Lesson 7

Lesson 7: Scale Factors and 3-D Objects

 

Focus

 

Moving can sometimes involve long road trips. Some passengers take this time to read, play games, or solve puzzles. One popular road-trip puzzle is the Rubik’s Cube.

 

The Rubik’s Cube is a six-sided 3-D puzzle. Each side of the original game includes 3 × 3 small cubes of the same colour. The objective of the game is to twist and turn the small cubes until the colours on each side are all mixed up, and then to twist and turn again until the colours are in their original state—one colour per side of the cube.

 

There are many versions of the original puzzle, including the Rubik’s Mini Cube, which is a 2 × 2 cube puzzle, and Rubik’s Revenge, a 4 × 4 cube with some special features that make the puzzle even harder to solve.

 

The 5 × 5 Rubik’s Professor’s Cube might be the toughest of the games. It has been calculated that there are 282 870 942 277 741 856 536 180 333 107 150 328 293 127 731 985 672 134 721 536 000 000 000 000 000 possible arrangements of the Professor’s Cube!

 

This lesson will help you answer the following critical questions:

• When a 3-D object is enlarged or reduced, what is the relationship between scale factor and the object’s surface area?
  
  
• When a 3-D object is enlarged or reduced, what is the relationship between scale factor and the object’s volume?

Assessment

• Math Lab: Scale Factors and Areas and Volumes of 3-D Objects

All assessment items you encounter need to be placed in your course folder.

 

Materials and Equipment

• calculator
• ruler