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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.

Tiling the Rectangle into Smallest Number of Squares of any Dimension

What is the smallest number of squares of any size we can dissect a rectangle of a given dimension? This was our challenge this week as we explored the strategy of breaking up rectangles into the largest squares possible in order to minimize the number of squares. 

Cake Method: Converting Any Decimal Number to Any Base Number Using Repeated Short Division

When I was your children’s age and I discovered the short division method, I became entranced with dividing any number by 2 and then dividing that quotient by 2 and so on. I began dividing each number right on top of the other and it resembled a multi-tiered cake.