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Before Class Work

Name. TG. 3/31/06. Before Class Work. Leon is building large cubes out of centimeter cubes . . If Leon builds a cube with an edge length of 2 cm, how many cm cubes does he need for the design? .

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Before Class Work

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  1. Name TG 3/31/06 Before Class Work Leon is building large cubes out of centimeter cubes. If Leon builds a cube with an edge length of 2 cm, how many cm cubes does he need for the design? If Leon builds a cube with an edge length of 3 cm, how many cm cubes does he need for the design? If Leon builds a cube with an edge length of 4 cm, how many cm cubes does he need for the design? ? If Leon builds a cube with an edge length of x cm, how many cm cubes does he need for the design?

  2. Frogs, Fleas, and Painted CubesInvestigation 5.1Analyzing Cube Puzzles

  3. Analyzing Cube Puzzles • As his midterm math project, Leon invented a puzzle. He made a large cube from 1,000 cm cubes and then painted the faces of the large cube. When the paint dried, he separated the puzzle into the original cm cubes. The object of Leon’s puzzle is to reassemble the cubes so that no unpainted faces are showing.

  4. Analyzing Cube Puzzles • When Leon examined the cm cubes, he noticed that some were painted on only one face, some on two faces, and some on three faces. Many of the cubes weren’t painted at all. Rubik’s Cube blindfolded Rubik’s Cube

  5. Name TG 3/31/06

  6. Cube with an edge length of 2

  7. Cube with an edge length of 3

  8. Cube with an edge length of 4

  9. Cube with an edge length of 5

  10. Cube with an edge length of 6

  11. Problem 5.1

  12. Name TG 4/3/06 Before Class Work Leon is building large cubes out of centimeter cubes. ? If Leon builds a cube with an edge length of 7 cm, how many cm cubes does he need for the design? ? If Leon builds a cube with an edge length of 15 cm, how many cm cubes does he need for the design? ? If Leon builds a cube with an edge length of 30 cm, how many cm cubes does he need for the design? ? If Leon builds a cube with an edge length of 100 cm, how many cm cubes does he need for the design?

  13. A large cube with edges of length n centimeters is built from centimeter cubes. The faces of the large cube are painted. • Write an equation for the number of centimeter cubes in the large cube. • What type of relationship is this? • How do you know?

  14. A large cube with edges of length n centimeters is built from centimeter cubes. The faces of the large cube are painted. • Write an equation for the number of centimeter cubes painted on 3 faces. • What type of relationship is this? • How do you know?

  15. A large cube with edges of length n centimeters is built from centimeter cubes. The faces of the large cube are painted. • Write an equation for the number of centimeter cubes painted on 2 faces. • What type of relationship is this? • How do you know?

  16. A large cube with edges of length n centimeters is built from centimeter cubes. The faces of the large cube are painted. • Write an equation for the number of centimeter cubes painted on 1 face. • What type of relationship is this? • How do you know?

  17. A large cube with edges of length n centimeters is built from centimeter cubes. The faces of the large cube are painted. • Write an equation for the number of centimeter cubes with no faces painted. • What type of relationship is this? • How do you know?

  18. He made a large cube from 1,000 cm cubes and then painted the faces of the large cube. Use your equations to determine the number of cubes in each blank space in the table.

  19. Number of cubes in the large cube C = n(n)(n) = n 3 This is a cubic relationship because the independent variable is being raised to the 3rd power.

  20. The 8 corners of each cube will have 3 faces painted.

  21. Number of cubes with three faces painted C = 8 This is a linear relationship because the table has a constant rate of change (+0).

  22. Number of cubes with two faces painted C = 12(n – 2) This is a linear relationship because the table has a constant rate of change (+12).

  23. 1 cube x 6 sides = 6. 16 cubes x 6 sides = 96. 4 cubes x 6 sides = 24. 9 cubes x 6 sides = 54.

  24. Number of cubes with one face painted 2 C = 6(n – 2) +6 +12 This is a quadratic relationship because the table has a constant second difference (+12). +18 +12 +30 +12 +42

  25. What’s on the inside?

  26. Number of cubes with zero faces painted 3 C = (n – 2) This is a cubic relationship because the independent variable is being raised to the 3rd power.

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