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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.

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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 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 Standards call for conceptual understanding of key concepts, such as place value and ratios. 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.

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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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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 PracticeMathematical 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

The Shelby County Schools curriculum maps are intended to guide planning, pacing, and sequencing, reinforcing the major work of the grade/subject. Curriculum maps are NOT meant to replace teacher preparation or judgment; however, it does serve as a resource for good first teaching and making instructional decisions based on best practices, and student learning needs and progress. Teachers should consistently use student data differentiate and scaffold instruction to meet the needs of students. The curriculum maps should be referenced each week as you plan your daily lessons, as well as daily when instructional support and resources are needed to adjust instruction based on the needs of your students.

How to Use the Mathematics Curriculum Maps

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 the 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 teachers' responsibility to examine the standards and skills needed in order to ensure student mastery of the indicated standard.

ContentWeekly and daily objectives/learning targets should be included in your plan. These 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 learning targets/objectives provide specific outcomes for that standard(s). Best practices tell us that making objectives measureable increases student mastery.

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District and web-based resources have been provided in the Instructional Support and Resources column. The additional resources provided are supplementary and should be used as needed for content support and differentiation.

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. 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 should be able to identify central angles, major and minor arcs, semicircles and find their measures. They will finish the quarter studying inscribed angles and intercepted arcs.

Content Standard Type of Rigor Foundational Standards Sample Assessment Items**G-SRT.A.2 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 Conceptual Understanding 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

G-SRT.C.6, 7, 8 Conceptual Understanding & Application 8.G.A.1, 2,3, 4,5 Mathshell: Hopewell Geometry

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G-C.A.1, 2 Conceptual Understanding 8.G.A.5; 8.G.B.7 Illustrative: Similar Circles; Illustrative: Neglecting the Curvature of the Earth

G-MG.A.3 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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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

Similarity and TransformationsRight Triangles and Trigonometry

(Allow approximately 5 weeks for instruction, review, and assessment)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.

Enduring Understanding(s) Polygons are similar if and only if

corresponding angles are congruent and corresponding sides are proportional.

Geometric figures can change size and/or position while maintaining proportional attributes

Essential Question(s) How is similarity defined by transformations? How can you prove two figures are similar?

Objective(s): Use proportions to Identify similar

polygons. Solve problems using the properties of

similar polygons. Identify similarity transformations. Verify similarity after a similarity

transformation.

Use the textbook resources to address procedural skill and fluency.Lesson 7.2 Similar Polygons pp.465-473Lesson 7.6 Similarity Transformations pp. 505-511

Use the following Lesson(s) 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? Engage ny Geometry Module 2, Topic C, Lesson 12 – Similarity Transformations Engage ny Geometry Module 2, Topic C, Lesson 14 – Similarity

Task(s):Illustrative Math: Are They Similar? G-SRT.A.2

VocabularySimilar polygons, similarity ratio, scale factordilation, similarity transformation, center of dilation, scale factor of a dilation, enlargement, reduction

Activity with DiscussionDraw 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

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

Writing in MathCompare and contrast congruent, similar, and equal figures.

Domain: G-MG Modeling with Geometry Cluster: Apply geometric concepts in

Enduring Understanding(s) Geometric figures can change size and/or

Use the textbook resources to address procedural skill and fluency.

Vocabulary

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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). ★

position while maintaining proportional attributes.

Essential Question(s) How can geometric properties and

relationships be applied to solve problems that are modeled by geometric objects?

How do you use proportions to find side lengths in similar polygons?

Objective(s): Create scale drawings of polygonal

figures by the ratio method. Use scale factors to solve problems.

Lesson 7.7 Scale Drawings and Scale Modelspp. 512-517

Use the following Lesson(s) to introduce concepts/build conceptual understanding.Engageny Geometry Module 2, Topic A, Lesson 2 – Making Scale Drawings

Task(s):Illustrative Math: Ice Cream Cone

Scale model, scale drawing, scale

Writing in MathFelix and Tamara are building a replica of their high school. The high school is 75 feet tall and the replica is 1.5 feet tall. Felix says the scale factor of the actual high school to the replica is 50:1, while Tamara says the scale factor is 1:50. Is either of them correct? Explain your reasoning.

Domain: G-SRT Similarity, Right Triangles and TrigonometryCluster(s): Understand similarity in terms of similarity transformations. Prove theorems involving similarity G-SRT.B.3 Use the properties of

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

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.

G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Enduring Understanding(s) Polygons are similar if and only if

corresponding angles are congruent and corresponding sides are proportional.

Essential Question(s) What relationships among sides and other

segments in a triangle are always true? How do you use proportions to find side

lengths in similar polygons? How do you show two triangles are similar?

Objective(s): Students will prove the angle-angle criterion

for two triangles to be similar and use it to solve triangle problems

Identify similar triangles and use their properties to solve problems.

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

Use the following Lesson(s) to introduce concepts/build conceptual understanding.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 Math Shell Lesson: Flood Light Shadows

Writing in MathContrast and compare the triangle congruence theorems with the triangle similarity theorems.

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESDomain: 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.

G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Enduring Understanding(s) Polygons are similar if and only if

corresponding angles are congruent and corresponding sides are proportional.

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

Essential Question(s) How do you use proportions to find side

lengths in similar polygons? How might the features of one figure be

useful when solving problems about a similar figure?

Objective(s): Prove that special segments in similar

triangles are proportional. Prove the Pythagorean Theorem by

using similar triangles. Recognize and use proportional

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

Use the Triangle Angle Bisector Theorem to find lengths of sides of similar triangles.

Use the textbook resources to address procedural skill and fluency.Lesson 7.4 Parallel Lines and Proportional Parts (mid-segments was previously covered in unit 2) pp. 484-492Lesson 7.5 Parts of Similar Triangles pp.495-503

Use the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Use the following Lesson(s) 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 18 – Triangle Angles Bisector Theorem Engage ny Geometry Module 2, Topic C, Lesson 19 – Parallel Lines and Proportional Segments

Task(s)Illustrative Math: Pythagorean Theorem Illustrative Math: Joining Two Midpoints of Sides of a Triangle

VocabularyMid-segment of a triangle

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

Find 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

Domain: G-SRT Similarity, Right Triangles and TrigonometryCluster: Prove theorems involving similarity

Enduring Understanding(s) Similar figures map one shape proportionally

onto another through non-rigid motions.

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

VocabularyGeometric mean

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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.

G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

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

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

triangle? How does geometric mean help us to find

the missing sides in a right triangle?

Objective(s): Students will prove the geometric mean

relationships in a triangle using similarity. Students will prove the triangle

proportionality theorem (side splitting theorem) using similarity.

Solve problems involving relationships between parts of a right triangle and the altitude to its hypotenuse.

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

Writing in MathHow does geometric mean help to find the missing sides in a right triangle?

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) The concept of similarity enables us to

explore geometric relationships and apply trigonometric ratios to solve real world problems.

Essential Question(s) How does the understanding of triangle

similarity develop an understanding of trigonometric ratios and relationships in triangles?

Objective(s): Compare common ratios for similar

right triangles and develop a

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

Use the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

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

Create your own triangles Learning Task

Activity with DiscussionExplain 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.

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relationship between the ratio and the acute angle leading to the trigonometry ratios.

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.

G-SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles.

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

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? 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.

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

Use the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Learnzillion: Apply Sine and Cosine FunctionsSimilar Right Triangles and Trig Ratios Lesson

Task(s)Discovering Trigonometric Ratio Relationships Learning Task p.22Inside Mathematics: Hopewell Geometry Performance Task

VocabularyTrigonometry, trigonometry ratio, sine, cosine, tangent, inverse sine, inverse cosine, inverse tangent

Activity with DiscussionExplain 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 right triangles in applied problems. ★

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? When you know the lengths of the sides of a

right triangle, how can you find the measures of the two acute angles?

Objective(s):

Use the textbook resources to address procedural skill and fluency.Lesson 8.5 – Angles of Elevation and Depression pp.574-581

Use the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Learnzillion Lesson: Develop an Understanding and Apply Right Triangle Rules

VocabularyAngle of elevation, angle of depression

Writing in MathHow is a right triangle used to find the sine and cosine of an acute angle? Is there a unique right triangle that must be used?

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Students will solve trigonometry and Pythagorean Theorem problems based on written descriptions.

Students will apply trigonometric ratios and Pythagorean Theorem to solve angle of elevation and angle of depression problems.

Learnzillion: Apply Relationships of Right Triangles Using Pythagorean Theorem

Task(s)Find that Side or Angle TaskTN Task :InterstateTN Task: Making Right Triangles

Illustrative Math: Ask the Pilot

Properties of Angles and Segments in Circles (Allow approximately 4 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 the 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

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?

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

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

Use the textbook resources to address procedural skill and fluency.Lesson 10.1 – Circles and Circumference pp.683-691

Use the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Learnzillion Lesson: G-CO.A.1Learnzillion Lesson: G-GMD.A.1

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

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

Writing in MathProvide examples of how distance traveled can depend on the circumference of a circle when used with vehicles.

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arguments.

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): Investigate and identify relationships

between parts of a circle and angles formed by parts of a circle

Use the textbook resources to address procedural skill and fluency.Lesson 10.2 Measuring Angles and Arcs pp.692-700

Use the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Use the following Lesson(s) 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

Task(s)Circles and their Relationships among Central Angles, Arcs and Chords Investigating Angle Relationships in Circles

Getting a Job Task (Click on HCPSS Task: Getting a Job)

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

Writing in MathDescribe how to use central angles to find other angles within a triangle

Discuss relationships between the arcs intercepted by an angle and the measure of that angle.

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

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)

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

Use the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and

VocabularyInscribed angle, intercepted arc

Writing in MathCompare and contrast inscribed angles and central angles of a circle. If they intercept

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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.

How are segments within circles, such as radii, diameters, and chords, related to each other?

What is the relationship of their measurements?

Objective(s): Identify and describe relationships involving

inscribed angles. Prove properties of angles for a

quadrilateral inscribed in a circle.

application) of the standards are met.

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

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

the same arc how are they related?

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

Comprehensive Geometry Help:

StandardsCommon Core Standards - Mathematics Common Core Standards - Mathematics Appendix A TN CoreCCSS Flip Book with Examples of each Standard Geometry Model Curriculum http://www.ccsstoolbox.org/

VideosMath TV VideosThe Teaching Channel Khan Academy Videos (Geometry)

Tasks

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RESOURCE TOOLBOXOnline Math Learning (Geometry) I LOVE MATHNCTM IlluminationsNew Jersey Center for Teaching & Learning (Geometry)

Others TN Ready Geometry BlueprintState ACT Resources

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

http://insidemathematics.org/index.php/high-school- geometry http://www.azed.gov/azcommoncore/mathstandards/hs math/ 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=571735North Carolina – Unpacking Common Core http://thegeometryteacher.wordpress.com/the- geometry-course/ http://math termind.blogspot.com/2012/07/common-core- geometry.html Utah Electronic School - Geometry Ohio Common Core Resources Chicago Public Schools Framework and Tasks

Mathy McMatherson Blog - Geometry in Common Core

Edutoolbox (formerly TNCore) Tasks Inside Math Tasks Mars Tasks Dan Meyer's Three-Act Math TasksNYC tasks Illustrative Math TasksUT Dana Center SCS Math Tasks

GSE Analytic Geometry Unit 1: Similarity, Congruence and Proofs

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

Shelby County Schools 2016/2017Revised 11/1/16

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