Geometry Semester 1                                                            Organized by Lisa Bejarano: @lisabej_manitou

 Unit 1: Constructions & Rigid Transformations CCSS 1.1 I Know and use precise definitions of geometric terms. G.CO.1 1.2 I can make formal geometric constructions sited in standards both by hand and using geometry software. G.CO 12,13 1.3 Given a geometric figure and a rotation, reflection and translation, I can draw the transformed figure. G.CO.5 1.4 I Understand and can explain the formal definition of rotation, reflection and translation. G.CO.4 1.5 I can represent transformations in the plane and describe transformations as functions that take points in the plane as inputs and give other points as outputs. G.CO.2 Enduring Understandings Essential Questions ·         You can use special geometric tools to make a figure that is congruent to an original figure without measuring.·         Construction is more accurate than sketching and drawing.·         Analyzing geometric relationships develops reasoning and justification skills.·         Objects in space can be transformed in an infinite number of ways and those transformations can be described and analyzed mathematically.·         Congruence of two objects can be established through a series of rigid motions.·         Properties of geometric objects can be analyzed and verified through geometric constructions.·         Judging, constructing, and communicating mathematically appropriate arguments are central to the study of mathematics. ·         What is the relationship between construction and congruency?·         How do the properties of lines and angles contribute to geometric understanding?·         How is visualization essential to the study of geometry?·         How does the rigid motion connect to congruence?·         How does geometry explain or describe the structure of our world?·         How do constructions enhance understanding of the geometric properties of objects?·         How can reasoning be used to establish or refute conjectures?·         What are the characteristics of a valid argument?·         What facts need to be verified in order to establish that two figures are congruent? Learning Target, Instructional task & Standards for Math Practice 1.1 Geometry VocabularyHigh Tech High Students engage with the academic language needed in this unit in a way that taps into their prior knowledge and provides a place to discuss and dialogue with their peers to activate their prior geometry experience. SMP.6 1.1 Starting with Definitionscrazymathteacherlady Using examples & non-examples, students complete Frayer models and collaborate on writing definitions. SMP.6SMP.7 1.2 Construction Design Project  crazymathteacherlady This activity provides an opportunity for students to familiarize themselves with the precision that can be generated using a straightedge and compass SMP.1SMP.8 1.2 Construction CastlesCheesemonkey “ I created this Constructions Castle project to give students plenty of practice doing constructions while also giving them a chance to develop their understanding of how shapes and angles fit together.” SMP.1SMP.8 1.2 http://sciencevsmagic.net/geo/Ancient Greek geometry A beautifully simple online tool that allows students to experiment with circles & lines to develop understanding of the capabilities of constructions. It's deceptively simple, and quite challenging. Can you construct a regular pentagon in 15 moves or less? And can you construct other regular polygons that are not shown in the challenges, like the 15-gon and 17-gon? SMP.5 1.2 Euclid, the Game!Geogebra This activity is a great introduction to geogebra as well as the basics of constructions while allowing students to develop methods instead of coping steps. Each level introduces a new geometric challenge to construct with only a virtual compass, ruler, and the previous abilities you've discovered. SMP.5 1.2 Introduction to ConstructionsHigh Tech High The purpose of this activity is to provide students with a teacher guided foundation of construction.  Additionally, students learn to use geometric tools for constructions, helping them to develop and understand how the tools can be used for later geometric work SMP.5 1.2 Pizza Delivery RegionNCTM Illuminations The trick to this task is in constructing perpendicular bisectors between locations to ensure customers receive pizzas from the nearest location.  Students must notice this structure and figure out how to apply bisector constructions to increasingly challenging models in to precisely divide the city grid for the pizza company. SMP.7SMP.6 1.2 Constructing ShapesHigh Tech High This activity builds on Introduction to Constructions but here students must build on the ideas from the previous activity to make sense of the problem at hand and must attend to precision in explaining why their construction makes the given shape based on how it was constructed and how this connects to the definition of the figure. SMP.1SMP.6 1.2 Constructing digitallyHigh Tech High Students use their prior knowledge of how to construct the given figures by hand to understand how to use geometric software. SMP.5 1.3 MATHHigh Tech High Activate students’ prior understanding of how to rotate, reflect and translate a given figure. In order to complete the fourth problem, students must look for and make use of structure found in the previous problems. SMP.7 1.3 Mrs. Pac Man, Robert Kaplinsky This lesson provides a real-life context for transformations including rotations, reflections, and translations, which are the foundation for students understanding congruence and similarity.  Rather than begin the lesson by defining the terms and identifying them in the game, the goal is to let students initially describe the movements in their own words and then guide them towards a mathematically precise definition. SMP.6 1.3 Transforming a Pentagon & Answer Key,  High Tech High This activity is useful in case students still struggle with visualizing given transformations and need more practice; this can provide students with an opportunity to demonstrate repeated reasoning and regularity in transformations. SMP.8 1.3 Reflected TrianglesIllustrative Mathematics This activity has students demonstrate their understanding of the line of reflection as the perpendicular bisector between any two corresponding points as well as a precise and accurate construction of a perpendicular bisector. SMP.6 1.4 Defining ReflectionsIllustrative Mathematics This task helps students transition to a technical mathematical definition of reflection.  This task requires time and patience and is ideally suited for in class group work. If there are mirrors present in the classroom the teacher may wish to have students experiment so that they can see first-hand how the mirror image is similar and how it differs from the original. SMP.5SMP.6 1.4 Defining RotationsIllustrative Mathematics At this point in the unit, students should be very familiar with the visual representation of rotation and should be able to use this task to help transition to the technical mathematical definition.  By providing four possible definitions and having students work through the validity and precision of each. SMP.6 1.31.5 Transforming 2D Figures, MARS Students describe transformations through writing and images and also see transformations as functions that take points in the plane as inputs and give other points as outputs. SMP.1SMP.7SMP.6 1.5 Horizontal Stretch of the Plane, Illustrative Mathematics Students compare a transformation of the plane (translation) which preserves distances and angles to a transformation of the plane (horizontal stretch) which does not preserve either distances or angles. SMP.2 1.31.4 Face Value, Mathalicious Here students are provided with an opportunity to grapple with the idea of something being symmetric and reflecting onto itself and must persevere through the calculations and analysis of the symmetry score.   This activity also provides students with an opportunity to model the ideas facial symmetry through reflection. SMP.1SMP.4

[a]I love your transition from rigid transformations to triangle congruence.  There is clearly a dearth of materials on this sequence and you have unearthed some great ones.

[b]It went well this year. I think that these materials are awesome, but there must also be teacher knowing their students and when to add some notes, journaling, practice, etc. it's also important to know what activities just won't work.

[c]I have difficulty in my class having students see something and retain it.  I like your follow up lessons and have struggled with an initial lesson.  My success with retaining quadrilateral knowledge has been with a 2-3 minute exercise called "What quadrilateral am I?".  Students ask questions and guess.  I restrict them later to types of qualities and over time.