Batch 3 - Class 198 - Meet the Cube

• (536Dudeney - 281) Two army motorcyclist, on the road at Adjbklmasdsj, wish to go to Bczrtswty, which are marked as A and B below. Pipipoff said" "I shall go to D, which is 6 miles, and then take the straight road to B, another 15 miles." But Sliponsky thought he would try the upper road by way of C. Curiously enough, they found that the distance either way was exactly the same. How far is A from C?

• Answer: 3(1/3) miles

• How would you describe a cube to an alien from a 2-Dimensional planet
• Hand out cubes to students, and let them answer bsaic facts - what are the main parts, number of faces, number of edges, number of vertices?
• Visual exploration - How many faces can you see simultaneously? Can you position the cube so that you can see three faces? Two? One? Four?
• Sketch a cube on a 2D surface, so that (a) only one face is visible; (b) two faces are visible; (c) three faces are visible
• On drawing three faces, you can choose to draw a realistic representation or a wireframe - which one works better for us? The solid cube is great visually, but we can't see the back edges. The wireframe is good to see those.

• Does the wireframe represent one cube, or are there other possibilities? To see those, try to draw wireframes and shade the front face.

• One solution is to draw a wireframe but use dashed lines for invisible edges

• Ask kids to hold the cube so that they can see it as illustrated under

• Can you fold the shapes below into cubes? The ones that can be folded into a cube are called cube-nets

• Can any connected six-squares be folded into a cube?
• Draw some other possible and impossible cube-nets

• Complete each of the two identical cube templates below into a different view of a cube

• Draw one of these so that you can see front, right and top faces
• Draw the second one so that you can see front, left and bottom faces

• Which of the following 2D shapes are cube nets?

• Marian made several 3D paper models of the cube from cutouts. On each assembled cube, she labeled the faces with letters T for top, B for bottom, and S for all the sides. Next, Marian unfolded the cutouts to store them. Later Marian's younger sister, Bella, erased some of the letters, so they look like under. Restore the missing letters.

• Which of the following are cube nets?

• Which of the cubes below could have been folded from the cube net sketched on the left?

• How many possible nets of a cube are there, without reversing? Can you find all of those?
• Answer: 11

• (536Dudeney - 326) I have three square blocks of side 16, 15 and 12 respectively, and I wish to construct a square of side 25, with least number of cuts. The cuts need not be straight, and can be of any shape. What's the least number of cuts to do this?
• Answer: Three cuts, 6 pieces.