Joanne+Crooks

Why do we need congruent triangles? |||| Related Lessons: || Students apply digital tools to gather, evaluate, and use information. Students: Students use critical thinking skills to plan and conduct research, manage products, solve problems, and make informed decisions using appropriate digital tools and resources. Students: 15 min. |||| Students will be introduced to the problem. Laid-back Larry works for Triangle Trusses Construction Inc. they make trusses to support simple roofs. His job is to ensure that all trusses are exactly the same. Because he is lazy, Larry wants the easiest way possible to do his job. Your job is to help him find the easiest way to show that two triangular trusses are equal in measure with as little work as possible. || Photos of various trusses used in construction || 120 min. |||| Students will be randomly assigned to groups of four. Each group will rotate through stations: 60 min. |||| Groups will report findings of congruent triangles in the real world. || Computer with internet access, projector || Students will be assigned to a partner for day one and pairs will be combined for days two and three. || I will monitor students’ work and provide soft scaffolding for students, pairs, and groups as needed. Review exit cards and provide feedback to students.
 * Daily Lesson GAME Plan ||
 * Lesson Title:
 * Grade Level: 9-12 |||| Unit: Congruent Triangles ||
 * GOALS ||
 * Content Standards:
 * // G.CO.6 //** Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
 * // G.CO.7 //** Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
 * // G.CO.8 //** Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. ||
 * ISTE NETS-S
 * // Research and Information Fluency //**
 * 1) locate, organize, analyze, evaluate, synthesize and ethically use information from a variety of sources and media
 * 2) process data and report results
 * // Critical Thinking, Problem Solving, and Decision Making //**
 * 1) collect and analyze data to identify solutions and/or make informed decisions ||
 * Instructional Objectives:
 * // Students will be able to: //**
 * 1) explain the definition of congruent triangles
 * 2) explain whey the shortcuts for proving triangles work
 * 3) use Geometer’s Sketchpad to investigate congruent triangles
 * 4) explain why it is necessary to assure congruency in the real world ||
 * ACTION ||
 * Before-Class Preparation:
 * 1) Create Geometer’s Sketchpad activity and save to the sahred drive on the school network
 * 2) Reserve computer lab
 * 3) Create and copy worksheets
 * 4) Copy and cut proofs ||
 * DURING CLASS ||
 * Time |||| Instructional Activities || Materials and Resources ||
 * **// Day 1 //**
 * 45 min. |||| Students will work independently through Geometer’s Sketchpad activity to determine which combinations of three pairs of congruencies are enough to ensure triangles are congruent. || Computer Lab, GSP v.5, GSP Activity, Student Worksheet ||
 * 10 min. |||| Students will work in pairs to share their findings. || None ||
 * 10 min. |||| Students will answer an exit reflection card. || Exit Card ||
 * **// Day 2 & 3 //**
 * 1) create a foldable in the shape of a triangle to record theorems and figures (20 min)
 * 2) research where congruent triangles are necessary in the real world (30 min)
 * 3) students will put paper strips in the correct order for proving two triangles congruent(20 min)
 * 4) students will match the corresponding parts of congruent triangles (20 min)
 * 5) students will apply algebra to congruent triangles (20 min) || Construction paper, graph paper, computers with internet access, proofs with figures, statements, and reasons cut into strips and algebra problems for congruent triangles ||
 * 10 min. each day |||| Students will write an exit reflection card || Exit card ||
 * **// Day 4 //**
 * 20 min. |||| Quiz administered to pairs || Quiz ||
 * ** Note students groupings, environmental modifications needed, etc.: **
 * MONITOR ||
 * __ Ongoing Assessment(s): __

__ Accommodations and Extensions: __ Will provide groups who finish early proofs to do on their own. For students having difficulty with how to order statements and line up reasons will provide hard scaffolding in the form of additional proofs to fill in missing parts leading to understanding of how to complete proofs.

__ Back-up Plan: __ If the technology is unavailable students will work in pairs with spaghetti noodles spray painted (red, blue, and green) each color will be a different length. Groups will need worksheets describing how to try and create congruent triangles using spaghetti noodles and a protractor. || Assess mastery of content by having students complete a quiz with their partner, day four. LESSON REFLECTIONS AND NOTES: ||
 * EVALUATE AND EXTEND ||
 * Be specific and include the evaluation that you will for this lesson:

Connections: Coordinates and Congruent Triangles |||| Related Lessons: Why do we need congruent triangles? || Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others. Students: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior. Students: 45 min |||| **// Whole class discussion: //** How would you convince someone two triangles are congruent if you were given the coordinates for the vertices? New Smart Notebook file || 20 min |||| **// Whole class discussion: //** Refrigerator repairpersons Rachel and Randy don’t understand the big deal about congruent figures! Can you explain to them in terms of their jobs why it is important to have congruent figures? ||  ||
 * Daily Lesson GAME Plan ||
 * Lesson Title:
 * Grade Level: 9-12 |||| Unit: Congruent Triangles ||
 * GOALS ||
 * Content Standards: Common Core State Standards – High School Geometry
 * Understand congruence in terms of rigid motions **
 * G-CO.7. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
 * G-CO.8. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. ||
 * ISTE NETS-S:
 * 2. Communication and Collaboration **
 * 1) interact, collaborate, and publish with peers, experts or others employing a variety of digital environments and media
 * 2) communicate information and ideas effectively to multiple audiences using a variety of media and formats
 * 3) develop cultural understanding and global awareness by engaging with learners of other cultures
 * 5. Digital Citizenship **
 * 1) advocate and practice safe, legal, and responsible use of information and technology
 * 2) exhibit a positive attitude toward using technology that supports collaboration, learning, and productivity
 * 3) demonstrate personal responsibility for lifelong learning ||
 * Instructional Objectives: Students will:
 * 1) be able to determine if two triangles are congruent given coordinates for vertices of triangles
 * 2) be able to explain why triangles are congruent
 * 3) use social media for educational networking ||
 * ACTION ||
 * **// Before-Class Preparation: //** Develop vertices for congruent triangles using GSP and rotations, reflections, and translations. Reserve computer lab for day 7 lesson. In advance I will share the class hashtag with my Twitter PLN and ask them to reply to tweets posted by my students. Create a stack containing a list of links for congruent figures in the real world. ||
 * DURING CLASS ||
 * Time |||| Instructional Activities || Materials and Resources ||
 * **// Day 6 //**
 * 1) What method(s) can you use?
 * 2) What formula(s) would you need to use?
 * 3) Which, if any, of these formulas indicate congruent angles?
 * 4) How (if at all) can you use Pythagorean theorem? || Computer/projector
 * 30 min |||| Students will work in groups of three – given the vertices of four triangles to calculate the lengths of each side of a triangle and the slopes of each side to determine which triangles may be congruent. Students will also check calculations with members of other groups to determine if any congruent triangles exist between the groups. || Graph paper, blank paper, vertices for triangles – enough for 10 groups ||
 * 10 min |||| Explain a new insight you gained today pertaining to congruent triangles, the use of the distance, slope, Pythagorean theorem, or the connection between congruent triangles and the formulas. || Index cards ||
 * **// Day 7 //**
 * 50 min |||| Students will sign into Twitter and using a hashtag created specifically for this class will post tweets to continue discussion and elicit responses from educators.

Students will be encouraged to be simultaneously researching ideas suggested by those outside the classroom sending tweets. || Computer Lab Use the projector & my computer to project feed for hashtag using Hootsuite || Students will post to the class wiki their answer to; What are the benefits to using a tool such as Twitter for learning? || Wiki page set up in Edublogs site. || Students will need to be placed in groups of three for day 6. || __ Accommodations and Extensions: __ Students without Internet access at home to answer the question for homework will be able to come in before school or during lunch to post their answer to the class Wiki. __ Back-up Plan: __ If the network is down, then I will have students use their cell phones to access Twitter. || I will evaluate the effectiveness of this lesson based on student responses posted to the Wiki. LESSON REFLECTIONS AND NOTES: ||
 * 10 min |||| Assign Homework
 * ** Note students groupings, environmental modifications needed, etc.: **
 * MONITOR ||
 * __ Ongoing Assessment(s): __ I will monitor group work without interference to assess student learning. Students’ Twitter posts will be closely monitored and assessed for contribution to discussion and learning by a feed following class hashtag.
 * EVALUATE AND EXTEND ||
 * Be specific and include the evaluation that you will for this lesson:

Show your Stuff! |||| Related Lessons: Why do we need congruent triangles? & Coordinates and Congruent Triangles || G-CO.8. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. || Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology. Students: Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others. Students: Students apply digital tools to gather, evaluate, and use information. Students: Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources. Students: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior. Students: Students will demonstrate mastery of content by demonstrating each of the 5 ways to prove triangles congruent and explain rigid motions used to move the image in the plane. Students will demonstrate understanding of congruent angles by creating a proof and showing a solution – the proof must incorporate two of the following: Students will demonstrate knowledge of both content and 21st Century technology tools to create a multi-media presentation. || Discuss with students the expectations for creating the digital story. Be open to allow students to adjust the product to fit their learning. || A collection of student created digital stories used to teach/share content. Copies of rubric. Photo-Story, Moviemaker. A list of websites with copyright free images as well as copyright free music. || (4-5) |||| Students will work in their groups over the next two weeks to develop their proofs and for digital story. || Computers in the classroom. Digital cameras, cell phones, etc. || Students will be grouped in pairs. ||
 * Daily Lesson GAME Plan ||
 * Lesson Title:
 * Grade Level: 9-12 |||| Unit: Congruent Triangles ||
 * GOALS ||
 * Content Standards: Common Core State Standards – High School Geometry
 * Understand congruence in terms of rigid motions **
 * G-CO.7. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
 * ISTE NETS-S:
 * 1) ** Creativity and Innovation **
 * 1) apply existing knowledge to generate new ideas, products, or processes
 * 2) create original works as a means of personal or group expression
 * 3) ** Communication and Collaboration **
 * 1) interact, collaborate, and publish with peers, experts, or others employing a variety of digital environments and media
 * 2) communicate information and ideas effectively to multiple audiences using a variety of media and formats
 * 3) contribute to project teams to produce original works or solve problems
 * 4) ** Research and Information Fluency **
 * 1) plan strategies to guide inquiry
 * 2) locate, organize, analyze, evaluate, synthesize, and ethically use information from a variety of sources and media
 * 3) evaluate and select information sources and digital tools based on the appropriateness to specific tasks
 * 4) ** Critical Thinking, Problem Solving, and Decision Making **
 * 1) plan and manage activities to develop a solution or complete a project
 * 2) ** Digital Citizenship **
 * 1) advocate and practice safe, legal, and responsible use of information and technology
 * 2) exhibit a positive attitude toward using technology that supports collaboration, learning, and productivity
 * 3) demonstrate personal responsibility for lifelong learning ||
 * Instructional Objectives:
 * vertical angles
 * perpendicular segments
 * midpoint
 * angle bisector
 * bisect each other
 * ACTION ||
 * Before-Class Preparation: Research examples of using digital storytelling created by students to teach, Copies of rubric for students, copies of storyboard worksheet. Create a schedule for groups to rotate time at computers in the classroom. ||
 * DURING CLASS ||
 * Time |||| Instructional Activities || Materials and Resources ||
 * 45 min |||| Introduce the activity – play examples of digital storytelling
 * 45 min |||| Students will work in pairs to begin the process of creating a storyboard. || Copies of worksheets to begin planning digital story. ||
 * 45 min
 * 90 min |||| Students will be provided with the opportunity to share their digital story. (15 groups will need approximately 60 minutes – an extra 30 minutes is allotted for time in between) || SmartBoard, projector, laptop, speakers. ||
 * ** Note students groupings, environmental modifications needed, etc.: **
 * MONITOR ||
 * Ongoing Assessment(s): teacher will observe students and keep field notes about progress, students will be encouraged to have other groups check their proofs for completeness.

Accommodations and Extensions: Students who are provided extended time according to their IEP, will be allotted extra time as schedule for computer time is designed. Students who wish to expand on this project will be the freedom to do so.

Back-up Plan: Will need to extend due date if there are issues with computers and access to the Internet. || LESSON REFLECTIONS AND NOTES: This is the first time I will be attempting this type of lesson I will need to be well prepared. I generally like to create the product myself so I understand what I am asking students to complete and have allotted an appropriate amount of time to complete. ||
 * EVALUATE AND EXTEND ||
 * Be specific and include the evaluation that you will for this lesson: I will use the attached rubric to evaluate student work.


 * CATEGORY  ||   4   ||   3   ||   2   ||   1   ||
 * **// Point of View – Purpose //** || Establishes a purpose early on and maintains as a clear focus throughout. || Establishes a purpose early on and maintains focus for most of the presentation. || There are a few lapses in focus, but the purpose is fairly clear. || It is difficult to figure out the purpose of the presentation. ||
 * **// Images //** || Images create a distinct atmosphere or tone that matches different parts of the story. The images may communicate symbolism and/or metaphors. || Images create an atmosphere or tone that matches some parts of the story. The images may communicate symbolism and/or metaphors. || An attempt was made to use images to create an atmosphere/tone but it needed more work. Image choice is logical. || Little or no attempt to use images to create an appropriate atmosphere/tone. ||
 * **// Voice - Consistency //** || Voice quality is clear and consistently audible throughout the presentation. || Voice quality is clear and consistently audible throughout the majority (85-95%) of the presentation. || Voice quality is clear and consistently audible through some (70-84%) of the presentation. || Voice quality needs more attention. ||
 * **// Duration of Presentation //** || Length of presentation was 4 minutes. || Length of presentation was 3 minutes. || Length of presentation was 2 minutes. || Presentation was less than 2 minutes long OR more than 4 minutes. ||
 * **// Diagrams //** || Clear, accurate diagrams are included. Diagrams are labeled neatly and accurately. || Diagrams are included but are missing a label. || Diagrams are not clear and are missing more than one label. || Not all diagrams are included OR are missing important labels. ||