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Unit Title: Geometry Unit 1Grade Level: HS Geometry

Timeframe: Marking Period 1

Unit Focus and Essential Questions

Unit Focus Experiment with transformations in the plane Understand congruence in terms of rigid motions Understand similarity in terms of similarity transformations Make geometric constructions Prove geometric theorems. Prove theorems involving similarity Use coordinates to prove simple geometric theorems Define trigonometric ratios and solve problems involving right triangles

Essential QuestionsWhat is congruence, and how can it be demonstrated and proven? What is similarity, and how can it be demonstrated and proven?What are the relationships between parts of right triangles?

New Jersey Student Learning Standards

Standards/Cumulative Progress Indicators (Taught and Assessed): G.CO.B.6G.CO.B.7G.CO.B.8G.SRT.A.1G.SRT.A.2G.SRT.A.3G.CO.C.9G.CO.C.10G.CO.C.11

G.GPE.B.4G.GPE.B.5G.GPE.B.6G.GPE.B.7G.SRT.C.6G.SRT.C.7G.SRT.C.8

Key: Green = Major Clusters; Blue = Supporting; Yellow = Additional Clusters

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Pacing – In the first grade level meeting or professional development day, teachers will create a pacing guide for the unit together. Teachers will backwards plan the marking period and come up with dates where they will assign each quarterly assessment question.

G.CO.B.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.

Objectives:SWBAT describe translations, reflections, rotations, and dilations that have been performed on object 1 to get to object 2

SWBAT predict effect of translations, reflections, rotations, and dilations on

Journal : Describe what you remember about transformations from grade 8: rotations, reflections, translations, and dilations.

Direct InstructionOption 1 – Use parts from: https://www.engageny.org/resource/geometry-module-1-topic-c-overviewGeometry Module 1, Topic C, Lessons 12-17 and 19-21;

Option 2 – https://njctl.org/courses/math/geometry/transformations/attachments/transformations-3/Slides 6-109, 153, 178-187.

Option 3 – https://www.khanacademy.org/math/basic-geo/basic-geo-transformations-congruence/basic-geo-reflections/v/introduction-to-transformationshttps://www.khanacademy.org/math/basic-geo/basic-geo-transformations-congruence/congruent-similar/v/testing-congruence-

Teachers will agree on common classwork problems in their

professional learning communities or grade level meetings. Problems

should be selected that most closely match the assessments in column 5.

The graph below shows the location

of and

Part A. Describe a set of transformations that can be used to

prove whether or not

and are congruent.

EngageNYhttps://www.engageny.org/resource/geometry-module-1-topic-c-overview

PMI/NJCTLhttps://njctl.org/courses/math/

geometry/transformations/attachments/transformations-3/

Khanacademy.orghttps://www.khanacademy.org/

math/basic-geo/basic-geo-transformations-congruence/basic-geo-

reflections/v/introduction-to-transformations

https://www.khanacademy.org/math/basic-geo/basic-geo-

transformations-congruence/congruent-similar/v/testing-

congruence-by-transformations-example

illustrative mathematics.orghttps://

www.illustrativemathematics.org/content-standards/tasks/1510

https://www.illustrativemathematics.org/

content-standards/tasks/1509https://

www.illustrativemathematics.org/HSG-CO

Pearson Geometry Common CoreGeometry Text: 9-1, 9-2, 9-3, 9-4, 9-5

Type II and Type III problems:G-CO.6 - Type 2-3 Questions [

Quarterly Assessment

Geometry Touchpoint - G-CO.6

Geometry OCRG-CO.6

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https://www.illustrativemathematics.org/HSG-CO



https://www.illustrativemathematics.org/content-standards/tasks/1509






https://www.khanacademy.org/math/basic-geo/basic-geo-transformations-congruence/congruent-similar/v/testing-congruence-by-transformations-example



https://www.khanacademy.org/math/basic-geo/basic-geo-transformations-congruence/basic-geo-reflections/v/introduction-to-transformations



https://njctl.org/courses/math/geometry/transformations/attachments/transformations-3/



https://www.engageny.org/resource/geometry-module-1-topic-c-overview

https://www.engageny.org/resource/geometry-module-1-topic-c-overview









object 1 to describe object 2.

SWBAT use the definition of congruence to determine if object 1 and object 2 are congruent.

by-transformations-example

Option 4 – Geometry Text: 9-1, 9-2, 9-3, 9-4, 9-5See activities and resourcesOption 5 https://learnzillion.com/lesson_plans/6658-describe-translations-using-coordinatesCentersTeacher Center – The teacher works in a small group with 1-4 students. [The engage NY lessons are written with teacher guidance and should also be implemented in the teacher center]Standards Based Problems Center – Students work in a group to solve the style of problems the assessments (Quarterly) will use to measure that standard. [Engage NY has excellent problems for this… as well as EdConnect Type 2 and Type 3 problems Individual Center – Students work on the individual skill that they need based on their pre-test data. Manipulative Center – Students work on creating transformations using protractor, compass, and straight-edge.Interdisciplinary Center – Students work on transformation problems

Part B. If is rotated counterclockwise about the origin and

then dilated by a scale factor of does the transformation result in a

triangle congruent to Explain.

Use words, numbers, and/or pictures to show your work.

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relating to video game graphics and programming.

Review Classwork

Exit Ticket

Standard/SWBAT and Pacing

Student Strategies Based on Instructional Framework

Formative Assessment

Activities and Resources Standards Based Assessment

G.CO.B.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.

SWBAT show that corresponding pairs of sides and angles are congruent, given that two triangles are congruent based on rigid motion,

SWBAT show, using rigid motion (transformations) that triangles are congruent, given that corresponding pairs of sides and angles of two triangles are congruent.

Math Journal : What does it mean when two figures are similar? What does it mean when two figures are congruent? How are they the same? How are they different?

Direct Instruction Option 1:https://www.engageny.org/resource/

geometry-module-1-topic-d-lesson-22Geometry Module 1, Topic D: Lessons 22;

24-27

Option 2: https://njctl.org/courses/math/geometry/congruent-triangles/attachments/congruent-triangles-2/

Option 3 – https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-triangle-congruence/v/finding-congruent-triangles

Option 4 – Geometry Text: Chapter 9-5

See activities and resources

Teachers will agree on common

classwork problems in their

professional learning

communities or grade level meetings.

Problems should be selected that

most closely match the

assessments in column 5.

The graph below shows the location

of

and

EngageNYhttps://www.engageny.org/resource/geometry-module-1-topic-d-overview

PMI/NJCTLhttps://njctl.org/courses/math/geometry/

congruent-triangles/attachments/congruent-triangles-2/

Khanacademy.orghttps://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-triangle-congruence/v/finding-congruent-triangles

Illustrative Mathematicshttps://www.illustrativemathematics.org/HSG-CO

https://www.illustrativemathematics.org/content-standards/HSG/CO/B/7/tasks/1637

Pearson Geometry Common CoreGeometry Text: Chapter 9-5

Type II and Type III problems:


Geometry OCR - G-CO.7


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https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-triangle-congruence/v/finding-congruent-triangles



https://njctl.org/courses/math/geometry/congruent-triangles/attachments/congruent-triangles-2/



https://www.engageny.org/resource/geometry-module-1-topic-d-overview


https://www.engageny.org/resource/geometry-module-1-topic-d-lesson-22

https://www.engageny.org/resource/geometry-module-1-topic-d-lesson-22

CentersTeacher Center – The teacher works in a small group with 1-4 students. [The engage NY lessons are written with teacher guidance and should also be implemented in the teacher center]

Standards Based Problems Center – Students work in a group to solve the style of problems the assessments (Quarterly) will use to measure that standard. [Engage NY has excellent problems for this… as well as EdConnect Type 2 and Type 3 problems:

Type 2-3 Question Bank Type 2-3 Question Bank

Individual Center – Students work on the individual skill that they need based on their pre-test data.

Interdisciplinary Center – Students work on transformation problems relating to video game graphics and programming.

Review Classwork

Exit Ticket

Part A. Describe a set of transformations that can be used to prove whether or

not

and are congruent.

Part B. If is rotated counterclockwise about the origin and then dilated by a scale factor

of does the transformation

G-CO.7 - Type 2-3 Question Bank

CAR © 2009

result in a triangle congruent

to Explain.


Student Learning Objective (SLO) Language Objective Language NeededSLO: 4CCSS:G.CO.6G.CO.7G.CO.8WIDA ELDS: 3SpeakingWriting

Use rigid transformations to determine, explain and prove congruence of geometric figures

Identify and explain congruence of geometric figures using rigid transformation, both orally and in writing, using an example, a sentence frame, partner and word wall.

VU: Preserve, rigid, rotate, reflect, criteria

LFC: Cause and effect transitional phrases, past tense

LC: Varies by ELP level

ELP 1 ELP 2 ELP 3 ELP 4 ELP 5Language Objectives

Identify and explain congruence of geometric figures orally and in writing in L1 and/or use gestures, examples and selected technical words.

Identify and explain congruence of geometric figures orally and in writing in L1 and/or use selected technical vocabulary in phrases and short sentences.

Identify and explain congruence of geometric figures orally and in writing using key, technical vocabulary in a series of simple sentences.

Identify and explain congruence of geometric figures orally and in writing using key technical vocabulary in expanded sentences.

Identify and explain congruence of geometric figures orally and in writing using technical vocabulary in complex sentences.

Learning Teacher Modeling Teacher Modeling Teacher Modeling Teacher Modeling Teacher Modeling

CAR © 2009

http://www.nj.gov/education/modelcurriculum/ela/ellscaffolding/GraphicOrganizersWorksheets.pdf





Supports DemonstrationPartner workWord/Picture Wall L1 text and/or support Pictures /illustrations

Partner workWord/Picture WallL1 text and/or supportSentence frames

Partner workSentence StarterWord wall

Partner work Partner work

G.CO.B.8. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

SWBAT show and explain: the criteria for Angle-

Side-Angle triangle congruence.

the criteria for Side-Angle-Side triangle congruence.

the criteria for Side-Side-Side triangle congruence.

the relation of the criteria for triangle congruence to congruence in terms of rigid motion.

Math Journal : How can you tell if two triangles are similar? How can you tell if they are congruent?

Direct Instruction Option 1:

https://www.engageny.org/resource/geometry-module-1-topic-d-overview -- lessons 22-27

Option 2:


Slides 5-124

Option 3 –

https://www.khanacademy.org/math/geometry-home/congruence#triangle-congruence

Option 4 – Geometry Text: 9-

Teachers will agree on common classwork problems in their professional learning communities or grade level meetings. Problems should be selected that most closely match the assessments in column 5.

is shown on the coordinate plane below.

Part A. Translate the triangle 2 units to the left and then reflect it across the x-axis. Label the image

EngageNYhttps://www.engageny.org/resource/geometry-module-1-topic-d-overview


congruent-triangles/attachments/congruent-triangles-2/

Khanacademy.orghttps://www.khanacademy.org/math/geometry-home/congruence#triangle-

congruence

Pearson Geometry Common CoreGeometry Text: 9-5

Illustrative Mathematicshttps://www.illustrativemathematics.org/

HSG-COhttps://www.illustrativemathematics.org/

HSG-CO.B.8

Type II and Type III problems:G-CO.8 - Type 2-3 Question Bank




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https://www.illustrativemathematics.org/HSG-CO.B.8

https://www.illustrativemathematics.org/HSG-CO.B.8













http://www.nj.gov/education/modelcurriculum/ela/ellscaffolding/InteractionSupports/PartnerWork.pdf


http://www.nj.gov/education/modelcurriculum/ela/ellscaffolding/ClassroomDisplays/WordWall.pdf

http://www.nj.gov/education/modelcurriculum/ela/ellscaffolding/GraphicOrganizersWorksheets/SentenceStarters.pdf


http://www.nj.gov/education/modelcurriculum/ela/ellscaffolding/GraphicOrganizersWorksheets/SentenceFrames.pdf

http://www.nj.gov/education/modelcurriculum/ela/ellscaffolding/L1Supports.pdf



http://www.nj.gov/education/modelcurriculum/ela/ellscaffolding/Visualizations/PicturesPhotographs.pdf




5






Review Classwork

as such that A is taken to X, B is taken to Y, and C is taken to Z.

Part B. Are the triangles congruent? Use the transformations from part A and congruence criteria to explain your answer. Use words, numbers, and/or pictures to show your work

CAR © 2009

Exit Ticket

Student Learning Objective (SLO) Language Objective Language NeededSLO: 4CCSS:G.CO.6G.CO.7G.CO.8WIDA ELDS: 3SpeakingWriting

Use rigid transformations to determine, explain and prove congruence of geometric figures

Identify and explain congruence of geometric figures using rigid transformation, both orally and in writing, using an example, a sentence frame, partner and word wall.

VU: Preserve, rigid, rotate, reflect, criteria

LFC: Cause and effect transitional phrases, past tense



Identify and explain congruence of geometric figures orally and in writing in L1 and/or use gestures, examples and selected technical words.

Identify and explain congruence of geometric figures orally and in writing in L1 and/or use selected technical vocabulary in phrases and short sentences.

Identify and explain congruence of geometric figures orally and in writing using key, technical vocabulary in a series of simple sentences.

Identify and explain congruence of geometric figures orally and in writing using key technical vocabulary in expanded sentences.

Identify and explain congruence of geometric figures orally and in writing using technical vocabulary in complex sentences.

Learning Supports

Teacher ModelingDemonstrationPartner workWord/Picture Wall L1 text and/or support Pictures /illustrations

Teacher ModelingPartner workWord/Picture WallL1 text and/or supportSentence frames

Teacher ModelingPartner workSentence StarterWord wall

Teacher ModelingPartner work

Teacher ModelingPartner work

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G.SRT.A.1. Verify experimentally the properties of dilations given by a center and a scale factor:

SWBAT determine the properties of dilation.

G.SRT.A.1a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.

SWBAT: dilate when the center of dilation is in, on and out of the shape.

SWBAT: dilate using both positive and negative scale factors.

SWBAT: construct a dilation.

G.SRT.A.1b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

SWBAT: dilate when given a center of dilation and a

Math Journal : How does a figure change when it is dilated by a number greater than one? Less than one?


https://www.engageny.org/resource/geometry-module-2-topic-b-overview

Lessons: Module 2, Topic B: Lesson 6, 7, 10, 11

Option 2: https://njctl.org/courses/math/geometry/transformations/attachments/transformations-3/

Slides: 188-244

Option 3 –

https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-dilations/v/dilating-one-line-onto-another

Option 4 – Geometry Text: Chapter 9: pp587-607




Mrs. Petrillo designed a new logo for her construction company and graphed the outline of the logo on the coordinate grid shown in Figure A below. Each square on the grid represents 1 square inch.

EngageNYhttps://www.engageny.org/resource/geometry-module-2-topic-b-overview


transformations/attachments/transformations-3/

Khanacademy.orghttps://www.khanacademy.org/math/

geometry/hs-geo-transformations/hs-geo-dilations/v/dilating-one-line-onto-another

Pearson Geometry Common Core

Illustrative Mathematicshttps://www.illustrativemathematics.org/HSG-

SRT.A

Pearson Geometry Common CoreGeometry Text: Chapter 9: pp587-607


G-SRT.1 - Type 2-3 Question Bank

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scale factor. SWBAT: The student will be able to use the dilation coordinate rules for dilations using any center of dilation.




Review Classwork

Exit Ticket

Part A. She dilates the logo by a scale

factor of so that it fits on the company’s envelopes that will be mailed to its customers. Graph the dilation of the logo for the envelopes with the center of the dilation at the origin.

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Part B. To promote some of the company’s new products, Mrs. Petrillo wants to print the new logo on some T-shirts and give one to each of her employees. She enlarges the logo she designed in Figure A by a scale

factor of to fit better on the T-shirts. Graph the

CAR © 2009

dilation of the logo for the T-shirts with the the center of the dilation at the origin.

Part C. Compare the side lengths of the logos designed for the company’s envelopes and T-shirts with the original logo shown in Figure A. Explain the relation between the scale factor

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and the change in the size.

Part D. Mrs. Petrillo also uses a larger image of the new logo to advertise on a digital billboard. If the base of the logo on the digital billboard is 4 feet, what is the scale factor of the dilation that was used to create the larger image?


Student Learning Objective (SLO) Language Objective Language NeededSLO: 2CCSS:G.SRT.1WIDA ELDS: 3Speaking

Justify the properties of dilations given by a center and a scale factor. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged (the dilation of a line segment is longer or shorter in the ratio given by the scale factor).

Demonstrate comprehension of the properties of dilations written word problems by drawing the model in order to answer questions using models, Charts and word/symbol banks.

Explain in writing the properties of dilations using word wall, Math Journal and sentence frames.

VU: Scale factor, image, dilation, origin, hypotenuse

LFC: Future tense, cause effect statements

CAR © 2009

http://www.nj.gov/education/modelcurriculum/math/ellscaffolding/MathJournal.pdf

http://www.nj.gov/education/modelcurriculum/ela/ellscaffolding/InteractionSupports/TeacherModeling.pdf


ReadingLC: Varies by ELP level


Demonstrate comprehension of written word problems in L1 and/or using simplified word problems with visuals.

Explain in writing the properties of dilations in L1 and/or use gestures, examples and selected technical words.

Demonstrate comprehension of written word problems in L1 and/or using simplified word problems.

Explain in writing the properties of dilations in L1 and/or use selected technical vocabulary in phrases and short sentences.

Demonstrate comprehension of written word problems by drawing the model in order to answer questions.

Explain in writing the properties of dilations using key technical vocabulary in a series of simple sentences.

Demonstrate comprehension of written word problems by drawing the model in order to answer questions.

Explain in writing the properties of dilations using key, technical vocabulary in some complex sentences.

Demonstrate comprehensionof written word problems by drawing the model in order to answer questions.

Explain in writing the properties of dilations using technical vocabulary in complex sentences.

Learning Supports

Teacher ModelingChartsIllustrations/diagrams/drawingsWord/Picture WallL1 text and/or supportMath Journal Cloze sentences

Teacher ModelingChartsIllustrations/diagrams/drawings Word/Picture Wall L1 text and/or supportSentence frames Math Journal

Teacher ModelingChartsSentence StarterWord wallMath Journal

Teacher ModelingChartsMath Journal

Teacher ModelingCharts



Formative Assessment Activities and Resources Standards Based Assessment

G.SRT.A.2. Given two figures, use the definition of similarity in terms of similarity transformations to decide if

Math Journal : How can you determine if two figures are similar?

Teachers will agree on common classwork problems in their professional learning communities or grade level meetings. Problems should be selected that most closely


PMI/NJCTL


CAR © 2009

http://www.nj.gov/education/modelcurriculum/ela/ellscaffolding/GraphicOrganizersWorksheets/ChartsPosters.pdf













http://www.nj.gov/education/modelcurriculum/ela/ellscaffolding/ClassroomDisplays/Wordpicturewall.pdf

http://www.nj.gov/education/modelcurriculum/ela/ellscaffolding/Visualizations/IllustrationsDiagramsDrawings.pdf














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.

SWBAT identify corresponding angles and sides based on similarity statements. SWBAT develop and write similarity statements for two polygons. SWBAT determine if two triangles are similar based on their corresponding parts. SWBAT establish a sequence of similarity transformations between two similar polygons.


https://www.engageny.org/resource/geometry-module-2-topic-c-lesson-12

Geometry Module 2 Topic C: Lessons 12-20

Option 2: https://njctl.org/courses/math/geometry/transformations/

Slides: 245-273

Option 3 – https://www.khanacademy.org/math/basic-geo/basic-geo-transformations-congruence/congruent-similar/v/testing-similarity-through-transformations

Option 4 – Geometry Text: Chapter 9-7:



match the assessments in column 5.

An artist is creating a sculpture made up of many different triangular pieces of wood. A sketch of her sculpture is shown on the coordinate plane below.

Part A. Can triangles

and be mapped onto each other using transformations? If so, explain the transformations. Are the triangles geometrically similar? Explain.

Part B. Can triangles and be mapped onto each other using transformations? If so, explain the transformations. Are the

https://njctl.org/courses/math/geometry/transformations/

Khanacademy.orghttps://www.khanacademy.org/

math/basic-geo/basic-geo-transformations-congruence/

congruent-similar/v/testing-similarity-through-transformations

Pearson Geometry Common CoreGeometry Text: Chapter 9-7:

Illustrative Mathematicshttps://

www.illustrativemathematics.org/HSG-SRT.A

Type II and Type III problems:G-SRT.2 - Type 2-3 Question Bank

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https://www.illustrativemathematics.org/HSG-SRT.A













Review Classwork

Exit Ticket

triangles geometrically similar? Explain.

Part C. A pair of similar triangles can be mapped onto each other through a translation of 3 units and a dilation by a scale factor of 3:5. Which triangles are they?

Part D. The artist wants to create a

triangle that is similar to

She dilates by a scale factor of 0.5 with the center of dilation at

the origin. Draw and the

resulting triangle,

CAR © 2009

Part E. What relationship do the side

lengths of and have? What is true about their angle measures? Use a protractor to measure and list the angle measures. Use properties of dilations to explain whether or not dilations of triangles always result in triangles that are similar to their original images.

Student Learning Objective (SLO) Language Objective Language NeededSLO: 3CCSS:G.SRT.2WIDA ELDS:3WritingReading

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.

Justify, answers by explaining, that two triangles are similar using the similarity transformations using a model, Math Journal, Sentence Starters, and Partner work.

VU: Given, valid, justify, coordinate plane, similarity statement

LFC: Cause and effect statements and signal words

LC: Varies by ELP levelELP 1 ELP 2 ELP 3 ELP 4 ELP 5

Language Objectives

Justify answers by explaining the similarity transformations in L1 and/or use gestures, examples and selected technical words.

Justify answers by explaining the similarity transformations in L1 and/or use selected technical vocabulary in phrases and short sentences.

Justify answers by explaining the similarity transformations using key, technical vocabulary in a series of simple sentences.

Justify answers by explaining the similarity transformations using key, technical vocabulary in expanded and some complex sentences.

Justify answers by explaining the similarity transformationsusing technical vocabulary in multiple, complex sentences.

Learning Supports

Teacher ModelingMath JournalPartner workWord/Picture WallL1 text and/or supportIllustrations Cloze sentences

Teacher ModelingMath JournalPartner workWord/Picture WallL1 text and/or supportSentence frames

Teacher ModelingMath JournalPartner workSentence StarterWord wall

Math JournalPartner work

Math Journal

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G.SRT.A.3. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

SWBAT prove two triangles to be similar using the minimum requirements of AA, SAS and SSS. SWBAT use the properties of similarity transformations to establish the AA, SAS and SSS criterion for two triangles to be similar.

Math Journal : What do you need to prove two triangles similar? What transformations can you use to help you with this?

Direct Instruction Option 1:https://www.engageny.org/resource/geometry-module-2-topic-c-lesson-15Lessons 15, 16

Option 2: https://njctl.org/courses/math/geometry/triangles/attachments/triangles-2/

Slides 135-232

Option 3 – https://www.khanacademy.org/math/geometry/hs-geo-similarity/hs-geo-triangle-similarity-intro/v/similar-triangle-basics

Option 4 – Geometry Text: 9-7



Standards Based Problems Center – Students work in a group to solve the style of problems the assessments (Quarterly)


An artist is creating a sculpture made up of many different triangular pieces of wood. A sketch of her sculpture is shown on the coordinate plane below.

EngageNYhttps://www.engageny.org/resource/geometry-module-2-topic-c-lesson-15


triangles/attachments/triangles-2/


geometry/hs-geo-similarity/hs-geo-triangle-similarity-intro/v/similar-triangle-basics

Pearson Geometry Common CoreGeometry Text: Chapter 9-7


SRT.A



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https://www.khanacademy.org/math/geometry/hs-geo-similarity/hs-geo-triangle-similarity-intro/v/similar-triangle-basics



https://njctl.org/courses/math/geometry/triangles/attachments/triangles-2/

https://njctl.org/courses/math/geometry/triangles/attachments/triangles-2/



will use to measure that standard. [Engage NY has excellent problems for this… as well as EdConnect Type 2 and Type 3 problems:



Review Classwork

Exit Ticket

Part A. Can

triangles

and be mapped onto each other using transformations? If so, explain the transformations. Are the triangles geometrically similar? Explain.

Part B. Can

triangles

and be mapped onto each other using transformations? If so, explain the

CAR © 2009

transformations. Are the triangles geometrically similar? Explain.

Part C. A pair of similar triangles can be mapped onto each other through a translation of 3 units and a dilation by a scale factor of 3:5. Which triangles are they?

Part D. The artist wants to create a triangle that is similar

to She

dilates by a scale factor of 0.5 with the center of dilation at the origin.

Draw and the resulting

triangle,

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Part E. What relationship do the side lengths

of

and have? What is true about their angle measures? Use a protractor to measure and list the angle measures. Use properties of dilations to explain whether or not dilations of triangles always result in triangles that are similar to their original images.

CAR © 2009

Student Learning Objective (SLO) Language Objective Language NeededSLO: 4CCSS:G.SRT.3.WIDA ELDS: 3SpeakingWriting

Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

Explain in writing how Justify the AA criterion for similar triangles using properties of similarity transformations can establish similarity in triangles using an applet, Manipulatives, a word wall and a model.

http://www.mathopenref.com/congruenttriangles.html

VU: Angle-angle criterion, ASA congruence test, similarityLFC: Cause and effect transitional phrases, prepositional phrasesLC: Varies by ELP level


Explain in writing how the AA criterion can establish similarity in triangles in L1 and/or use gestures, examples and selected technical words.

Explain in writing how the AA criterion can establish similarity in triangles in L1 and/or use selected technical vocabulary in phrases and short sentences.

Explain in writing how the AA criterion can establish similarity in triangles using key, technical vocabulary in simple sentences.

Explain in writing how the AA criterion can establish similarity in triangles using key technical vocabulary in expanded sentences.

Explain in writing how the AA criterion can establish similarity in triangles using technical vocabulary in complex sentences.

Learning Supports

AppletTeacher ModelingManipulativesPartner workWord wallL1 text and/or supportPictures /illustrations Cloze sentences

AppletTeacher ModelingManipulatives Partner workWord wallL1 text and/or supportSentence frames

AppletTeacher ModelingManipulativesPartner workSentence StarterWord wall

AppletTeacher ModelingPartner work

AppletTeacher ModelingPartner work





G.CO.C.9: Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior

Math Journal : Why do you think mathematicians need to prove theorems? What is necessary for a proof to be valid?

Direct Instruction Option 1: https://www.engageny.org/ccls-

Teachers will agree on common classwork problems in their professional learning communities or

EngageNYhttps://www.engageny.org/ccls-math/gco9

PMI/NJCTLhttps://njctl.org/courses/math/geometry/parallel-lines/attachments/parallel-lines-3/




CAR © 2009

https://njctl.org/courses/math/geometry/parallel-lines/attachments/parallel-lines-3/









http://www.nj.gov/education/modelcurriculum/ela/ellscaffolding/Visualizations/Manipulatives.pdf














http://www.mathopenref.com/congruenttriangles.html



angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.

SWBAT prove and apply that vertical angles are congruent. SWBAT prove and apply the angle relationships formed when two parallel lines are cut by a transversal.

SWBAT prove that all points on a perpendicular bisector of a segment are equidistant from the segment endpoints. SWBAT know all of the relationships between pairs of angles.

math/gco9Geometry Module 1, Topic G, lessons 33-34Geometry Module 1 Topic E, lessons 29-30Geometry Module 1, Topic B, lessons 6-11

Option 2:


Option 3 –

https://www.khanacademy.org/math/basic-geo/basic-geo-angle/angles-between-lines/v/angles-formed-by-parallel-lines-and-transversals

Option 4 – Geometry Text: 2-6,3-2,5-2




grade level meetings. Problems should be selected that most closely match the assessments in column 5.

Given use the image below to answer the questions.

Part A. Write a two-column proof to prove

Part B.

If

what is Show your work.

Khanacademy.orghttps://www.khanacademy.org/math/basic-

geo/basic-geo-angle/angles-between-lines/v/angles-formed-by-parallel-lines-and-

transversals

Pearson Geometry Common CoreGeometry Text: 2-6,3-2,5-2


CO


CAR © 2009





Review Classwork

Exit Ticket


Student Learning Objective (SLO) Language Objective Language NeededSLO: 5CCSS:G.CO.9G.CO.10G.Co.11WIDA ELDS: 3Speaking

Create proofs of theorems involving lines, angles, triangles, and parallelograms.* (Please note G.CO.10 will be addressed again in unit2 and G.CO.11 will be addressed again in unit 4)

Create and explain orally the proofs of theorems using a model, a Charts/Posters, a sentence frame and word wall.

VU: Proof, prove, consecutive, interior, quadrilateral

LFC: Cause and effect transitional phrases



Create and explain orally the proofs of theorems in L1 and/or use gestures, examples and selected technical words.

Create and explain orally the proofs of theorems in L1 and/or use selected technical vocabulary in phrases and short sentences.

Create and explain orally the proofs of theorems using key technical vocabulary in a series of simple sentences.

Create and explain orally the proofs of theorems using key, technical vocabulary in expanded and some complex sentences.

Create and explain orally the proofs of theorems using technical vocabulary in multiple, complex sentences.

Learning Supports

Teacher ModelingDemonstrationStudent-generated dictionaryPartially completed proofSmall group/triads

Teacher ModelingStudent-created dictionaryPartially completed proofSmall group/triadsWord/Picture WallL1 text and/or support

Teacher ModelingSmall group/triadsSentence StarterWord wall

Teacher ModelingSmall group/triads

Teacher Modeling

CAR © 2009


http://www.nj.gov/education/modelcurriculum/ela/ellscaffolding/InteractionSupports/InTriadsOrSmallGroups.pdf













Word/Picture Wall L1 text and/or support Pictures /illustrations

Sentence frames

CAR © 2009









G.CO.C.10: Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; 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

.SWBAT prove and apply that the sum of the interior angles of a triangle is 180°. SWBAT prove and apply that the base angles of an isosceles triangle are congruent.

SWBAT prove and apply the midsegment (midline) of triangle theorem. SWBAT prove that the medians of a triangle meet at a point, a point of concurrency. SWBAT prove and apply that the exterior angle theorem.

Math Journal : Suppose you connected the midpoints of a triangle to form a second triangle. What relationships exist between the new triangles formed?


math/gco10Module 1, Topic G, Lesson 29, 30, 33, 34

Option 2: https://njctl.org/courses/math/geometry/analytic-geometry/attachments/analytic-geometry-2/

Slides 1-114

https://njctl.org/courses/math/geometry/triangles/

Slides 1-134

Option 3 –

https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-congruence-theorems/v/congruent-legs-and-base-angles-of-isosceles-triangles

https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-working-with-triangles/v/another-isosceles-example-problem


The pennant for a local high school football team, the American Eagles, is shown below.

Part 1. Write a two-column proof to prove that the given pennant is in


PMI/NJCTLhttps://njctl.org/courses/math/geometry/analytic-geometry/attachments/analytic-

geometry-2/

Khanacademy.orghttps://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-working-with-triangles/v/another-isosceles-example-problem

https://www.khanacademy.org/math/basic-geo/basic-geometry-shapes/triangle-angles/v/proof-sum-of-measures-of-angles-in-a-triangle-are-180

https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-congruence-theorems/v/congruent-legs-and-base-angles-of-isosceles-triangles

Pearson Geometry Common CoreGeometry Text: 3-5, 4-5, 5-1, 5-4


CO

Type II and Type III problems:




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https://www.engageny.org/ccls-math/gco10

https://njctl.org/courses/math/geometry/analytic-geometry/attachments/analytic-geometry-2/





SWBAT determine the conditions for forming a triangle, when given three lengths.

https://www.khanacademy.org/math/basic-geo/basic-geometry-shapes/triangle-angles/v/proof-sum-of-measures-of-angles-in-a-triangle-are-180

Option 4 – Geometry Text: 3-5, 4-5, 5-1, 5-4






Review Classwork

Exit Ticket

the shape of an isosceles triangle.

Part 2. If the measure of the vertex angle of the pennant is 25°, what are the measures of the other two angles?

Part 3. The model of a rival school’s pennant is drawn on the coordinate

G-CO.10 - Type 2-3 Question Bank

CAR © 2009

plane shown below. Is this pennant also an isosceles triangle? Use the distance formula to support your answer.


Student Learning Objective (SLO) Language Objective Language NeededSLO: 5CCSS:G.CO.9

Create proofs of theorems involving lines, angles, triangles, and parallelograms.* (Please note



CAR © 2009


G.CO.10G.Co.11WIDA ELDS: 3Speaking

G.CO.10 will be addressed again in unit2 and G.CO.11 will be addressed again in unit 4)









Learning Supports

Teacher ModelingDemonstrationStudent-generated dictionaryPartially completed proofSmall group/triadsWord/Picture Wall L1 text and/or support Pictures /illustrations

Teacher ModelingStudent-created dictionaryPartially completed proofSmall group/triadsWord/Picture WallL1 text and/or supportSentence frames



Teacher Modeling

CAR © 2009






















G.CO.C.11: 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.

SWBAT prove properties of parallelograms and then apply them.

SWBAT prove the properties of rectangles and then apply them. SWBAT prove the properties of rhombi and then apply them. SWBAT prove the properties of squares and then apply them. SWBAT classify a quadrilateral by its properties. SWBAT identify the conditions necessary to prove that a quadrilateral is a parallelogram.

Math Journal : What are parallelograms? How are triangles and parallelograms related? What properties of triangles can you to prove quadrilaterals are parallelograms?


math/gco11Geometry Module 1, Topic G, Lesson 34Geometry Module 1, Topic E, Lesson 28

Option 2: https://njctl.org/courses/math/geometry/quadrilaterals/attachments/quadrilaterals-2/

Slides 60-163

Option 3 –

https://www.khanacademy.org/math/geometry-home/quadrilaterals-and-polygons#geometry-quads

https://www.khanacademy.org/math/geometry-home/quadrilaterals-and-polygons#quadrilaterals

Option 4 – Geometry Text: 6-2, 6-3, 6-4, 6-5



Consider the quadrilateral with vertices

Part A.

One way to prove that the quadrilateral is a parallelogram is to show that the diagonals bisect each other. Explain two other different methods that can be used to prove that the quadrilateral is a parallelogram.



quadrilaterals/attachments/quadrilaterals-2/


geometry-home/quadrilaterals-and-polygons#geometry-quads

https://www.khanacademy.org/math/geometry-home/quadrilaterals-and-

polygons#quadrilaterals

Pearson Geometry Common CoreGeometry Text: 6-2, 6-3, 6-4, 6-5


CO





CAR © 2009






https://njctl.org/courses/math/geometry/quadrilaterals/attachments/quadrilaterals-2/

https://njctl.org/courses/math/geometry/quadrilaterals/attachments/quadrilaterals-2/











Review Classwork

Exit Ticket

Part B.

Explain how Part A illustrates the claim that the diagonals of a parallelogram bisect each other.

Quadrilateral MATH includes the pointsM(2,-4) and A(5,-2).

Part A: Find coordinates for T and H such that quadrilateral MATH is a rectangle.

Part B: Prove that the resulting quadrilateral is a rectangle.

Student Learning Objective (SLO) Language Objective Language NeededSLO: 5CCSS:G.CO.9

Create proofs of theorems involving lines, angles, triangles, and parallelograms.* (Please note



CAR © 2009


G.CO.10G.Co.11WIDA ELDS: 3Speaking

G.CO.10 will be addressed again in unit2 and G.CO.11 will be addressed again in unit 4)









Learning Supports

Teacher ModelingDemonstrationStudent-generated dictionaryPartially completed proofSmall group/triadsWord/Picture Wall L1 text and/or support Pictures /illustrations

Teacher ModelingStudent-created dictionaryPartially completed proofSmall group/triadsWord/Picture WallL1 text and/or supportSentence frames



Teacher Modeling





G.GPE.B.4: 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; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).

SWBAT establish

Math Journal : What would you need to prove to determine that quadrilateral ABCD is a rectangle. How could you do this if you were given the coordinates?


math/ggpe4Geometry Module 4, Topic D, lessons 12-14Geometry Module 4, Topic B, lessons 5, 8

Option 2:

https://njctl.org/courses/math/geometry/


EngageNYhttps://www.engageny.org/ccls-math/ggpe4


analytic-geometry/


geometry/hs-geo-analytic-geometry/hs-geo-distance-and-midpoints/e/midpoint_formula

Pearson Geometry Common CoreGeometry Text: 6-9


Geometry Touchpoint - G-GPE.4

Geometry OCR - G-GPE.4

CAR © 2009

https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-distance-and-midpoints/e/midpoint_formula



https://njctl.org/courses/math/geometry/analytic-geometry/


https://www.engageny.org/ccls-math/ggpe4





















relationships and /or characteristics of geometric shapes using coordinate geometry. SWBAT classify a quadrilateral through use of coordinate analysis.

analytic-geometry/Slides 134-146

Option 3 – https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-distance-and-midpoints/e/midpoint_formula

Option 4 – https://www.illustrativemathematics.org/content-standards/HSG/GPE/B/4/tasks/605






The town officials in Justin's town are making plans to expand the services offered to residents. The map below shows the current location of the high school, H; the library, L; and the recreation center, R.

Part A. A developer wants to build a


GPE.B

https://www.illustrativemathematics.org/content-standards/HSG/GPE/B/4/tasks/605

Type II and Type III problems:G-GPE.4 - Type 2-3 Questions

CAR © 2009



https://www.illustrativemathematics.org/HSG-GPE.B




Review Classwork

Exit Ticket

gas station, G, that is located southeast of the high school so that right triangle LHG is formed with the high school and the library. If the coordinates of the gas station are positioned such

that and are only whole number values, what are the possible locations of the gas station?

Part B. Town regulations state that a gas station cannot be built within 0.5 mile of a school. Graph the location of the gas station, G, on the coordinate grid above if each coordinate represents 0.2 mile. Explain why the developer will need to build the gas station at this location.

Part C. A new CAR © 2009

park, P, is going to be built centered

at with a circular boundary that passes through

point If Justin’s house, J, is located

at does he live on the boundary of the park? Explain.

Part D. Justin claims that the location of the mall, M, being built

at forms a parallelogram with his house, the park, and the recreation center. Prove whether or not Justin is correct using the coordinate grid above to justify your answer. Do these locations form any other type of special quadrilateral? Explain why or why not.

CAR © 2009

Part E. The new mall is planned to cover a rectangular area that measures 0.96 square mile with a width of 0.8 mile. If the center of the mall is located

at on the coordinate grid, what is one possible set of coordinates that could be the locations of the vertices that make up the rectangular area of the mall? Explain using the coordinate grid above to justify your answer.

Student Learning Objective (SLO) Language Objective Language NeededSLO: 7CCSS:G.GPE.4 WIDA ELDS: 3ListeningReadingWriting

Use coordinates to prove simple geometric theorems algebraically.

Demonstrate comprehension of how to use coordinates to prove simple geometric theorems algebraically by explaining the process using a Teacher Modeling, Charts/Posters and Partner work.

VU: Theorems, rhombus, parallelogram, quadrilateral

LFC: Embedded clauses



Demonstrate comprehension of how to use coordinates to prove

Demonstrate comprehension of how to use coordinates to prove simple geometric

Demonstrate comprehension of how to use coordinates to prove simple geometric theorems

Demonstrate comprehension of how to use coordinates to prove simple geometric

Demonstrate comprehension of how to coordinates to prove simple geometric

CAR © 2009




simple geometric theorems algebraically by explaining the process in L1 and/or use gestures, examples and selected technical words.

theorems algebraically by explaining the process in L1 and/or use selected technical vocabulary in phrases and short sentences.

algebraically by explaining the process using key vocabulary in simple sentences.

theorems algebraically by explaining the process using key, technical vocabulary in expanded sentences.

theorems algebraically by explaining the process using technical vocabulary in complex sentences.

Learning Supports

Teacher ModelingMath JournalDemonstrationCharts/PostersWord/Picture WallL1 text and/or supportPictures /illustrations

Teacher ModelingMath JournalCharts/PostersWord/Picture WallL1 text and/or supportSentence Frame

Teacher ModelingMath JournalCharts/PostersSentence StarterWord Wall

Teacher ModelingMath JournalCharts/Posters

Teacher Modeling





G.GPE.B.5: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

SWBAT prove that parallel lines have congruent slopes and its converse. SWBAT prove that perpendicular lines have negative reciprocal slopes and its converse. SWBAT determine the slope of a line. SWBAT determine whether two slopes represent

Math Journal : What do you remember about the slope of a line?

Direct Instruction Option 1: Geometry Module 4, Topic B,

Lessons 6-8

Option 2: https://njctl.org/courses/math/geometry/analytic-geometry/

Slides 115-132

Option 3 –

https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-parallel-perpendicular-eq/e/line_relationships

https://www.khanacademy.org/math/


Read "Designing a Hotel" and answer the questions.

From her study of architecture, Yasmin knows that diagonal bracing

EngageNYGeometry, Module 4, Topic B Overview


analytic-geometry/

Khanacademy.orghttps://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-parallel-perpendicular-eq/e/line_relationships

https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-parallel-perpendicular-lines/e/classifying-lines-as-parallel--perpendicular--or-neither

https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-parallel-perpendicular-eq/e/writing-equations-for-parallel-or-perpendicular-lines




CAR © 2009





































parallel or perpendicular relationships.

SWBAT classify geometric shapes using slopes and/or distances.

geometry/hs-geo-analytic-geometry/hs-geo-parallel-perpendicular-lines/e/classifying-lines-as-parallel--perpendicular--or-neither


Option 4 – Geometry Text: 3-8, 7-3, 7-4





Interdisciplinary Center – Students work

makes buildings more stable. She wants to make the building stronger. She likes the pattern the diagonal supports add to the front of the building, so she strategically places the diagonal supports on the front face of the hotel.

Part A. What is the slope of the support passing through the points labeled A andC? What is the slope of the support passing through the points labeled B and D? Explain and show your work.

Part B. Compare the slopes of these two supports. What does the slope tell you about the relationship between these two supports? Using slope, explain why

Pearson Geometry Common CoreGeometry Text: 3-8, 7-3, 7-4


GPE.B

Type II and Type III problems:G-GPE.5 - Type 2-3 Questions

CAR © 2009








on transformation problems relating to video game graphics and programming.

Review Classwork

Exit Ticket

this relationship must be true. How would the relationship between the supports change if the location of point B was moved up 1 unit on the grid? Explain.


CAR © 2009





G.GPE.B.6: Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

SWBAT to partition a line segment based on a provided ratio.

Math Journal : Explain how to find out where to make the cuts on a board if you were asked to cut it so that fit a specific ratio (such as 1:3)

Direct Instruction Option 1:https://www.engageny.org/resource/geometry-module-4-topic-d-lesson-12

Option 2:


Slides 49-72

Option 3 – https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-dividing-segments/v/finding-a-point-part-way-between-two-points

Option 4 – Geometry Text: 1-3, 1-7




Legend has it that there is buried treasure on Geometry Island deep in the Caribbean. The legend describes the island as having only three palm trees and says that if a curiously smart pirate were to find the centroid of the triangle formed by the trees, then that pirate would suddenly find great riches! From the southernmost palm tree, a

EngageNYhttps://www.engageny.org/resource/geometry-module-4-topic-d-lesson-12

PMI/NJCTLhttps://njctl.org/courses/math/geometry/analytic-geometry/

Khanacademy.orghttps://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-dividing-segments/v/finding-a-point-part-way-between-two-points

Pearson Geometry Common CoreGeometry Text: 1-3, 1-7


GPE.B

Type II and Type III problems:G-GPE.6 - Type 2-3 Question Bank




CAR © 2009



https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-dividing-segments/v/finding-a-point-part-way-between-two-points













Review Classwork

Exit Ticket

second palm tree is 12 paces north and 6 paces west. The third tree is 6 paces north and 8 paces east of the southernmost tree.

Part A

Using graph paper, draw a suitable model of the island, detailing the coordinates of the trees. Plot the southernmost palm tree at the origin and let each unit on the coordinate grid represent one pace.

Part B

Research the definition of a centroid and draw the special segments of a triangle that form the centroid on your graph paper.

Part C

Using the fact that a centroid divides each of the three special segments of the triangle in a

CAR © 2009

ratio of 2:1, find the coordinates of the buried treasure. Explain each step using words and your graph.

Student Learning Objective (SLO) Language Objective Language NeededSLO: 1CCSS:G.GPE.6WIDA ELDS: 3ListeningReading

Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

After listening to an oral explanation and reading the directions, demonstrate comprehension by finding the point on a directed line segment between two points that divides the segment in a given ratio using White Boards, Charts/Posters, Teacher Modeling and a Partner work.

VU: Partition, coordinate plane, equal interval, directed line segmentLFC: Wh-questions, should be placed,

LC: Varies by ELP levelELP 1 ELP 2 ELP 3 ELP 4 ELP 5

Language Objectives

After listening to oral explanation and reading the directions in L1 and/or using gestures, graphs and selected technical words, demonstrate comprehension by finding the point on a directed line segment.

After listening to oral explanation and reading the directions using L1 and/or selected technical vocabulary in phrases and short sentences, demonstrate comprehension by finding the point on a directed line segment.

After listening to oral explanation and reading the directions using key, technical vocabulary in simple sentences, demonstrate comprehension by finding the point on a directed line segment.

After listening to oral explanation and reading the directions using key, technical vocabulary in expanded sentences, demonstrate comprehension by finding the point on a directed line segment.

After listening to oral explanation and reading the directions using technical vocabulary in complex sentences, demonstrate comprehension by finding the point on a directed line segment.

Learning Supports

Teacher ModelingWhite BoardCharts/PostersMath Journal/dictionaryDemonstrationPartner workWord/picture wallL1 text and/or supportPictures /illustrations

White BoardCharts/PostersTeacher ModelingMath Journal/dictionaryPartner workWord/picture wallL1 text and/or support

White BoardCharts/PostersTeacher ModelingMath Journal/dictionaryPartner work

White BoardMath Journal/dictionary Partner work

White BoardMath Journal/dictionary

CAR © 2009


http://www.nj.gov/education/modelcurriculum/math/ellscaffolding/Whiteboards.pdf











http://www.nj.gov/education/modelcurriculum/ela/ellscaffolding/InteractionSupports/PartnerWork.pdfhttp:/www.nj.gov/education/modelcurriculum/ela/ellscaffolding/InteractionSupports/PartnerWork.pdf





















G.GPE.B.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

SWBAT determine the perimeter and area of various shapes on the coordinate grid. SWBAT use a variety of techniques to determine the area of a shape.

Math Journal : What do you remember about area and perimeter?

Direct Instruction Option 1: https://www.engageny.org/resource/geometry-module-4-topic-c-overviewGeometry Module 4, Topic C: Lessons 9,

10, 11

Option 2: https://njctl.org/courses/math/geometry/area-of-figures/attachments/area-of-figures-2/

Slides 129-152

Option 3 – https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-dist-problems/e/find-area-and-perimeter-on-the-coordinate-plane

https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-dist-problems/e/coordinate-plane-word-problems-with-polygons

Option 4 – Geometry Text: 6-7, 10-1


Centers


Read “College Apartments” and answer the questions.

Part A. Find the area of the Campus East Apartment complex.

Part B. Find the area of the Campus West Apartment complex. Explain



area-of-figures/attachments/area-of-figures-2/


geometry/hs-geo-analytic-geometry/hs-geo-dist-problems/e/find-area-and-perimeter-on-

the-coordinate-plane

https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-

dist-problems/e/coordinate-plane-word-problems-with-polygons

Pearson Geometry Common CoreGeometry Text: 6-7, 10-1


GPE.B

Type II and Type III problems:G-GPE.7 - Type 2-3 Question Bank




CAR © 2009






https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-dist-problems/e/find-area-and-perimeter-on-the-coordinate-plane



https://njctl.org/courses/math/geometry/area-of-figures/attachments/area-of-figures-2/











Teacher Center – The teacher works in a small group with 1-4 students. [The engage NY lessons are written with teacher guidance and should also be implemented in the teacher center]




Review Classwork

Exit Ticket

how you divided the complex into shapes you knew how to find the area of.

Part C. The footprint of each of the smaller apartment buildings Nancy is designing is 100 meters by 150 meters. The footprints of Michael’s buildings are both 620 meters long by 120 meters wide. Based on this information and the information in the passage, which apartment complex should have Nancy’s smaller apartments and which apartment complex should have Michael’s apartment buildings? Use calculations and information from the passage to defend your answer.

CAR © 2009


Student Learning Objective (SLO) Language Objective Language NeededSLO: 8CCSS:G.GPE.7 WIDA ELDS: 3ListeningReading

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.★

Demonstrate comprehension of area and perimeter problems by computing perimeters of polygons and areas of triangles and rectangles using the distance formulas using Multilingual Math Glossary, Math Journal, Word Wall and Visuals.

VU: Heron’s formula, distance formula, semiperimeter

LFC: Cause/effect



Demonstrate comprehension of area and perimeter problems by computing perimeters of polygons and areas of triangles and rectangles in L1 and/or use gestures, examples and selected technical words.

Demonstrate comprehension of area and perimeter problems by computing perimeters of polygons and areas of triangles and rectangles in L1 and/or use selected technical vocabulary in phrases and short sentences.

Demonstrate comprehension of area and perimeter problems by computing perimeters of polygons and areas of triangles and rectangles using key vocabulary in simple sentences.

Demonstrate comprehension of area and perimeter problems by computing perimeters of polygons and areas of triangles and rectangles using key, technical vocabulary in expanded sentences.

Demonstrate comprehension of area and perimeter problems by computing perimeters of polygons and areas of triangles and rectangles using technical vocabulary in complex sentences.

Learning Supports

Multilingual Math GlossaryMath JournalDemonstrationWord/Picture WallL1 text and/or supportPictures /illustrations Visuals

Multilingual Math GlossaryMath JournalWord/Picture WallL1 text and/or supportSentence FrameVisuals

Multilingual Math GlossaryMath JournalSentence StarterWord WallVisuals

Multilingual Math GlossaryMath Journal

Math Journal

CAR © 2009



http://www.glencoe.com/sec/math/mlg/

http://www.nj.gov/education/modelcurriculum/ela/ellscaffolding/Visualizations/Visuals.pdf






















G.SRT.C.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

SWBAT label a triangle in relation to the reference angle (opposite, adjacent & hypotenuse). SWBAT determine the most appropriate trigonometric ratio (sine, cosine, and tangent) to use for a given problem based on the information provided. SWBAT solve for sides and angles of right triangles using trigonometry.

Math Journal : What do you remember about right triangles? List vocabulary and properties.

Direct Instruction Option 1: https://www.engageny.org/resource/geometry-module-2-topic-e-overviewGeometry Module E Lessons 25, 26, 29

Option 2: https://njctl.org/courses/math/geometry/similar-triangles-trigonometry/attachments/similar-triangles-trigonometry-2/

Slides 1-35 (review)

Slides 36-141

Option 3 – http://www.geometrycommoncore.com/content/unit2/gsrt6/gsrt6.html

Option 4 – Geometry Text: CB 8-3: pp506-513


CentersTeacher Center – The teacher works in a small group with 1-4 students. [The engage NY lessons are written with teacher guidance and should also be implemented


Keegan’s high school is planning to create a smaller version of the football team’s pennant to sell to fans during its home games. The diagram below shows the dimensions of the original pennant and the plans for the smaller version.

EngageNYhttps://www.engageny.org/resource/geometry-module-2-topic-e-overview


similar-triangles-trigonometry/attachments/similar-triangles-trigonometry-2/

Geometry Common Corehttp://www.geometrycommoncore.com/

content/unit2/gsrt6/gsrt6.html

Pearson Geometry Common CoreGeometry Text: CB 8-3: pp506-513


SRT



Geometry Touchpoint - G-SRT.6

Geometry OCR - G-SRT.6

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https://www.illustrativemathematics.org/HSG-SRT


https://njctl.org/courses/math/geometry/similar-triangles-trigonometry/attachments/similar-triangles-trigonometry-2/






in the teacher center]




Review Classwork

Exit Ticket

Part A. What needs to be true about the measure of the angles in order for the smaller pennnant, triangle DEF, to be geometrically similar to the original, triangle ABC? Explain using one set of corresponding angles to justify your answer.

Part B. Based on the dimensions given in the diagram, Keegan does not believe that the plans for the smaller version of the pennant create a triangle

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similar to the original. Is Keegan correct? Explain why or why not.

Part C. The school created triangle XYZ in an attempt to create a larger triangle similar to triangle ABC.

If and

, use trigonometric ratios to test whether

.

Part D. The cheerleading team is making a triangular board with their team’s logo printed on it to also display in the football stadium. It is shaped like an equilateral triangle with a side length of 8 feet. They plan to divide the board into two parts by drawing the

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altitude of the triangle and then placing the team’s logo on one half and the team’s name on the other half. What is the height of the triangular board to the nearest hundredth of a foot? Draw a diagram to support your answer.






G.SRT.C.7: Explain and use the relationship between the sine and cosine of complementary angles.SWBAT explain the co-function nature of sine and cosine. SWBAT calculate values that would make sine and cosine equal.

Math Journal : What do you remember about the lengths of the sides of a right triangle, the angles of the right triangle, their measurements, and their relationships?


https://www.engageny.org/resource/geometry-module-2-topic-e-overview

Geometry Module 2, Topic E, Lessons: 27-28

Teachers will agree on common classwork problems in their professional learning communities or grade level meetings. Problems should be selected that most closely match the




Geometry Common Core

http://www.geometrycommoncore.com/content/unit2/gsrt7/gsrt7.html




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Option 2: https://njctl.org/courses/math/geometry/similar-triangles-trigonometry/attachments/similar-triangles-trigonometry-2/

Slides 1-35 (review)

Slides 36-141

Option 3 – http://www.geometrycommoncore.com/content/unit2/gsrt7/gsrt7.html




Standards Based Problems Center – Students work in a group to solve the style of problems the assessments (Quarterly) will use to measure that standard. [Engage NY has excellent problems for this… as well as EdConnect Type 2 and Type 3 problems: Individual Center – Students work on the

assessments in column 5.

Use the following image to complete the parts below.

Part A. What is the relationship between the

measures of

and in

right Explain your reasoning.

Part B. What is the

value of Explain your reasoning.

Part C. What is the

value of Explain your reasoning.

Part D. Based on the relationship

Pearson Geometry Common Core Geometry Text: 8-3


SRT

Type II and Type III problems: G-SRT.7 - Type 2-3 Question Bank

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individual skill that they need based on their pre-test data.


Review Classwork

Exit Ticket

between

and that you found in part A, along with the

values of

and that you determined in parts B and C, write a general trigonometric rule describing the relationship between those angles.


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G.SRT.C.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

SWBAT interpret the word descriptions into lengths and angles of a right triangle so that they can diagram the relationship. SWBAT solve trigonometry and Pythagorean Theorem problems based on written descriptions.

Math Journal : What can you recall about the Pythagorean Theorem? How do you use it to solve problems regarding right triangles?



Geometry Module 2, Topic E: Lessons 28, 30-34

Option 2: https://njctl.org/courses/math/geometry/similar-triangles-trigonometry/attachments/similar-triangles-trigonometry-2/Slides: 142-252

Option 3 – https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-modeling-with-right-triangles/v/angle-to-aim-to-get-alien

https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-special-right-triangles/v/45-45-90-triangles

Option 4: Geometry Text: 8-1, 8-2, 8-3, 8-4, CB 8-4


CentersTeacher Center – The teacher works in a small group with 1-4 students. [The engage


Jeremy likes to ride his bike to his friend Khaleel’s house. If he takes the road, he rides 3.6 miles east and then 1.5 miles north. There is also a path that goes through the woods directly from Jeremy’s house to Khaleel’s house.

Part A. To the




Khanacademy.org

https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-modeling-with-right-triangles/v/angle-to-aim-to-get-alien

https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-special-right-

triangles/v/45-45-90-triangles

Pearson Geometry Common Core Geometry Text: 8-1, 8-2, 8-3, 8-4, CB 8-4


SRT

Type II and Type III problems:G-SRT.8 - Type 2-3 Question Bank (COPY)




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