8.2.4Ma


 * Grade: 8 Unit: 2 Week: 4 Dates: 10/22-10/26 **
 * Content: Parallel Lines Cut by a Transversal **


 * 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 angles formed by parallel lines that are cut by a transversal? **


 * 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 special angle relationships that are formed when parallel lines are intersected by a transversal to find the values of the angles.
 * The student will use their knowledge to determine if lines cut by a transversal are parallel or non-parallel lines.


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

At the completion of this lesson, the students will have worked with six of the eight Mathematical Practices. We must continue to encourage the children’s thinking to help make these practices part of their way of approaching mathematics.

Students should be provided the opportunity to explore and investigate the special angle relationships, using such items as rulers and protractors, patty paper, TI84 geometry app (Cabri Jr.), and/or software such as GeoGebra or Geometer’s Sketchpad. It is our intention to give students resources that they can add to their toolbox and they can use as needed.

We need to be prepared to review the following:
 * How to use a protractor?
 * Classifying the types of lines (i.e. parallel, perpendicular, intersect, etc).
 * Classifying angles (i.e., acute, scalene, etc).
 * Naming lines (segments, rays, and angles).
 * Define complementary, supplementary, and adjacent angles.

We suggest that you select problems dealing with finding angles of parallel lines that use the solving equation techniques.



@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 ) **

In Grade 7, students develop an understanding of the special relationships of angles and their measures (complementary, supplementary, adjacent, and vertical). Now, the focus is on learning about the sum of the angles of a triangle and using it to, find the measures of angles formed by transversals (especially with parallel lines), find the measures of exterior angles of triangles and informally prove congruence.

Further examples can be explored to verify these relationships and demonstrate their relevance in real life.

Informal arguments are justifications based on known facts and logical reasoning. Students should be able to appropriately label figures, angles, lines, line segments, and congruent parts. Students are expected to use logical thinking, expressed in words using correct terminology. They are NOT expected to use theorems, axioms, postulates or a formal format of proof as in two-column proofs.


 * Assessment **
 * Product **
 * Students should begin 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 **
 * Given parallel lines cut by a transversal, which angle pairs are congruent and which angle pairs are supplementary?
 * Why are angles of parallel lines cut by a transversal either congruent or supplementary, only?


 * Observable Student Behaviors **
 * The student can find angles formed by parallel lines cut by a transversal.
 * The student can identify angles for lines cut by a transversal.
 * The students can use parallel lines cut by transversals to find angles.
 * By using the angles formed by lines cut by a transversal, the student can determine if the lines are/are not parallel lines.

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 **

Transversal, Exterior, Interior, Corresponding angles, Alternate interior angles, alternate exterior angles, Same-side interior angles, vertical angles, supplementary angles, complementary angles, congruent.
 * 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]
 * On Core Mathematics Unit 5-1, p. 113-116
 * Introductory Unit- ABC Mastering the Common Core in Mathematics Chapter 10-1 through 10-6, p.149-159
 * ABC Mastering the Common Core in Mathematics Chapter 10-7 through 10-8, p. 160-162
 * ** 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 3 p. 222
 * JBHM-7th GP3 (p. 281-314)
 * Glencoe Pre-Algebra Line and Angle Relationships 10-1 (p. 492)
 * Glencoe Geometry Parallel Lines and Transversals (p.126)
 * @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


 * 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 Text **


 * 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


 * Videos **
 * Discovery Learning @http://www.discoveryeducation.com/

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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