Draw pictures for yourselves to model each situation. Use points to represent people and line segments to represent connections such as a handshake or a conversation.
- How many diagonals can you draw from ONE vertex in a polygon with 35 sides?
- If you place 35 points on a piece of paper so that NO THREE are in a line, how many line segments are necessary to connect each point to all the others?
- What's the TOTAL number of diagonals in a 35 sided figure?
- If you draw 35 lines on a piece of paper so that no 2 lines are parallel to each other and no three pass through the same point, how many times will they intersect?
- Is there a geometrical relationship between the first 4 problems?
- If there are 20 ppl sitting around a table, how many different pairs of ppl can have conversations during dinner?
- If 40 houses in a community all had to have direct lines to one another in order to have telephone service, how many lines would be necessary? Would it be practical? Is there a more practical alternative?
- If each team in a 10 team league plays each of the other teams four times in a season, how many league games are played during one season? What geometric figures can you use to model teams and games played?
- Each person at a dinner table shakes hands with everyone EXCEPT the 2 ppl on either side of him (this means he won't shake hands with either the person directly to his left and the person directly to his right). How many handshakes will there be among 20 diners?
- A polygon has six diagonals leaving each vertex. How many sides does it have?
- A polygon has 90 diagonals. How many sides does it have?
- Each person at a party shook hands with everyone else exactly once. There were 66 handshakes. How many ppl were at the party?
- Find the nth term: 1, 6, 15, 28, 45, 66
- Find the nth term: 4, 7, 10, 13, 16, 19
- Find the nth term: -4, 3, 16, 35, 60, 91
- Find the nth termL -1, 0, 9, 26, 51, 84
- 33+35+37+...+351=?
- 48+50+52+...+688=?
- 45+46+47+...+986=?
- Find the next term in the sequence: 1, 246, 546, 909, 1344, 1861
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