The Cube Challenge

Three Cubes

Have pairs of students make one 3D structure composed of 3 multilink cubes. 

• Tell students each cube must line up with adjacent cubes so that all the edges are flush – no twisted cube structures allowed
• Ensure each pair is working with only one cube colour
• Ask students to create one unique structure with 3 cubes and put it in front of them.
• Challenge students to use 3 more cubes to create a second different object. When they are finished, they will place it next to their first structure.
• Ask students whether they think it is possible to create any other unique structures. Some students may try to create a third structure that is congruent with another structure – meaning has the same shape and size as another structure if flipped or rotated.
• Discuss the ideas of congruency and incongruency (a less formal term like sameness may work for younger students) so that students understand that there can only be 2 unique structures made of 3 cubes.

Four Cubes

Challenge groups of four to five students to make as many unique structures as they can with 4 multilink cubes.

• Ask students to estimate how many unique structures they think they can make with 4 cubes.
  What makes them think that?
• Challenge students to create as many unique structures as they can.
• Remind students to check to see if each structure is congruent with one of their previous structures if rotated or flipped
• There are 8 unique structures that students can find.
• Ask students some of the following questions as they work:
• How do you know when you have all the combinations?
• Are these two objects the same or different? How do you know?
  • Is there a way of building the structures so that they can’t lie flat on the ground and have cubes sticking in another direction?
• Have each pair of students compare their structures with another pair of students.
  • Ask the group of four to put each unique structure on a designated area (e.g., a mat).
• Check as a class that students have found every possible structure. Students can describe their structures while each group checks if they have built that structure too.
• Make a class collection of structures: take one team’s collection and ask the other groups to add the structures that are missing. There should be 8 structures in total.

Five Cubes

Challenge students to make as many unique structures as they can with 5 multilink cubes, following the same lesson sequence as above.

• There are 29 unique structures that students can find. Students may benefit from a class chart or table so that they can identify new structures.
• You can ask students to describe how to build their structure to practice their spatial communication skills, or to pick a structure and describe why it is their favorite.