Last week, we used magnetic plastic shapes (Picasso Tiles) to explore and see the relationships between squares and square roots. We built squares of areas, 1, 2, 4, 8, 16, 32, 64, even 128 (tried to, but we ran out of triangles). We then discussed given the number of triangles that we actually did have between the two boxed sets, what was the biggest square we could construct completely with the materials that we did have (area was 72). We looked how radicals (of multiples of square roots of 2) simplified and what that meant in terms of addition and multiplication. Thus we were able to build other squares besides those of powers of 2, which were areas of 18, 50, and 72.

Thursday and Friday of last week and Monday and Tuesday of this week, we exploring tessellations and what shapes will tessellate the plane with no gaps (triangles, squares/rectangles, hexagons, parallelograms). We also then explored what other regular polygons in conjunction with other shapes could tessellate the plane with no gaps (octagons with squares, 12-gons with hexagons, etc). We have also explored what is a tessellating unit (shape or combination of shapes that tessellate the plane with no gaps or overlaps). Today, we briefly explored the fact that if we take one of the four basic shapes and cut from one and glue that missing piece to the opposite side, we can create a new tessellating unit, which means we can create a wide variety (infinitely-many) units that will cover the plane.