210 likes | 391 Views
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). Justin’s way (cube). Calculating surface area of a rectangular prism. S = 2 lw + 2 lh + 2 wh.
E N D
What would Justin do? Algebra outside of“the box” WATERTOWN MIDDLE SCHOOL Lesson Study Open House April 11, 2006
Calculating surface area of a rectangular prism • S = 2lw + 2lh + 2wh
Justin’s way: • S = 2lw + 2lh + 2wh • S = l(2w + 2h) + 2wh
If you picked up this prism, how many exposed faces could you count?
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?
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.