What is the greatest number of pieces you can get if you cut a circular pizza from edge to edge using 5 straight lines?

What strategies are you trying? Are they random? Is there a way to be more systematic?

Lets try to simplify things. What is the most number of pizza slices for 1 cut? 2 cuts?

Do you see a pattern? Is it reasonable that the pattern will continue? Why?

Handshake problem

Solve the following using a similar technique as the third grade students in the video.

There are eight people in a room. Each person shakes hands with each of the other people once and only once. How many handshakes are there?

What if there are 20 people in the room?

Do you see a pattern? Is it reasonable that the pattern will continue? Why?

Triangular numbers

The triangular numbers are whole numbers that represent triangular arrays of dots. The first four triangular numbers are shown (along with square and pentagonal numbers).

How many dots will be in the seventh triangular number?

Do you see a pattern? Is it reasonable that the pattern will continue? Why?

Is there a triangular number that has 91 dots in its shape? If so, which one?

Is there a triangular number that has 150 dots in its shape? If so, which one?