8.5.3Ma


 * Grade: 8 Unit: 5 Week: 3 **
 * Content: Dilations **
 * Transformations with Symmetry **
 * Dates: 3/25-3/28 **

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


 * Essential Questions: **
 * How do dilations affect two-dimensional figures in the coordinate plane?
 * What is the connection between transformations and similar figures?


 * Standards **


 * ** 8. G.3 Describe ** the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
 * ** 8.G.4 ** **Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them**.


 * Objectives **
 * The student will use coordinates to describe and explain the results of dilation.
 * The student will calculate or determine the scale factor of dilation.
 * The student will analyze and evaluate two-dimensional figures by rotation, reflection, translation, and dilation to determine if they are congruent or similar.

In this lesson, it is essential that students use various approaches to explore, study, and develop logical arguments in their investigations of properties of dilation. It is imperative students use such items as 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 **

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


 * 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 finalizing their design work.
 * Week 4: Museum Walk.

__ Alternative Product: Park the Car __ 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.


 * Key Questions **
 * How do you use coordinates to describe and explain the result of dilation?
 * How do you calculate or determine the scale factor of a dilation?
 * How do transformations and dialations affect congruent and similar figures?


 * Observable Student Behaviors **
 * The student can find the coordinates and explain the results of a dilation.
 * The student can calculate or determine the scale factor of a dilation.
 * The student provided a viable argument for the affect of transformations and dilations on congruent and similar figures.

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 **

Gizmo Lessons __ Teaching the Common Core Math Standards with Hands-On Activities __ by Judith Muschla Glencoe Pre-Algebra – p. 512 Glencoe Algebra 1- p. 197-203 Nothing available at this timeThe 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 4.4, p. 99-102
 * ABC Mastering the Common Core in Mathematics, Chapter 9.7 p142-143 and Chapter 12.4 p.195-199
 * 8.G.3
 * Dilations
 * Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in (x, y) form and in matrix form.
 * G.3 p. 210
 * G.4 p. 215
 * 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. Students have a bit of background knowledge on similar figures. This lesson takes their knowledge and applies it to the real world and how we use proportions and similar figures. Rotations, Translations, Reflections, and Dilations
 * SMART Board Lessons, Promethean Lessons **
 * [|Smartboard Resource Website] Smartboard lesson search engine
 * 8.G. 3 Symmetry
 * 8.G. 3 Rotation
 * 8.G. 3 Translation
 * 8.G.4 Similar Figures, Indirect Measurement and Scale Drawings
 * 8.G.4 Rotations, Translations, Reflections, and Dilations/Math by Ed


 * 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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