7.4.3Ma


 * Grade: 7 Unit: 4 Week: 3 **
 * Content: Cross Sections **
 * Angle Pairs **
 * Dates: 2/4 – 2/8 **


 * __ Theme Essential Question __**** : **
 * How can you use formulas and geometry to solve real-world and mathematical problems? **


 * __ Essential Questions __**** : **
 * How can you identify cross sections of three-dimensional figures?
 * How can you use angle pairs to solve problems?


 * __ Standards __**** : **
 * ** 7.G. 3 ** Describe the two-dimensional figures that results from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
 * ** 7.G.5 ** Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to solve simple equations for an unknown angle in a figure.


 * __ Objectives __**** : **
 * 1) The student will identify figures formed by cross sections.
 * 2) The student will sketch cross sections of three dimensional figures.
 * 3) The student will identify and construct supplementary, complementary, vertical and adjacent angles.
 * 4) The student will apply knowledge of supplementary, complementary, vertical and adjacent angles to solve multi-step problems and simple equations for an unknown angle.

This week will focus on two different concepts; cross-sections of three dimensional figures and angle pairs. In order to facilitate student product, //Teaching the Common Core Math Standards with Hands-on Activities,// will be used as the primary resource. The discussion provided below from Ohio Department of Education will be very useful in the development of lesson and activities.
 * __ Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team __**

Recommended: For a quick overview of the standard(s) to be addressed in this Unit, see Arizona’s Content Standards Reference Materials at[|**http://www.azed.gov/educator-certification/**]
 * __ Background: __**


 * Taken from __Ohio Dept of Education Mathematics Model Curriculum 6-28-2022__ **

Cross-Sections: Slicing three-dimensional figures helps develop three-dimensional visualization skills. Students should have the opportunity to physically create some of the three-dimensional figures, slice them in different ways, and describe in pictures and words what has been found. For example, use clay to form a cube, then pull string through it in different angles and record the shape of the slices found. Challenges can also be given: “See how many different two-dimensional figures can be found by slicing a cube” or “What three-dimensional figure can produce a hexagon slice?” This can be repeated with other three-dimensional figures using a chart to record and sketch the figure, slices and resulting two-dimensional figures.

Angle Pairs: In previous grades, students have studied angles by type according to size: acute, obtuse and right, and their role as an attribute in polygons. Now angles are considered based upon the special relationships that exist among them: supplementary, complementary, vertical and adjacent angles. Provide students the opportunities to explore these relationships first through measuring and finding the patterns among the angles of intersecting lines or within polygons, then utilize the relationships to write and solve equations for multi-step problems.

//Teaching the Common Core Math Standards with Hands-on Activities:// Use Acitivity #2, Slicing Figures, page 120 Use Activity, What’s the Angle?, page 124
 * __ Assessment __**** : **
 * Product **
 * 1) Cross-Sections:
 * Allow students to work in groups and assign a different shape to each group.
 * Recommended shapes rectangular prism, cone, cylinder, sphere, triangular pyramid, rectangular pyramid. (other prisms and pyramids as needed).
 * Slice shape to find as many cross sections, as noted in the activity instructions, and present their cross sections to the class.
 * If a student(s) have the aptitude to prepare sketches, allow this student(s) to roam the class producing sketches of the cross sections to be use as classroom displays.
 * 1) Angle Pairs:
 * Conduct the activity and display student work as indicated.


 * Key Questions **
 * What geometric figures are formed from a cross section of a three dimensional shape?
 * What are the characteristics of supplementary, complementary, vertical and adjacent angles?
 * How do you apply supplementary, complementary, vertical and adjacent angles to solve multi-step problems and simple equations for an unknown angle?


 * Observable Student Behaviors **
 * The student can viualize and describe the two-dimensional figures that results from slicing three-dimensional shapes.
 * The student can use and apply supplementary, complementary, vertical, and adjacent angles in a multi-step problem to solve simple equations for an unknown angle.

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 **


 * __ Vocabulary __**** : **

Congruent angles Vertical angles Adjacent angles Complementary angles Congruent angles Supplementary angles ||
 * ** Math ** ||
 * Intersection Cross section

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. @http://www.discoveryeducation.com/free-puzzlemaker/?CFID=1276695&CFTOKEN=75709576
 * __ Suggested Activities __** :
 * // Houghton Mifflin On Core Mathematics Middle School // Grade 7
 * Unit 4-3, Cross Sections, p. 97-98
 * Unit 4-4, Angle Pairs, p. 99-102
 * ABC //Mastering the Common Core in Mathematics//
 * Solid Figures, Chapter 13.1, p. 159
 * Cross Sections, Chapter 13.2, p. 160-161
 * Adjacent angles, Chapter 10.2, p. 118
 * Vertical angles, Chapter 10.3, p. 119
 * Complementary and Supplementary Angles, Chapter 10.4, p. 120
 * Finding angles in figures, Chapter 10.5, p. 121
 * Chapter 10 Review and Test, p. 122-123
 * Gizmo Correlation:
 * 7.G.5
 * Investigating Angles Theorems-Activity A
 * Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure.
 * // Teaching the Common Core Math Standards with Hands-On Activities, //
 * // 7.G.3 – Activity #1, p.119 //
 * // 7.G.3 – Activity #2, p.120 //
 * // 7.G.5 – Activity, p.124 //
 * **Highly Recommended** None Available at this time
 * Glencoe, Pre-Algebra, Chapter 11.4, p. 581
 * Glencoe, Geometry, p. 639, 640, 641, 648
 * Create a puzzle with unit vocabulary words.


 * Diverse Learners **
 * Odyssey (teacher discretion)
 * Skills Tutor (teacher discretion)


 * __ Homework __**** : ( ** Teachers Discretion**)**
 * See appropriate Glencoe On Core, JBHM and ABC Materials under Suggested Activities


 * __ 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: __**

@http://sci.tamucc.edu/~eyoung/geometry_literature.html @http://sci.tamucc.edu/~eyoung/measure_literature.html Click on the following link, @http://libguides.nl.edu/mathinchildrenslit, then look under __Math and Literature Bibliographies__. Many books include websites with __lesson ideas__. @http://sci.tamucc.edu/~eyoung/middle_school_literature.html @http://sci.tamucc.edu/~eyoung/Literature%20webpages/Leonor/index.html @http://sci.tamucc.edu/~eyoung/literature.html
 * __ Literary Texts __**
 * Geometry and Literature Titles:
 * Measurement and children'e Literature/Ratios
 * Mathematics in Children's Literature:Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annontated Lists of Children's Literature including the math concepts and grade levels.
 * ** Middle & High School: Literature in Mathematics **
 * ** Lesson Plans for Using Literature in Middle and High School Mathematics (developed by Leonor and edited by Elaine) **
 * Miscellaneous Math and Children's Literature


 * Informational Texts **


 * Art, Music, and Media **


 * __ Manipulatives: __**
 * http://nlvm.usu.edu Geometry software Versa Tiles
 * Cross Sections
 * Slicing Sections
 * String
 * Modeling Clay
 * Grid paper
 * Nets
 * http://www.learner.org/courses/learningmath/geometry/session9/part_c/index.html


 * __ Games __**
 * @http://www.mathchimp.com/7thGrade.php
 * @http://www.sumdog.com/ A variety of games covering many math topics
 * @http://www.mathplayground.com/SMP_index.html


 * **Videos** **
 * Discovery Learning @http://www.discoveryeducation.com/
 * The Teaching Channel
 * The teaching Channel currently offers videos of K-12 mathematics teaching aligned with the Common Core Sate Standards, which would be perfect for professional development with teacher teams.
 * https://www.teachingchannel.org/videos?categories=topics common-core
 * @https://www.teachingchannel.org/videos/visualizing-geometry-lesson

Describe, analyze and reason about the properties of rectangular prisms. Contruct rectangular prisms and flat patterns using a variety of materials and tools.
 * __ SMART Board Lessons, Promethean Lessons __**
 * 7. G. 3 Rectangular Prisms

__ @http://www.shodor.org/interactivate/guide/ __ __Activities and tools:__ @http://www.shodor.org/interactivate/activities/
 * __ Other Activities, etc. __**
 * Puzzle Maker
 * @http://www.discoveryeducation.com/free-puzzlemaker/?CFID=1276695&CFTOKEN=75709576
 * // Interactivate // is a set of free, online courseware for exploration in science and mathematics. It is comprised of activities, lessons, and discussions. The site is structured around collections of activities, lessons, and discussions.

Language Arts ||=  ||=   ||= Week 1 ||= Week 2 ||= Week 3 ||= Week 4 ||= Week 5 ||= Week 6 || 7 Matrix ||= Accelerated 7 Matrix ||= Week 1 ||= Week 2 ||= Week 3 ||= Week 4 ||= Week 5 ||= Week 6 || Home K-2 ||= Home 3-6 ||= Home 6-8 ||= Unit 1 ||= Unit 2 ||= Unit 3 ||= Unit 4 ||= Unit 5 ||= Unit 6 ||
 * = English
 * = Math ||= [[image:commoncorepcssd6/Actions-insert-table-icon.png link="@http://inst.pcssd.org/math/CCSS/7/Math7TeachingMatrix.xls"]]
 * = [[image:commoncorepcssd6/PCSSDlogo.JPG link="commoncorepcssd/PCSSD"]]