ISOMETRIES IN THE COORDINATE PLANE Docente: Cutillo Silvia Presso ITC Caruso NA Prof.ssa Castagneto Laura Liceo Scientifico Labriola Na Content Isometries in the coordinate plane Studentage 15-16 y.o. Teaching aims: to enable learners to understand that different types of isometries to develop their ability to perform and describe transformations of a 2-D shape in all 4 quadrants of a Cartesian plane to increase their skills to observe regularities in different examples and to deduce mathematical laws Learning outcomes MOST LEARNERS SHOULD KNOW... BE ABLE TO … BE AWARE … demonstrate an understanding of transformations (translations, rotations, and reflections) of 2-D shapes in all four quadrants of the Cartesian plane carry out transformations (translations, reflections and rotations) on a Cartesian plane. Model with mathematics. definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. describe the effect of dilations, translations,rotations,and reflections on two-dimensional figures using coordinates. Reason abstractly quantitatively transformations as functions that take points in the plane as inputs and give other points as outputs to extend their findings to understand that a series of transformations can be calculated using multiple rules Look for and express regularity in repeated reasoning. Given two 2-D shapes, describe transformations that could be used to take one shape to the other and vice versa. and Competence Description Communicative Can describe different types of plane transformations Linguistic Can use language to observe and analyse Artistic Can recognise symmetries in monuments, paintings Digital Can use Geogebra Mathematical Can reason and solve problems mathematically Social Can cooperate with others GLOSSARY Function Let A and B sets, a function from A to B is a rule in which to every element x of A assigns an unique element in B Transformation of a plane Let A the set of points in the plane. A transformation in the plane is a one-to-one mapping from A to A Isometry An isometry is a transformation of the planethat preserves the distance between points Rotation (turn) Rotation is defined by stating the centre of rotation, amount of turning in degrees and the direction of rotation (clockwise or anticlockwise) Translation (slide) A translation is defined by specifying the distance and the direction of a movement Reflection(flip) reflection over a line is a transformation in which each point of the original figure has an image that is the same distance from the line of reflection as the original point but is on the opposite side of the line. Wordlist Function Funzione Collinear point Puntallineati Range Immagine x coordinate ascissa Symmetric points with respect to a point (line) Punti simmetrici rispetto ad un punto (una retta) y coordinate ordinata X -axis Asse delle ascisse Midpoint of a line segment Punto medio di un segmento Invariant point Punto unito Y-axis Asse ordinate Quadrant Quadrante Rotation Rotazione delle Transformations in the plane coordinate Trasformazioni del piano Axis of symmetry Asse di simmetria Half line Semiretta Reflection across a line Simmetria assiale Point reflection Simmetria centrale Centre of symmetry Centro di simmetria Symmetric figure with rispect to a point Figura simmetrica rispetto ad un punto Transformation of a plane Trasformazioni piane Symmetric figure with rispect to a line Figura simmetrica rispetto ad una retta Translation Traslazione Perpendicular bisector in a line segment Asse di segmento Perpendicular line through a point to a given line Perpendicolare da un punto ad una retta data un Horizontal component of a vector Componente di un vettore secondo l’asse x Vertical component of a vector Componente di un vettore secondo l’asse y Vector norm Modulo vettore di un Composition of isometries Composizione isometrie di Ordered pair Coppia ordinata Distance from a point to a line Distanza di un puntoda una retta Congruent figures Figurecongruenti Isometry Isometria Lunghezza Lenght Opposite oppoto Curly brackets Parentesi graffe Resources A little mirror Worksheets Interactive whiteboard PC ( to use Geogebra ) Colored paper Squared math paper PPT presentations Procedure Groups Activity using worksheet and/or simple objects from everyday life Whole class Class discussion on preceeding activity Summary of the discussion by drawing mind map or other visuals Glossary writing Individually Writing observations and feedback on worksheets Students are divided in groups with the help of English teacher in order to balance both language and mathematical skills (i.e. the best students in mathematics, the best English speaking people should not belong to all to one or few groups ) Lesson 1 Activating prior knowledge Lesson 2 -3 Introduction to plane transformation Reflection Learning outcomes to carry out reflections to write the coordinate of image of a 2D shape after a reflection of the shape has been completed Lesson 4-5 Translation and Rotation Learning outcomes to carry out translations and rotations to write the coordinate of image of a 2D shape after a translation/rotation of the shape has Lesson 6 Consecutive plane transformations Learning outcomes • been completed • • To perform consecutive transformations on a 2-D shape using Geogebra and identify coordinates of the vertices of the image to describe a sequence of transformations to carry a certain figure onto another to use the new vocabulary Lesson 1 Activating prior knowledge Learners are encouraged to produce content language at the start of the lesson. It is expected that students will have prior knowledge/experience related to the concepts and skills identified below. It may be necessary to pre-assess in order to determine if time needs to be spent on conceptual activities that help students develop a deeper understanding of these ideas. plotting points on a coordinate plane - congruence of geometric figures and the correspondence of their vertices, sides, and angles interpreting and sketching views from different perspectives calculate the perimeter and area of fundamental geometric plane figures LESSON 1 •Activating prior knowledge •Developing communication skills Cognitive skills: Remembering, Defining Learning skills: cooperating with others, organizing information •Building specific vocabulary Students are asked to complete worksheets and write the a glossary of key words they can find on the worksheet Class discussion and preparation of a poster with key words to be hanged in the classroom Reflection Material : 1 plane mirror with a support, 2 pencils, 1 piece of blank paper, 1 centimeter ruler 1. Hold a pencil in a vertical position about 10 cm in front of a flat mirror, as in the photograph. Look into the mirror and you will see an image of the pencil. 2. Moving a second pencil around behind the mirror, it will be possible to have a complete view of the object: its lower part as reflected in the mirror and the top with a direct view, 3. What is the appropriate distance that makes it possible ? ( Use a centimeter ruler to measure these distances: (a) From the first pencil to the mirror surface and (b) From the mirror surface to the image). 4. Try using other distances from the first pencil to the mirror surface. Rotation Explore Rotational Symmetry by Making Rose Windows A photo of a rose window will be given to each group. The task is to determine how many degrees each rose window rotates before it appears the same. Translation A picture similar to the following will be given to each group. Students have to answer to the following questions : How many birds you have to translate to obtain this image? Describe the translations http://www.tess-elation.co.uk/birds---an-introduction LESSON 6 Activity 1 http://www.geogebra.org/en/wiki/index.php/Transform ations_English

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# ISOMETRIES IN THE COORDINATE PLANE