1. 5. Representing Areas of Rectangles.notebook December 03, 2012
Representing Areas of
Rectangles
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2. 5. Representing Areas of Rectangles.notebook December 03, 2012
Happy Monday! Please do as
much as you can of page 1 of the
warm­up.
If you finish early, please take
out Challenges 1­5
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3. 5. Representing Areas of Rectangles.notebook December 03, 2012
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4. 5. Representing Areas of Rectangles.notebook December 03, 2012
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5. 5. Representing Areas of Rectangles.notebook December 03, 2012
Last week, we talked about expressions. What did we say
it means to "express" something in Algebra?
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6. 5. Representing Areas of Rectangles.notebook December 03, 2012
On Friday, we expressed the number of girls in the room
as boys minus 2. What is the expression of the number of
girls in the room today, in terms of the number of boys?
What is the expression of the number of boys in the
room today, in terms of the number of girls?
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7. 5. Representing Areas of Rectangles.notebook December 03, 2012
On Friday, we also expressed some of the eighth graders
in terms of how they like to express themselves. Who
was ...
... the girl with the glittery uggs?
... the girl with the Spongebob lunch box?
... the boy with the furry winter hat that gets passed
around to everyone else?
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8. 5. Representing Areas of Rectangles.notebook December 03, 2012
What is another way to express two $1 bills?
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9. 5. Representing Areas of Rectangles.notebook December 03, 2012
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10. 5. Representing Areas of Rectangles.notebook December 03, 2012
We need someone to read Page 19, loudly and clearly.
Does this trade seem fair? Why or why not?
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11. 5. Representing Areas of Rectangles.notebook December 03, 2012
How can you find the area of these two plots of land to
see which one has more space?
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12. 5. Representing Areas of Rectangles.notebook December 03, 2012
In this problem you will test several cases and record
your data in a table. Your table will help you to see
patterns that will tell you more about situations like
these.
If the side length of the square is n, and we add 2 to the
length, how can we express the new length?
If the side width of the square is n, and we subtract 2
from the width, how can we express the new width?
If the original area could be expressed as length x width,
how can we express the new area?
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13. 5. Representing Areas of Rectangles.notebook December 03, 2012
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14. 5. Representing Areas of Rectangles.notebook December 03, 2012
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15. 5. Representing Areas of Rectangles.notebook December 03, 2012
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16. 5. Representing Areas of Rectangles.notebook December 03, 2012
What patterns do you see in the table?
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17. 5. Representing Areas of Rectangles.notebook December 03, 2012
What would be the length and width of a new rectangle
if the original square had sides of 100 feet?
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18. 5. Representing Areas of Rectangles.notebook December 03, 2012
What is the equation for the area of the orginal square?
(#3)
What do you notice about the area of the new rectangles
compared to the original square? (#2)
How can we write the equation of the area of the new
rectangle? (#4)
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19. 5. Representing Areas of Rectangles.notebook December 03, 2012
What is the equation for the area of the orginal square?
(#3)
What do you notice about the area of the new rectangles
compared to the original square? (#2)
How can we write the equation of the area of the new
rectangle? (#4)
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20. 5. Representing Areas of Rectangles.notebook December 03, 2012
Original Square Lot vs. New Rectangular Lot
a = n2 a = n2 ­ 4
Length Area Length Area
­10 ­10
­9 ­9
­8 ­8
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21. 5. Representing Areas of Rectangles.notebook December 03, 2012
Modeling Polynomials with Algebra Tiles
(2x2 + 3x + 1) + (x2 + 2x ­ 2)
1 ­1
x ­x
x2 ­x2
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22. 5. Representing Areas of Rectangles.notebook December 03, 2012
Modeling Polynomials with Algebra Tiles
(2x2 ­ 3x + 1) ­ (3x2 + 2x ­ 2)
1 ­1
x ­x
x2 ­x2
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23. 5. Representing Areas of Rectangles.notebook December 03, 2012
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