Topic: Faces, edges and corners (vertices) of cubes

Today we studied a little more about cube, and learned that it has:

• 6 faces
• 12 edges
• 8 vertices

When counting cubes, their faces, edges and vertices, we continue to use the following strategies:

• Counting by layer
• Use symmetry to help "see" the hidden part

Homework

1. Claire uses cubes to build a large brick. Some of the small cubes are red, and the rest of the cubes are blue. The outside of the large brick is completely red, but the inside cubes are all blue. How many blue cubes did Claire use?

A) 12    B) 24              C) 36           D) 40            E) 48

2. In the class, we looked at the following structure. Try to build it yourself with 10 cubes at home, and then count how many faces of small cubes can be painted. Try using the following two methods:

• Count by layers. For example, starting with the top layer which has 5 faces.
• Count faces by viewing from side. Remember there are 6 sides: top, bottom, left, right, font and back.

Topic: “Seeing” and counting 3D cubes

Today we learned how to “see” and count 3D cubes.

• Visualize the 3D cubes in your brain
• Know there are hidden parts (blocked from view)
• Get help from the visible part to learn about the hidden part (e.g. using symmetry)

Homework

Note: homework are due next week. We will check it at the beginning of the next class.

1. Amy wants to build a big cube from small ones, so that the edge of the big cube is made up from 3 small cubes. When she takes a break, she has completed the following part using 7 small cubes. How many more small cubes will she still needs to complete the big cube?

2. 3 mini rubic cubes (each of them is 2x2x2) are connected one after another in the following picture. Some parts of them overlap each other. Can you tell altogether how many small cubes are there?