Distribute and follow the directions on the How Many Triangles? activity sheet.
Initially, students should attempt the activity sheet individually. You may wish for students to work together after they have had a chance to work independently.
Ask the following questions to stimulate a whole class discussion:
- How did your triangle change?
- How did you find out the number of triangles that were possible?
- What did you notice about the number patterns?
Solutions to the Activity Sheet:
Students should see the following pattern emerge for Triangle 1:
Stage...Number of Triangles
1......1
2......4
3......16
4......64
Students should see the following pattern emerge for Triangle 2:
Stage...Number of Shaded Triangles (and Reason)
1......3 (3 to the power of 1)
2......9 (3 to the power of 2)
3......27 (3 to the power of 3)
4......81 (3 to the power of 4)
Ask students if they have heard the term fractal previously. Students who are familiar with the term will know that a fractal is a geometric shape that can be split into parts, where the parts are smaller versions of the original geometric shape. Introduce the Fractal Tool, which allows students to explore and create their own fractals.
