rigorous curriculum design - dekalb county school …...math department is seeking support from...

Rigorous Curriculum DesignmdashUnit Planning Organizer Blank

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1

DEKALB COUNTY SCHOOL DISTRICT

RIGOROUS CURRICULUM DESIGN

UNIT PLANNING ORGANIZER

Subject(s) Mathematics

Grade and Course

Grade 10 - Analytic Geometry

Unit of Study Unit 2 ndash Similarity Congruence and Proofs

Pacing Traditional 7 weeks Block 35 weeks

ldquoUnwrappedrdquo Priority Georgia Standards of Excellence

Skills and Concepts

Understand similarity in terms of similarity transformations MGSE9-12GSRT2 Given two figures USE the definition of similarity in terms of similarity transformations to DECIDE if they are similar EXPLAIN using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides Prove theorems involving similarity MGSE9-12GSRT5 USE congruence and similarity criteria for triangles to SOLVE problems and to PROVE relationships in geometric figures Understand congruence in terms of rigid motions MGSE9-12GCO6 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 Prove geometric theorems MGSE9-12GCO10 PROVE theorems about triangles Theorems include measures of interior angles of a triangle sum to 180 degrees base angles of isosceles triangles are congruent the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length the medians of a triangle meet at a point MGSE9-12GCO11 PROVE theorems about parallelograms Theorems include opposite sides are congruent opposite angles are congruent the diagonals of a parallelogram bisect each other and

conversely rectangles are parallelograms with congruent diagonals



2

ldquoUnwrappedrdquo Priority Standards

ldquoUnwrappedrdquo Skills (Students Need

to Be Able to Do)

ldquoUnwrappedrdquo Concepts

(Students Need to Know)

Bloomrsquos Taxonomy Levels

DOK (For Overall Standard)

MGSE9-12GSRT2 USE DECIDE EXPLAIN

The definition of similarity in terms of similarity transformations If 2 figures are similar The meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides

3 (Apply) 4 (Analyze) 4 (Analyze)

2 (SkillConcept)

MGSE9-12GSRT5 USE SOLVE PROVE

Congruence and similarity criteria for triangles Problems Relationships in geometric figure

3 (Apply) 3 (Apply) 5 (Evaluate)

3 (StrategicReasoning)

MGSE9-12GCO6 USE TRANSFORM PREDICT USE DECIDE

Geometric descriptions of rigid motions Figures The effect of a given rigid motion on a given figure The definition of congruence in terms of rigid motions If 2 figures are congruent

3 (Apply) 3 (Apply) 4 (Analyze) 3 (Apply) 5 (Evaluate)

2 (SkillConcept)

MGSE9-12GCO10 PROVE INCLUDE

Theorems about triangles Measures of interior angles of a triangle sum to 180 degrees Base angles of isosceles triangles are congruent The segment joining midpoints of two sides of a triangle is parallel to

5 (Evaluate) 5 (Evaluate)

4 (Extended Thinking)



3

the third side and half the length The medians of a triangle meet at a point


Theorems about parallelograms Opposite sides are congruent opposite angles are congruent The diagonals of a parallelogram bisect each other Rectangles are parallelograms with congruent diagonals



Supporting Standards

Understand similarity in terms of similarity transformations MGSE9-12GSRT1 Verify experimentally the properties of dilations given by a center and a scale factor a The dilation of a line not passing through the center of the dilation results in a parallel line and leaves a line passing through the center unchanged b The dilation of a line segment is longer or shorter according to the ratio given by the scale factor MGSE9-12GSRT3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar Prove theorems involving similarity MGSE9-12GSRT4 Prove theorems about triangles Theorems include a line parallel to one side of a triangle divides the other two proportionally (and its converse) the Pythagorean Theorem using triangle similarity Understand congruence in terms of rigid motions MGSE9-12GCO7 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 MGSE9-12GCO8 Explain how the criteria for triangle congruence (ASA SAS and SSS) follow from the definition of congruence in terms of rigid motions (Extend to include HL and AAS) Prove geometric theorems MGSE9-12GCO9 Prove theorems about lines and angles Theorems include vertical angles are congruent when a transversal crosses parallel lines alternate interior angles are congruent and corresponding angles are congruent points on a perpendicular bisector of a line segment are exactly those equidistant from the segmentrsquos endpoints Make geometric constructions MGSE9-12GCO12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge string reflective devices paper folding dynamic geometric software etc) Copying a segment copying an angle bisecting a segment bisecting an angle constructing perpendicular lines including the perpendicular bisector of a line segment and constructing a line parallel to a given line through a point not on the line



4

MGSE9-12GCO13 Construct an equilateral triangle a square and a regular hexagon each inscribed in a circle MGSE9-12GGPE4 Use coordinates to prove simple geometric theorems algebraically For example prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle (focus on quadrilaterals right triangles)



5

Standards of Mathematical Practice

1 Make sense of problems and persevere in solving them (Daily) 2 Reason abstractly and quantitatively (Daily) 3 Construct viable arguments and critique the reasoning of others 4 Model with mathematics 5 Use appropriate tools strategically (Daily) 6 Attend to precision 7 Look for and make use of structure 8 Look for and express regularity in repeated reasoning

Essential Questions Corresponding Big Ideas

bull What is a dilation and how does this transformation affect a figure in the coordinate plane

bull What strategies can I use to determine missing side lengths and areas of similar figures

bull What are isometric transformations and how do they differ from dilation

bull How do I prove geometric theorems involving lines angles triangles and parallelograms

bull How can I solve for unknown measures in geometric figures

bull How do I apply my understanding of geometric principles to create constructions

bull Dilation is a similarity transformation

bull Proportions can be used to solve for missing information in similar figures

bull Isometric transformations are rigid motions The image is congruent to the pre-image

bull Construct formal mathematical arguments

using definitions properties postulates related

to lines angles triangles and parallelograms

bull Apply theorem postulates definitions and geometric properties to solve for unknown values in geometric figures

bull Use tools to construct segments angles bisectors perpendicular and parallel lines



6



7

Unit Assessments

Pre-Assessment Post-Assessment

Student Version 10__AnalyticGeometry_Unit2_pre-assessment SUdoc Teacher Version 10__AnalyticGeometry_Unit2_pre-assessment TEdoc

Student Version

Dekalb Benchmark Assessment

Teacher Version



8

Performance Assessment

Engaging Scenario

Situation

Math Department is seeking support from students in creating a mural to illustrate mathematical creativity and to promote real-world applications of understanding congruence in terms of rigid motions making geometric constructions and proving theorems involving lines angles figures similarity transformations and congruence

Challenge Create a mathematically accurate mural using geometric shapes and the concepts derived around properties of lines angles figures transformations similarity and congruent figures

Student Role Project Manager Community Liaison Artist and all will be Problem-Solver(s) using the language of the standards and skills acquired throughout the learning process

Intended Audience Math Department Principal District Possibly other High Schools

Product or Performance Students will create a portfolio of evidence of geometric understanding along with a geometric mural design that could possibly be used in the school

Teacher Script ldquoYour Principal wishes to display a new mural in the hallway Instead of hiring an outside company to design and create a mural heshe want the students of ______ High School to create a mathematical mural You as students have the opportunity to propose a mural design to the principal Before you do this you must prove that your mural contains geometric designs that highlight the properties of lines figures and their relationship to each other To provide evidence of your understanding of these properties you will incorporate principles you learn from class performance tasks Your group will create a mural design and a report that explains how you have applied geometric properties in your muralrdquo



9

Performance Task Synopses

Task 1 Dilations In the Coordinate Plane (Unit 1 state Frameworks pg 158 ndash 168) MGSE9-12GSRT1 MGSE9-12GSRT2 Standards of Mathematical Practice 1 4 7 and 8 In this task students will explore properties of similar figures and dilation using graph paper to illustrate the changes shapes undergo when students dilate or stretch them

Task 2 Line and Parallelogram Proofs MGSE9-12GCO11 MGSE9-12GCO9 Students will complete the three activities for each special quadrilateral Students will list properties of quadrilaterals construct quadrilaterals and label the properties and create a story song poem or essay about special quadrilaterals Task 3 Triangle Proofs MGSE9-12GCO10 In this task students assemble strips and individual puzzle pieces of statements and proofs pertaining to a given triangle All unit standards Task 4 Completed Mural Design and Proposal Students will apply skills from the previous tasks to complete their mural design and present a proposal to the class



10

Performance Task 1 In Detail

Understand similarity in terms of similarity transformations MGSE9-12GSRT1 Verify experimentally the properties of dilations given by a center and a scale factor a The dilation of a line not passing through the center of the dilation results in a parallel line and leaves a line passing through the center unchanged b The dilation of a line segment is longer or shorter according to the ratio given by the scale factor MGSE9-12GSRT2 Given two figures USE the definition of similarity in terms of similarity transformations to DECIDE if they are similar EXPLAIN using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides Standards of Mathematical Practice 1 Make sense of problems and persevere in solving them 4 Model with mathematics 7 Look for and make use of structure 8 Look for and express regularity in repeated reasoning

Extensions MGSE9-12GSRT1 Verify experimentally the properties of dilations given by a center and a scale factor

MGSE9-12GSRT3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar

MGSE9-12GSRT4 Prove theorems about triangles Theorems include a line parallel to one side of a triangle divides the other two proportionally (and its converse) the Pythagorean Theorem using triangle similarity

MGSE9-12GCO10 Prove theorems about triangles Theorems include measures of interior angles of a triangle sum to 180 degrees base angles of isosceles triangles are congruent the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length the medians of a triangle meet at a point Circumstances of Performance In-Class (Approximate Time 75-90 minutes) Plotting the order pairs can be given the night before for homework In this task students will explore properties of similar figures and dilation using graph paper to illustrate the changes shapes undergo when students dilate or stretch them

Task 1 Student Directions Per the directions on the GA Performance Task ldquoDilations in the

Coordinate Plane ndash pages 168 ndash 169 on httpswwwgeorgiastandardsorgGeorgia-

StandardsFrameworksAnalytic-Geometry-Unit-1pdf students will

Plot the order pairs to create 6 figures Determine which figures are similar by using the definition of similarity Compare corresponding sides and angles Create general rules for similar figures Determine the effects of multiplying coordinates (including fractions less than 1) Perform a dilation whose center is not the origin



11


Students will incorporate what they learn about similarity in this performance task into the production of the mural They should investigate appropriate scale factors for the actual mural dimensions based upon available wall space and proposed size of blueprint

Task 1 Teacher Notes The entire task is described on pages 158-168 in the Georgia Frameworks for Unit 1 httpswwwgeorgiastandardsorgGeorgia-StandardsFrameworksAnalytic-Geometry-Unit-1pdf Note Teacher may choose to require students to perform a dilation of a student-selected designimage from their mural blueprint

Extensions

Re-vamp the plots of the noses so that they create triangles Use the triangles to aid in teaching of standards

Performance Task 1 Scoring Guide

4 Advanced 3 Proficient 2 Basic 1 Below Basic

All Proficient criteria plus o Correctly described

all 4 of the proficient concepts

o Correctly created and identifies points in problem 7

o Correctly completed all 6 figures

o Correctly answered and provides proper reasoning to questions 1 4 and 5

o Correctly described 3 of the following 4 concepts o Congruent

angles o Equal ratios of

sides o Enlargement

vs Reduction o Same shape

but not necessarily the same size

o Did not complete all 6 figures

o Answers were partially correct and math reasoning were hard to follow with little explanation

o Correctly described 2 of the 4 concepts

o Responses were incorrect or incomplete

o Provided explanations andor mathematical representations that are not clearly understood or interpreted



12


Prove geometric theorems MGSE9-12GCO11 PROVE theorems about parallelograms Theorems include opposite sides are congruent opposite angles are congruent the diagonals of a parallelogram bisect each other and

conversely rectangles are parallelograms with congruent diagonals MGSE9-12GCO9 Prove theorems about lines and angles Theorems include vertical angles are congruent when a transversal crosses parallel lines alternate interior angles are congruent and corresponding angles are congruent points on a perpendicular bisector of a line segment are exactly those equidistant from the segmentrsquos endpoints Circumstances of Performance In class and Out of Class (Approximate Time 3-4 hours) Task 2 Special Quadrilateral Properties Project Task 2 Student Directions Part I Students will complete the three activities below for each special quadrilateral (parallelogram rectangle rhombus and square) First activity List all the properties of each special quadrilateral Second activity Using a ruler protractor pencil and colored pencils construct the quadrilateral and correctly label ALL the properties of each special quadrilateral Third activity Find and attach a copy of a photo or picture that shows an example of an actual real world object that is or contains the listed special quadrilateral Identify the quadrilateral by outlining it with a marker Below the picture describe the quadrilateralrsquos use in the real-life situation and explain how you know it is the specified special quadrilateral After completing the tasks for the 5 quadrilaterals complete Part II Part II Write a story song poem or essay on one of the following subjects 1 The similarities and differences of the 5 quadrilaterals 2 How quadrilaterals and triangles are related 3 What the world would be like if we did not have quadrilaterals Task 2 Teacher Notes Students will take what they have learned about the real world quadrilaterals and incorporate it into a portion of their mural In Resources there is the student handout to complete the activities


All Proficient criteria plus o Constructions

were neat colorful and creatively

o All properties were listed for each special quadrilateral

o Quadrilaterals were constructed

o Some properties were listed for each special quadrilateral

o Missing one of the products (properties

o Some quadrilaterals did

not have any properties listed

o Constructions were incomplete or nonexistent



13


labeled and precise

o Explanations of real world objects used mathematical examples and language to accurately articulate all properties of the quadrilateral

o Story song

poem or essay was creative insightful and well presented

neatly accurately and all properties are labeled

o Real-world

example matches the special quadrilateral and were correctly outlined

o Description of

real world example was clear concise and accurate

o The explanation

of the real-world object was correct

o Story song

poem or essay was topical and mathematically accurate

real world examples or storysongpoemessay)

o Description of the real

world example was not completely clear or accurate

o There a couple of

inaccuracies in the storysongpoemessay)

o Provided explanations

andor mathematical representations that were not clearly understood or interpreted

o Missing two or more products (properties real world examples or storysongpoemessay)


Prove geometric theorems MGSE9-12GCO10 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 Circumstances of Performance In class (Approximate Time 90 -120 minutes) Task 3 Triangle Proofs Task 3 Student Directions Students will assemble proof puzzles of increasing difficulty Stage 1 ndash students will put strips that include both statement and reason in the correct order to generate a valid proof Stage 2 ndash students will sequence reasons and corresponding statements written on separate cards in order to generate a valid proof Stage 3- students will assemble a proof where some cards are blank and they must provide the missing statement(s) or reason(s) Extension ndash Convert table proofs to flow diagram and paragraph proofs



14


Task 3 Teacher Notes Teacher should activate prior knowledge by creating a proof for an algebraic equation (eg prove x=5 given 2x+3=13) Once students understand the structure and flow of a proof instruct them to work in pairs to assemble the proof puzzles Teacher should ensure that the proof puzzles include proofs related directly to the standard for triangle proofs (GCO10) Teacher should review puzzles at each stage before students move to the next stage Address misconceptions Refer to the Planning and Managing a Mural Project PP for an example to project during this task Teachers will have to create problems for all stages for students



All Proficient criteria plus o A flowchart that

demonstrated the assembled proof in stage 3

o A paragraph proof that demonstrated the assembled proof in stage 3

o By stage 3 the student was able to assemble a proof with appropriate statements and reasons

o Assembled Stage 1

and 2 correctly with valid justification but the student could not complete Stage 3 independently

o Assembled Stage 1 correctly but the student could not complete Stage 2 or 3 independently


Task 4 Student Directions In groups students will create a proposal for a mural The proposal must include a small-scale version of the mural and a corresponding scale factor that would allow it to fit in the space allotted by the school The written description should include how the mural incorporates the following mathematical principles learned in this unit similarity congruence parallel lines transversals parallelograms triangles angles and associated properties and transformations in the coordinate plane Task 4 Teacher Notes The teacher should communicate expectations when introducing the engaging scenario so that students can work on their designs throughout the unit as they complete the performance tasks for this unit The teacher should review progress on the mural design with students at designated checkpoints (possibly after each of the 4 key performance tasks) Teacher should encourage students to research art and mathematics online to get ideas for their murals



All Proficient criteria plus o Design was

creative visually appealing colorful and ready for implementation

o Students calculated and provided the correct dimensions and scale factor for the mural design in comparison to the canvas space

o Met 3 or fewer of the Proficient criteria

o Mural had 4 or less of the 6 concepts represented in the design


o Mural contained 2 or less of the 6 concepts represented in the design



15


o Mural contained all 6 concepts in its design

o Mural had a representation of 5 of each the following concepts

bull similarity

bull congruence

bull parallel lines and transversals

bull parallelograms

bull triangles and angles

bull associated properties of each

o Description of mural

articulated how the previous incorporated concepts are within the mural design

o Design was complete accurate and precise



16

Instructional Strategies Instructional Strategies

Research-Based Effective Teaching Strategies

21st Century Learning Skills

Learning Objectives (posted and referenced)

Identifying Similarities and Differences

Summarizing and Note Taking

Reinforcing Effort Providing Recognition

Homework and Practice

Nonlinguistic Representations

Cooperative Learning

Purposeful small group instruction

Increased think time

Setting Objectives Providing Feedback

Check for Understanding

Generating and Testing Hypotheses

Cues Questions and Advance Organizers

Interdisciplinary Non-Fiction Writing

Teamwork and Collaboration

Initiative and Leadership

Curiosity and Imagination

Innovation and Creativity

Critical thinking and Problem Solving

Flexibility and Adaptability

Effective Oral and Written Communication

Accessing and Analyzing Information

Other



17

Intervention Strategies Intervention Strategies

(Tiers 1 2 3) Additional Supports in

Classroom

Specially Designed Instruction for Special

Education Students

Strategies for English Language Learners

Re-voicing

Explaining

Prompting for participation

Challenging or countering

Asking ldquoWhyrdquo ldquoHowrdquo

Reread

Practice new academic vocab

Assistive technology

Pre-teach amp re-teach in a different way

Repetition

Use of manipulatives

Collaborative work

Directexplicit instruction

ldquoChunkingrdquo

Accommodating different

learning styles

Create differentiated text sets

Providing additional guided practice

Conferencing

Additional time

Small group collaboration

Modify quantity of work

Take studentrsquos dictation

Scaffold information

Differentiated content process or product

Consistent reward system

Refer to studentsrsquo IEP or 504 plan


VisualsRealia

Front-loading

EchoingChoral response

Color-coding

Multiple exposures in

different media

Pair-share

Modeling

Language scaffolds eg sentence frames

Deconstruct complex sentences and texts

L1 support

increased opportunities for student-student talk

Strategic vocabulary instruction

Additional think time



18

Strategies for Gifted Learners

Tier 1 Low Preparation Tier 2 Medium Preparation

Flexible-Learning Groups by Readiness Interest Learning Profiles

Gifted Education Cluster Classes

Choice of Books Gifted Education Collaboration Classes

Homework Options Tiered Activities and Products

Use of Reading Buddies Use of Literature Clubs

Various Journal Prompts Multiple Testing Options

StudentTeacher Goal Setting Multiple Texts

Varied Pacing with Anchor Options Alternative Assessments

Work Alone or Together Subject Advancement within class

Flexible Seating Curriculum Compacting

Varied Scaffolding Tiered Centers

Varied Computer Programs Spelling by Readiness

Design-A-DAY Varying Organizers

Varied Supplemental Materials Community Mentorships

Computer Mentors Stations

Think-Pair-Share by Readiness Interest Learning Profiles

Group Investigations

Open-ended Activities Students are Assessed in Multiple Ways

Explorations by Interest Student choice in selecting learning activities

Options for Competition Simulations

Tier 3 High Tier 4 AdvancedAutonomous

Advanced Content Englishlanguage arts mathematics science andor social studies courses

Above grade level accelerated Englishlanguage arts mathematics science andor social studies courses

Resource Classes Advanced Placement Classes

IndependentDirected Study International Baccalaureate Classes

Socratic Seminars InternshipMentorships

Whole Grade Acceleration

Instructional Resources and Materials Suggested Resources Suggested Technology Resources



19

Math Tools

o Graph paper o Colored pencils o Protractor o Ruler o Mini Whiteboards o Mini Expo markers

Refer to the Unit 1 Planning and Managing a Mural Projectppt Power Point to accompany this Units Performance Tasks in the Resource Folder

Refer to myhrwcom Teacher Center for Reading Strategies and Success for every learnerrdquo before each Priority Standard See Resource Folder

List of GeometryMath Symbols

State Framework Unit 1

Khan Academy Unit 1 see resource folder Khanacademyorg Geogebraorg Kahootcom Plickerscom Prezicom Learnzillioncom Desmosorg Socrative virtualnerdcom

Unit Vocabulary

Unit Vocabulary Terms Interdisciplinary

Connections

Academic Tier 2 Unit-Specific Domain Tier 3



20

angle conjecture contrapositive dilation distance exterior Interior length measure mural Illustrate accurate shapes project manager community liaison portfolio

acute angle altitude altitude bisector centroid circumcenter circumscribed concurrent consecutive conditional statement congruent construction coordinate corresponding corresponding angles corresponding sides counterexample dilation dilation distance exterior incenter incenter of a triangle inscribed interior inverse isometry length line locus logically equivalent statements measure median of a triangle midpoint midsegment of a triangle obtuse angle obtuse angle orthocenter of a triangle plane parallel lines parallelogram perpendicular bisector perpendicular lines point of concurrency polygon proof quadrilateral rectangle remote interior angle constant rhombus right angle rigid transformation scale factor

VAHSDRC1 Applies information from other disciplines to enhance the understanding and production of artworks a Uses inspiration from other disciplines to influence idea development in art b Identifies specific knowledge and skills from other discipline that informs the planning and execution of drawing c Understands how knowledge of art enriches and enhances learning in other core disciplines d Makes interdisciplinary connections applying art skills knowledge and habits of mind to improve understanding in other disciplines e Develops the ability to integrate visual and verbal skills to communicate clearly and eloquently



21

segment bisector similar polygons similarity ratio similarity transformation square square theorem straight angle transversal triangle vertex



22

Weekly Planner Course Analytic Geometry Unit Unit 2 Similarity Congruence and Proofs

Pacing Priority (in bold) and Supporting Standards

Engaging Learning Experiences

Core Instruction (in bold) and additional resources

Formative Assessments

Mathematical Literacy The ability to read listen think creatively and communicate about problem situations mathematical representations and the validation of solutions will help students to develop and deepen their understanding of mathematics (National Council of Teachers of Mathematics 2000)

7 weeks ndash Traditional 35 weeks - Block

Make modifications to the pacing based upon student pre-assessment results and the daily

analysis of student work

See CAAG for a listing of all standards Instruction should be supported with the implementation of the Standards for Mathematical Practice (SMP)

Students should complete the listed experiences to support understanding and mastery of the math standards Students are expected to exhibit the SMP

Teachers should implement the listed experiences to support core instruction on the math standards Teachers should model the SMP during the 3-Part Lesson Structure

Teachers should use the assessments to support student learning at all levels The unit pre-assessment should be administered prior to unit instruction for diagnostic purposes

o Differentiate instruction based upon the pre-assessment results o Make modifications to the pacing based upon student pre-assessment results and the daily analysis of student work o Implement the Formative Assessment Lesson (FAL) to monitor the progress of students during the instructional unit o Introduce the learning targets on a daily basis in kid friendly language using ldquoI Canrdquo statements o Provide instruction using the Concrete-Representational-Abstract (CRA) sequence of instruction o Utilize the Gradual Release Model of Responsibility (I do We do You do) during instruction to support student learning of

conceptsskills o Use UPS Check and the 3 Read Protocol for the Problem Solving Process o Use Newmanrsquos Prompt to diagnose the hurdles students face while problem solving o Incorporate Mathematical Visualization to model math concepts skills and problem solving o Remind students that mistakes are respected expected and inspected in the mathematics classroom

Unit Expectations o Performance Assessment (4 Tasks and Scoring Guide) o Formative Assessment Lessons o GADOE Instructional Tasks

o Weekly core instruction should include the implementation of instructional tasks from the Georgia Department of Education (GADOE) located at wwwgeorgiastandardsorg along with other district and supplemental instructional resources Included in the planner are possible suggestions for GADOE tasks



23





Week 1

MGSE9-12GSRT2 MGSE9-12GSRT5 MGSE9-12GCO6 MGSE9-12GSRT1 MGSE9-12GSRT3

Intro Engaging Scenario Off the Wall Mural Project and Task 1 Dilations in the Coordinate Plane from Georgia Framework

Transformations in

Coordinate Plane ndash Activate

prior knowledge review rigid

motion ndash translations

reflections rotation

Use Geogebra (free) or Gizmos

(subscription required)

Dilations Use Geogebra Use Matt Winking Dilations Lab Similarity Use Matt Winking Similar Figures or other comparable resources

Pre-Assessment (Unit Pre-Assessment) Discussion of the Essential Questions (throughout unit) Task 1 scoring guide Cooperative Group Presentation Suggested informal progress monitoring checks (throughout the unit)

bull Questioning

bull Homework check

bull Student-led class discussion

bull Exit slip

bull Socrative Question

Week 2

MGSE9-12GSRT2 MGSE9-12GSRT5 MGSE9-12GCO6 MGSE9-12GCO7 MGSE9-12GCO8

Introducing Congruence (Spotlight Task) From Georgia Framework Formative Assessment Lesson Analyzing Congruency Proofs from Georgia Framework

Triangle Congruence Use Math Illuminations Congruence Theorems (free) Of Gizmos Proving Triangles Congruent (subscription required) Use Showing Triangles Congruent Using Rigid Motion

Task 2 scoring guide Cooperative Group Presentation Khan Academy practicedoc Individual white boards



24





Week 3

MGSE9-12GCO11 MGSE9-12GCO9 MGSE9-12GGPE4

Introductory Activity (Spotlight Task) Georgia Framework Task 3 Start Quadrilaterals Properties Project

Basic geometry terms Use pp 4-7 VA_DOE_geometry_vocab Parallel Lines amp Transversals Use free interactive tools on parallel lines amp transversals Or hand-held Exploragons (must be purchased) Use pp 24-29 VA_DOE_geometry_vocab Properties of Quadrilaterals Use graphic organizer QuadrilateralFamilyTreeKeypdf

Task 3 scoring guide Thumbs Up and Thumbs Down Active Expressions

Week 4 MGSE9-12GCO11 MGSE9-12GCO9 MGSE9-12GGPE4

Task 3 Finish Quadrilaterals Properties Project Task Lunch Line from Georgia Framework

Properties of Quadrilaterals and Special Parallelograms Use free interactive tools such as Math is Fun Quadrilaterals Or hand-held Exploragons (must be purchased) Use Matt Winkings Quadrilateral Properties or other comparable activity

Graphic Organizer Cooperative Group Presentation

Week 5

MGSE9-12GCO10 MGSE9-12GCO9 MGSE9-12GSRT4

Task 4 Triangle Proofs

Purpose and Structure of Proofs An Introduction to Mathematical Theorems Understand Properties of triangles angles and lines Angle Sums Illuminations Math Warehouse vertical angles interactive CK-12 Midsegment Lesson

Task 4 scoring guide Graphic Organizer Cooperative Group Presentation



25





Develop proofs about triangles angles and lines Use pp 3132344043-46 in Analytic Geometry EOC StudyResource Guide

Week 6 MGSE9-12GCO10 MGSE9-12GCO9 MGSE9-12GSRT4

Culminating Task Off the Wall Mural Project

Develop proofs about triangles angles and lines Use pp 3132344043-46 in Analytic Geometry EOC StudyResource Guide Culminating Task Use Planning and Managing a Mural Project presentation

Task 5 scoring guide

Week 7

MGSE9-12GSRT2 MGSE9-12GSRT5 MGSE9-12CO6 MGSE9-12CO10 MGSE9-12CO11 MGSE9-12GSRT1 MGSE9-12GSRT3 MGSE9-12GSRT4 MGSE9-12GCO7 MGSE9-12GCO8 MGSE9-12GCO9 MGSE9-12GCO12 MGSE9-12GCO13

Culminating Task Finish Off the Wall Mural Project

Constructions Use interactive construction tools Use pp 47-58 in Analytic Geometry EOC StudyResource Guide Cumulative Review Revisit preceding activities and tasks Use pp 22-46 in Analytic Geometry EOC StudyResource Guide

Cooperative Group Presentation Post Assessment (District Benchmark)

DeKalb County School District

Rigorous Curriculum Design

Unit Planning Organizer

Unit Assessments


Instructional Strategies

Intervention Strategies

Instructional Resources and Materials

Unit Vocabulary

Weekly Planner



2

ldquoUnwrappedrdquo Priority Standards

ldquoUnwrappedrdquo Skills (Students Need

to Be Able to Do)

ldquoUnwrappedrdquo Concepts

(Students Need to Know)

Bloomrsquos Taxonomy Levels

DOK (For Overall Standard)

MGSE9-12GSRT2 USE DECIDE EXPLAIN

The definition of similarity in terms of similarity transformations If 2 figures are similar The meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides

3 (Apply) 4 (Analyze) 4 (Analyze)

2 (SkillConcept)

MGSE9-12GSRT5 USE SOLVE PROVE

Congruence and similarity criteria for triangles Problems Relationships in geometric figure

3 (Apply) 3 (Apply) 5 (Evaluate)

3 (StrategicReasoning)

MGSE9-12GCO6 USE TRANSFORM PREDICT USE DECIDE

Geometric descriptions of rigid motions Figures The effect of a given rigid motion on a given figure The definition of congruence in terms of rigid motions If 2 figures are congruent

3 (Apply) 3 (Apply) 4 (Analyze) 3 (Apply) 5 (Evaluate)

2 (SkillConcept)


Theorems about triangles Measures of interior angles of a triangle sum to 180 degrees Base angles of isosceles triangles are congruent The segment joining midpoints of two sides of a triangle is parallel to





3










4




5




















6



7

Unit Assessments



Student Version


Teacher Version



8


Engaging Scenario

Situation









9






10













11




Extensions











sides o Enlargement










12
















13


labeled and precise


o Story song



o Real-world


o Description of


o The explanation


o Story song





o There a couple of









14









o Assembled Stage 1
















15




bull similarity

bull congruence


bull parallelograms








16


























Other



17



Classroom


Education Students


Re-voicing

Explaining




Reread




Repetition


Collaborative work


ldquoChunkingrdquo


learning styles



Conferencing

Additional time









VisualsRealia

Front-loading


Color-coding


different media

Pair-share

Modeling



L1 support






18

































19

Math Tools







Unit Vocabulary


Connections




20






21




22




















23





Week 1



Transformations in









bull Questioning

bull Homework check


bull Exit slip


Week 2







24





Week 3









Week 5







25










Week 7








Unit Assessments





Unit Vocabulary

Weekly Planner



3










4




5




















6



7

Unit Assessments



Student Version


Teacher Version



8


Engaging Scenario

Situation









9






10













11




Extensions











sides o Enlargement










12
















13


labeled and precise


o Story song



o Real-world


o Description of


o The explanation


o Story song





o There a couple of









14









o Assembled Stage 1
















15




bull similarity

bull congruence


bull parallelograms








16


























Other



17



Classroom


Education Students


Re-voicing

Explaining




Reread




Repetition


Collaborative work


ldquoChunkingrdquo


learning styles



Conferencing

Additional time









VisualsRealia

Front-loading


Color-coding


different media

Pair-share

Modeling



L1 support






18

































19

Math Tools







Unit Vocabulary


Connections




20






21




22




















23





Week 1



Transformations in









bull Questioning

bull Homework check


bull Exit slip


Week 2







24





Week 3









Week 5







25










Week 7








Unit Assessments





Unit Vocabulary

Weekly Planner



4




5




















6



7

Unit Assessments



Student Version


Teacher Version



8


Engaging Scenario

Situation









9






10













11




Extensions











sides o Enlargement










12
















13


labeled and precise


o Story song



o Real-world


o Description of


o The explanation


o Story song





o There a couple of









14









o Assembled Stage 1
















15




bull similarity

bull congruence


bull parallelograms








16


























Other



17



Classroom


Education Students


Re-voicing

Explaining




Reread




Repetition


Collaborative work


ldquoChunkingrdquo


learning styles



Conferencing

Additional time









VisualsRealia

Front-loading


Color-coding


different media

Pair-share

Modeling



L1 support






18

































19

Math Tools







Unit Vocabulary


Connections




20






21




22




















23





Week 1



Transformations in









bull Questioning

bull Homework check


bull Exit slip


Week 2







24





Week 3









Week 5







25










Week 7








Unit Assessments





Unit Vocabulary

Weekly Planner



5




















6



7

Unit Assessments



Student Version


Teacher Version



8


Engaging Scenario

Situation









9






10













11




Extensions











sides o Enlargement










12
















13


labeled and precise


o Story song



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o Description of


o The explanation


o Story song





o There a couple of









14









o Assembled Stage 1
















15




bull similarity

bull congruence


bull parallelograms








16


























Other



17



Classroom


Education Students


Re-voicing

Explaining




Reread




Repetition


Collaborative work


ldquoChunkingrdquo


learning styles



Conferencing

Additional time









VisualsRealia

Front-loading


Color-coding


different media

Pair-share

Modeling



L1 support






18

































19

Math Tools







Unit Vocabulary


Connections




20






21




22




















23





Week 1



Transformations in









bull Questioning

bull Homework check


bull Exit slip


Week 2







24





Week 3









Week 5







25










Week 7








Unit Assessments





Unit Vocabulary

Weekly Planner



6



7

Unit Assessments



Student Version


Teacher Version



8


Engaging Scenario

Situation









9






10













11




Extensions











sides o Enlargement










12
















13


labeled and precise


o Story song



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o There a couple of









14









o Assembled Stage 1
















15




bull similarity

bull congruence


bull parallelograms








16


























Other



17



Classroom


Education Students


Re-voicing

Explaining




Reread




Repetition


Collaborative work


ldquoChunkingrdquo


learning styles



Conferencing

Additional time









VisualsRealia

Front-loading


Color-coding


different media

Pair-share

Modeling



L1 support






18

































19

Math Tools







Unit Vocabulary


Connections




20






21




22




















23





Week 1



Transformations in









bull Questioning

bull Homework check


bull Exit slip


Week 2







24





Week 3









Week 5







25










Week 7








Unit Assessments





Unit Vocabulary

Weekly Planner



7

Unit Assessments



Student Version


Teacher Version



8


Engaging Scenario

Situation









9






10













11




Extensions











sides o Enlargement










12
















13


labeled and precise


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o There a couple of









14









o Assembled Stage 1
















15




bull similarity

bull congruence


bull parallelograms








16


























Other



17



Classroom


Education Students


Re-voicing

Explaining




Reread




Repetition


Collaborative work


ldquoChunkingrdquo


learning styles



Conferencing

Additional time









VisualsRealia

Front-loading


Color-coding


different media

Pair-share

Modeling



L1 support






18

































19

Math Tools







Unit Vocabulary


Connections




20






21




22




















23





Week 1



Transformations in









bull Questioning

bull Homework check


bull Exit slip


Week 2







24





Week 3









Week 5







25










Week 7








Unit Assessments





Unit Vocabulary

Weekly Planner



8


Engaging Scenario

Situation









9






10













11




Extensions











sides o Enlargement










12
















13


labeled and precise


o Story song



o Real-world


o Description of


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o There a couple of









14









o Assembled Stage 1
















15




bull similarity

bull congruence


bull parallelograms








16


























Other



17



Classroom


Education Students


Re-voicing

Explaining




Reread




Repetition


Collaborative work


ldquoChunkingrdquo


learning styles



Conferencing

Additional time









VisualsRealia

Front-loading


Color-coding


different media

Pair-share

Modeling



L1 support






18

































19

Math Tools







Unit Vocabulary


Connections




20






21




22




















23





Week 1



Transformations in









bull Questioning

bull Homework check


bull Exit slip


Week 2







24





Week 3









Week 5







25










Week 7








Unit Assessments





Unit Vocabulary

Weekly Planner



9






10













11




Extensions











sides o Enlargement










12
















13


labeled and precise


o Story song



o Real-world


o Description of


o The explanation


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o There a couple of









14









o Assembled Stage 1
















15




bull similarity

bull congruence


bull parallelograms








16


























Other



17



Classroom


Education Students


Re-voicing

Explaining




Reread




Repetition


Collaborative work


ldquoChunkingrdquo


learning styles



Conferencing

Additional time









VisualsRealia

Front-loading


Color-coding


different media

Pair-share

Modeling



L1 support






18

































19

Math Tools







Unit Vocabulary


Connections




20






21




22




















23





Week 1



Transformations in









bull Questioning

bull Homework check


bull Exit slip


Week 2







24





Week 3









Week 5







25










Week 7








Unit Assessments





Unit Vocabulary

Weekly Planner



10













11




Extensions











sides o Enlargement










12
















13


labeled and precise


o Story song



o Real-world


o Description of


o The explanation


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o There a couple of









14









o Assembled Stage 1
















15




bull similarity

bull congruence


bull parallelograms








16


























Other



17



Classroom


Education Students


Re-voicing

Explaining




Reread




Repetition


Collaborative work


ldquoChunkingrdquo


learning styles



Conferencing

Additional time









VisualsRealia

Front-loading


Color-coding


different media

Pair-share

Modeling



L1 support






18

































19

Math Tools







Unit Vocabulary


Connections




20






21




22




















23





Week 1



Transformations in









bull Questioning

bull Homework check


bull Exit slip


Week 2







24





Week 3









Week 5







25










Week 7








Unit Assessments





Unit Vocabulary

Weekly Planner



11




Extensions











sides o Enlargement










12
















13


labeled and precise


o Story song



o Real-world


o Description of


o The explanation


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o There a couple of









14









o Assembled Stage 1
















15




bull similarity

bull congruence


bull parallelograms








16


























Other



17



Classroom


Education Students


Re-voicing

Explaining




Reread




Repetition


Collaborative work


ldquoChunkingrdquo


learning styles



Conferencing

Additional time









VisualsRealia

Front-loading


Color-coding


different media

Pair-share

Modeling



L1 support






18

































19

Math Tools







Unit Vocabulary


Connections




20






21




22




















23





Week 1



Transformations in









bull Questioning

bull Homework check


bull Exit slip


Week 2







24





Week 3









Week 5







25










Week 7








Unit Assessments





Unit Vocabulary

Weekly Planner



12
















13


labeled and precise


o Story song



o Real-world


o Description of


o The explanation


o Story song





o There a couple of









14









o Assembled Stage 1
















15




bull similarity

bull congruence


bull parallelograms








16


























Other



17



Classroom


Education Students


Re-voicing

Explaining




Reread




Repetition


Collaborative work


ldquoChunkingrdquo


learning styles



Conferencing

Additional time









VisualsRealia

Front-loading


Color-coding


different media

Pair-share

Modeling



L1 support






18

































19

Math Tools







Unit Vocabulary


Connections




20






21




22




















23





Week 1



Transformations in









bull Questioning

bull Homework check


bull Exit slip


Week 2







24





Week 3









Week 5







25










Week 7








Unit Assessments





Unit Vocabulary

Weekly Planner



13


labeled and precise


o Story song



o Real-world


o Description of


o The explanation


o Story song





o There a couple of









14









o Assembled Stage 1
















15




bull similarity

bull congruence


bull parallelograms








16


























Other



17



Classroom


Education Students


Re-voicing

Explaining




Reread




Repetition


Collaborative work


ldquoChunkingrdquo


learning styles



Conferencing

Additional time









VisualsRealia

Front-loading


Color-coding


different media

Pair-share

Modeling



L1 support






18

































19

Math Tools







Unit Vocabulary


Connections




20






21




22




















23





Week 1



Transformations in









bull Questioning

bull Homework check


bull Exit slip


Week 2







24





Week 3









Week 5







25










Week 7








Unit Assessments





Unit Vocabulary

Weekly Planner



14









o Assembled Stage 1
















15




bull similarity

bull congruence


bull parallelograms








16


























Other



17



Classroom


Education Students


Re-voicing

Explaining




Reread




Repetition


Collaborative work


ldquoChunkingrdquo


learning styles



Conferencing

Additional time









VisualsRealia

Front-loading


Color-coding


different media

Pair-share

Modeling



L1 support






18

































19

Math Tools







Unit Vocabulary


Connections




20






21




22




















23





Week 1



Transformations in









bull Questioning

bull Homework check


bull Exit slip


Week 2







24





Week 3









Week 5







25










Week 7








Unit Assessments





Unit Vocabulary

Weekly Planner



15




bull similarity

bull congruence


bull parallelograms








16


























Other



17



Classroom


Education Students


Re-voicing

Explaining




Reread




Repetition


Collaborative work


ldquoChunkingrdquo


learning styles



Conferencing

Additional time









VisualsRealia

Front-loading


Color-coding


different media

Pair-share

Modeling



L1 support






18

































19

Math Tools







Unit Vocabulary


Connections




20






21




22




















23





Week 1



Transformations in









bull Questioning

bull Homework check


bull Exit slip


Week 2







24





Week 3









Week 5







25










Week 7








Unit Assessments





Unit Vocabulary

Weekly Planner



16


























Other



17



Classroom


Education Students


Re-voicing

Explaining




Reread




Repetition


Collaborative work


ldquoChunkingrdquo


learning styles



Conferencing

Additional time









VisualsRealia

Front-loading


Color-coding


different media

Pair-share

Modeling



L1 support






18

































19

Math Tools







Unit Vocabulary


Connections




20






21




22




















23





Week 1



Transformations in









bull Questioning

bull Homework check


bull Exit slip


Week 2







24





Week 3









Week 5







25










Week 7








Unit Assessments





Unit Vocabulary

Weekly Planner



17



Classroom


Education Students


Re-voicing

Explaining




Reread




Repetition


Collaborative work


ldquoChunkingrdquo


learning styles



Conferencing

Additional time









VisualsRealia

Front-loading


Color-coding


different media

Pair-share

Modeling



L1 support






18

































19

Math Tools







Unit Vocabulary


Connections




20






21




22




















23





Week 1



Transformations in









bull Questioning

bull Homework check


bull Exit slip


Week 2







24





Week 3









Week 5







25










Week 7








Unit Assessments





Unit Vocabulary

Weekly Planner



18

































19

Math Tools







Unit Vocabulary


Connections




20






21




22




















23





Week 1



Transformations in









bull Questioning

bull Homework check


bull Exit slip


Week 2







24





Week 3









Week 5







25










Week 7








Unit Assessments





Unit Vocabulary

Weekly Planner



19

Math Tools







Unit Vocabulary


Connections




20






21




22




















23





Week 1



Transformations in









bull Questioning

bull Homework check


bull Exit slip


Week 2







24





Week 3









Week 5







25










Week 7








Unit Assessments





Unit Vocabulary

Weekly Planner



20






21




22




















23





Week 1



Transformations in









bull Questioning

bull Homework check


bull Exit slip


Week 2







24





Week 3









Week 5







25










Week 7








Unit Assessments





Unit Vocabulary

Weekly Planner



21




22




















23





Week 1



Transformations in









bull Questioning

bull Homework check


bull Exit slip


Week 2







24





Week 3









Week 5







25










Week 7








Unit Assessments





Unit Vocabulary

Weekly Planner



22




















23





Week 1



Transformations in









bull Questioning

bull Homework check


bull Exit slip


Week 2







24





Week 3









Week 5







25










Week 7








Unit Assessments





Unit Vocabulary

Weekly Planner



23





Week 1



Transformations in









bull Questioning

bull Homework check


bull Exit slip


Week 2







24





Week 3









Week 5







25










Week 7








Unit Assessments





Unit Vocabulary

Weekly Planner



24





Week 3









Week 5







25










Week 7








Unit Assessments





Unit Vocabulary

Weekly Planner



25










Week 7








Unit Assessments





Unit Vocabulary

Weekly Planner

rigorous curriculum design - dekalb county school …...math department is seeking support from...

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