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I don't really undertand what the problems are asking me can someone help? 142 Chapter 8....


142 Chapter 8. Algebraic Thinking EXTENSION 1. Unit cubes are used to build a larger cube that has edges 3 units long. Then t

I don't really undertand what the problems are asking me can someone help?

142 Chapter 8 - Algebraic Thinking EXTENSION 1. Unit cubes are used to build a larger cube that has edges 3 units long. Then
142 Chapter 8. Algebraic Thinking EXTENSION 1. Unit cubes are used to build a larger cube that has edges 3 units long. Then the six faces of the larger cube are painted. When this cube is taken apart, how many of the unit cubes will have exactly 3 painted faces? 2 painted faces? I painted face? no painted faces? This unit cube has exactly 3 painted faces 2. Repeat Exercise 1 for cubes with edges 4 units and 5 units long. Record your results in the table. 3 units 4 units 5 units n units Length of edge 3 painted faces 2 painted faces 1 painted face O painted faces Number of unit cubes with 3. Look for patterns that lead to expressions that represent the number of unit cubes with 3 painted faces, 2 painted faces, 1 painted face, and no painted faces in a cube with an edge n units long. Write the expressions in the table. 4. a. What is the length of an edge of a large cube made up of 729 unit cubes? b. How many of the unit cubes will have 3 painted faces? 2 painted faces? 1 painted face? no painted faces? 5. Explain what each of your expressions in Exercise 3 represents physically with the cubes.
142 Chapter 8 - Algebraic Thinking EXTENSION 1. Unit cubes are used to build a larger cube that has edges 3 units long. Then the six faces of the larger cube are painted. When this cube is taken apart, how many of the unit cubes will have exactly 3 painted faces? 2 painted faces? I painted face? no painted faces? This unit cube has exactly 3 painted faces. 2. Repeat Exercise 1 for cubes with edges 4 units and 5 units long. Record your results in the table. 3 units 4 units 5 units ... n units Number of unit cubes with Length of edge 3 painted faces 2 painted faces 1 painted face O painted faces 3. Look for patterns that lead to expressions that represent the number of unit cubes with 3 painted faces, 2 painted faces, 1 painted face, and no painted faces in a cube with an edge nt units long. Write the expressions in the table. 4. a. What is the length of an edge of a large cube made up of 729 unit cubes? b. How many of the unit cubes will have 3 painted faces? 2 painted faces? 1 painted face? no painted faces? 5. Explain what each of your expressions in Exercise 3 represents physically with the cubes.
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Mit cubes & Lx 1 x 1 units. They build a larger cube 3x3x3 units = 27 units Total cubes required. 27. 27 sq cubes 6 faces pai3 units 4 unita 5 ta 3 painted 12(2-2) 2 pansted 36 12 4 54 I paunted (h-2) 6 24 painted 1 a 27 n-fblas / n²-{(6x-2)) + 12 (n

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