gr8_tessellations

= Tessellations Portfolio =

//It is expected that students will://
 * **Prescribed Learning Outcomes**

C6 Demonstrate an understanding of tessellation by:
 * explaining the properties of shapes that make tessellating possible
 * creating tessellations
 * identifying tessellations in the environment. [C, CN, PS, T, V]

C1 Develop and apply the Pythagorean theorem to solve problems. [CN, PS, R, T, V] ||
 * **Planning for Assessment** || **Assessment Strategies** ||
 * Have students create a portfolio in which they demonstrate their understanding of tessellations. Note that drawings may be done with actual shapes and pencil and paper, or, where technology is available, with a computer program/virtual manipulative. Include items such as the following:
 * Explain what is meant when it is said that "a shape tessellates" using a definition, examples and non-examples.
 * Test all regular polygons having three through eight sides (triangles through octagons) to see which will tessellate. Include angle measurements for each figure and explain why particular shapes will or will not tessellate. Make a prediction about regular n-gons with more than 8 sides and justify your prediction.
 * Draw five non-regular triangles (including scalene, obtuse, isosceles, and right triangles) and test these to see if they tessellate. Explain your findings and generate a rule.
 * Draw three irregular quadrilaterals and test these to see if they tessellate. Explain your findings and generate a rule.
 * Using the figure provided (figure 1), identify a translation, reflection, and rotation. Explain the process of each transformation using pictures or sketches to clarify. If each side of the square has a length of two, calculate the perimeter and area of each small triangle. Calculate the total length of all line segments in the figure. Use your area measurements to explain the principle of conservation of area when performing a translation,reflection or rotation.
 * Using the shapes from a set of pattern blocks, create a tessellation using two or more different shapes. Describe the tessellation in terms of transformations.
 * Draw a rectangle, triangle, parallelogram, or square. Beginning at one corner, draw an irregularly curved line through the figure's area, ending at an adjacent corner (see example in figure 2). Cut out this section, and attach it along one of the figure's other sides matching straight edges and corners (see examples in figures 3 and 4). You may wish to alter two sides (see example in figure 5). Use this new shape to create a tessellation. Describe the resulting tessellation in terms of transformations.
 * Collect at least 6 pictures showing tessellations in the environment. You may take personal photographs of things around you if you wish. You may also use pictures from magazines or from the internet. For each picture describe the shapes that make up the tessellated area. || Look for evidence that students are able to explain that a regular hexagon, with an interior angle on 120 degrees, is the largest n-gon that will tessellate since overlap will occur in all n-gons with more that 6 sides. Students should also be able to explain why pentagons cannot tessellate, since their interior angles of 108 degrees cannot surround a point.

Verify that students can identify a translation, a reflection, and a rotation in the image provided and in an image that they create. ||
 * {outline the background information to explain the classroom context, opportunities for students to gain and practise learning, and suggestions for preparing the students for assessment} || {describe the assessment task, the method of gathering assessment information, and the assessment criteria as defined by the learning outcomes and achievement indicators.} ||