8.2.5Ma


 * Grade: 8 Unit: 2 Week: 5 Dates: 10/29-11/2 **
 * Content: Triangle Angle Theorems **


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


 * Essential Questions: **
 * ** What can you conclude about the measures of angles of a triangle? **


 * 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 use the sum of the interior angle measures in a triangle to calculate missing angle measurements.
 * The student will use an informal argument to explain the sum of the interior angle measurement is 180 °.
 * The student will develop an informal argument and use their argument to apply the relationship between the exterior angle of a triangle with their corresponding remote interior angles.

Students should continue to approach this lesson as indicated in the discussion for lesson 2-4.
 * 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. **
 * (Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2011 ) **

By using three copies of the same triangle labeled and placed so that the three different angles form a straight line, students can: explore the relationships of the angles, learn the types of angles (interior, exterior, alternate interior, alternate exterior, corresponding, same side interior, same side exterior), and Explore the parallel lines, triangles and parallelograms formed.


 * 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.
 * Students can also take “Where in the park is Xander?” and extend and/or recreate a new scenario.


 * Key Questions **
 * Why does the sum of the interior angles of a triangle equal 180 ° ?
 * Why does an exterior angle of a triangle equal the sum of the remote interior angles?
 * How do you apply the sum of the interior angles of a triangle equal 180 ° ?
 * How do you apply that an exterior angles of a triangles equal the sum of the remote interior angles


 * Observable Student Behaviors **
 * The student can provide a viable argument to justify the facts about the angle sum and exterior angles of triangles.
 * The student can determine the measurement of the interior and exterior angles of triangles.

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 **

Interior angles, Exterior angles, Remote interior angles
 * 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:
 * Suggested Activities ** [see Legend to highlight MCO and HYS]
 * On Core Mathematics Unit 5-2, p. 117-120
 * ABC Mastering the Common Core in Mathematics Chapter 11-1 through 11-2, p. 167-169
 * ** 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 1(interior) p. 220, Activity 2 (exterior) p. 221
 * JBHM-7th GP3 (p. 281-314)
 * Glencoe Geometry Angles of Triangles (Angle Sum Theorem) 4-2 (p.185)
 * Glencoe Geometry Angles of Triangles (Exterior Angle Theorem) 4-2 (p.186)
 * @http://illustrativemathematics.org/illustrations/59 (G.5)
 * @http://illustrativemathematics.org/illustrations/56 (G.5)

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.


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


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


 * 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 **
 * 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. **

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