find the Number Guided Practice Distributing the Negative Sign Distributing.](https://reader036.fdocuments.in/reader036/viewer/2022081515/56649f4a5503460f94c6c062/html5/thumbnails/3.jpg)
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
![Page 4: Symbolic Exploration Day 3 (Module 15) Level IX of IX Distribution Warm Up Find the Number Guided Practice Distributing the Negative Sign Distributing.](https://reader036.fdocuments.in/reader036/viewer/2022081515/56649f4a5503460f94c6c062/html5/thumbnails/4.jpg)
–(– x + 2) = – 6-
x – 2 = – 6
x – 2 + 2 = – 6 + 2
x = – 4
Distributing the Negative Sign (Tiles and Abstract)
Distribution(Guided Practice)
1
![Page 5: Symbolic Exploration Day 3 (Module 15) Level IX of IX Distribution Warm Up Find the Number Guided Practice Distributing the Negative Sign Distributing.](https://reader036.fdocuments.in/reader036/viewer/2022081515/56649f4a5503460f94c6c062/html5/thumbnails/5.jpg)
– (– x + 3) = 2
x – 3 = 2
x – 3 + 3 = 2 + 3
x = 5
Distributing the Negative Sign (Abstract)
Distribution(Guided Practice)
2
![Page 6: Symbolic Exploration Day 3 (Module 15) Level IX of IX Distribution Warm Up Find the Number Guided Practice Distributing the Negative Sign Distributing.](https://reader036.fdocuments.in/reader036/viewer/2022081515/56649f4a5503460f94c6c062/html5/thumbnails/6.jpg)
3
Distribution(Guided Practice)
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
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3(2x+4) = – 63
+ 12 = –6
6x + 12 – 12 = –6 – 126x = –18
x = –3
6x
Distribution(Guided Practice)
Distributing a Coefficient (Tiles and Abstract)
3
![Page 8: Symbolic Exploration Day 3 (Module 15) Level IX of IX Distribution Warm Up Find the Number Guided Practice Distributing the Negative Sign Distributing.](https://reader036.fdocuments.in/reader036/viewer/2022081515/56649f4a5503460f94c6c062/html5/thumbnails/8.jpg)
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
Distribution(Guided Practice)
Distributing a Coefficient (Abstract)
4
![Page 9: Symbolic Exploration Day 3 (Module 15) Level IX of IX Distribution Warm Up Find the Number Guided Practice Distributing the Negative Sign Distributing.](https://reader036.fdocuments.in/reader036/viewer/2022081515/56649f4a5503460f94c6c062/html5/thumbnails/9.jpg)
–2
Distribution(Guided Practice)
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
![Page 10: Symbolic Exploration Day 3 (Module 15) Level IX of IX Distribution Warm Up Find the Number Guided Practice Distributing the Negative Sign Distributing.](https://reader036.fdocuments.in/reader036/viewer/2022081515/56649f4a5503460f94c6c062/html5/thumbnails/10.jpg)
–12 = –2(– 2x + 4)
– 2
– 12 = 4x – 8
– 12 + 8 = 4x – 8 + 8
– 4 = 4x
– 1 = x
Distribution(Guided Practice)
Distributing a Negative Coefficient (Tiles and
Abstract)
6
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Distribution(Guided Practice)
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
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1_2
Distribution(Guided Practice)
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
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–12 = (– 2x + 4)
–
– 12 = 1x – 2
– 12 + 2 = x – 2 + 2
– 10 = x
1_2
2
1
Distribution(Guided Practice)
Distributing a Fraction (Tiles and Abstract)
9
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1_2
Distribution(Guided Practice)
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
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Distribution(Guided Practice)
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
![Page 16: Symbolic Exploration Day 3 (Module 15) Level IX of IX Distribution Warm Up Find the Number Guided Practice Distributing the Negative Sign Distributing.](https://reader036.fdocuments.in/reader036/viewer/2022081515/56649f4a5503460f94c6c062/html5/thumbnails/16.jpg)
6
?
12
Distribution(Guided Practice)
Anything New?
![Page 17: Symbolic Exploration Day 3 (Module 15) Level IX of IX Distribution Warm Up Find the Number Guided Practice Distributing the Negative Sign Distributing.](https://reader036.fdocuments.in/reader036/viewer/2022081515/56649f4a5503460f94c6c062/html5/thumbnails/17.jpg)
THE END