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Pick's Theorem to find Area of Polygon on Grid (January 24-27)


The children did a great job last week of determining area and perimeter in terms of square units and linear units, respectively.  They did this using our City A through City D plus their own creations.

Area and Perimeter -- Rectangular City Planning (January 18-20)

We explored how the children identified a rectangle on a geoboard.  The children learned the most general attibute is a "polygon," "quadrilateral,"  a "parallelogram," then a "rectangle." 'How do you name this rectangle?' was the next question. We learned that you name rectangles by their dimensions.  Two dimensions, "length and width," "base and height." For example, a 3x5 rectangle.

Geoboard Polygons (January 10,11, and 13)

We explored the use of geoboards with pegs and rubberbands to create unusual polygons.  

After they completed their creations, they had to count the number of sides to name the polygon.

Then they were given large graph paper for them to try to replicate their geoboard polygon.  They did extraordinarily well once they were able to plan where they would start their drawing.

I gave them extra sheets of this large graph paper (see attached pdf) with instructions for during the week to 1. Create, 2. Color, and 3. Cutout.

Knight's Polygons (January 3-6)

Using a variation on Knight's Tours, in 2004, I created a challenge to find Knight's Polygons.  The goal is to create a polygon with the most number of sides on an 8x8 chess board moving like a knight.  You start on anyone of the 64 squares from the middle of the square and make a straight segment to the center of the next square moving like a knight.

Knights Tours (December 20-23)

All of the Mathletes learned about or rediscovered the mystery and challenge of Knights Tours.  This is an ancient puzzle that challenges us to place a number anywhere on an 8x8 grid and move as a Knight on a chess board (2-1 L shape) until you reach 64. As only a Knight can do, it may jump over other numbers but may not repeat a square. If you are stuck, use the method of recursion where we erase the last number on which we hit a wall until we can travel more moves in a different direction.