2D Shapes, Scaling, and Tessellations Name(s): Sarah Hunter Title of lesson: How do different shapes fit together? Date of lesson: Week 2, Day 5 Length of lesson: 50 Minutes (1 Class Period) Description of the class: Name of course: Geometry Grade level: 10 th Grade Honors or regular: Regular Source of the lesson: http://mathforum.org/sum95/suzanne/whattess.html http://www.rtc.edu/cce/resources/products/mathtoolbox/files/8_lprati oscale3.pdf TEKS addressed: Geometry (5) Geometric patterns. The student uses a variety of representations to describe geometric relationships and solve problems. The student is expected to: (B) Use numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles; (C) Use properties of transformations and their compositions to make connections between mathematics and the real world, such as tessellations; and I. Overview Scaling is used many times throughout science and mathematics. Architects use scales and ratios when drawing the design of a building, which, in turn, allows them to communicate that design and layout to others using a smaller version of the building. Along with scaling, different shapes fit together in certain ways. We will explore how certain shapes can sit side by side, while others cannot. The creation of using the same shape, which fits together in such a way that does not leave gaps, is called a tessellation. In this project, students will learn how to make a scale based on the dimensions of their perfect school in order to draw and construct their school on paper, and using their knowledge about tessellations, the students will decide on what shapes to use.
II. Performance or learner outcomes Students will be able to: 1. Define tessellation and scaling 2. Use tessellations and scaling when drawing sketches of their perfect school III. Resources, materials and supplies needed 1. Toy flat blocks of different sizes and shapes 2.Graph/Blueprint paper 3. Pencils IV. Supplementary materials, handouts. (Also address any safety issues Concerning equipment used) Tessellation Handout V. Safety Issues 1. Do not put the shapes in your mouth 2. Do not scrape the objects across anyone VI. Accommodations for learners with special needs (ELLs, Special Ed, 504, G&T)
Five-E Organization Teacher Does Probing Questions Student Does Engage: Teacher begins class by putting different pictures of mosaics (where the pieces actually fit nicely together) on the projector. What do you notice about the art work made by the artist? What do you notice about the organization of those different shapes? He/she used many different shapes and they are all different sizes. The pieces fit together and there are no gaps between any two pieces. Approx. Time 5 mins Assessment): Explore: Have the students sit in their project groups. Give each group a piece of blueprint paper. Hand out two of three bags of the plastic blocks to each group. Have each group sketch out the school their school (the one they are presently in).the students are to sketch the school out by using the different shapes in the bags. Bring the class back together. Have two groups present their drawing and tell what shapes they chose to use along with their reasoning. Question and answer. [call on student] How are you going to sketch your school? [call on two groups, allow any group to volunteer] If the class is able to answer the questions with correct and intelligent responses. If they are not able to, then we will go back through it and have another class discussion We will be using the blueprint paper and blocks to draw the school. We chose to use because the shapes are.
Earlier, you mentioned that some shapes were bigger than others. Now we are going to take those blueprints and make the drawings twice as big. Approx. Time 20 mins Assessment): Explain: How do you propose you will make your drawings twice as big as they are right now? Presentations from groups What do you think the connection is between the mosaics we were looking at and your project of building the perfect school? We can take the shapes, find the measurements of each side and then multiply by two. The students explanations as to why they chose the shapes and how they made the sketch twice as big. If there seems to be some confusion, then we will go through one of the groups sketches together as a class so that everyone understands the concept before moving on. We need to find out what type of shapes fit together so that when we building our school, we will not have gaps between rooms and buildings. Okay, the main thing that the class has seemed to observe in the mosaics is that different objects fit well next to each other. A tessellation is created when a shape is repeated over and over again covering a plane, part of the blueprint, without any gaps or overlaps. So in the previous activity, you each used different shapes and tried to fit them together, but sometimes you ran into a little problem. Does anyone know what the word is that describes this sort of idea???? Tessellation
Give students the Tessellation Handout Let s take a look at the handout. One of the things stated in the handout is that tessellations are created from using the same shape. Now, as a group, try and make a tessellation of this classroom using the same shapes that you have, or, if you want a challenge, sketch your tessellation using whatever shapes you would like. Make sure that you are careful; because you need to make sure you keep track of the scale that you use for each figure. Did any group construct a tessellation that did not use a single shape? How were you able to use all of them? Why would you have to keep track of the scale that you use for each shape? Our group used octagons, squares, and triangles. Since the octagons, squares, and triangles have similar edges, all flat and straight, we can put them side by side. Because if you put one shape next to another, but are using a different scale, they may not fit next to each other correctly. Approx. Time 10 mins Assessment) Extend / Elaborate: So we have learned about scaling, dilation, and tessellations today. Now, we have some time left in the class period so that you can apply what you have Questions and answers: What is a tessellation? Why would you use the idea of tessellations in our big project? Are the groups able to explain how they used tessellations in their construction of the classroom? Answers Presentations
learned to your project. Each group has a few bags of plastic blocks. It is your groups job to construct the blueprint that looks like the perfect school that you are building. Each group must dilate their sketch by whatever factor they would like. On a separate sheet of paper, your group is to explain why you chose to use those shapes and why you chose that layout. Approx. Time 10 mins Assessment): Evaluate: Is the group able to explain how they used tessellations in their sketch? Is the group able to explain what a tessellation is? Did the group demonstrate the use of dilation in their diagram? Did they give a key for the scale? Presentations of the groups sketches Three questions The students show a clear understanding of what a tessellation is and can explain how they used it in their sketch. The students will turn in their sketches and be graded on their explanation of how they incorporated tessellations, and dilations into their sketch. Approx. Time 5 mins