Page 154 - NUMINO Challenge_C1
P. 154
Problem solving 4 Number of small cubes with two colored faces:
1 The cube has 12 edges. Each edge has 2 small the cube has 12 edges, and each edge has 10
small cubes. 12 10 120
cubes with two colored faces. Therefore, there Number of small cubes with no colored faces: it
are 12 2 24 small cubes with 2 colored faces. is the remaining number of small cubes after
subtracting the outside cubes. Therefore, it is
2 The 6 faces of the larger cube equal to the total number of small cubes in the
large cube with a length of 10, a width of 10,
have 150 small cubes with one and a height of 10.
colored face. Therefore, each
face of the larger cube has 150 10 10 10 1000
6 25 small cubes. Since
there are 7 small cubes on the length, width and
height of the larger cube, there are 7 7 7
343 small cubes.
Creative Thinking p.66~p.67
1 8 Nets p.68~p.69
All the figures have in common.
When you look at the position of the added Example 3, 1, ,
cube on each , is different from the TryItAgain If a square is drawn on or , there will be
three overlapped faces, so this is not a cube
other four figures. net. If a square is drawn on , , or , four
faces will meet at a vertex on , and ,
2 5 is not the opposite face to 3, 8, 4, and 6, so a cube net cannot be drawn. Therefore, to
complete the net of a cube, a square should
therefore 7 is its opposite face. (5 7) be drawn in , , and .
8 is not the opposite face to 3, 5, 4, and 7,
therefore 6 is the opposite face. (8 6)
Therefore, 4 is the opposite face to 3.
3 Example 6 3, 8
In the figure above, will have two colored
faces, will have five colored faces, and
will have four colored faces. Therefore, the
number of cubes with four colored faces is 5.
Answers will vary.
Answer Key
1 The cube has 12 edges. Each edge has 2 small the cube has 12 edges, and each edge has 10
small cubes. 12 10 120
cubes with two colored faces. Therefore, there Number of small cubes with no colored faces: it
are 12 2 24 small cubes with 2 colored faces. is the remaining number of small cubes after
subtracting the outside cubes. Therefore, it is
2 The 6 faces of the larger cube equal to the total number of small cubes in the
large cube with a length of 10, a width of 10,
have 150 small cubes with one and a height of 10.
colored face. Therefore, each
face of the larger cube has 150 10 10 10 1000
6 25 small cubes. Since
there are 7 small cubes on the length, width and
height of the larger cube, there are 7 7 7
343 small cubes.
Creative Thinking p.66~p.67
1 8 Nets p.68~p.69
All the figures have in common.
When you look at the position of the added Example 3, 1, ,
cube on each , is different from the TryItAgain If a square is drawn on or , there will be
three overlapped faces, so this is not a cube
other four figures. net. If a square is drawn on , , or , four
faces will meet at a vertex on , and ,
2 5 is not the opposite face to 3, 8, 4, and 6, so a cube net cannot be drawn. Therefore, to
complete the net of a cube, a square should
therefore 7 is its opposite face. (5 7) be drawn in , , and .
8 is not the opposite face to 3, 5, 4, and 7,
therefore 6 is the opposite face. (8 6)
Therefore, 4 is the opposite face to 3.
3 Example 6 3, 8
In the figure above, will have two colored
faces, will have five colored faces, and
will have four colored faces. Therefore, the
number of cubes with four colored faces is 5.
Answers will vary.
Answer Key
