8.5.4Ma


 * Grade: 8 Unit: 5 Week:4 **
 * Content: Problem Solving Connections **
 * Dates: 4/1-4/5 **

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


 * Essential Questions: **
 * How are coordinates used to describe the results of translations, reflections, and rotations?
 * 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?
 * How do dilations affect two-dimensional figures in the coordinate plane?
 * What is the connection between transformations and similar figures?


 * 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.
 * ** 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.


 * Objective: **
 * 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.
 * The student will verify the properties of a figure that are preserved under a translation, reflection or rotation.
 * The student will combine transformations and compare the size and shape of the final image.
 * The student will analyze and evaluate two-dimensional figures by rotation, reflection or translation to determine if they are congruent.
 * 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.


 * 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 are the coordinates of a pre-image affected by a translation, reflection, and rotation?
 * How do you verify experimentally the properties of rotations, reflections, and translations?
 * 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?
 * 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 dilations affect congruent and similar figures?


 * Observable Student Behaviors **
 * Student can perform the transformation and describe the effects of a translation, reflection, and rotation.
 * The student will provide a viable argument to justify the properties of rotations, reflections, and translations.
 * The student will compare the size and shape of the final image that has underwent combined transformations.
 * The student will connect transformations with congruency.
 * 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 JBHM 8th GP3 p. 63-70, 73-78, 83-103
 * Suggested Activities ** [see Legend to highlight MCO and HYS]
 * Houghton Mifflin OnCore Mathematics Middle School Grade 8 Problem Solving Connections Unit 4, p. 105-108, Test Prep p. 109-110
 * ABC Mastering the Common Core in Mathematics Chapter 9 Review and Test p. 144-148
 * 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.
 * Rotations, Reflections and Translations
 * Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure.
 * Similar Figures-Activity A
 * 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.
 * Translations
 * Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation.
 * 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.
 * 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.
 * G.1 p. 201
 * G.2 Activity 1 p. 205, Activity 2 p. 206
 * G.3 p. 210
 * G.4 p. 215

Glencoe Algebra 1- p. 197-203 @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.
 * Highly Recommended:


 * Diverse Learners **
 * Odyssey (teacher discretion)
 * <span style="font-family: 'Arial','sans-serif'; font-size: 15px;">Skills Tutor (teacher discretion)
 * <span style="font-family: 'Arial','sans-serif'; font-size: 15px;">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

** 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)
 * Terminology for Teachers **
 * ** 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) **<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.
 * ** Transformations- Dilation (NLVM) **<span style="font-family: 'Verdana','sans-serif'; font-size: 15px;">Dynamically interact with and see the result of a dilation transformation.
 * ** Tranformations - Reflections (NLVM) **<span style="font-family: 'Verdana','sans-serif'; font-size: 15px;">Dynamically interact with and see the result of a reflection transformation.
 * ** Transformations- Rotation (NLVM) **<span style="font-family: 'Verdana','sans-serif'; font-size: 15px;">Dynamically interact with and see the result of a rotation transformation.
 * ** Transformations- Translation (NLVM) **<span style="font-family: 'Verdana','sans-serif'; font-size: 15px;">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/

The objectives are to translate figures in the coordinate plane and to describe the translation. The objectives are to identify, describe and perform reflections in the coordinate plane. Use pattern blocks to explore the relationships between a variety of polygons. Explore similar and congruent shapes. Explore flips, slides, and turns. Rotations, Translations, Reflections, and Dilations 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. 1 Translation
 * 8.G.1 Reflection
 * 8.G. 2 Polygons and Patten Blocks
 * 8.G. 2 Rotations, Translations, Reflections, and Dilations/Math by Ed
 * 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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