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 = 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?

Fill in the chart below 1. Number of cubes in the prism Number of exposed faces N

Fill in the chart below 1. Number of cubes in the prism Number of exposed faces 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?

: 1 cube wide 2 cubes wide 3 cubes wide 1 cube long 2 cubes long N

: 1 cube wide 2 cubes wide 3 cubes wide 1 cube long cubes long N 4N + 26N + 48N + 6

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.