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Fractals in Pascal's Triangle (5s, 1s, 2s, 4s in 1, 2, and 3 digits; multiples of 10, 2, 4, and 8)

We created beautiful fractals last week from mere triangles, quadrilaterals and inscribed circles. The children did a wonderful job of mimicking nature’s obsession with fractals. I showed them the following video of 15 plants that form spectacular fractals. 

Fractals: Self-Similarity--Inscribed Triangles, Circles, Quadrilaterals, Right Triangles

Fractals are self-similar objects. What does self-similarity mean? If you look carefully at a fern leaf, you will notice that every little leaf - part of the bigger one - has the same shape as the whole fern leaf. You can say that the fern leaf is self-similar.

Constructing Regular Hexagons, Equilateral Triangles, and Derivative Works

Last week, we explored the three regular polygons that tessellate: the square, the equilateral triangle, and the regular hexagon. Creating a regular hexagon or an equilateral triangle can be done with only a compass and straight edge. This was the only way the ancient Greeks explored geometry.

Tessellations of Regular Polygons and Irregular Escher-like Shapes

A Tessellation is a repeating pattern of polygons that covers a plane with no gaps or overlaps. Typically, the shapes that make up a tessellation are polygons or similar regular shapes. The only regular polygons that tessellate on their own are equilateral triangles, squares, and regular hexagons. Regular polygons have equal sides and equal angles. 

Tiling Rectangles with Integer-Sided Squares Algebra and Perfect Rectangles

Algebra is the mathematics of using letters to represent possible numbers to solve complex problems.

We had the K-3rd graders look at one or two values of square dimension and then fill in the rectangle with all square dimensions using the information given. For example, if a square shared a side with two other squares with dimensions of 3 and 4, that larger square has a dimension of 7. If a square has a dimension that is the difference between a larger square of 10 and a smaller square of 3, its dimension is 7. Then we use a "work around" strategy to complete the puzzle.