Ideas about area and perimeter can be combined for students to discover how they are different without using formulas. Later students could be given one or two tiles as a unit of measure and using them they could calculate the area of a large design. They could make with an area of six rectangles (or any other specified area). Students could look for shapes with specified sizes. Students could compare many different shapes within a design and try to figure out which shape is bigger by using the idea that area is a measure of covering. Students could trace around a small set of tiles in a pattern and find that by counting the tiles they can tell how big the shape is Tiles that are arranged so there are no holes or gaps can be used to teach students that area is a measure of covering. Another thing that students could do is to find a shape that has exactly 10 units (or any other specified number of units) for the perimeter. One thing that the students could do is to calculate the distance from one point to another in a tessellation if they hĪd to walk a certain path on the cracks between the tiles. Ts could use the lengths to calculate perimeter of the different tiles or the perimeter of the shapes that they used the tiles to make. The tiles could be used to talk about perimeter. Once students know what the length is of the sides of the different tiles, they could use the information to measure distances. Tiles used in tessellations can be used for measuring distances. S are not the usual geometric shapes the students could sketch a picture of the design or shape that they found. Students could possibly find how many different shapes they could make with six (or any number) tiles. So students could find some tiles that make a square, a large triangle, a hexagon, etc. Two or more tiles usually make some other shape. Students could count how many tiles are in a certain row (or square, or group, or triangle), they could count how many of the tiles arĮ colored a certain color, or they could find a group of eight diamonds (or any other specified shape). Since tessellations have patterns made from small sets of tiles they could be used for different counting activities. G the tessellation patterns, makes it worth the time spent on teaching about them. Just the problem solving, that is part of creatin The older the students, the more complicated the artwork and patterns can be. All students have an equal chance to make wonderful artwork and patterns with tessellations. Creating tessellations does not depend largely on numerical skills therefore students with many different levels of mathe They can be used from kindergarten to high school. You can click and drag the corners of the triangle to change its shape, find the midpoint between two points, and rotate a shape around a point.Tessellations can be very useful in education and in teaching mathematics. You might find the interactivity below useful for this: If your answer is yes, can you explain how you know that all triangles tessellate, and can you give an algorithm (a series of instructions) that you can use on any triangle to produce a tessellation? If your answer is no, can you give an example of a triangle which doesn't tessellate and explain why it doesn't? Now try drawing some triangles on blank paper, and seeing if you can find ways to tessellate them. You can print off some square dotty paper, or some isometric dotty paper, and try drawing different triangles on it. You could also draw some triangles using this interactive. Let's think about other triangles which tessellate: We say that a shape tessellates if we can use lots of copies of it to cover a flat surface without leaving any gaps.įor example, equilateral triangles tessellate like this:
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