This is a Level 3 Geometry activity from the Figure It Out Series.
A PDF of the student activity is included.
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make nets for three dimensional shapes.
Isometric dot paper
FIO, Level 2-3, Geometry, Boxes of Tricks, page 8
Scissors
Tape
Activity One
Pentominoes are combinations of five squares joined side to side. Penta is the prefix that means five.
Most students will need to cut the pentominoes out of squared paper to find out whether they will fold to make a cube. Encourage them to visualise the folding before attempting to fold each pentomino. The pentomino in question 2 will not fold to make an open cube (a cube box with no lid):
Faces 1 and 5 will overlap.
The Answers section shows the 12 possible pentominoes and whether they form open cubes.
Activity Two
Students will find the different triangular shapes by trial and improvement after drawing them on the isometric dot paper.
The two shapes labelled “yes” above will fold to form a tetrahedron; the other shapes will not.
Answers to Activities
Activity One
1. Pentominoes are combinations of five squares
joined side to side.
2. No. An open cube is a cube box with no lid.
3. 12
4.
5.
Activity Two
1. 4:
2. The first two shown in the answer to question 1
will fold to form a tetrahedron.