Geometric Problem Solving with Snap Cubes

Geometric Problem Solving

Problem solving in mathematics is critical to understanding geometric concepts and also making connections with other mathematics concepts.

The following activities cause students to use critical thinking and problem solving skills – often referred to as inquiry-based teaching and learning.

Inquiry Math Activity

Materials – 27 one inch snap cubes for each student

Procedures – Part 1

Give each student 27 snap cubes

Ask them to determine how many different ways can they can join three cubes face-to-face? (These are called “tri-cubes”)

Tell them that if a tri-cube can be flipped or repositioned (reflected, rotated) in such a way that it is exactly like a tri-cube already made, it is not different from the other one.

Notes

There are only two different tri-cubes – rectangular and non-rectangular.

Have students retain the non-rectangular tri-cube.

Procedures – Part 2

Ask students to find all possible non-rectangular tetra-cubes (4 unit cubes joined face-to-face).

Note

There are only six different tetra cubes – see picture (the picture also contains the one non-rectangular tri-cube).

Tetra-Cubes

Discussion

Ask the following questions:

Are any of the pieces reflections of each other? (If you put a mirror next to one piece, will you see the other in the mirror?)

Which pieces can be placed so that they are only one unit high?

Which pieces must occupy space that is 2 units high?

Which pieces have a line of symmetry on a given face?

Procedures – Part 3

Ask students to find the surface area and volume of each of the six tetra-cubes and the non-rectangular tri-cube – recording their data in a data table.

Discussion

Ask the following questions:

Did the pieces with the same volume have the same surface area?

Did the pieces with the same surface area have the same volume?

Procedures – Part 4

Ask to make a SOMA Cube by connecting their non-rectangular tri-cube and 6 tetra-cubes into a 3 by 3 cube without altering the shape of the tri-cube or tetra-cubes.

Ask students to record and share how they created a SOMA Cube with the class.

Note

There are 214 different ways.

Extension

Ask students to create other shapes using the non-rectangular tri-cube and 6 tetra-cubes without altering the shape of the tri-cube or tetra-cubes. (See picture for examples)