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

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

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

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  1. What would Justin do? Algebra outside of“the box” WATERTOWN MIDDLE SCHOOL Lesson Study Open House April 11, 2006

  2. Let’s go back to Justin…

  3. Calculating surface area (of a cube)

  4. Justin’s way (cube)

  5. Calculating surface area of a rectangular prism • S = 2lw + 2lh + 2wh

  6. Justin’s way: • S = 2lw + 2lh + 2wh • S = l(2w + 2h) + 2wh

  7. If you picked up this prism, how many exposed faces could you count?

  8. Fill in the chart below • 1.

  9. Fill in the chart below • 1.

  10. How did you get your answer?

  11. 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?)

  12. How might you get…? • 6N –2(N –2) – 2

  13. How might you get…? • 6N –2(N –2) – 2 • N+N+N+N+2

  14. How might you get…? • 6N –2(N –2) – 2 • N+N+N+N+2 • 5N –2(N –2)

  15. What happens if, instead of a prism that is one cube wide, we create prisms that are two cubes or three cubes wide?

  16. :

  17. :

  18. How can you describe the exposed faces of a prism in terms of the width (W) AND the length (N)?

  19. How can you describe the exposed faces of a prism in terms of the width (W) AND the length (N)? • 2WN + 2W + 2N

  20. 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?!)

  21. Determine the number of exposed faces of a prism that is N cubes long, W cubes wide, and H cubes high.