8.5.1Ma


 * Grade: 8Unit: 5 Week: 1**
 * Content:Translations, Reflections, and Rotations**
 * Dates: 3/4-3/8**


 * Theme Essential Question **** : **
 * How are transformations a visual representation of an object moving in our three-dimensional world? **

How are coordinates used to describe the results of translations, reflections, and rotations?
 * Essential Questions: **


 * Standards **
 * ** 8.G.3 ** Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.


 * Objectives **
 * The student will apply translational moves to pre-images and describe these moves by adjusting the shift in the x- and y- coordinate. This will include using translational notation.
 * The student will apply reflectional moves to pre-images and describe these moves by adjusting the shift in the x- and y- coordinate. This will include reflections over x- axis, y-axis, the line y = x, and the line y = -x.
 * The student will apply rotational moves to pre-images and describe these moves by adjusting the shift in the x- and y- coordinate. This will include rotation about a point other than the origin.

Students should be provided the opportunity to explore and investigate the transformations and relationships using such items as rules and protractors, patty paper, TI84 geometry app (Cabri Jr.), and/or software such as GeoGebra or Geometer’s Sketchpad.
 * Reflections and/or Comments from your PCSSD 8th Grade Curriculum Team **

@http://www.azed.gov/wp-content/uploads/PDF/MathGr8.pdf
 * Background Information **
 * Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials. **

Transformational geometry is about the effects of rigid motions, rotations, reflections and translations on figures. Initial work should be presented in such a way that students understand the concept of each type of transformation and the effects that each transformation has on an object before working within the coordinate system. For example, when reflecting over a line, each vertex is the same distance from the line as its corresponding vertex. This is easier to visualize when not using regular figures. Time should be allowed for students to cut out and trace the figures for each step in a series of transformations. Discussion should include the description of the relationship between the original figure and its image(s) in regards to their corresponding parts (length of sides and measure of angles) and the descriptionof the movement, including the atributes of transformations (line of symmetry, distance to be moved, center of rotation, angle of rotationand the amount of dilation).The case of distance – preserving transformation leads to the idea of congruence It is these distance-preserving transformations that lead to the idea of congruence. Work in the coordinate plane should involve the movement of various polygons by addition, subtraction and multiplied changes of the coordinates. For example, add 3 to x, subtract 4 from y, combinations of changes to x and y, multiply coordinates by 2 then by 12. Students should observe and discuss such questions as ‘What happens to the polygon?’ and ‘What does making the change to all vertices do?’. Understandings should include generalizations about the changes that maintain size or maintain shape, as well as the changes that create distortions of the polygon (dilations). Example dilations should be analyzed by students to discover the movement from the origin and the subsequent change of edge lengths of the figures. Students should be asked to describe the transformations required to go from an original figure to a transformed figure (image). Provide opportunities for students to discuss the procedure used, whether different procedures can obtain the same results, and if there is a more efficient procedure to obtain the same results. Students need to learn to describe transformations with both words and numbers. Through understanding symmetry and congruence, conclusions can be made about the relationships of line segments and angles with figures. Students should relate rigid motions to the concept of symmetry and to use them to prove congruence or similarity of two figures. Problem situations should require students to use this knowledge to solve for missing measures or to prove relationships. It is an expectation to be able to describe rigid motions with coordinates.
 * (Taken from [|Ohio Dept of Education Mathematics Model Curriculum 6-28-2011] –page 17) **


 * Assessment **
 * Product **
 * [|Mathematics behind the Art of MC Escher] ** Explore the transformations using principles of MC Escher from this website, and have students work to create a similar art project with examples of each type of transformation included.This will be an ongoing project over several weeks. Recommended schedule for project development:
 * Week 1: Students are to explore the principles of MC Escher.
 * Week 2: Students are to study the development of design and prepare their initial sketch.
 * Week 3: Students are finalize their design work.
 * Week 4: Museum Walk.


 * Key Questions **
 * How are the coordinates of a pre-image affected by a translation, reflection, and rotation?


 * Observable Student Behaviors **
 * The student can perform the transformation and describe the effects of a translation, reflection, and rotation.

1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||
 * **Mathematical Practices **

Transformation, pre-image, image, translation, reflection, line of reflections, and rotation
 * Vocabulary **

Gizmo Lessons __ Teaching the Common Core Math Standards with Hands-On Activities __ by Judith Muschla JBHM 8th GP3 p. 63-70, 73-78, 83-103 Glencoe Pre-Algebra- p. 506-511 Glencoe Algebra 1- p. 197-203 Nothing available at this time (G.3)The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
 * Suggested Activities ** [see Legend to highlight MCO and HYS]
 * Houghton Mifflin OnCore Mathematics Middle School Grade 8 Unit 4.1, p. 91-94
 * ABC Mastering the Common Core in Mathematics 9.3-9.5, p.135-141
 * 8.G.3
 * Reflections
 * Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated.
 * Translations
 * Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation.
 * p. 210
 * Highly Recommended:


 * Diverse Learners **
 * Odyssey (teacher discretion)
 * Skills Tutor (teacher discretion)
 * Math’scool: Unit B Module 11

Suggested:
 * Homework **
 * @http://www.kutasoftware.com/free.html to print assignments on variety of topics
 * See appropriate Glencoe, OnCore, JBHM, and ABC materials


 * Terminology for Teachers **

** E ** thnicity/**C**ulture | **I**mmigration/**M**igration | **I**ntercultural **C**ompetence | **S**ocialization | **R**acism/**D**iscrimination ** High Yield Strategies ** ** S ** imilarities/**D**ifferences | **S**ummarizing/**N**otetaking | **R**einforcing/**R**ecognition | **H**omework/**P**ractice | ** N ** on-**L**inguistic representation | **C**ooperative **L**earning | **O**bjectives/**F**eedback | ** G ** enerating-**T**esting **H**ypothesis | **C**ues, **Q**uestions, **O**rganizers  || Lesson Plan in Word Format (Click Cancel if asked to Log In)
 * ** Multicultural Concepts **


 * Resources **


 * Professional Texts **


 * Literary Texts **

@http://schools.nyc.gov/Academics/CommonCoreLibrary/SeeStudentWork/default.htm
 * Informational Texts****
 * See New York Common Core Aligned Task (other resources)


 * Art, Music, and Media****


 * Manipulatives **
 * Transformations- Composition (National Library of Virtual Manipulatives) Explore the effect of applying a composition of translation, rotation, and reflection transformations to objects.
 * Transformations- Dilation (NLVM) Dynamically interact with and see the result of a dilation transformation.
 * Tranformations - Reflections (NLVM) Dynamically interact with and see the result of a reflection transformation.
 * Transformations- Rotation (NLVM) Dynamically interact with and see the result of a rotation transformation.
 * Transformations- Translation (NLVM) Dynamically interact with and see the result of a translation transformation.
 * Mathematics behind the Art of MC Escher Explorations of all transformations using principles of MC Escher
 * http://nlvm.usu.edu/ National Library of Virtual Manipulatives
 * Algebra: Function Machine, Function Transformations
 * Graphing calculators


 * Games **


 * Videos **
 * Discovery Learning @http://www.discoveryeducation.com/

This Smart Board activity explores the concepts of line symmetry and rotational symmetry. The closure of the lesson has students create their own logo for a fictitious company. The objectives are to identify and perform rotations in the coordinate plane. The objectives are to translate figures in the coordinate plane and to describe the translation.
 * SMART Board Lessons, Promethean Lessons **
 * [|Smartboard Resource Website] Smartboard lesson search engine
 * 8.G. 3 Symmetry
 * 8.G. 3 Rotation
 * 8.G. 3 Translation


 * Websites **
 * @http://illustrativemathematics.org/standards/k8 PARCC Online (released items)
 * http://www.khanacademy.org Online tutorials
 * @http://www.tli.net/ TLI Quiz Builder


 * Other Activities, etc. **

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