filling the triangle
I introduced Pascal's triangle by getting boys and girls to the front of the class, finding different ways of arranging them on rows of 2,3,4 … chairs.
I did not tell them what we were doing or what it was called; they found that out for themselves later.
Through this, we discovered the values in the first few rows of the triangle, then students found the next few rows for homework and posted them on my year 7 class blog, finding for themselves the method for generating the next row in the triangle (as well as finding out about Blaise Pascal)
Next lesson, we did Pascal's cube.
By drawing the triangle on isometric paper, it became clear that we could ‘walk’ around the triangle. So next lesson I put hula hoops in a triangle. Individual students were given a card that directs them from the top of the triangle to a hoop in a different way to all the other students.
The video on the right shows my year 7 students doing this task. With any luck, by the end the numbers of students in each hoop should represent the numbers in Pascal's triangle!
Good questions to ask include:
- what do you notice about the people in your group?
- what about the people on the edges?
- how is this related to boys and girls sitting in a row?