What shape/shapes have been repeated to create the tessellations? What colours are used in the designs? How are patterns created using colour? What shapes are used together to cover the space? What shapes are the tiles in the designs? Place the brochures around the room and allow students time to browse.Ensure that they know that a tiling/tessellation means that all of the wall area is to be covered. Explain that you have been to a tiling shop and got some brochures for ideas and you would like the students to help you explore possible design ideas. Introduce the concept of tiling by explaining that you are renovating your bathroom and want to make one of the walls interesting by creating a tile pattern.See the image attribution section for more information.In the first part of this unit we look at the idea of tessellations and use one design element to make a tessellation. Openly licensed images remain under the terms of their respective licenses. This site includes public domain images or openly licensed images that are copyrighted by their respective owners. The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics. Spanish translation of the "B" assessments are copyright 2020 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). The second set of English assessments (marked as set "B") are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). Īdaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).Īdaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics®, and is copyright 2017-2019 by Open Up Resources. Privacy Policy | Accessibility Information Point out that this activity provides a mathematical justification for the “yes” in the table for triangles and hexagons. (It shows a tessellation with equilateral triangles.) You can make infinite rows of triangles that can be placed on top of one another-and displaced relative to one another.)Ĭonsider showing students an isometric grid, used earlier in grade 8 for experimenting with transformations, and ask them how this relates to tessellations. “Are there other tessellations of the plane with triangles?” (Yes.“How does your tessellation with triangles relate to hexagons?” (You can group the triangles meeting at certain vertices into hexagons, which tessellate the plane.).“Why is there no space between six triangles meeting at a vertex?” (The angles total 360 degrees, which is a full circle.).“How did you find the angle measures in an equilateral triangle?” (The sum of the angles is 180 degrees, and they are all congruent so each is 60 degrees.).Consider asking the following questions to lead the discussion of this activity:
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