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We want to make a quilt pattern. Imagine the triangles on the left are half squares where one half of the square is colored (the triangle), and the other half of the square is blank, or white. When you piece these together in a 4-square block, don't overlap them: one triangle per one square. You need to identify 4 different kinds of patterns (one for each 4-square block) as follows: 1. A pattern that has ONLY ONE axis of symmetry along a diagonal. 2. A pattern that has ONLY ONE axis of symmetry along a vertical. (if you come up with a horizontal axis of symmetry, rotate it to be vertical) 3. A pattern that has BOTH horizontal and vertical axes of symmetry. 4. A pattern that has BOTH diagonals as axes of symmetry. For these last two, it's OK to have axes of symmetry that are horizontal/vertical and diagonal/diagonal. Drag triangles at the left by using the Move tool and selecting the point on the triangle. Change the color by selecting the triangle and using the "menu" (bottom 3 lines at top right).
Try to find a pattern that has NO reflective symmetry but that has rotational symmetry. 1. With only 180 degree rotational symmetry. (2 possible combinations) 2. With 90, 180 and 270 degree rotational symmetry (2 possible combinations) 3. Now, come up with a pattern that has reflective symmetry along both diagonals and vertically and horizontally. 4. Finally, come up with a unique patterns that have no rotational or reflective symmetry. (There are a lot more of these than anything else.) Again, you may color the triangles in your quilt blocks.


This is an activity created by Mark E. Vasicek. It is intended to replace optional lesson 18 from illustrative mathematics, geometry, unit 1. It is to check student understanding of 1) reflection symmetry and 2) rotational symmetry.