7.4.1Ma


 * Grade: 7 Unit: 4 Week: 1 **
 * Content: Geometric Drawing (Manually) **
 * Dates: 1/22 – 1/25 (4 days) **


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

How can geometrically draw shapes, help determine that a given set conditions will produce a specific shape?
 * __ Essential Questions __**** : **


 * __ Standards __**** : **
 * ** 7.G.2 ** Draw (freehand, with ruler and protractor) geometricshapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine unique triangle, more than one triangle, or no triangle.

Review Recommended:
 * __ Objectives __**** : **
 * The students will describe types of angles.
 * The student will measure and draw angles using a protractor.
 * The student will describe types of polygons.
 * The student will explain the properties associated with triangles and quadrilateral.
 * The student will draw triangles given certain sets of conditions, such as
 * The measures of two angles and the included side (ASA),
 * The measures of two angles and the non-included side, associated with one of the specific angle (AAS),
 * The measures of two sides and the included angle (SAS),
 * The measures of all three sides (SSS),
 * The measures of all three angles (AAA),
 * The measure of two sides and the non-included angle, associated with one of the specific sides (SSA)
 * To determine is a unique triangle, more than one triangle, or no triangle will always be produced.
 * The student will conclude that for a triangle to result the sum of any two side lengths must be greater than the third side length (this concept is needed in the 8th grade geometry unit).
 * The student will conclude that the sum of the three angles must equal 180 degrees.


 * __ Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team __**

The curriculum team has provided two weeks for drawing of geometric figures. It is advisable that before beginning this unit, that students review and practice previous learning dealing with triangles and their properties. Assure that students are capable of properly drawing and measuring line segments and angles. These will be essential skills.

**Even though the Teacher Matrix denotes two independent weeks, one for manual exploration and the other for technological exploration, it would be appropriate to blend the weeks to obtain maximum impact in the teaching/learning process.**


 * The definition for a unique triangle is provided for clarity: **

Examples
 * A **unique triangle **is a triangle that can only be drawn one way. This means there is not another triangle that has the exact dimensions or shape. The set of facts or conditions that you need to know to create a unique triangle:SSS, SAS, ASA and AAS. **
 * If you are given: •3 sides (SSS) e.g. 5 cm, 3 cm, 7 cm •2 sides and the included angle (SAS) e.g. 4 cm, 50°, 6 cm •2 angles and the side between (ASA) e.g. 40°, 5 cm, 60° •1 angle and 2 sides (AAS) e.g. 40°, 50°, 7 cm **

__ Background Information __

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/**] **

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


 * Constructions facilitate understanding of geometry. Provide opportunities for students to physically construct triangles with straws, sticks, patty paper, or geometric apps. prior to using rulers and protractors to discover and justify the side and angle conditions that will form triangles. Explorations should involve giving students: the conditions noted above to determine if a unique triangle, no triangle or an infinite set of triangles results. Through discussion of their exploration results, students should conclude that triangles cannot be formed by any three arbitrary side or angle measures. Students should be able to transfer from these explorations to reviewing measures of three side lengths or three angle measures and determining if they are from a triangle justifying their conclusions with both sketches and reasoning **
 * They should realize that for a triangle to result the sum of any two side lengths must be greater than the third side length (this concept is needed in the 8th grade geometry unit), or the sum of the three angles must equal 180 degrees. **
 * This cluster is related to the following Grade 7 cluster “Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.” **


 * Extension of Student Learning: **
 * Further construction work can be replicated with quadrilaterals, determining the angle sum, noticing the variety of polygons that can be created with the same side lengths but different angle measures, and ultimately generalizing a method for finding the angle sums for regular polygons and the measures of individual angles. For example, subdividing a polygon into triangles using a vertex (N-2)180° or subdividing a polygons into triangles using an interior point 180°N - 360° where N = the number of sides in the polygon. An extension would be to realize that the two equations are equal. **

**Recommended:** Students can prepare a viable argument to justify when three sides results in a triangle and when three sides do not result in a triangle.
 * Assessment: **
 * Product ****
 * Students are to work in groups of twos or threes.
 * Students will be creating a more detail summary chart as shown in the OnCore Teacher Guide page 95 with justifying drawings and/or constructions.
 * Students are to address each of the following conditions:
 * The measures of two angles and the included side (ASA),
 * The measures of two angles and the non-included side, associated with one of the specific angle (AAS),
 * The measures of two sides and the included angle (SAS),
 * The measures of all three sides (SSS)
 * The measures of all three angles (AAA),
 * The measure of two sides and the non-included angle, associated with one of the specific sides (SSA)
 * Students are to determine if a unique triangle, no triangle or an infinite set of triangles result for the given condition.
 * 1) Enrichment: Students can prepare a viable arugment for the Angle Sum Theorem, S = (n – 2) 180.
 * 2) Students have the flexibility in the design and display of the project using their creativity.
 * 3) NOTE: Students will be allowed to extent their project to include lesson 4-2, and use technology.


 * Key Questions **
 * What are the properties of a triangle?
 * What is a “unique” triangle?
 * How do you know a triangle is “unique”?
 * Do three given lengths always create a triangle?
 * If three given sides make a triangle, is the triangle always unique?


 * Observable Student Behaviors **
 * The student can determine when a given set of conditions will produce a unique triangle, no triangle, or infinite set of triangles.
 * Extension:
 * The students can provide a viable argument to justify when three given sides will produce a triangle.
 * The student can provide a viable argument to justify the angle sum theorem, s = (n-2)180

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 __**** : **


 * ** Math ** ||
 * Protractor Compass Unique triangle Adjacent Angles Complementary Angles Congruent Angles Cross Section Intersection Supplementary Angles Vertical Angles Degrees ||

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 __** :
 * ABC //Mastering the Common Core in Mathematics//
 * Types of Angles, Chapter 10.1, p. 116
 * Types of triangles, Chapter 11.1, p. 124
 * Types of Quadrilaterals, Chapter 11.2, p. 125
 * Quadrilaterals and their Properties, Chapter 11.3, p. 126
 * Types of Polygons, Chapter 11.4, Chapter 11.4, p. 127
 * Drawing Shapes, Chapter 11.5, p. 128-134
 * // Houghton Mifflin On Core Mathematics Middle School // Grade 7 Unit 4-2, p. 93-96
 * Gizmo Correlation: None Available at this time
 * // Teaching the Common Core Math Standards with Hands-On Activities, //
 * // 7.G.2 – Activity p.80 //
 * **Highly Recommended** None Available at this time
 * Glencoe 7th Grade //Mathematics Application and Concepts Course 2//, Chapter 10.4b, p. 432-433
 * Create a puzzle with unit vocabulary words.


 * Diverse Learners **
 * Odyssey (teacher discretion)
 * Skills Tutor (teacher discretion)
 * Math Cool Mod 8


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

Unique triangle (figure)
 * __ 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, and 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’s 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 annotated 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: __**
 * Triangle Cutouts
 * Straws cut in different lengths
 * Rulers (Straightedge)
 * Protractor
 * Compas s
 * Versa Tiles


 * __ 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

Classifying triangles by sides and angles, finding missing angle measures. Students will observe which side lengths make a triangle and investigate the theorem stating that the largest angle is opposite the longest side of a triangle. @http://exchange.smarttech.com/details.html?id=1764f052-3804-448f-9f12-95bc5646a2ea @http://exchange.smarttech.com/details.html?id=050e54ad-0dea-4080-ae54-975d93487209
 * __ SMART Board Lessons, Promethean Lessons __**
 * Smart Board rational number lessons
 * 7.G.2 All About Triangles
 * 7.G.2 Triangle Inequalities
 * Rational numbers Smart Board lessons

__ @http://www.shodor.org/interactivate/guide/ __
 * __ 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.

__ Activities and tools: __ @http://www.shodor.org/interactivate/activities/

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