Differentiated Product Project: Tessellation

Transcription

1 1 Brianna Myers and Adriana Pena Doctor Loughmiller SPED April 2013 Differentiated Product Project: Tessellation Definition: Tessellation (or Tilling)- is when you cover a surface with a pattern of flat shapes so that there are no overlaps or gaps. Intended Grade Levels: 6 th, 7 th, or 8 th Grade TEKS: 6.8 Expressions, equations, and relationships. The student applies mathematical process standards to use geometry to represent relationships and solve problems. 7.9 Expressions, equations, and relationships. The student applies mathematical process standards to solve geometric problems Two-dimensional shapes. The student applies mathematical process standards to develop transformational geometry concepts. Levels of Learning: Kinesthetic Learner-This activity will satisfy students who are this type of smart; they can be hands-on making the tessellation. Vocabulary: Visual Learner-The students who prefer images, pictures, and colors will enjoy this activity because of the different colored patterns that are involved to make the tessellations. Logical Learner-This activity is perfect for students who enjoy dealing with patterns and connections consisting of mathematical content such as, tessellation, transformation, rotation, translation, concave, convex, basic shapes, and in-depth shapes. Linguistic Learner-The students who are this type of smart will be able to use their strengths because of the written and verbal part of this activity. Intrapersonal Learner-Students get to work in a group to make the tessellation. Interpersonal Learner-Students get to work individually when doing the reflection. Tessellation (or Tilling)- is when you cover a surface with a pattern of flat shapes so that there are no overlaps or gaps. Examples: rotating or translating a figure. Transformations ways of moving a figure. Rotation-a figure moves in a circular path around a point. Translation-a figure moves up, down, left, right, or diagonally by sliding it.

2 2 Concave-the curving in or hollowed inward. Convex-the curving out or bulging outward. Basic Shapes-common geometric figures. Examples: triangle, square, rectangle, and trapezoid. In-Depth Shapes-uncommon/unique geometric figures. Instructions: Lowest Level-tessellating four basic geometry shapes Average Level-tessellating two basic shapes and one in-depth shape Highest Level-tessellating at least three basic shapes and at least three in-depth shapes The Lowest-level group will get a 7-inch square that has instructions on it for how to make the shape and then they will translate the shape as much as they can on half a sheet of poster board. The Average-level group will get a 6-inch square and will have to cut out two basic shapes on the right side of the square and one in-depth shape on the left side of the square. Then they will rotate this shape as many times as they can on the poster board. The Highest-level group will get a 5-inch square and will have to cut out at least two basic shapes and one in-depth shape on the right side of the square. Then cut out at least two in-depth shapes and one basic shape on the bottom side of the square. Then the student will translate the shape as much as they can on half a sheet of poster board. Modifications: This tessellation assignment is something all levels of students can do, but in order for each group level to succeed at the assignment, modifications need to be taken into consideration. The idea we had in mind was to have three different tables focusing on different complex or simple tessellation. The idea is to key our modifications as discrete as possible, we do not want any group of children to feel insecure or discouraged about what they are capable of and what they may be too complex for them. When the Lowest group switches to work on the Average or Highest group activity, their modifications will consist of patterns already formulated and they will have to tessellate the figures onto the poster board, whereas the Average and Highest group would have to cut the shapes and draw the patterns before they could answer any further question about the assignment. The modifications/instructions will take place for each group no matter what tessellation they did. Follow Up Activity/Next Day: The Lowest-level learners will answer multiple-choice questions to reflect on the project. The Average-level learners will have a word bank of the vocabulary words that will help them write a reflection on the project. The Highest-level learners will write a description of what they learned from doing this activity, as well as using the vocabulary they learned.

3 3 7-Inch Square Tessellation Project Materials needed: One 7-Inch Instruction Square A pencil Scissors Tape Half of a White Poster Board Markers or Color Pencils Instructions: You will get a 7-inch square that has instructions on it for how to make the shape Next you will trace the shape on the lower right side of the poster board Then trace the shape again to the left of it and again After that trace the shape on top, so that the shapes look like a puzzle (also known as, a tessellation) Finally color each shape a different color Yay you created a tessellation by moving (also known as, transforming) the shape up, down, left, and right by sliding it (also known as, translation)!

4 End Result of a 7-Inch Tessellation 4

5 5 6-Inch Square Tessellation Project Materials needed: One 6-Inch Square A pencil Scissors Tape Half of a White Poster Board Markers or Color Pencils Instructions: Draw with your pencil and cut out two basic shapes (ex: triangles, squares, rectangles, and rhombuses) on the right side of the 6-inch square Take the shapes you cut out and place them exactly how you cut them, but this time have them sticking out of the top of the square (this object is convex) Then tape the convex objects on top, so the right side would have the concave of the shapes and the top side would have convex of the two basic shapes Next trace and cut out one in-depth shape on the left side of the square Then take the shape you cut out and place it exactly how you cut it, but this time have it convex at the bottom of the square Next you will put and trace the your unique geometric shape on the top left corner of the white poster board Then they will rotate this shape to the right and trace it again and continue this as many times as they can on the poster board Finally color each figure a different color from the one next to it Yay you created a tessellation by moving (transforming) the geometric figure through rotation!

6 End Result of a 6-Inch Tessellation 6

7 7 5-Inch Square Tessellation Project Materials needed: One 5-Inch Square A pencil Scissors Tape Half of a White Poster Board Markers or Color Pencils Vocabulary: Tessellation (or Tilling)- is when you cover a surface with a pattern of flat shapes so that there are no overlaps or gaps. Examples: rotating or translating a figure. Transformations ways of moving a figure. Rotation-a figure moves in a circular path around a point. Translation-a figure moves up, down, left, right, or diagonally by sliding it. Concave-the curving in or hollowed inward. Convex-the curving out or bulging outward. Basic Shapes-common geometric figures. Examples: triangle, square, rectangle, and trapezoid. In-Depth Shapes-uncommon/unique geometric figures. Instructions: Draw with your pencil and cut out at least two basic shapes and one in-depth shape on the right side of the 5-inch square Take the shapes you cut out and place them exactly how you cut them, but this time put them so they are convex on the left side of the square Then tape the convex objects on the left side, so the right side would be concave and the left side would be, the opposite, convex Next trace and cut out at least two in-depth shapes and one basic shape on the bottom side of the square Then take the shape you cut out and place it exactly how you cut it, but this time have it convex at the top of the square Next you will put and trace the your unique geometric shape on the top right corner of the white poster board Then they will translate this shape left, right, up, and down as many times as you can to create a unique geometric tessellation Finally color each figure a different color from the one next to it Yay you created a tessellation by transforming the unique geometric figure through translation!

8 End Result of a 5-Inch Tessellation 8