What are Penrose Tiles?

Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Kindergarten||Mathematical Practices|||K.G.1. Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.||Common Core Mathematics||Kindergarten||Geometry||Identify And Describe Shapes (Squares, Circles, Triangles, Rectangles, Hexagons, Cubes, Cones, Cylinders, And Spheres)|||K.G.2. Correctly name shapes regardless of their orientations or overall size.||Common Core Mathematics||Kindergarten||Geometry||Identify And Describe Shapes (Squares, Circles, Triangles, Rectangles, Hexagons, Cubes, Cones, Cylinders, And Spheres)|||K.G.3. Identify shapes as two-dimensional (lying in a plane, “”flat””) or three- dimensional (“”solid””).||Common Core Mathematics||Kindergarten||Geometry||Identify And Describe Shapes (Squares, Circles, Triangles, Rectangles, Hexagons, Cubes, Cones, Cylinders, And Spheres)|||K.G.4. Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/””corners””) and other attributes (e.g., having sides of equal length).||Common Core Mathematics||Kindergarten||Geometry||Analyze, Compare, Create, And Compose Shapes|||K.MD.1. Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.||Common Core Mathematics||Kindergarten||Measurement And Data||Describe And Compare Measurable Attributes|||K.MD.2. Directly compare two objects with a measurable attribute in common, to see which object has “”more of””/””less of”” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.||Common Core Mathematics||Kindergarten||Measurement And Data||Describe And Compare Measurable Attributes|||K.MD.3. Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.3||Common Core Mathematics||Kindergarten||Measurement And Data||Classify Objects And Count The Number Of Objects In Each Category|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 1||Mathematical Practices|||1.G.1. Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.||Common Core Mathematics||Grade 1||Geometry||Reason With Shapes And Their Attributes|||1.G.2. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.4||Common Core Mathematics||Grade 1||Geometry||Reason With Shapes And Their Attributes|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 2||Mathematical Practices|||Reason With Shapes And Their Attributes||Common Core Mathematics||Grade 2||Geometry|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 3||Mathematical Practices|||Reason With Shapes And Their Attributes||Common Core Mathematics||Grade 3||Geometry|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 4||Mathematical Practices|||Draw And Identify Lines And Angles, And Classify Shapes By Properties Of Their Lines And Angles||Common Core Mathematics||Grade 4||Geometry|||4.OA.5. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “”Add 3″” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.||Common Core Mathematics||Grade 4||Operations And Algebraic Thinking||Generate And Analyze Patterns|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 5||Mathematical Practices|||5.G.3. Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.||Common Core Mathematics||Grade 5||Geometry||Classify Two-Dimensional Figures Into Categories Based On Their Properties|||5.G.4. Classify two-dimensional figures in a hierarchy based on properties.||Common Core Mathematics||Grade 5||Geometry||Classify Two-Dimensional Figures Into Categories Based On Their Properties|||Solve Real-World And Mathematical Problems Involving Area, Surface Area, And Volume||Common Core Mathematics||Grade 6||Geometry|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 6||Mathematical Practices|||Draw, Construct, And Describe Geometrical Figures And Describe The Relationships Between Them||Common Core Mathematics||Grade 7||Geometry|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 7||Mathematical Practices|||Solve Real-Life And Mathematical Problems Involving Angle Measure, Area, Surface Area, And Volume||Common Core Mathematics||Grade 7||Geometry|||Understand Congruence And Similarity Using Physical Models, Trans- Parencies, Or Geometry Software||Common Core Mathematics||Grade 8||Geometry|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 8||Mathematical Practices|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||High School||Mathematical Practices