Q3 12_7_16 Rev CH.do… · Web vie

Major Content Supporting Content Additional Content

Curriculum and Instruction – Office of Mathematics

Quarter 3 GEOMETRY

Introduction

In 2014, the Shelby County Schools Board of Education adopted a set of ambitious, yet attainable goals for school and student performance. The District is committed to these goals, as further described in our strategic plan, Destination2025. By 2025,

80% of our students will graduate from high school college or career ready 90% of students will graduate on time 100% of our students who graduate college or career ready will enroll in a post-secondary opportunity

In order to achieve these ambitious goals, we must collectively work to provide our students with high quality, college and career ready aligned instruction. The Tennessee State Standards provide a common set of expectations for what students will know and be able to do at the end of a grade. College and career readiness is rooted in the knowledge and skills students need to succeed in post-secondary study or careers. The TN State Standards represent three fundamental shifts in mathematics instruction: focus, coherence and rigor.

Shelby County Schools 2016/2017Revised 12/1/16

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Focus

The Standards call for a greater focus in mathematics. Rather than racing to cover topics in a mile-wide, inch-deep curriculum, the Standards require us to significantly narrow and deepen the way time and energy is spent in the math classroom. We focus deeply on the major work of each grade so that students can gain strong foundations: solid conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the math classroom. For geometry, the major clusters, account for 65% of time spent on instruction.Supporting Content - information that supports the understanding and implementation of the major work of the grade.Additional Content - content that does not explicitly connect to the major work of the grade yet it is required for proficiency.

Coherence

Thinking across grades:The TN Standards are designed around coherent progressions from grade to grade. Learning is carefully connected across grades so that students can build new understanding on to foundations built in previous years. Each standard is not a new event, but an extension of previous learning. Linking to major topics:Instead of allowing additional or supporting topics to detract from the focus of the grade, these concepts serve the grade level focus. For example, instead of data displays as an end in themselves, they are an opportunity to do grade-level word problems.

Rigor

Conceptual understanding: The TN Standards call for conceptual understanding of key concepts. Students must be able to access concepts from a number of perspectives so that they are able to see math as more than a set of mnemonics or discrete procedures. Procedural skill and fluency: The Standards call for speed and accuracy in calculation. While high school standards for math do not list high school fluencies, there are fluency standards for algebra 1, geometry, and algebra 2..Application: The Standards call for students to use math flexibly for applications in problem-solving contexts. In content areas outside of math, particularly science, students are given the opportunity to use math to make meaning of and access content.



Quarter 3 GEOMETRY

The Standards for Mathematical Practice describe varieties of expertise, habits of minds and productive dispositions that mathematics educators at all levels should seek to develop in their students. These practices rest on important National Council of Teachers of Mathematics (NCTM) “processes and proficiencies” with longstanding

importance in mathematics education. Throughout the year, students should continue to develop proficiency with the eight Standards for Mathematical Practice.

This curriculum map is designed to help teachers make effective decisions about what mathematical content to teach so that, ultimately our students, can reach Destination 2025. To reach our collective student achievement goals, we know that teachers must change their practice so that it is in alignment with the three mathematics instructional shifts.

Throughout this curriculum map, you will see resources as well as links to tasks that will support you in ensuring that students are able to reach the demands of the standards in your classroom. In addition to the resources embedded in the map, there are some high-leverage resources around the content standards and mathematical practice standards that teachers should consistently access:


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Quarter 3 GEOMETRY

The TN Mathematics StandardsThe Tennessee Mathematics Standards:https://www.tn.gov/education/article/mathematics-standards

Teachers can access the Tennessee State standards, which are featured throughout this curriculum map and represent college and career ready learning at reach respective grade level.

Standards for Mathematical Practice Mathematical Practice Standardshttps://drive.google.com/file/d/0B926oAMrdzI4RUpMd1pGdEJTYkE/view

Teachers can access the Mathematical Practice Standards, which are featured throughout this curriculum map. This link contains more a more detailed explanation of each practice along with implications for instructions.

Purpose of the Mathematics Curriculum Maps

This curriculum framework or map is meant to help teachers and their support providers (e.g., coaches, leaders) on their path to effective, college and career ready (CCR) aligned instruction and our pursuit of Destination 2025. It is a resource for organizing instruction around the TN State Standards, which define what to teach and what students need to learn at each grade level. The framework is designed to reinforce the grade/course-specific standards and content—the major work of the grade (scope)—and provides a suggested sequencing and pacing and time frames, aligned resources—including sample questions, tasks and other planning tools. Our hope is that by curating and organizing a variety of standards-aligned resources, teachers will be able to spend less time wondering what to teach and searching for quality materials (though they may both select from and/or supplement those included here) and have more time to plan, teach, assess, and reflect with colleagues to continuously improve practice and best meet the needs of their students.

The map is meant to support effective planning and instruction to rigorous standards; it is not meant to replace teacher planning or prescribe pacing or instructional practice. In fact, our goal is not to merely “cover the curriculum,” but rather to “uncover” it by developing students’ deep understanding of the content and mastery of the standards. Teachers who are knowledgeable about and intentionally align the learning target (standards and objectives), topic, task, and needs (and assessment) of the learners are best-positioned to make decisions about how to support student learning toward such mastery. Teachers are therefore expected--with the support of their colleagues, coaches, leaders, and other support providers--to exercise their professional judgment aligned to our shared vision of effective instruction, the Teacher Effectiveness Measure (TEM) and related best practices. However, while the framework allows for flexibility and encourages each teacher/teacher team to make it their own, our expectations for student learning are non-negotiable. We must ensure all of our children have access to rigor—high-quality teaching and learning to grade-level specific standards, including purposeful support of literacy and language learning across the content areas.

Additional Instructional SupportShelby County Schools adopted our current math textbooks for grades 9-12 in 2010-2011. The textbook adoption process at that time followed the requirements set forth by the Tennessee Department of Education and took into consideration all texts approved by the TDOE as appropriate. We now have new standards;


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https://drive.google.com/file/d/0B926oAMrdzI4RUpMd1pGdEJTYkE/view

https://www.tn.gov/education/article/mathematics-standards



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therefore, the textbook(s) have been vetted using the Instructional Materials Evaluation Tool (IMET). This tool was developed in partnership with Achieve, the Council of Chief State Officers (CCSSO) and the Council of Great City Schools. The review revealed some gaps in the content, scope, sequencing, and rigor (including the balance of conceptual knowledge development and application of these concepts), of our current materials. The additional materials purposefully address the identified gaps in alignment to meet the expectations of the CCR standards and related instructional shifts while still incorporating the current materials to which schools have access. Materials selected for inclusion in the Curriculum Maps, both those from the textbooks and external/supplemental resources (e.g., engageny), have been evaluated by district staff to ensure that they meet the IMET criteria.

How to Use the Mathematics Curriculum Maps

OverviewAn overview is provided for each quarter. The information given is intended to aid teachers, coaches and administrators develop an understanding of the content the students will learn in the quarter, how the content addresses prior knowledge and future learning, and may provide some non-summative assessment items.

Tennessee State StandardsThe TN State Standards are located in the left column. Each content standard is identified as the following: Major Work, Supporting Content or Additional Content.; a key can be found at the bottom of the map. The major work of the grade should comprise 65-85% of your instructional time. Supporting Content are standards that supports student’s learning of the major work. Therefore, you will see supporting and additional standards taught in conjunction with major work. It is the teacher’s responsibility to examine the standards and skills needed in order to ensure student mastery of the indicated standard.

ContentTeachers are expected to carefully craft weekly and daily learning objectives/ based on their knowledge of TEM Teach 1. In addition, teachers should include related best practices based upon the TN State Standards, related shifts, and knowledge of students from a variety of sources (e.g., student work samples, MAP, etc.). Support for the development of these lesson objectives can be found under the column titled ‘Content’. The enduring understandings will help clarify the “big picture” of the standard. The essential questions break that picture down into smaller questions and the objectives provide specific outcomes for that standard(s). Best practices tell us that clearly communicating and making objectives measureable leads to greater student mastery.

Instructional Support and ResourcesDistrict and web-based resources have been provided in the Instructional Resources column. Throughout the map you will find instructional/performance tasks and additional resources that align with the standards in that module. The additional resources provided are supplementary and should be used as needed for content support and differentiation.


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Topics Addressed in Quarter Similarity and Transformations Using Similar Triangles Right Triangles with Trigonometry Properties of Angles and Segments in Circles

OverviewDuring the third quarter students formalize their understanding of similarity, which was informally studied prior to geometry. Similarity of polygons and triangles is explored and triangle similarity postulates and theorems are formally proven. The proportionality of corresponding sides of similar figures is applied. Similarity is extended to the side-splitting, proportional medians, altitudes, angle bisectors, and segments theorems. The geometric mean is defined and related to the arithmetic mean. The special right triangles of 30-60-90 and 45-45-90 are also studied. Students are introduced to the right-triangle trigonometric ratios of sine, cosine, and tangent, and their applications. Angles and the sine, cosine, and tangent functions are defined in terms of a rotation of a point on the unit circle. Students will end the quarter by starting their study of circles. They will quickly review circumference and then identify central angles, major and minor arcs, semicircles and find their measures. They will finish the quarter studying inscribed angles and intercepted arcs.

Year at a Glance Document

Content Standard Type of Rigor Foundational Standards Sample Assessment Items**G-SRT.A.2 Procedural Skill and Fluency , Conceptual

Understanding 8.G.A.1, 2,3, 4,5 Illustrative: Are They Similar; Illustrative:

Congruent and Similar Triangles; Illustrative: Similar Triangles

G-SRT.B.4, 5 Procedural Skill and Fluency , Conceptual Understanding & Application

8.G.A.1, 2,3, 4,5 Illustrative: Joining Two Midpoints of Sides of a Triangle ; Illustrative: Pythagorean Theorem; Illustrative: Bank Shot; Illustrative: Points From Directions


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https://www.illustrativemathematics.org/content-standards/HSG/SRT/B/5/tasks/1002







http://tennessee.gov/assets/entities/education/attachments/std_math_geometry.pdf

https://www.illustrativemathematics.org/content-standards/HSG/SRT/A/2/tasks/1890






https://drive.google.com/file/d/0B6PC3EhLszWHRUkybXlCeVlxSlE/view?usp=sharing



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G-SRT.C.6, 7, 8 Procedural Skill and Fluency , Conceptual Understanding & Application

8.G.A.1, 2,3, 4,5 Math shell: Hopewell Geometry

G-C.A.1, 2 Procedural Skill and Fluency , Conceptual Understanding & Application

8.G.A.5; 8.G.B.7 Illustrative: Similar Circles; Illustrative: Neglecting the Curvature of the Earth

G-MG.A.3 Procedural Skill and Fluency , Conceptual Understanding & Application

8.G.A.5; 8.G.B.7 Illustrative: Ice Cream Cone; Illustrative: Satellite

** TN Tasks are available at http://www.edutoolbox.org/ and can be accessed by Tennessee educators with a login and password.

Fluency The high school standards do not set explicit expectations for fluency, but fluency is important in high school mathematics. Fluency in algebra can help students get past the need to manage computational and algebraic manipulation details so that they can observe structure and patterns in problems. Such fluency can also allow for smooth progress toward readiness for further study/careers in science, technology, engineering, and mathematics (STEM) fields. These fluencies are highlighted to stress the need to provide sufficient supports and opportunities for practice to help students gain fluency. Fluency is not meant to come at the expense of conceptual understanding. Rather, it should be an outcome resulting from a progression of learning and thoughtful practice. It is important to provide the conceptual building blocks that develop understanding along with skill toward developing fluency.

The fluency recommendations for geometry listed below should be incorporated throughout your instruction over the course of the school year. G-SRT.B.5 Fluency with the triangle congruence and similarity criteria G-GPE.B.4,5,7 Fluency with the use of coordinates G-CO.D.12 Fluency with the use of construction tools

References: http://www.tn.gov/education/article/mathematics-standards http://www.corestandards.org/ http://www.nctm.org/ http://achievethecore.org/


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http://achievethecore.org/

http://www.nctm.org/Standards-and-Positions/Position-Statements/Procedural-Fluency-in-Mathematics/

http://www.corestandards.org/

http://www.tn.gov/education/article/mathematics-standards

http://www.edutoolbox.org/

https://www.illustrativemathematics.org/content-standards/HSG/MG/A/3/tasks/416




https://www.illustrativemathematics.org/content-standards/HSG/C/A/2/tasks/1345




http://map.mathshell.org/tasks.php?unit=HA05&collection=9&redir=1




Quarter 3 GEOMETRY

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

Similarity and Transformations (Allow approximately 3 weeks for instruction, review, and assessment)

Domain: G-MG Modeling with Geometry Cluster: Apply geometric concept in modeling situationsG-MG.A.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). ★

Enduring Understanding(s)Polygons are similar if and only if corresponding angles are congruent and corresponding sides are proportional.

Essential Question(s)What is the difference between a ratio and a proportion?What operations are used to solve a proportion?

Objective(s):• Write ratios• Write and solve proportions

Use the following lesson(s) first to introduce concepts/build conceptual understanding. Better Lesson: Comparing Sequences

Use the textbook resources to address procedural skill and fluency.Lesson 7.1 Ratios and Proportions pp. 457 - 464 Graphing Technology Lab - Fibonacci Sequence and Ratios p. 464

VocabularyRatio, extended ratios, proportion, extremes, means, cross products

Activity with DiscussionResearch and Report- The Fibonacci Sequence and the Golden Ratio - what are they, why are they important, and how are they related.

Domain: G-SRT Similarity, Right Triangles and TrigonometryCluster: Understand similarity in terms of similarity transformations G-SRT.A.2 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


Essential Question(s)How do you use proportions to find side lengths in similar polygons?How do you identify corresponding parts of similar triangles?

Use the following lesson(s) first to introduce concepts/build conceptual understanding. engage ny Geometry Module 2, Topic C, Lesson 12 – Similarity Transformations Use the textbook resources to address procedural skill and fluency.Lesson 7.2 Similar Polygons pp.465-473

Use the following resources to deepen

VocabularySimilar polygons, similarity ratio, scale factor

Activity with Discussionp. 472 #54 Draw two regular pentagons that are different sizes. Are the pentagon’s similar? Will any two regular polygons with the same number of sides be similar? Explain

Writing in Math/DiscussionShelby County Schools 2016/2017

Revised 12/1/167 of 19

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


http://betterlesson.com/lesson/449193/comparing-sequences-by-form-and-by-pattern-of-change



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the proportionality of all corresponding pairs of sides. Objective(s):

• Use proportions to Identify similar polygons

• Solve problems using the properties of similar polygons

students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.HS Flip Book with examples of each Standard(Designed as a resource tool to assist teachers in deepening their understanding of what each standard means in terms of what students must know and be able to do. It outlines only a sample of instructional strategies and examples. Links to conceptual categories and specific standards in the document can be accessed from page 5 Mathematics Standards for High School.)

p. 472 #55 Compare and contrast congruent, similar, and equal figures.

Domain: G-SRT Similarity, Right Triangles and TrigonometryCluster: Understand similarity in terms of similarity transformations G-SRT.A.2 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.

Domain: G-SRT Similarity, Right Triangles and TrigonometryCluster: Define trigonometric ratios and solve problems involving right triangles 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.

Enduring Understanding(s)Geometric figures can change size and/or position while maintaining proportional attributes.

Essential Question(s)How do you show two triangles are similar?

Objective(s):• Identify similarity transformations• Verify similarity after a similarity

transformation

Use the following lesson(s) first to introduce concepts/build conceptual understanding. engage ny Geometry Module 2, Topic A, Lesson 2 – Scale Drawings by Ratio Method engage ny Geometry Module 2, Topic A, Lesson 3 – Scale Drawings by the Parallel Method engage ny Geometry Module 2, Topic B Lesson 6 – Dilations engage ny Geometry Module 2, Topic B, Lesson 7 – Do Dilations Map Segments?

Use the textbook resources to address procedural skill and fluency.Lesson 7.6 Similarity Transformations pp. 505-511

Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.HS Flip Book with examples of each

Vocabularydilation, similarity transformation, center of dilation, scale factor of a dilation, enlargement, reduction

Activity with DiscussionExplain how you can use scale factor to determine whether a transformation is an enlargement, a reduction, or a congruence transformation.


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http://www.azed.gov/azccrs/files/2013/11/high-school-ccss-flip-book-usd-259-2012.pdf

https://www.engageny.org/resource/geometry-module-2-topic-b-lesson-7




https://www.engageny.org/resource/geometry-module-2-topic-a-lesson-3









Quarter 3 GEOMETRY


Standard

Domain: G-MG Modeling with Geometry Cluster: Apply geometric concepts in modeling situationsG-MG.A.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). ★

Enduring Understanding(s)Geometric figures can change size and/or position while maintaining proportional attributes.

Essential Question(s)How do you use proportions to find side lengths in similar polygons?

Objective(s):• Interpret scale models• Use scale factors to solve problems

Use the following lesson(s) first to introduce concepts/build conceptual understanding. engage ny Geometry Module 2, Topic A, Lesson 1 – Scale Drawings

Use the textbook resources to address procedural skill and fluency.Lesson 7.7 Scale Drawings and Scale Models pp. 512-517

VocabularyScale model, scale drawing, scale

Writing in Math/DiscussionCompare and contrast scale and scale factor.

You can produce a scale model of a certain object by extending each dimension by a constant. What must be true of the shape of the object? Explain your reasoning.

Using Similar Triangles (Allow approximately 3 weeks for instruction, review, and assessment)

Domain: G-SRT Similarity, Right Triangles and TrigonometryCluster: Prove theorems involving similarity G-SRT.B.4 Prove theorems about

triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.

Domain: G-SRT Similarity, Right Triangles and TrigonometryCluster: Prove theorems involving similarity G-SRT.B.5 Use congruence and

similarity criteria for triangles to solve problems and to prove relationships in geometric figures.


Essential Question(s)How do you use proportions to find side lengths in similar polygons? How do you show two triangles are similar?

Objective(s):• Identify and prove similar triangles

using the AA Similarity Postulate and the SSS and SAS similarity Theorems

• Use similar triangles to solve problems

Use the following lesson(s) first to introduce concepts/build conceptual understanding. engage ny Geometry Module 2, Topic C, Lesson 14 – Similarity engage ny Geometry Module 2, Topic C, Lesson 15 – AA Similarity engage ny Geometry Module 2, Topic C, Lesson 17 – SSS & SAS Similarity engage ny Geometry Module 2, Topic C, Lesson 16 – Applying Similar Triangles

Use the textbook resources to address procedural skill and fluency.Lesson 7.3 Similar Triangles pp. 474-483

Writing in Math/DiscussionContrast and compare the triangle congruence theorems with the triangle similarity theorems.


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Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.HS Flip Book with examples of each Standard






Essential Question(s)How do you use proportions to find side lengths in similar polygons?

Objective(s):• Use proportional parts within triangles• Use proportional parts with parallel lines

Use the following lesson(s) first to introduce concepts/build conceptual understanding. engage ny Geometry Module 2, Topic A, Lesson 4 – Triangle Side Splitter Theorem engage ny Geometry Module 2, Topic B, Lesson 10 – Dividing a Line Segment into Equal Parts engage ny Geometry Module 2, Topic C, Lesson 19 – Parallel Lines and Proportional Segments

Use the textbook resources to address procedural skill and fluency.Lesson 7.4 Parallel Lines and Proportional Parts (midsegments was previously covered in unit 2) pp. 484-492

Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.

HS Flip Book with examples of each Standard

VocabularyMid-segment of a triangle

Activity with DiscussionUse multiple representations to explore angle bisectors and proportions. See p. 492, #47


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Quarter 3 GEOMETRY


Task(s)See Mathematics, Instructional Resources, Geometry, Task Arc: Investigating Coordinate GeometryPartitioning However You Want to Slice It Comparing Shapes

Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.HS Flip Book with examples of each Standard (Designed as a resource tool to assist teachers in deepening their understanding of what each standard means in terms of what students must know and be able to do. It outlines only a sample of instructional strategies and examples. Links to conceptual categories and specific standards in the document can be accessed from page 5 Mathematics Standards for High School.)



Domain: G-SRT Similarity, Right Triangles

Enduring Understanding(s)• Similar figures map one shape

proportionally onto another through non-rigid motions.

• Congruence and similarity criteria for triangles are used to solve problems and prove relationships of geometric figures.

Use the following lesson(s) first to introduce concepts/build conceptual understanding. engage ny Geometry Module 2, Topic D, Lesson 21 – Special Relationships within Right Traingles engage ny Geometry Module 2, Topic D, Lesson 24 – Prove the Pythagorean Theorem Using Similarity

VocabularyGeometric mean

Writing in Math/DiscussionWhat is an arithmetic mean and a geometric mean of two numbers? Are they ever equal? Justify your answer.


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https://www.engageny.org/resource/geometry-module-2-topic-d-lesson-24








http://edutoolbox.org/rasp/678?route=tntools/list/grade/819/955/9-10





Quarter 3 GEOMETRY

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESand TrigonometryCluster: Prove theorems involving similarity G-SRT.B.5 Use congruence and


Essential Question(s) Can the geometric mean be used in any

triangle? Why does geometric mean help us to find

the missing sides in a right triangle?

Objective(s):• Find the geometric mean between two

numbers• Solve problems involving relationships

between parts of a right triangle and the altitude to its hypotenuse

Use the textbook resources to address procedural skill and fluency.Lesson 8.1 Geometric Mean pp.531-539






Enduring Understanding(s)• Similar figures map one shape

proportionally onto another through non-rigid motions.

• Congruence and similarity criteria for triangles are used to solve problems and prove relationships of geometric figures.

.Essential Question(s)How might the features of one figure be useful when solving problems about a similar figure?

Objective(s):• Recognize and use proportional

relationships of corresponding angle bisectors, altitudes, and medians of similar triangles

• Use the Triangle Angle Bisector Theorem

Use the following lesson(s) first to introduce concepts/build conceptual understanding. engage ny Geometry Module 2, Topic C, Lesson 18 – Triangle Angles Bisector Theorem

Use the textbook resources to address procedural skill and fluency.Lesson 7.5 Parts of Similar Triangles pp.495-503


Activity with DiscussionFind a counterexample: If the measure of an altitude and side of a triangle are proportional to the corresponding altitude and corresponding side of another triangle, then the triangles are similar


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Quarter 3 GEOMETRY


ACT Practice (sample problems to prepare for the ACT)

Glencoe, pp.456-457

Right Triangles and Trigonometry (Allow approximately 1.5 weeks for instruction, review, and assessment)t)



Enduring Understanding(s)Trigonometry can be used to measure sides and angles indirectly in right triangles.

Essential Question(s)How do you find a side length or angle measure in a right triangle?

Objective(s):• Identify and apply side ratios in 45-45-

90 right triangles.• Identify and apply side ratios in 30-60-

90 right triangles

Use the following lesson(s) first to introduce concepts/build conceptual understanding. engage ny Geometry Module 2, Topic D, Lesson 24 - Prove the Pythagorean Theorem Using Similarity

Use the textbook resources to address procedural skill and fluency.Lesson 8.3 Special Right Triangles pp.552-559


Task(s)Discovering Special Right Triangles Learning TaskFinding Right Triangles in your Environment Learning Task

Create your own triangles Learning Task

Activity with Discussionp.559 #50Explain how you can find the lengths of two legs of a 30-60-90 triangle in radical form if you are given the length of the hypotenuse.

Domain: G-SRT Similarity, Right Triangles Enduring Understanding(s) Use the following lesson(s) first to Vocabulary


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http://troup612resources.troup.k12.ga.us/curriculum1/mathematics/accel_coord_alg/8_right_triangle_trig/8_create_your_own_triangles_setask.pdf

http://troup612resources.troup.k12.ga.us/curriculum1/mathematics/accel_coord_alg/8_right_triangle_trig/8_finding_right_triangles_environment_setask.pdf

http://troup612resources.troup.k12.ga.us/curriculum1/mathematics/accel_coord_alg/8_right_triangle_trig/8_finding_right_triangles_environment_setask.pdf

http://troup612resources.troup.k12.ga.us/curriculum1/mathematics/accel_coord_alg/8_right_triangle_trig/8_discovering_special_triangles_setask.pdf

http://troup612resources.troup.k12.ga.us/curriculum1/mathematics/accel_coord_alg/8_right_triangle_trig/8_discovering_special_triangles_setask.pdf








Quarter 3 GEOMETRY

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESand TrigonometryCluster: Define trigonometric ratios and solve problems involving right triangles G-SRT.C.7 Explain and use the

relationship between the sine and cosine of complementary angles.

Domain: G-SRT Similarity, Right Triangles and TrigonometryCluster: Define trigonometric ratios and solve problems involving right triangles G-SRT.C.8 Use trigonometric ratios

and the Pythagorean Theorem to solve right triangles in applied problems. ★



Trigonometry can be used to measure sides and angles indirectly in right triangles.

Essential Question(s)How do you find a side length or angle measure in a right triangle?How do trigonometric ratios relate to similar right triangles?

Objective(s):• Define trigonometric ratios for acute

angles in right triangles• Use trigonometric rations and Pythagorean

Theorem to solve right triangles• Use the relationship between the sine and

cosine of complementary angles.

introduce concepts/build conceptual understanding. engage ny Geometry Module 2, Topic E Lesson 25: Incredibly Useful Ratios Lesson 26: The Definition of Sine, Cosine, and Tangent Lesson 27: Sine and Cosine of Complementary Angles and Special Angles Lesson 28: Solving Problems Using Sine and Cosine Lesson 29: Applying Tangents Lesson 30: Trigonometry and the Pythagorean Theorem

Use the textbook resources to address procedural skill and fluency.Lesson 8.4 Trigonometry pp.562-271


Task(s)Discovering Trigonometric Ratio Relationships learning task p.22

Trigonometry, trigonometry ratio, sine, cosine, tangent, inverse sine, inverse cosine, inverse tangent

Activity with Discussionp.570 #65Explain how you can use ratios of the side lengths to find the angle measures of the acute angles in a right triangle.

Domain: G-SRT Similarity, Right Triangles and TrigonometryCluster: Define trigonometric ratios and solve problems involving right triangles G-SRT.C.8 Use trigonometric ratios

and the Pythagorean Theorem to solve

Enduring Understanding(s)Trigonometry can be used to measure sides and angles indirectly in right triangles.

Essential Question(s)How do you find a side length or angle measure

Use the following lesson(s) first to introduce concepts/build conceptual understanding. engage ny Geometry Module 2, Topic D, Lesson Lesson 31: Using Trigonometry to Determine Area

VocabularyAngle of elevation, angle of depression

Writing in Math/Discussionp.580 #25


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https://www.engageny.org/resource/geometry-module-2-topic-e-lesson-31



https://www.georgiastandards.org/Frameworks/GSO%20Frameworks/Acc-Math-II-Unit-4-SE-Right-Triangle-Trig.pdf

https://www.georgiastandards.org/Frameworks/GSO%20Frameworks/Acc-Math-II-Unit-4-SE-Right-Triangle-Trig.pdf



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












Quarter 3 GEOMETRY


right triangles in applied problems. ★ in a right triangle?How do trigonometric ratios relate to similar right triangles?

Objective(s):• Solve problems involving angles of elevation. • Solve problems involving angles of

depression.

Lesson 32: Using Trigonometry to Find Side Lengths of an Acute TriangleLesson 33: Applying the Laws of Sines and Cosines Lesson 34: Unknown Angles Use the textbook resources to address procedural skill and fluency.Lesson 8.5 – Angles of Elevation and Depression pp.574-581


Task(s)Find that Side or Angle TaskEdutoolbox: Interstate Task

ACT Practice (sample problems to prepare for the ACT)

Glencoe, pp.618-619

Classify the statement below as true or false. Explain. “As a person moves closer to an object he or she is sighting, the angle of elevation increases”

Properties of Angles and Segments in Circles (Allow approximately 1.5 weeks for instruction, review, and assessment)t)

Domain: G-C Circles Cluster: Understand and apply theorems about circles G-C.A.1 Prove that all circles are similar.

Domain: G-CO Congruence Cluster: Experiment with transformations in

Enduring Understanding(s)The concept of similarity as it relates to circles can be extended with proof.

Essential Question(s)What role do circles play in modeling the word around us?

Use the following lesson(s) first to introduce concepts/build conceptual understanding. engage ny Geometry Module 3, Topic A, Lesson 4 – Proving the Area of a Disk

Use the textbook resources to address

VocabularyCircle, center, radius, chord, diameter, congruent circles, concentric circles, circumference, pi, inscribed, circumscribed

Writing in Math/Discussion


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http://images.pcmac.org/SiSFiles/Schools/GA/CarrollCounty/CentralHigh/Uploads/DocumentsCategories/Documents/07%20-%20Find%20That%20Side%20or%20Angle%20Task.pdf










Quarter 3 GEOMETRY

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESthe plane G-CO.A.1 Know precise definitions of

angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

Domain: G-GMD Geometric Measurement and DimensionCluster: Explain volume formulas and use them to solve problems G-GMD.A.1 Give an informal

argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.

Objective(s):• Give an argument to justify the formula

for the circumference of a circle.• Prove that all circles are similar.

procedural skill and fluency.Lesson 10.1 – Circles and Circumference pp.683-691


Task(s)Illustrative Math: Similar Circles TaskAll Circles are Similar Task

p.690 #54Research and write about the history of pi and its importance to the study of geometry.

Domain: G-C Circles Cluster: Understand and apply theorems about circles G-C.A.2 Identify and describe

relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

Enduring Understanding(s)• Relationships between angles, radii and

chords will be investigated. • Similarities will be applied to derive an arc

length and a sector area.

Essential Question(s)When lines intersect a circle, or within a circle, how do you find the measures of resulting angles, arcs, and segments?

Objective(s):• Identify central angles, major arcs, minor

arcs, and semicircles and find their measures.

Use the following lesson(s) first to introduce concepts/build conceptual understanding. . engage ny Geometry Module 5, Topic A, Lesson 4 – Explore Relationships between Inscribed Angles, Central Angles and their Intercepted Arcs

Use the textbook resources to address procedural skill and fluency.Lesson 10.2 Measuring Angles and Arcs pp.692-700Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-

VocabularyCentral angle, arc, minor arc, major arc, semicircle, congruent arcs, adjacent arcs, arc length

Writing in Math/Discussionp.699 #62Describe the three different types of arcs in a circle and the method for finding the measure of each one.


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http://www.cpm.org/pdfs/state_supplements/Similar_Circles.pdf

https://www.illustrativemathematics.org/content-standards/tasks/1368





Quarter 3 GEOMETRY


routine problems.HS Flip Book with examples of each Standard

Task(s)Circles and their Relationships among Central Angles, Arcs and Chords (p. 15) Investigating Angle Relationships in Circles (pp. 46 & 52)

Domain: G-C Circles Cluster: Understand and apply theorems about circles G-C.A.2 Identify and describe

relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

Enduring Understanding(s)• Relationships between angles, radii and

chords will be investigated. • Similarities will be applied to derive an arc

length and a sector area.

Essential Question(s)When lines intersect a circle, or within a circle, how do you find the measures of resulting angles, arcs, and segments?

Objective(s):• Identify and describe relationships involving

inscribed angles.• Prove properties of angles for a quadrilateral

inscribed in a circle.

Use the following lesson(s) first to introduce concepts/build conceptual understanding. Engage ny Geometry Module 5, Topic A, Lesson 5 – Prove Inscribed Angle Theorem

Use the textbook resources to address procedural skill and fluency.Lesson 10.4 Inscribed Angles pp.709-716


Task(s)Illustrative Math: Opposite angles in a cyclic quadrilateral

VocabularyInscribed angle, intercepted arc

Writing in Math/Discussionp.715 #50Compare and contrast inscribed angles and central angles of a circle. If they intercept the same arc, how are they related?


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https://www.georgiastandards.org/Georgia-Standards/Frameworks/Analytic-Geometry-Unit-3.pdf







Quarter 3 GEOMETRY

RESOURCE TOOLBOXThe Resource Toolbox provides additional support for comprehension and mastery of subject-level skills and concepts. While some of these resources are embedded in the map, the use of these categorized materials can assist educators with maximizing their instructional practices to meet the needs of all students.

Textbook ResourcesConnectED Site - Textbook and Resources Glencoe Video Lessons Hotmath - solutions to odd problems

Comprehensive Geometry Help: Online Math Learning (Geometry) I LOVE MATHNCTM Illuminations

StandardsCommon Core Standards - Mathematics Common Core Standards - Mathematics Appendix A TN CoreHS Flip Book with Examples of each Standard (The Flip Book is designed as a resource tool to assist teachers in deepening their understanding of what each standard means in terms of what students must know and be able to do. It outlines only a sample of instructional strategies and examples. Links to conceptual categories and specific standards in the document can be accessed from page 5 Mathematics Standards for High School.)

Geometry Model Curriculum http://www.ccsstoolbox.org/

Videos Math TV VideosThe Teaching Channel Khan Academy Videos (Geometry)

TasksEdutoolbox (formerly TNCore) Tasks Inside Math Tasks Mars Tasks Dan Meyer's Three- NYC tasks Illustrative Math Tasks


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https://www.illustrativemathematics.org/search?query=tasks#by_sections

http://schools.nyc.gov/Academics/CommonCoreLibrary/TasksUnitsStudentWork/default.htm

https://docs.google.com/spreadsheet/ccc?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWnM2YWxWYVM1UWowTEE#gid=0

http://map.mathshell.org/materials/tasks.php

http://www.insidemathematics.org/performance-assessment-tasks

http://www.insidemathematics.org/performance-assessment-tasks

http://tncore.org/math/instructional_resources/domains/hs_algdomain.aspx

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

https://www.teachingchannel.org/

http://www.mathtv.com/videos_by_topic

http://www.ccsstoolbox.org/

https://education.ohio.gov/getattachment/Topics/Academic-Content-Standards/Mathematics/High-School-Model-Curriculum-for-Mathematics-%E2%80%93-Geometry-pdf.pdf.aspx


http://www.corestandards.org/assets/CCSSI_Mathematics_Appendix_A.pdf

http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf

http://illuminations.nctm.org/

http://www.ilovemath.org/index.php?option=com_docman&Itemid=31

http://www.onlinemathlearning.com/geometry-help.html

http://hotmath.com/help/bookindexes/cumminsgtn12/

http://glencoe.mcgraw-hill.com/sites/0078884845/sitemap.html?resource=personaltutor

http://connected.mcgraw-hill.com/connected/login.do



Quarter 3 GEOMETRY

RESOURCE TOOLBOXThe Resource Toolbox provides additional support for comprehension and mastery of subject-level skills and concepts. While some of these resources are embedded in the map, the use of these categorized materials can assist educators with maximizing their instructional practices to meet the needs of all students.

New Jersey Center for Teaching & Learning (Geometry) http://insidemathematics.org/index.php/high-school- geometry http://learnzillion.com/common_core/math/hs http://www.livebinders.com/play/play/454480https://www.livebinders.com/play/play?id=464831 http://www.livebinders.com/play/play?id=571735 Utah Electronic School - Geometry Ohio Common Core Resources Chicago Public Schools Framework and Tasks

ACT TN ACT Information & Resources

ACT College & Career Readiness Mathematics Standards

UT Dana Center GSE Analytic Geometry Unit 1: Similarity, Congruence and Proofs

CalculatorFinding Your Way Around TI-83+ & TI-84+ (mathbits.com) Texas Instruments Calculator Activity ExchangeTexas Instruments Math NspiredSTEM ResourcesCasio Education for Teachers*Graphing Calculator Note: TI tutorials are available through Atomic Learning and also at the following link: Math Bits - graphing calculator steps Some activities require calculator programs and/or applications.

Use the following link to access FREE software for your MAC. This will enable your computer and TI Calculator to communicate: Free TI calculator downloads

NWEA MAP Resources:https://teach.mapnwea.org/assist/help_map/ApplicationHelp.htm#UsingTestResults/MAPReportsFinder.htm - Sign in and Click the Learning Continuum Tab – this resources will help as you plan for intervention, and differentiating small group instruction on the skill you are currently teaching. (Four Ways to Impact Teaching with the Learning Continuum)

https://support.nwea.org/khanrit - These Khan Academy lessons are aligned to RIT scores.

Interactive ManipulativesGeoGebra – Free software for dynamic math and science learningNCTM Core Math Tools http://www.keycurriculum.com/products/sketchpad (Not free) Any activity using Geometer’s Sketchpad can also be done with any software that allows construction of figures and measurement, such as Cabri, Cabri Jr. on the TI-83 or 84 Plus,TI-92 Plus, or TI-Nspire.

Literacy Resources Literacy Skills and Strategies for Content Area Teachers (Math, p. 22)Glencoe Reading & Writing in the Mathematics ClassroomGraphic Organizers (9-12) (teachervision.com)


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https://www.teachervision.com/tv/tvsearch/site=TV&lowest_grade=109&highest_grade=112&type=graphic-organizer

http://www.glencoe.com/sec/teachingtoday/downloads/pdf/ReadingWritingMathClass.pdf

http://www.valrc.org/resources/docs/MHS_Literacy_Strategy_Book.pdf

http://www.keycurriculum.com/products/sketchpad

http://www.nctm.org/resources/content.aspx?id=32702

http://www.geogebra.org/cms/en/

https://exchange.scsk12.org/owa/redir.aspx?SURL=6B8d_6h_R679_RRR092tkVCu6l4IQBJpWBWrHsYK6X5LQ9b-xEbTCGgAdAB0AHAAcwA6AC8ALwBzAHUAcABwAG8AcgB0AC4AbgB3AGUAYQAuAG8AcgBnAC8AawBoAGEAbgByAGkAdAA.&URL=https%3A%2F%2Fsupport.nwea.org%2Fkhanrit

https://exchange.scsk12.org/owa/redir.aspx?SURL=CLLmD5S_czDWmSJtkFdGHOvdUMjXEJiEYOAo04PK_1BLQ9b-xEbTCGgAdAB0AHAAcwA6AC8ALwB0AGUAYQBjAGgALgBtAGEAcABuAHcAZQBhAC4AbwByAGcALwBhAHMAcwBpAHMAdAAvAGgAZQBsAHAAXwBtAGEAcAAvAEEAcABwAGwAaQBjAGEAdABpAG8AbgBIAGUAbABwAC4AaAB0AG0AIwBVAHMAaQBuAGcAVABlAHMAdABSAGUAcwB1AGwAdABzAC8ATQBBAFAAUgBlAHAAbwByAHQAcwBGAGkAbgBkAGUAcgAuAGgAdABtAA..&URL=https%3A%2F%2Fteach.mapnwea.org%2Fassist%2Fhelp_map%2FApplicationHelp.htm%23UsingTestResults%2FMAPReportsFinder.htm

https://exchange.scsk12.org/owa/redir.aspx?SURL=CLLmD5S_czDWmSJtkFdGHOvdUMjXEJiEYOAo04PK_1BLQ9b-xEbTCGgAdAB0AHAAcwA6AC8ALwB0AGUAYQBjAGgALgBtAGEAcABuAHcAZQBhAC4AbwByAGcALwBhAHMAcwBpAHMAdAAvAGgAZQBsAHAAXwBtAGEAcAAvAEEAcABwAGwAaQBjAGEAdABpAG8AbgBIAGUAbABwAC4AaAB0AG0AIwBVAHMAaQBuAGcAVABlAHMAdABSAGUAcwB1AGwAdABzAC8ATQBBAFAAUgBlAHAAbwByAHQAcwBGAGkAbgBkAGUAcgAuAGgAdABtAA..&URL=https%3A%2F%2Fteach.mapnwea.org%2Fassist%2Fhelp_map%2FApplicationHelp.htm%23UsingTestResults%2FMAPReportsFinder.htm

http://education.ti.com/educationportal/downloadcenter/SoftwareDetail.do?website=US&amp%3BtabId=1&amp%3BappId=286

http://mathbits.com/MathBits/TISection/Openpage.htm


http://movies.atomiclearning.com/k12/search?p=25&amp%3Blang=en*&amp%3Bq=TI%2B84&amp%3Bsubmit=Go!

http://www.casioeducation.com/educators

http://www.stemresources.com/

http://www.ti-mathnspired.com/

http://education.ti.com/educationportal/activityexchange/activity




http://www.utdanacenter.org/k12mathbenchmarks/secondary/index.php

http://www.act.org/content/dam/act/unsecured/documents/CCRS-MathStandards.pdf

http://www.tn.gov/education/topic/act-sat

http://cmsi.cps.k12.il.us/ViewProgramDetails.aspx?pid=4577

http://www.ohiorc.org/standards/commoncore/mathematics/resources.aspx?id=5277

https://share.ehs.uen.org/view-content-unit/234

http://www.livebinders.com/play/play?id=571735

https://www.livebinders.com/play/play?id=464831

http://www.livebinders.com/play/play/454480

http://learnzillion.com/common_core/math/hs

http://insidemathematics.org/index.php/high-school-geometry

http://insidemathematics.org/index.php/high-school-geometry

http://www.njctl.org/courses/math/geometry/year-long-plan-geometry/