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What would Justin do? Algebra outside of
“the box”
WATERTOWN MIDDLE SCHOOL
Lesson Study Open House
April 11, 2006
Let’s go back to Justin…
Calculating surface area (of a cube)
€
S = 6x 2
Justin’s way (cube)
€
S = ( 4 x ) x + x2
+ x2
€
S = 6 x2
Calculating surface area of a rectangular prism
• S = 2lw + 2lh + 2wh
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Justin’s way:
• S = 2lw + 2lh + 2wh
• S = l(2w + 2h) + 2wh
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
If you picked up this prism, how many exposed faces
could you count?
Fill in the chart below1.Number of cubes in
the prismNumber of exposed
faces
1
2
3
100
500
N
Fill in the chart below1.Number of cubes in
the prismNumber of exposed
faces
1 6
2 10
3 14
100 402
500 2002
N 4N + 2
How did you get your answer?
Try to find two other correct algebraic expressions for the number of exposed faces in a
prism formed by N cubes - by thinking about the problem
differently.(i.e.: what would Justin do?)
How might you get…?
• 6N – 2(N – 2) – 2
How might you get…?
• 6N – 2(N – 2) – 2
• N+N+N+N+2
How might you get…?
• 6N – 2(N – 2) – 2
• N+N+N+N+2
• 5N – 2(N – 2)
What happens if, instead of a prism that is one cube wide, we create prisms that are two cubes
or three cubes wide?
3 cubes wide2 cubes wide
• :
1 cube wide
2 cubes wide
3 cubes wide
1 cube long
2 cubes long
3
4
10
100
500
N
• :
1 cube wide
2 cubes wide
3 cubes wide
1 cube long 6 10 14
2 cubes long
10 16 22
3 14
4 18
10 42
100 402
500 2002
N 4N + 2 6N + 4 8N + 6
How can you describe the exposed faces of a prism in terms of the width (W) AND
the length (N)?
How can you describe the exposed faces of a prism in terms of the width (W) AND
the length (N)? • 2WN + 2W + 2N
How can you describe the exposed faces of a prism in terms of the width (W) AND
the length (N)? • F(W,N) = 2WN + 2W + 2N
(A function of two variables?!)
Determine the number of exposed faces of a prism that is N cubes long, W cubes wide, and H
cubes high.
4 cubes long4 cubes wide3 cubes high4 cubes long3 cubes wide2 cubes high
