Finish “Grasshopper Games” for 9 pieces (p=9) and boards with sidelengths of 3, 4, 5, 6, 7, 8 and 9. Use a table to track your progress and write a rule that relates the moves (M) to the sidelength of the board (S).

Several of you also need to re-do the 3D patterns HW from last week – it must be done on a piece of graph paper with each of the four steps (draw, write, table, equation) done.

Those of you who finished that assignment can use this time to try the challenge:

Complete the attached 3D patterns.  Follow the same four steps as the last assignment.  The last pattern is an optional challenge – try it!

We won’t meet again until the Friday after Thanksgiving Break, so you have plenty of time.  Make your work neat, clear and thorough.  See me by Wednesday 11/28 if you have quesitons.

Complete the Patterns Worksheet for the square pattern, s-pattern, and star pattern.  Remember to do each of the four steps described in the worksheet.

We looked more closely this week at patterns from the boat problem.

Looking at the numbers of jumps and slides for different numbers of people, we looked for a pattern that defines the total number of moves for any number of people.  We saw, for example that for

1 pair:

SJS = 3 moves

2 pairs:

SJSJJSJS = 8 moves

Continue to diagram and record the slides, jumps and moves for at least up to 6 pairs or until you are able to describe a rule.  Explain your rule that relates the number of slides, jumps and total moves to the number of pairs.  Then use the rule to discover how many moves you would need to have 100 pairs of people switch places on a boat.

This is due the week you return from Williamsburg.

HAVE A WONDERFUL TIME!  Don’t forget the hot cider!

Sorry for the technical difficulty! Because I wasn’t able to get the blog up in time, I’m extending the help deadline – you can come see me either Thursday or Friday.

People In A Boat

Five people on each side of a boat, ten in total. There is one space between them. The five on one side need to switch places with the five on the other side. A person can slide forward to an empty space, but not back. They can jump over one person, but not jump backwards.

What patterns do you notice? (Look at the number of moves, the order of slides versus jumps, which “color” piece moves, etc) Record your observations neatly and thoroughly on a piece of graph paper.