8.2.6Ma


 * Grade: 8 Unit: 2 Week: 6 Dates: 11/5-11/7 (3 days) **
 * Content: Similar Triangles and Similar Triangles with Slope **


 * Theme Essential Question: **
 * How does mathematical reasoning apply to the attributes of two- and three- dimensional figures as seen in everyday life? **


 * Essential Questions: **
 * ** How can you determine when two triangles are similar? **


 * Standards **
 * ** 8. G.5. ** Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.


 * Note: This standard has been divided into three lessons to allow for ample time for students to obtain fluency. **


 * Objectives **
 * The student will construct a viable argument for Angle-Angle Similarity.
 * The student will use the Angle-Angle Similarity to find missing measures in similar triangles.


 * Reflections and/or Comments from your PCSSD 8th Grade Curriculum Team **

As you can tell from the objectives, Mathematical Practice #3 is utilized extensively. Due to the amount of exploration and investigation required in these last lessons of unit 2, we have decided to postpone the introduction of the last two Mathematical Practices. They will be developed in Unit 3, functions.

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


 * Assessment **
 * Product **
 * Students should continue reviewing the problem solving connections on page 137-140 in the OnCore book. The final presentation of the “Where in the park is Xander?” can be presented as a PowerPoint, poster, etc. This will conclude the end of this unit.


 * Key Questions **
 * How is the concept of similar triangles applied to real world problems?


 * Observable Student Behaviors **
 * The student can support the development of the concept of AA similarity and slope using a viable argument.
 * The students can apply the concepts of similarity to real world problems.

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 **

Similarity, congruent, theorem, corresponding, ratio, proportion
 * Vocabulary **

Gizmo Lessons Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. Derive the sum of the angles of a polygon by dividing the polygon into triangles and summing their angles. Vary the number of sides and determine how the sum of the angles changes. Dilate the polygon to see that the sum is unchanged. (Student Exploration Sheet & Teacher Guide Available) Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Measure the angles of a triangle and find the sum. Then reshape and resize the triangle and confirm that the sum of angle measures is the same for all triangles. Highly Recommended: 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 5-3 p. 121-124
 * ABC Mastering the Common Core in Mathematics Chapter 12-1 through 12-2, p. 185-188
 * ** Investigating Angle Theorems-Activity A **
 * ** Polygon Angle Sum-Activity B **
 * ** Similar Polygons **
 * ** Triangle Angle Sum-Activity A **
 * __ Teaching the Common Core Math Standards with Hands-On Activities __ by Judith Muschla
 * 8.G.5- Activity 4 p. 223
 * JBHM-7th GP3 (p. 315-350)
 * JBHM-8th GP3 (p. 106 and corresponding notes)
 * Glencoe Pre-Algebra Similar Triangles and Indirect Measurement 9-7 (p. 471-475)
 * Glencoe Geometry Similar Triangles 6-3 (298-306)
 * @http://illustrativemathematics.org/illustrations/59 (G.5)
 * @http://illustrativemathematics.org/illustrations/56 (G.5)


 * Diverse Learners **
 * Odyssey (teacher discretion)
 * Skills Tutor (teacher discretion)
 * Math’scool: Unit B Module 8

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

** 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 || ||
 * Terminology for Teachers **
 * ||  ** Multicultural Concepts **

Lesson Plan in Word Format (Click Cancel if asked to Log In)


 * 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 **
 * http://nlvm.usu.edu/ National Library of Virtual Manipulatives


 * Games **
 * www.sumdog.com

Discovery Learning []
 * Videos **

SMART Board Resource Website SMART Board lesson search engine
 * SMART Board Lessons, Promethean Lessons **


 * Websites **
 * @http://illustrativemathematics.org/standards/k8 PARCC Online (released items)
 * Discovery Education (Discovering Math: Advanced: Number Concepts) Contains 15 different segments you can choose from. GREAT HOOK FOR YOUR LESSONS!!
 * @http://www.khanacademy.org/math Online tutorials
 * @http://www.tli.net/ TLI Quiz Builder


 * Other Activities, etc. **

Language Arts ||=  ||=   ||= Week 1 ||= Week 2 ||= Week 3 ||= Week 4 ||= Week 5 ||= Week 6 || Week 7 || Week 8 || Matrix ||=  ||= Week 1 ||= Week 2 ||= Week 3 ||= Week 4 ||= Week 5 ||= Week 6 || Week 7 || Week 8 || Home K-2 ||= Home 3-6 ||= Home 6-8 ||= Unit 1 ||= Unit 2 ||= Unit 3 ||= Unit 4 ||= Unit 5 ||= Unit 6 ||  ||   ||
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