It’s quite difficult for us to imagine what something looks like from different viewpoints. Yet this is a wonderful skill we can try to develop in each of our students. A part of your daily mental Warm-ups, hold up a 3D object and ask your students to imagine what this looks like from on top or below of from the back. You might even ask them to sketch it on some scrap paper and then compare their sketches with a partner. Here is a triangular pyramid, for example, made from wooden balls.You can see it from 3 different angles.
These balls demonstrate tetrahedral numbers too. The first 5 tetrahedral numbers are 1, 4, 10, 20 and 35. This one is made from 20 wooden balls stacked together. The base starts with 4 balls on each side.You need 35 wooden balls to make a triangular pyramid with sides 5 balls long. You need only 4 balls to make a triangular pyramid with sides 2 balls long at the base. One ball doesn’t really look like a triangular pyramid but the idea is there!!! By the way, in the Song “The 12 Days of Christmas my true love sent to me …” the total number of gifts is 364 – the twelfth tetrahedral number!