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## What would Justin do? Algebra outside of “the box”

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**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.