![]() ![]() ![]() ![]() See the image attribution section for more information. If you have folded this, and have a copy online, would you consider. As mentioned on the flickr page- Where did I first see this Is it yours I have seen it many places, but I can’t seem to recall (or find) the first one I ever saw. Openly licensed images remain under the terms of their respective licenses. Uses offset square twists in the back to make the open squares in the front. 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. Make a fish tessellation coloring page: Now take the sticky note fish and trace. B) Cut from the mark to the top left corner and from the mark to the top right corner of the note. Make a mark at the halfway point of the vertical fold line. Point out that this activity provides a mathematical justification for the “yes” in the table for triangles and hexagons. Make the body of the fish: A) Fold the note in half horizontally again. (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.).The tessellations shown here are from Suad, Alim, Mohamed, Ruhan and Era.Consider asking the following questions to lead the discussion of this activity: At the end of the inquiry, I displayed some of the tessellations under a visualiser, which elicited an intriguing question from one of the students who had noticed the angles chosen for the quadrilaterals were all less than 180 o : "Would it work if the quadrilateral has a reflex angle?" I encouraged students to write in the angles that met at a point to verify that they summed to 360 o. They had to think carefully about how to transform the shape. The quadrilaterals presented a challenge even to the students with the highest prior attainment, particularly when the size of the angles were similar. Īs our time was limited, I directed the students to cut out a triangle or quadrilateral from card and, after measuring and noting down the interior angles, tessellate their shape on paper. To tessellate is to cover a surface with a pattern of repeated shapes, especially polygons, that fit together closely without gaps or overlapping. We compared their ideas with a formal definition (below) and agreed that they were consistent. Will it work with all the types of triangles?Īfter showing them pictures of tessellations, the students began to construct an understanding of the concept: They had no prior knowledge of tessellations and, unsurprisingly, that was their first question about the prompt:ĭoes it mean that triangles fit into quadrilaterals? Do they "perfectly overlap"?ĭo triangles and quadrilaterals do it in the same way? The prompt gave them an opportunity to see angle facts in a new context. Andrew Blair reports on how the inquiry progressed: A year 7 mixed attainment class at Haverstock school (Camden, UK) inquired into the prompt during a 50-minute lesson. ![]()
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