Half turn rotations are common in Escher type tessellations. Half turn rotations are when the amount of the rotation is 180 o. The centre of rotation may or may not be a point on the figure itself. S has been rotated to a new position in the plane (object S’). In the picture below, the figure is rotated 90o clockwise about the point P. The properties of size, shape and orientation remain invariant (unchanged) under the operation of rotation. In this activity students are learning about rotations.Ī rotation involves turning a figure in a plane about a given point in the plane, called the centre of rotation. Using rotation to create a tessellation.This session explores learning to create a base pattern for a tessellation that has rotation (and translation). For example:Īlternatively, they might write ABCD maps to A’B’C’D’ under translation 2.1cm to the right ABCD maps to A’’B’’C’’D’’ under translation 2.1cm down. When students are working on the activities Using Translation to Tessellate they should show on their completed tessellation the direction(s) and distances of the translations used in their tessellation. If students work with a 5cm square piece of card, create a pattern to repeat on a sheet of A4 paper to create a tessellation (as in the instruction card), what area does their pattern cover… (the new shape still has the same area as the square).
Key ideas to reinforce in this include the conservation of area, perimeter and orientation. Students can then practice and have a go at making their own using Copymaster 2. Have a selection of pictures of Escher’s work to leave on your board. Ideas around creativity can be mentioned here by the teacher. Other ideas include altering a side and translating the alteration across the square, both ideas are explored in the student activities given later.ĭemonstrate this using an example or two, for example: These instructions use the idea of taking a nibble and translating that across the square. Use the Escher type tessellations instructions card above to show how a tessellating tile can be made using translation. Making a base template with translation only. If a more in-depth look at translation was wanted teachers could explore Session 2, Activity 1 “teacher and student activity using translations” in the Transforming Shapes unit of work. Translation allows us to repeat patterns. The properties of size, shape and orientation remain invariant (unchanged) under the operation of translation. We would say quadrilateral ABCD maps to quadrilateral A’B’C’D’ under translation to the right of 6.5cm. Note that lines AA’, BB’, CC’ and DD’ are all parallel. In the figure above, quadrilateral ABCD has been translated to a new position in the plane (A’B’C’D’). Translations involve a linear shift or slide of a figure in a plane. In this activity students are learning about translations. Using translation to create a tessellation.This session explores learning to create a base pattern for a tessellation that has translation only. Shapes are equilateral triangle, square, rectangle, rhombus, parallelogram, kite and hexagon. You may wish to add additional activities while they are doing the beginning tessellations activities so you can teach shape recognition and the properties of the shapes used in this unit. While students are working on the tessellation activities, there is a great opportunity to circulate around your classroom and discuss the shapes the students are going to meet during this unit. Use the activities to draw out the ideas around invariant properties of tessellations – specifically area and length remain the same. Students complete the activities Stingrays, Hexastars, and Butterflies ( Copymaster 1). Discussions can include examples of other places students see tessellations in the real world, for example, paving patterns, ceramic tiles, beehives, wallpaper. Students are introduced to the idea of tessellations, referring to the examples given in the introduction.
An outline of the unit of work is given, explaining what is required of students in each subject. Introduction to Escher’s work, both his wider art and his art based on tessellations through a PowerPoint.
Setting the scene for the unit and making the connection between the mathematics and how it will be used in art.Outline of unit of work by teachers explaining what is required of students in each subject. This unit of work has most of the mathematics front-loaded to support students’ ideas for their piece of art. The teacher supports this work with examples of art that are based on the ideas of the mathematics being explored. It is also expected that any session may extend beyond one teaching period.
#TRANSLATION TESSELLATION SERIES#
This unit of work is presented as a series of six sessions, however, more sessions than this may be required.
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