8.5.2Ma


 *  Grade: 8 Unit: 5 Week: 2 **
 *  Content: Properties of Transformations **
 *  Transformations and Congruency **
 *  Dates: 3/11-3/14 (4 days) **

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


 *  Essential Questions: **
 *  What properties of a figure are preserved under a translation, reflection, or rotation?
 *  What is the connection between transformations and figures that have the same shape and size?


 *  Standards **
 * ** 8.G.1 ** Verify experimentally the properties of rotations, reflections, and translations:
 * a. Lines are taken to lines, and line segments to line segments of the same length.
 * b. Angles are taken to angles of the same measure.
 * c. Parallel lines are taken to parallel lines.
 * ** 8.G.2  ** Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.


 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Objectives **
 * <span style="font-family: arial,helvetica,sans-serif;">The student will verify the properties of a figure that are preserved under a translation, reflection or rotation.
 * <span style="font-family: arial,helvetica,sans-serif;">The student will combine transformations and compare the size and shape of the final image.
 * <span style="font-family: arial,helvetica,sans-serif;">The student will analyze and evaluate two-dimensional figures by rotation, reflection or translation to determine if they are congruent.

<span style="font-family: arial,helvetica,sans-serif; font-size: 15px;">In this lesson, it is essential that students use various approaches to explore, study, and develop logical arguments in their investigations of properties of transformation. It is imperative students use such items as rulers and protractors, patty paper, TI84 geometry app (Cabri Jr.), and/or software such as GeoGebra or Geometer’s Sketchpad.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Reflections and/or Comments from your PCSSD 8th Grade Curriculum Team **

It is recommended that every student be exposed to the works of MCEscher. We have added an alternative product for the **struggling-learner** having difficulties with the creation of their individual MC Escher design.


 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Assessment **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Product **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> [|Mathematics behind the Art of MC Escher] **<span style="font-family: arial,helvetica,sans-serif; font-size: 15px;">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:
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Week 1: Students are to explore the principles of MC Escher.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Week 2: Students are to study the development of design and prepare their initial sketch.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Week 3: Students are finalizing their design work.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Week 4: Museum Walk.

__<span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Alternative Product: Park the Car __ <span style="font-family: arial,helvetica,sans-serif; font-size: 15px;">Students are to plot a car 2 units by 4 units in quadrant I, they are to plot a garage 1 unit by 2 unit in quadrant III. They are to use each transformation at least once (translation, rotation, reflection, and dilation) to park their car into the garage. Each translation should be noted using correct notation with corresponding coordinates.


 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Key Questions **
 * <span style="font-family: arial,helvetica,sans-serif;">How do you verify experimentally the properties of rotations, reflections, and translations?
 * <span style="font-family: arial,helvetica,sans-serif;">How can a two-dimensional figure be congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations?


 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Observable Student Behaviors **
 * <span style="font-family: arial,helvetica,sans-serif;">The student will provide a viable argument to justify the properties of rotations, reflections, and translations.
 * <span style="font-family: arial,helvetica,sans-serif;">The student will compare the size and shape of the final image that has underwent combined transformations.
 * <span style="font-family: arial,helvetica,sans-serif;">The student will connect transformations with congruency.

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. ||
 * **<span style="font-family: 'Gotham-Medium','sans-serif'; font-size: 15px;">Mathematical Practices **

<span style="font-family: arial,helvetica,sans-serif; font-size: 15px;">Gizmo Lessons
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Suggested Activities **<span style="font-family: arial,helvetica,sans-serif; font-size: 15px;"> [see Legend to highlight MCO and HYS]
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Houghton Mifflin OnCore Mathematics Middle School Grade 8 Unit 4.2-4.3, p. 95-98
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> ABC Mastering the Common Core in Mathematics 9.3-9.5, p. 135-141 and 12.3 189-194
 * <span style="font-family: Arial,sans-serif; font-size: 15px;">8.G.1
 * 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.
 * <span style="font-family: Arial,sans-serif; font-size: 15px;">Rotations, Reflections and Translations
 * <span style="font-family: 'Arial','sans-serif'; font-size: 15px;">Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure.
 * <span style="font-family: Arial,sans-serif; font-size: 15px;">Similar Figures-Activity A
 * <span style="font-family: 'Arial','sans-serif'; font-size: 15px;">Vary the scale factor and rotation of an image and compare it to the pre-image. Determine how the angle measures and side lengths of the two figures are related.
 * <span style="font-family: Arial,sans-serif; font-size: 15px;">Translations
 * <span style="font-family: 'Arial','sans-serif'; font-size: 15px;">Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation.
 * __ Teaching the Common Core Math Standards with Hands-On Activities __ by Judith Muschla
 * G.1 p. 201
 * G.2 Activity 1 p. 205, Activity 2 p. 206
 * JBHM 8th GP3-p. 63-70, 73-78, 83-103
 * JBHM 8th GP3-p. 63-70, 73-78, 83-103


 * Glencoe Pre-Algebra – p. 500-504


 * Glencoe Algebra 1- p. 197-203

<span style="font-family: arial,helvetica,sans-serif; font-size: 15px;">@http://illustrativemathematics.org/illustrations/646 (G.2)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.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Highly Recommended:


 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Diverse Learners **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"><span style="font-family: 'Arial','sans-serif'; font-size: 15px;">Odyssey (teacher discretion)
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"><span style="font-family: 'Arial','sans-serif'; font-size: 15px;">Skills Tutor (teacher discretion)
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"><span style="font-family: 'Arial','sans-serif'; font-size: 15px;">Math’scool: Unit B Module 11

<span style="font-family: arial,helvetica,sans-serif; font-size: 15px;">Suggested:
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Homework **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;">** @http://www.kutasoftware.com/free.html ** to print assignments on variety of topics
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> See appropriate Glencoe, OnCore, JBHM, and ABC materials


 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> 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 **


 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Resources **


 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Professional Texts **

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 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Literary Texts **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;">

<span style="font-family: arial,helvetica,sans-serif; font-size: 15px;">@http://schools.nyc.gov/Academics/CommonCoreLibrary/SeeStudentWork/default.htm
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 15px;">**Informational Texts** **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> See New York Common Core Aligned Task (other resources)

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 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Art, Music, and Media **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;">


 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Manipulatives **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;">** Transformations- Composition (National Library of Virtual Manipulatives) **<span style="font-family: 'Verdana','sans-serif'; font-size: 15px;">Explore the effect of applying a composition of translation, rotation, and reflection transformations to objects.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;">** Transformations- Dilation (NLVM) **<span style="font-family: 'Verdana','sans-serif'; font-size: 15px;">Dynamically interact with and see the result of a dilation transformation.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;">** Tranformations - Reflections (NLVM) **<span style="font-family: 'Verdana','sans-serif'; font-size: 15px;">Dynamically interact with and see the result of a reflection transformation.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;">** Transformations- Rotation (NLVM) **<span style="font-family: 'Verdana','sans-serif'; font-size: 15px;">Dynamically interact with and see the result of a rotation transformation.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;">** Transformations- Translation (NLVM) **<span style="font-family: 'Verdana','sans-serif'; font-size: 15px;">Dynamically interact with and see the result of a translation transformation.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;">** Mathematics behind the Art of MC Escher ** Explorations of all transformations using principles of MC Escher
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> http://nlvm.usu.edu/ National Library of Virtual Manipulatives
 * Algebra: Function Machine, Function Transformations
 * Graphing calculators

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 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Games **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;">


 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Videos **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Discovery Learning @http://www.discoveryeducation.com/

<span style="color: #333333; font-family: arial,helvetica,sans-serif;"> The objectives are to translate figures in the coordinate plane and to describe the translation. <span style="color: #333333; font-family: arial,helvetica,sans-serif; font-size: 15px;">The objectives are to identify, describe and perform reflections in the coordinate plane. <span style="color: #333333; font-family: arial,helvetica,sans-serif; font-size: 15px;">Use pattern blocks to explore the relationships between a variety of polygons. Explore similar and congruent shapes. Explore flips, slides, and turns. <span style="color: #333333; font-family: arial,helvetica,sans-serif;"> Rotations, Translations, Reflections, and Dilations **<span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Websites **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> SMART Board Lessons, Promethean Lessons  **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> [|Smartboard Resource Website] Smartboard lesson search engine
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"><span style="font-family: arial,helvetica,sans-serif; font-size: 15px;">8.G. 1 <span style="color: #333333; font-family: arial,helvetica,sans-serif; font-size: 15px;">Translation
 * 8.G.1 Reflection
 * 8.G. 2 Polygons and Patten Blocks
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 15px;">8.G. 2 <span style="color: #333333; font-family: arial,helvetica,sans-serif; font-size: 15px;">Rotations, Translations, Reflections, and Dilations/Math by Ed
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> @http://illustrativemathematics.org/standards/k8 PARCC Online (released items)
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> http://www.khanacademy.org Online tutorials
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> @http://www.tli.net/ TLI Quiz Builder


 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Other Activities, etc. **

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