Geometry Unit 1 Geometric Transformations Lesson Plan (10 days) Stage 1 Desired Results Learning Goal: Students will be able to draw, describe, specify the sequence, develop definitions, and predict the effect of transformations by using appropriate academic vocabulary. Essential Questions: What effects do transformations have on geometric figures? What is the relationship between reflections, translations, and rotations? How do you determine the type of transformation that has occurred? Unit Objectives: SWBAT Describe the terms point, line, and be able to: distance along a line in a plane. Define perpendicular lines, parallel lines, line segments, and angles. Describe the different types of transformations including translations, reflections, rotations, and dilations. Describe transformations as functions that take points in the coordinate plane as inputs and give other points as outputs. Represent transformations in the plane. Write functions to represent transformations. Compare transformations that preserve distance and angle to those that do not (e g, translation vs. horizontal stretch). Describe rotations and reflections that carry a rectangle, parallelogram, and trapezoid, or regular polygon onto it. Determine the line of reflection of a segment is the perpendicular bisector. Determine the center of rotation, direction of rotation (distance preserving), and number of degrees rotated (angle preserving). Understand in a translation the length and degree measure of the angle of the vector. Create a parallel line by rotating a line 180 degrees through a point not on the line. Define rotations, reflections, and translations. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure. Draw a transformed figure and specify the sequence of transformations that were used to carry the given figure onto the other. Use geometric descriptions of rigid motions to transform figures. Standards (see How Tested at the end of document) (circles are saved for later): MAFS.912.G-CO.1.1 (DOK 1) Know precise definitions of angle, circle, perpendicular lines, parallel lines, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. (Unit 8) MAFS.912.G-CO.1.2 (DOK 2) Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). MAFS.912.G-CO1.3 (DOK2) Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. MAFS.912.G-CO.1.4 (DOK 3) Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. Understand rigid motion maps segments onto segments of equal lengths and angles onto angles of equal measure. MAFS.912.G-CO.1.5 (DOK 2) Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. MAFS.912.G-CO.2.6 (DOK 2) 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.
Use geometric descriptions of rigid motions to predict the effect of a given motion on a given figure. Determine if two figures are congruent using the definition of congruence in terms of rigid motions. Knowledge: Students will know Definitions of: Point Line Line segment Perpendicular Bisector Translation Reflection Rotation Transformation Rigid motion Distance preserving Angle preserving Angle of rotation Center of rotation Direction Pre-image Image Horizontal stretch Congruence Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. Skills: Students will be able to Know precise definitions of angle, perpendicular lines, parallel lines, and line segment, based on the undefined notions of point, line Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. 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.
Scales: 4.0 3.0 Transformations In addition to score 3.0 performance, the student demonstrates in-depth inferences and applications that go beyond what was taught. 3.5 The student will: In addition to score 3.0 performance, partial success at score 4.0 content Describe the rotations and reflections that carry a given rectangle, parallelogram, trapezoid or regular polygon on to itself (HSG-CO.A.3) Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments (HSG-CO.A.4) Specify the sequence of transformations that will carry a given figure onto another (HSG- CO.A.5) 2.0 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure (HSG-CO.B.6) 2.5 No major errors or omissions regarding score 2.0 content, and partial success at score 3.0 content The student will recognize or recall specific vocabulary, such as: Angle, circle, definition, distance, figure, function, geometric, graph paper, horizontal stretch, input, line, line segment, output, parallel, parallelogram, perpendicular, plane, point, polygon, predict, preserve, rectangle, reflection, regular, represent, rigid motion, rotation, sequence, software, tracing paper, transform, transformation, translation, trapezoid (HSG-CO.A.1) The student will perform basic processes, such as: Describe transformations as functions that take points in the plane as inputs and give other points as outputs (HSG-CO.A.2) Represent transformations in the plane using, for example, transparencies and geometry software (HSG-CO.A.2) Compare transformations that preserve distance and angle to those that do not (for example, translation vs. horizontal stretch) (HSG-CO.A.2) 1.0 0.0 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, for example, graph paper, tracing paper, or geometry software (HSGCO.A.5) 1.5 Partial success at score 2.0 content, and major errors or omissions regarding score 3.0 content With help, partial success at score 2.0 content and score 3.0 content 0.5 With help, partial success at score 2.0 content but not at score 3.0 content Even with help, no success
Performance Tasks: 1. Unit Test K: drive 2. Formative Assessments: http://www.cpalms.org/resources/publicpreviewr esourcecollection.aspx?resourcecollectionid=202 3. Formative Quizzes 4. Group Presentations 5. Higher Order Question Writing Assignments 6. Projects Stage 2 Assessment Evidence Other Evidence: 1. Socrative Survey 2. Bell work 3. Group work 4. Notebook check (Cornell Notes) 5. Homework Stage 3 Learning Plan Learning Activities & Instructional Strategies (*indicates highly recommended): Textbook Sections: 1.2, 1.3, 1.4, 9.1, 9.2, 9.3, 9.4, 9.6 High School Flip Book: http://katm.org/wp/wp-content/uploads/flipbooks/high-school-ccss-flip-book-usd- 259-2012.pdf Pages: 158-166 *Transformation Grapher: http://www.shodor.org/interactivate/activities/transmographer/ Definitions: https://www.math.ku.edu/~jmartin/courses/math105-f11/lectures/chapter11-part3.pdf Demonstrating Rotations Worksheet: http://www.cpalms.org/public/previewresource/preview/59161 Interactive Rotations: http://nlvm.usu.edu/en/nav/frames_asid_299_g_3_t_3.html?open.instructions *EngageNY: https://www.engageny.org/resource/high-school-geometry Daily Lessons/Mini-tasks: Day 1/Task(s) Day 2/Task(s) Day 3/Task(s) Day 4/Task(s) Day 5/Task(s) Day 6/Task(s) Day 7/Task(s) Day 8/Task(s) Day 9/Task(s) Day 10/Task(s)
Higher Order Thinking Questions & Writing Tasks: 1. Using geometric figures and single transformations, is it possible to accomplish the same movement of an object using different rigid motion movements? Give a reason for your answer. 2. List a daily activity you do that represents rigid motion movements? What movements are you using and when? 3. Write a general transformation using 3 different types of rigid motions that will move any object back to its original location as if it never moved? Stage 4 Remediation or Enrichment MTSS RTI Interventions for remediation Teachers will meet in PLC to compare Unit Test Results and collaborate on suggestions for improvement Test Retakes or Corrections Data Chats Alternate or extra remediation assignments with different expectations for struggling students, especially if indicated in a 504, or IEP. Additional or re-teaching on standards that are not met for struggling students with extension and enrichment for students who have met the standards. Phone calls home with emails to grade level administrator and counselor for both grading and attendance issues Use of pre-test and post-test with mini assessments throughout unit to assess understanding of individual standards Problem-based instruction in class with small group activities throughout unit Lessons developed on Florida Standards After-school tutoring and remediation for more individualized instruction as needed Use of County Benchmark tests with EOC at the end to check student data Ensure at least 80% of students are meeting standards in each unit. Tutoring outside of the school Check vertical progression on blueprints for where these topics will be seen again to push curriculum Find real-world contextual problems to engage the students in higher level problems.
MAFS.912.G-CO.1.1 Item Types Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. Graphic response May require drawing a figure. Hot text response May require dragging text to complete a justification. Multiple-choice response May require selecting a definition. Multi-select response May require selecting responses. Natural Language response May require explaining the validity of a definition. Clarifications Selectable text response May require highlighting a definition from an informal argument. Students will use the precise definitions of angles, circles, perpendicular lines, parallel lines, and line segments, basing the definitions on the undefined notions of point, line, distance along a line, and distance around a circular arc. Assessment Limit Stimulus Attributes Items may ask students to analyze possible definitions to determine mathematical accuracy. Items may ask students to use definitions for justifications when choosing examples or nonexamples. Items may ask students to use properties of rotations, reflections, and translations as steps to a formal definition. Response Attribute Calculator Neutral
MAFS.912.G-CO.1.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Also assesses MAFS.912.G-CO.1.4 Item Types Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. Drag and drop response May require completing a table. Graphic response May require constructing transformations, mapping vertices to each other, or graphing a figure or a line of reflection. Multiple-choice response May require selecting a value or an expression from a list. Multi-select response May require selecting responses. Natural Language response May require explaining the differences and similarities between different transformations or describing rotations, reflections, and/or translations. Selectable text response May require highlighting a definition of rotation, reflection, or translation from an informal or formal geometric argument. Clarifications Simulation response May require generating tables and constructing transformations. Students will represent transformations in the plane. Students will describe transformations as functions that take points in the plane as inputs and give other points as outputs. Students will compare transformations that preserve distance and angle to those that do not. Students will use definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
Assessment Limits Items may require the student to be familiar with using an algebraic description,, for transformations. Items should not use matrices to describe transformations. Items should not require the student to use the distance formula. Items may require the student to find the distance between two points or the slope of a line. Stimulus Attributes Response Attributes In items that require the student to represent transformations, at least two transformations should be applied. Items may ask students to determine if a transformation is rigid. Items may ask students to determine if steps that are given can be used to develop a definition of an angle, a circle, perpendicular lines, parallel lines, or line segments by using rotations, reflections, and translations. Students may be asked for a coordinate of a transformed figure. Students may be asked to use a function to describe a transformation. Items may ask students to determine if verbal description of a definition is valid. Items may ask students to determine any flaws in verbal description of a definition. Students may be asked to use a function to describe a transformation. Students may be asked to give a line of reflection and/or degree of rotation that carry a figure onto itself. Calculator Students may be required to draw a figure using a description of a translation. Neutral
Geometry Unit 1 Lesson Plans MAFS.912.G-CO.1.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. Also assesses MAFS.912.G-CO.1.3 Item Types Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. Graphic response May require constructing a transformed figure or graphing a figure or a line of reflection. Hot text response May require reordering steps of a transformation. Multiple-choice response May require selecting a value or an expression from a list. Multi-select response May require selecting responses. Natural Language response May require describing rotations and reflections. Simulation response May require generating a table and constructing a transformed figure. Clarifications Students will apply two or more transformations to a given figure to draw a transformed figure. Students will specify a sequence of transformations that will carry a figure onto another. Students will describe rotations and reflections that carry a geometric figure onto itself. Assessment Limits Items should not require the student to use the distance formula. Items may require the student to be familiar with using an algebraic description,, for transformations. Items should not use matrices to describe transformations. In items in which the line of reflection is given, it should be in slopeintercept form. In items in which the student has to write the line of reflection, any form of a line can be used. If the line is not a vertical line or a horizontal line, then the line of reflection should be graphed as a dotted line so that the slope and the y-intercept can be determined.
Stimulus Attributes Geometry Unit 1 Lesson Plans Students may be given a sequence of transformations to determine if a figure will carry one figure on top of another. Students may be asked to determine if an attribute of a figure is the same after a sequence of transformations has been applied. Response Attributes Students may be asked to use a function to describe a transformation. Students may be asked to give a line of reflection and/or degree of rotation that carry a figure onto itself. Students may be required to draw a figure using a description of a transformation. Students may be required to graph a figure using a description of a rotation and/or reflection. In items in which the student has to write the line of reflection, any line can be used. If the line is not a vertical line or a horizontal line, then the line of reflection should be graphed as a dotted line so that the slope and the y-intercept can be determined. Students may be asked to write a line of reflection that will carry a figure onto itself. Students may be asked degree of rotation that will carry a figure onto itself. Calculator Neutral MAFS.912.G-CO.2.6 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.
Item Types Geometry Unit 1 Lesson Plans Graphic response May require constructing a transformed figure. Hot text response May require reordering steps of a transformation or selecting text that proves congruence between triangles. Movable text response May require dragging and dropping text to complete a viable geometric argument. Multiple-choice response May require selecting a value, an expression from a list, or from choices of transformations. Multi-select response May require identifying transformed figures. Natural Language response May require justifying why two figures are congruent. Simulation response May require generating a table and constructing a transformed figure. Clarifications Students will use rigid motions to transform figures. Students will predict the effect of a given rigid motion on a given figure. Students will use the definition of congruence in terms of rigid motions to determine if two figures are congruent. Students will explain triangle congruence using the definition of congruence in terms of rigid motions. Students will apply congruence to solve problems. Students will use congruence to justify steps within the context of a proof. Assessment Limits Items may require the student to justify congruence using the properties of rigid motion. Items should not require the student to use the distance formula. Items may require the student to be familiar with using an algebraic description,, for transformations. Items should not use matrices to describe transformations. Stimulus Attribute Items may require the student to determine the rigid motions that show that two triangles are congruent.
Response Attributes Geometry Unit 1 Lesson Plans Items may ask students to name corresponding angles and/or sides. Students may be asked to use a function to describe a transformation. In items in which the student has to write the line of reflection, any line can be used. If the line is not a vertical line or a horizontal line, then the line of reflection should be graphed as a dotted line so that the slope and the y-intercept can be determined. Items may require the student to name corresponding angles or sides. Items may require the student to determine the transformations required to show a given congruence. Items may require students to list sufficient conditions to prove triangles are congruent. Items may require students to determine if given information is sufficient for congruence. Items may require students to give statements to complete formal and informal proofs. Calculator Neutral