51_Maths_Y5(1)

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Mathematics Year 5: Fitting shapes together.

Introduction: This lesson is about encouraging children to look at shapes that tessellate. They will then move on to create their own shape(s) and to tessellate it. In doing this they will have an opportunity to think creatively rather than purely geometrically.

Resources  A computer with an art or drawing program available.  An interactive whiteboard for whole class/large group teaching.  Digital camera (optional)  Tessellations Resource file (included) Previous learning Children need to be familiar with the concept of tiling. They may have used stamps or templates before to cover a page in a regular pattern.

Children need to be able to describe polygons, and to understand about angle and symmetry.

They will need to be familiar with an art or drawing program to create their basic template.

Learning Objectives  Children will learn to look at shapes and to see which ones tessellate on their own, which ones need a ‘partner’ shape (semi-regular tessellations) and which don’t tessellate at all.  Children will create their own tessellation patterns. They will use the computer to create an accurate template (which can be easily resized) and then produce the pattern by hand.

What to do Take a group of children on a town trail or a walk around the school grounds and photograph as many tessellation patterns that they can find (brick work – how many different designs do they see?), tiling patterns on the floor of shopping malls, pavers on front drives, mock leaded windows, etc.)

The photographs can then be projected on to an interactive whiteboard and the basic shapes traced over.

Alternatively, you could use a very good PowerPoint presentation on tessellations. This can be freely downloaded from: http://www.numeracysoftware.com/tessellation.pps If the children have used the digital camera as suggested above, it will be interesting for them to compare their images with those referenced in the PowerPoint presentation.

Next, take the children through the website at: http://www.tessellations.org/linemethod-ex1-1.htm This now opens up three possibilities. Some pupils may be happy trying to tessellate one or more of the pentominoes. Others may decide to tessellate one of the 7-pin polygons. A third group may decide to create their own more imaginative design based on the methodology described in the website.

Ask the children to use the computer to produce an accurate template, to decide upon the sizing of it, print it out and glue it on to card. They should then cut around it to give them their template.

Differentiation This has been discussed above. Depending upon ability, the children might work with the pentominoes, the 7-pin polygons or the creative shapes based upon the triangle.

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Maths Y5: Fitting shapes together 2008

The role of ICT Often tessellations fail because of the inaccuracies with which the template is drawn. The use of ICT here allows for a precise template which can be adjusted and resized before being printed out.

Follow-up suggestions Some pupils will be able to tessellate some of the polygons and state which of them need a ‘partner’ and what shape the ‘partner’ would be. The attached file gives some ideas and a program to achieve these results can be found at: http://nlvm.usu.edu/en/nav/grade_g_1.html (scroll down to the Tessellations program in the geometry section - some notes regarding the use of this program are given below) Others might care to try a non-symmetrical arrow head (an irregular quadrilateral). This will always tessellate but is not easy to achieve. (The secret is to draw round the template and then to rotate it around the mid-point of any side. This gives you the position of the next shape.)

Assessment The complexity of the pattern achieved is one measure of how well the children have grasped the topic.

They should also discuss how they found the process. Could they design their own shapes? How difficult was it to decide where to reposition the template each time? Were they successful in covering the page?

Weblinks Some other useful websites and sources of ideas are at: http://www.tessella.com/literature/Tessellations/WhatareTessellations/index.htm http://www.nrich.maths.org.uk/public/viewer.php?obj_id=4832&part=index&refpage=monthindex.php http://www.mathsisfun.com/geometry/tessellation.html http://mathforum.org/sum95/suzanne/whattess.html http://www.coolmath.com/tesspag1.htm Additional note on the use of: http://nlvm.usu.edu/en/nav/grade_g_1.html  Any of the basic polygons can be added to the workspace simply by clicking on one and then dragging it around the workspace  Click on the vertex of a polygon and move the mouse in a circular motion and the polygon will rotate  Click on a polygon, and then a colour on the toolbar, and the colour will be changed  Click on a polygon and then the delete key and it will be erased The program contains a short cut for covering the whole of the screen and the children will need to master this technique; in effect they can group together a number of polygons and then ‘clone’ the set.  Click above and to the left of the polygons to be grouped and holding down the mouse button, drag to the bottom right hand corner. A box will be displayed. When the box surrounds the polygons you want to group, release the mouse button. A group will be created containing the polygons that were included in the box. The group can be moved in the same way as a single polygon. Copies of a single polygon, or a group, can be created by clicking on the Clone button.

This lesson idea was first published as part of the Becta Direct2U subscription service for teachers, (c) Becta, 2005-2006

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Maths Y5: Fitting shapes together 2008