Welcome to this month’s edition of Problems to Ponder! Pose them in your classroom as a challenge, or try them out yourself. Have an interesting student (or teacher) solution? Send it to thevariable@smts.ca for publication in a future issue of The Variable, our monthly periodical.
Grade 7-8 Problem: Painted cube
Math Challenge 2016
A cube is made up of 27 smaller cubes. Suppose that all of the faces of the larger cube are painted red, and then it is taken apart. How many of the small cubes would have no faces painted red? One face painted red? Two faces painted red? Three faces painted red?
Grade 9-10 Problem: More (cubes) than meets the eye
Math Challenge 2016
a) How many cubes are there in a 3 x 3 cube?
b) How many rectangular prisms are there in a 3 x 3 cube?
c) How many cubes are there in a 9 x 9 cube after a 3 x 3 cube has been removed from the center?
Solutions will be posted at the end of the month in the SMTS newsletter. If you try a problem with your students, leave a comment below. We’d love to hear your stories, extensions, and/or frustrations (but no spoilers, please).
