Curriculum and Instruction – Mathematics

Quarter 3 Bridge Math

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 11/28/16

1 of 17

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 concepts of each subject 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 Bridge Math, account for 65-75% of time spent on the major conccepts of algebra 1, geometry and algebra 2.The supporting and additional content from algebra 1, geometry and algebra 2 are incorporated into the subject to provide more understanding about the major concepts of those courses.

Coherence

Thinking across grades/courses:learning of mathematics is carefully connected across grades and subjects 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/subject level focus.

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. Students are given opportunities to practice core functions such as solving one-and two-step equations so that they have access to more complex concepts and procedures.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.

Curriculum and Instruction – Mathematics

Quarter 3 Bridge Math

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:

Shelby County Schools 2016/2017Revised 11/28/16

2 of 17

Curriculum and Instruction – Mathematics

Quarter 3 Bridge Math

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

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 Support

Shelby County Schools 2016/2017Revised 11/28/16

3 of 17

Curriculum and Instruction – Mathematics

Quarter 3 Bridge Math

Shelby 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; 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 Resources

Shelby County Schools 2016/2017Revised 11/28/16

4 of 17

Curriculum and Instruction – Mathematics

Quarter 3 Bridge Math

District 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.

Topics Addressed in Quarter Basic Geometry Similar Triangles Measurement

Overview This quarter introduces and reviews some basic geometry to students including angles, triangles and polygons. Students study angle relationships, classifications of triangles and their theorems and then the special angles and relationships in polygons and solve problems involving angles, triangles and polygons. Students then review measurement including perimeter, circumference, area of two-dimensional figures and surface area and volume of three-dimensional figures and solve problems using these figures, including the use of geometric probabilities. The quarter concludes with students studying solving real-world problems involving similar triangles and their properties and theorems.

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

Shelby County Schools 2016/2017Revised 11/28/16

5 of 17

Curriculum and Instruction – Mathematics

Quarter 3 Bridge Math

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.

References: https://www.engageny.org/ http://www.corestandards.org/ http://www.nctm.org/ http://achievethecore.org/

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESBasic Geometry

Chapter 4 - McGraw-Hill Bridge MathMcGraw Hill Glencoe Geometry

PLEASE NOTE: TN CURRICULUM EMPHASIZES PROBLEM SOLVING ASPECTS, NOT THE PROOFS.(Allow approximately 2 weeks for instruction, review, and assessment)

Conceptual Category: Ways of Looking: Revisiting Concepts

Domain: Verbal Mathematics (W-VM)

W-VM3. Use several angle properties to find an unknown angle measure (i.e. supplementary, complementary, vertical, angles along a transversal, and sum of angles in a polygon.)

Enduring Understanding(s): Many relationships exist between the

measure of the angles of a triangle and the measure of the sides of the triangle.

The properties of triangles create a basis for understanding and reasoning that extends to other geometric figures.

Essential Question(s): How do the properties of triangles

contribute to the geometric understanding of the world around us?

What can you say about the interior and exterior angles of a triangle and other polygons?

How do you use coordinate geometry to find relationships within triangles?

How do you solve problems that involve measurements of triangles?

McGraw-Hill GeometryReview of angles1-5 Angle Relationships4-1 Classifying Triangles4-2 Angles of Triangles

McGraw-Hill Bridge Mathpp.152-153, Refresh Your Math Skills4-1 Triangles and Triangle Theorems4-2 Congruent TrianglesGeometry Lab: Angles of Triangles, p. 243

Task(s):Mathematics Vision Project- Module 5, Geometric Figures (select from the eight tasks)

Additional Lessons/Resources:Engageny Geometry Module 1, Topic B, Lesson 6 – Solve for Unknown Angles – Angles and Lines at a Point

Vocabulary:Angles, polygon, triangle, vertex, side, interior angle, exterior angle, postulate, included angle, included side

Writing in Math/Discussion: How many exterior angles does a triangle

have? Draw a triangle and label all of its exterior angles.

Explain why classifying an equiangular triangle as an acute equiangular triangle is unnecessary.

Explain why a triangle cannot have an obtuse, acute, and a right exterior angle.

Shelby County Schools 2016/2017Revised 11/28/16

6 of 17

Curriculum and Instruction – Mathematics

Quarter 3 Bridge Math

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

Objective(s): Students will identify and use special pairs

of angles. Students will identify perpendicular lines. Students will solve equations to find the

measure of angles. Students classify triangles according to their

sides or angles. Students will prove triangles are congruent.

Complementary & Supplementary Lesson 1 NCTM Illuminations: Triangle ClassificationLearnzillion Lesson: Angle Sum TheoremLearnzillion Lesson: Exterior angle theorem

CPalms: Discovering Triangle Sum Khan Academy Videos: Angles Khan Academy Videos: Triangle Congruence Khan Academy: Working with Triangles

Conceptual Category: Ways of Looking: Revisiting Concepts

Domain: Verbal Mathematics (W-VM)

W-VM3. Use several angle properties to find an unknown angle measure (i.e. supplementary, complementary, vertical, angles along a transversal, and sum of angles in a polygon.)

Enduring Understanding(s): Two figures are congruent if, through a

sequence of rigid motions and/or constructions, one shape maps exactly onto another.

Many relationships exist between the measure of the angles of a triangle and the measure of the sides of the triangle.

The properties of triangles create a basis for understanding and reasoning that extends to other geometric figures.

Essential Question(s): How do the properties of triangles

contribute to the geometric understanding of the world around us?

What can you say about the interior and exterior angles of a triangle and other polygons?

How do you solve problems that involve measurements of triangles?

Objective(s): Students will establish congruence between

two triangles to show that corresponding parts are congruent.

McGraw-Hill Bridge Math4-3 Congruent Triangles and Proofs

McGraw-Hill Geometry4-6 Isosceles and Equilateral Triangles

Task(s):CPalms Task: Are the Triangles Congruent?TN Task Arc - Investigating Congruence in Terms of Rigid Motion, Task 5Mathematics Vision Project- Module 5, Geometric Figures (select from the eight tasks)

Additional Lessons/Resources:Engage ny Geometry Module 1, Topic D, Lesson 22 – Triangle Congruence Equilateral and Isosceles Triangle

Vocabulary: legs, base, base angles, vertex angles, corollary, theorem

Writing in Math/Discussion:Have students create multiple representations of binomial multiplication.Have students write a response to the following: Can the product of two binomials ever have more than three terms? Explain your thinking.

Shelby County Schools 2016/2017Revised 11/28/16

7 of 17

Curriculum and Instruction – Mathematics

Quarter 3 Bridge Math

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES Students will find angle and side measures

of triangles.Conceptual Category: Ways of Looking: Revisiting Concepts

Domain: Verbal Mathematics (W-VM)

W-VM3. Use several angle properties to find an unknown angle measure (i.e. supplementary, complementary, vertical, angles along a transversal, and sum of angles in a polygon.)W-VM4. Describe, compare, and contrast plane and solid figures using their attributes.

Enduring Understanding(s):There exist certain patterns in the angle measures of polygons.

Essential Question(s):Is there a limit to the sum of the interior/exterior angles of a polygon why or why not?

Objective(s): Students will find and use the measures of

interior angles of polygons. Students will find and use the measures of

exterior angles of polygons.

McGraw-Hill Bridge Math4-7 Polygons and Angles

McGraw-Hill Geometry6-1 Angles of PolygonsSpreadsheet Lab Angles of Polygon, p. 398

Task(s):CPalms Task: Interior Angles of a PolygonIllustrative: Sum of Angles in a Polygon

Additional Lessons/Resources:Khan Academy: Triangle Angles Illuminations : Angle Sums

Vocabulary:Polygon, vertex, convex, concave, interior angles, exterior angles, consecutive sides, consecutive vertices, diagonal, the Polygon-Sum Theorem ( Polygon Interior Angles Sum Theorem), the Polygon Exterior Angle Theorem

Writing in Math/Discussion:As the number of sides of a regular polygon becomes larger and larger, what happens to the measure of each exterior angle of the polygon?

As the number of sides of a regular polygon becomes larger and larger, what happens to the measure of each interior angle of the polygon?

Explain how triangles are related to the Polygon-Sum Theorem (Polygon Interior Angles Sum Theorem).

Conceptual Category: Ways of Looking: Revisiting Concepts

Domain: Verbal Mathematics (W-VM)W-VM4. Describe, compare, and contrast plane and solid figures using their attributes.

Enduring Understanding(s):The properties of quadrilaterals help you to categorize quadrilaterals.

Essential Question(s):What can you conclude about the sides, angles, and diagonals of a parallelogram?

Objective(s):Students will apply properties of parallelograms to find missing lengths and angle measures.

McGraw-Hill Bridge Math4-8 Special Quadrilaterals: Parallelograms

McGraw-Hill Geometry6-3 Tests for Parallelograms

Task(s)TN Task: Expanding Triangles TN Task: Parallelograms MARS Task: Floor PatternMathematics Vision Project- Module 5, Geometric Figures (select from the eight tasks)

Additional Lessons/Resources:CPalms: Quadrilateral Classification GameCPalms: To Be or Not to Be a Parallelogram

Vocabulary:Opposite sides, opposite angles, parallelogram, rectangle, rhombus, square, The Parallelogram-Side Theorem, The Parallelogram-Angle Theorem, The Parallelogram-Diagonal Theorem, The Rectangle-Diagonal Theorem, The Rhombus-Diagonal Theorem

Writing in Math/Discussion:Are two parallelograms congruent if they both have four congruent angles? Justify your answer.Suppose that you are asked to prove the parallelogram-diagonal theorem. Write a paragraph that explains how you would proceed.

Shelby County Schools 2016/2017Revised 11/28/16

8 of 17

Curriculum and Instruction – Mathematics

Quarter 3 Bridge Math

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESCharacteristics of Quadrilaterals (Do not write the two-column proof.)

Conceptual Category: Ways of Looking: Revisiting Concepts

Domain: Verbal Mathematics (W-VM)W-VM4. Describe, compare, and contrast plane and solid figures using their attributes. .

Enduring Understanding(s):Properties of angles, triangles, quadrilaterals, and polygons are connected.

Essential Question(s):What are the properties of kites and trapezoids?

Objective(s):Students will apply properties of trapezoids to find missing lengths and angle measures.

McGraw-Hill Bridge Math4-9 Special Quadrilaterals: TrapezoidsGraphing Technology Lab: The Triangle Inequality, p.195aSpreadsheet Lab: Angle of Polygons, 195b

McGraw-Hill Geometry6-6 Trapezoids and Kites

Task(s)TN Task: Getting in ShapeTN Task: Go Fly a Kite

Additional Lessons/Resources:Khan Academy: Quadrilaterals- Kites As Geometric Shape

ACT Practice(sample problems to prepare for the ACT)

McGraw-Hill Bridge Math, pp. 200-201McGraw-Hill Geometry, pp.388-389

Vocabulary:Trapezoid, bases, base angles, legs, median, isosceles trapezoid, kite, The Isosceles Trapezoid Theorem

Writing in Math/Discussion:Differentiate between the word median when used in geometry to the word median used in statistics.

Compare the median of a trapezoid to the median of a triangle. How are they alike? How are they different?

MeasurementChapter 5 -McGraw-Hill Bridge Math

McGraw Hill Glencoe Geometry (Allow approximately 3.5 weeks for instruction, review, and assessment)

Conceptual Category: Ways of Looking: Revisiting Concepts

Domain: Diagrammatic Mathematics (W-DM)

W-DM4. Compute the perimeter of simple

Enduring Understanding(s):Relationships exist among angles, segments, lengths, perimeter and area of a polygons, and circumference and area of circles.

McGraw-Hill Bridge Math5-2 & Perimeter, Circumference, and Area

McGraw-Hill Geometry1-6 Two-Dimensional Figures

Vocabulary:Perimeter, circumference, area

Writing in Math/Discussion:Since is an irrational number, many calculations involving are found using approximations 3.14

Shelby County Schools 2016/2017Revised 11/28/16

9 of 17

Curriculum and Instruction – Mathematics

Quarter 3 Bridge Math

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCEScomposite geometric figures with unknown side lengths.W-DM5. Apply a variety of strategies to determine the circumference and the area for circles.

Essential Question(s): How do you find the area of a polygon

or find the circumference and area of a circle?

How do perimeters and areas of similar polygons compare?

Objective(s):Students will apply perimeter, circumference and area formulas.

Task(s):Illustrative: Eight CirclesInside Math: Pizza Crusts

Additional Lessons/Resources:Khan Academy: Language-and-notation-of-the-circleKhan Academy: Area and PerimeterKhan Academy: Area and Circumference of CirclesCPalms: Area and Circumference 1CPalms: Area and Circumference 2CPalms: Area and Circumference 3

or 227. When might it be easier to use 22/7 rather than 3.14 to estimate area or circumference?

Conceptual Category: Applications: Ways of Looking at the World

Domain: Applications with Data (A-AD)

A-AD3. Solve problems involving geometric probabilities. .

Enduring Understanding(s):The probability of an event can be expressed as the ration of the number of favorable outcomes to the number of possible outcomes.

Essential Question(s):How can you explain the concepts of probability and use probability to solve real-world problems?

Objective(s):Students will determine probabilities using areas.

McGraw-Hill Bridge Math5-3 Probability and Area

McGraw-Hill Geometry13-3 Geometric Probability

Task(s):Inside Math: Marble Game

Additional Lessons/Resources:Khan Academy: Probability Basics

Vocabulary:probability

Writing in Math/Discussion:The probability of an event is a number between 0 and 1. What is the probability that an event will always occur? What is the probability of an impossible event? Give an example of each.

Conceptual Category: Making Connections

Domain: Symbolic & Diagrammatic Mathematics (M-SD)

M-SD5. Apply a variety of strategies using relationships between perimeter, area, and volume to calculate desired measures in composite figures.

Enduring Understanding(s):More difficult problems can be solved by decomposing the problems into smaller solvable problems.

Essential Question(s):How can you break a more complex problem into smaller problems?

McGraw-Hill Bridge Math5-4 Problem Solving Skills: Irregular Shapes

McGraw-Hill Geometry11-4 Area of Regular Polygons and Composite Figures

Task(s):NCTM Illuminations: Finding the Area of Irregular

Writing in Math/Discussion:Create your own problem involving the area of irregular figures that can be solved by first solving a simpler problem or problems.

Shelby County Schools 2016/2017Revised 11/28/16

10 of 17

Curriculum and Instruction – Mathematics

Quarter 3 Bridge Math

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESObjective(s):Students will solve problems involving irregular shapes.

Figures

Additional Lessons/Resources:Khan Academy: Perimeter-and-Area-of-a-Non-Standard-PolygonLearnZillion: Finding the Area of an Irregular Figure

Conceptual Category: Applications: Ways of Looking at the World

Domain: Applications with Geometry (A-AG)

A-AG3. Solve problems involving surface areas and volumes of 3-dimensional figures, including maximization, scale, and increment problems.

Enduring Understanding(s):More difficult problems can be solved by decomposing the problems into smaller solvable problems.

Essential Question(s):How can you break a more complex problem into smaller problems?

Objective(s):Students will analyze space figures.

McGraw-Hill Bridge Math5-5 Three-dimensional Figures and Loci

McGraw-Hill Geometry12-1 Representations of Three-Dimensional Figures

Additional Lessons/Resources:NCTM Illuminations: 3-D InteractiveKhan Academy: 2D vs, 3D ObjectsPlatonic Solids Ornaments

Vocabulary:Polyhedron, faces, edge, vertex, prism, base, pyramid, lateral faces, lateral edges, cylinder, axis, cone, sphere

Writing in Math/Discussion:A polyhedron is a regular polyhedron if all of its faces are congruent regular polygons. The Greek scholar, Plato, studied these figures, also known as the five Platonic solids. What are they and how have you seen examples of these in the real world?

Conceptual Category: Applications: Ways of Looking at the World

Domain: Applications with Geometry (A-AG)

A-AG3. Solve problems involving surface areas and volumes of 3-dimensional figures, including maximization, scale, and increment problems.

Enduring Understanding(s): Visualization can help you connect

properties of real objects with two-dimensional drawings of these objects.

Some attributes of geometric figures, such as length, area, volume, and angle measure, are measureable. Units are used to describe these attributes.

Essential Question(s): How can you determine the

intersection of a solid and a plane? How do you find the surface area and

volume of a solid?

Objective(s): Students will find the surface area of

three-dimensional figures. Students will find the volume of three-

McGraw-Hill Bridge Math5-6 Surface Area of Three-dimensional Figures5-7 Volume of Three-dimensional Figures

McGraw-Hill Geometry12-2 Surface Area of Prisms & Cylinders12-3 Surface Area of Pyramids & Cones12-4 Volumes of Pyramids and Cones12-5 Volumes of Prisms & Cylinders

Task(s):Bedroom RemodelMARS: Fruit Boxes

Additional Lessons/Resources:Khan Academy: Cylinder Volume and Surface-AreaSurface Area of Pyramids and ConesKhan Academy: Volume of a Sphere

Vocabulary:Surface area, volume

Writing in Math/Discussion:The surface area of a rectangular prism is 178 in2. What is the height of the figure if its length is 3 in. and its width is 4 in.? Explain how you got your answer.

How are the formulas for the volume of a prism and the volume of a cylinder similar? How are they different?

Shelby County Schools 2016/2017Revised 11/28/16

11 of 17

Curriculum and Instruction – Mathematics

Quarter 3 Bridge Math

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESdimensional figures. LearnZillion: finding Surface Area of Three-

Dimensional FiguresLearnZillion: Using Nets to Find Surface AreaLearnZillion: Volume LessonsLearnZillion: Solve Real-World Problems-Surface Area and Volume of Rectangular PrismsInteractive: Isometric Drawing ToolIlluminations: Finding Surface Area and Volume

ACT Practice(sample problems to prepare for the ACT)

McGraw-Hill Bridge Math, pp. 242-243McGraw-Hill Geometry, pp.456-457

Similar TrianglesChapter 7 - McGraw-Hill Bridge Math

McGraw Hill Glencoe Geometry (Allow approximately 3.5 weeks for instruction, review, and assessment)

Conceptual Category: Making ConnectionsDomain: Symbolic & Numeric Mathematics (M-SV)

M-SV3. Write ratios, proportions, and solve proportions in a contextual setting for an unknown value.

Enduring Understanding(s):Many types/varieties of situations in life depend on or require the application of proportional reasoning.

Essential Question(s):How do we use proportional relationships in solving real-world problems?

Objective(s):Students will use ratios and rates to solve problems.

McGraw-Hill Bridge Math5-1 Ratios and Units of Measure

McGraw-Hill Geometry7-1 Ratios and Proportions7-1 Graphing Technology Lab - Fibonacci Sequence and Ratios p. 464

Task(s)Dan Myer 3-Act Tasks – Ratios and Proportions

Additional Lessons/Resources:Khan Academy: Ratios, Rates and Proportions

Vocabulary:Measurement, customary, metric, compass, protractor, calipers, micrometers, precision, greatest possible error (GPE), ratio, rate, unit rate, unit price.

Writing in Math/Discussion:Compare and contrast a ratio and a proportion. Explain how you would use both to solve a problem.

Conceptual Category: Applications: Ways of Looking at the WorldDomain: Applications with Numbers (A-AN)A-AN3. Solve rate, distance, and work problems using proportions and percentages.

Conceptual Category: Making ConnectionsDomain: Symbolic & Verbal Mathematics (M-SV)

Enduring Understanding(s):Ratios can be used to describe proportional situations.

Essential Question(s): Why are ratios and proportions important? How are they used in the real world?

McGraw-Hill Bridge Math7-1 Ratios and Proportions

McGraw-Hill Geometry7-1 Ratios and Proportions

Task(s):

Vocabulary:Equivalent ratios, proportion, terms, extremes, means, cross products

Writing in Math/Discussion:If a/b = c/d, is it always true that a/c = b/d? Explain.

Shelby County Schools 2016/2017Revised 11/28/16

12 of 17

Curriculum and Instruction – Mathematics

Quarter 3 Bridge Math

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESM-SV3. Write ratios, proportions, and solve proportions in a contextual setting for an unknown value.

Objective(s): Students will find equivalent ratios. Students will use ratios and proportions to

solve problems.

TN Task Arc: Reasoning With Ratios and Rates(Select from Tasks 1 through 8)

Additional Lessons/Resources:Khan Academy: RatiosKhan Academy: Writing ProportionsKhan Academy: Ratio and Proportion

Conceptual Category: Applications: Ways of Looking at the WorldDomain: Applications with Geometry (A-AG)

A-AG1. Solve problems involving ratios in geometric settings, such as similar figures and right triangle distance problems.

Enduring Understanding(s):The use of proportional relationships between similar figures can help solve problems.

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

lengths in similar polygons?

Objective(s): Students will identify similar polygons. Students will find missing measures of

similar polygons.

McGraw-Hill Bridge Math7-2 Similar Polygons

McGraw-Hill Geometry7-2 Similar Polygons

Task(s):TN Task: Ratios, Proportions, and Similar Figures

Additional Lessons/Resources:Similar Polygons - Lesson & WorksheetsLesson: Congruent and Similar Figures

Vocabulary:Similar

Writing in Math/Discussion:When given two similar figures, how can you tell which angles are corresponding angles?

Conceptual Category: Applications: Ways of Looking at the WorldDomain: Applications with Geometry (A-AG)

A-AG1. Solve problems involving ratios in geometric settings, such as similar figures and right triangle distance problems.

Enduring Understanding(s):The use of proportional relationships between similar figures can help solve problems.

Essential Question(s):How do you use proportions to find real and scale measurements?

Objective(s):Students will find actual or scale length using scale drawings.

McGraw-Hill Bridge Math7-3 Scale Drawings

McGraw-Hill Geometry7-7 Scale Drawings and Models

Task(s):

Additional Lessons/Resources:LearnZillion: Scale Drawings Lesson 1 (Procedural Skills)LearnZillion: Scale Drawings Lesson 2 (Conceptual)LearnZillion: Scale Drawings Lesson 3 (Application)LearnZillion: Areas of Scale Drawings

Vocabulary:Scale drawing, scale

Writing in Math/Discussion: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.

Shelby County Schools 2016/2017Revised 11/28/16

13 of 17

Curriculum and Instruction – Mathematics

Quarter 3 Bridge Math

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

Conceptual Category: Applications: Ways of Looking at the WorldDomain: Applications with Geometry (A-AG)

A-AG1. Solve problems involving ratios in geometric settings, such as similar figures and right triangle distance problems.

Enduring Understanding(s):There exist methods for proving triangles similar.

Essential Question(s): What does the SAS Triangle Congruence

Theorem tell you about triangles? What does the SSS Triangle Congruence

Theorem tell you about triangles?

Objective(s):Students will use the AA, SSS, and SAS similarity postulates to determine if two triangles are similar and solve problems using similar triangles.

McGraw-Hill Bridge Math7-4 Postulates for Similar Triangles

McGraw-Hill Geometry7-3 Similar Triangles

Task(s):Select appropriate tasks from GSE Analytic Geometry Unit 1: Similarity, Congruence and Proofs

Additional Lessons/Resources:Engage ny Geometry Module 1, Topic D, Lesson 22 – Triangle Congruence

Engageny Geometry Module 1, Topic D, Lesson 24 – Congruence Criteria for Triangles – ASA and SSS

Khan Academy - Similar Triangle Basics

Vocabulary:The AA Similarity Postulate, the SSS Similarity Theorem, the SAS Similarity Theorem

Writing in Math/Discussion:Compare and contrast the AA Similarity Postulate, the SSS Similarity Theorem, and the SAS Similarity Theorem

Given a triangle, explain a process you can use to draw a similar triangle that is twice as large.

Conceptual Category: Ways of Looking: Revisiting ConceptsDomain: Verbal Mathematics (W-VM)

W-VM1. Understand that a line parallel to one side of a triangle divides the other two sides proportionally, and conversely.

W-VM2. Apply similar triangles to solve problems, such as finding heights and distances.

Enduring Understanding(s):There exist theorems for finding similar triangles’ lengths of proportional segments.

Essential Question(s): If a segment connects the midpoint of

two sides of a triangle, what is known about the length of the third side?

What is the relationship between the altitudes of two similar triangles?

If two triangles are similar, what is known about their medians in relation to the corresponding sides of the triangles?

Objective(s):

McGraw-Hill Bridge Math7-5 Triangles and Proportional Segments

McGraw-Hill Geometry7-5 Parts of Similar Triangles

Task(s):Illustrative: Congruent and Similar TrianglesIllustrative: Similar Triangles

Additional Lessons/Resources:LearnZillion: Triangle Similarity by Checking for Congruent AnglesKhan Academy: Triangle SimilarityMARS: Identifying Similar Triangles

Writing in Math/Discussion:If two rectangles are similar, do you think their diagonals are proportional to corresponding sides? Explain.

Shelby County Schools 2016/2017Revised 11/28/16

14 of 17

Curriculum and Instruction – Mathematics

Quarter 3 Bridge Math

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES Students will prove theorem involving

similar triangles. Students will find unknown lengths of

sides of triangles.Conceptual Category: Applications: Ways of Looking at the WorldDomain: Applications with Geometry (A-AG)

A-AG1. Solve problems involving ratios in geometric settings, such as similar figures and right triangle distance problems

Enduring Understanding(s):There exist theorems for finding lengths of proportional segments involving parallel lines.

Essential Question(s): If a line is parallel to one side of a

triangle and intersects the other sides at any points except the vertex, what is known about that line?

What do you know about the median of a trapezoid in relation to the lengths of the bases?

Objective(s): Students will use theorems involving

parallel lines and proportional segments to find unknown lengths.

Students will divide a line segment into congruent parts.

Students will solve problems using indirect measurement.

McGraw-Hill Bridge Math7-6 Parallel Lines and Proportional Segments7-7 Problem Solving Skills: Indirect Measurements

McGraw-Hill Geometry7-4 Parallel Lines and Proportional Parts7-5 Extend: Geometry Lab: Fractals

Task(s):Illustrative: Midpoints of Triangle Sides

Additional Lessons/Resources:Brightstorm: Proportional Segments Between Parallel linesBrightstorm: Indirect Measurement

ACT Practice(sample problems to prepare for the ACT)

McGraw-Hill Bridge Math, pp. 294-295; pp.336-337McGraw-Hill Geometry, pp.456-457; pp. 532-533

Vocabulary:Median

Writing in Math/Discussion:Construct the following segment as directed:

A segment separated into two segments in which their lengths have a ratio of 1 to 3.

Shelby County Schools 2016/2017Revised 11/28/16

15 of 17

Curriculum and Instruction – Mathematics

Quarter 3 Bridge Math

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.

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.Textbook Resourceshttp://www.connected.mcgraw-hill.com/http://www.pearsonsuccessnet.com/

StandardsCom m on Core S tand a rds - Math e matics Com m on Core S tand a rds - Math e matics A pp e ndix A Edutoolbox (formerly TNCore)ht t p: / /ww w . cc ss t oolbo x . o r g / Common Core LessonsTennessee State StandardsTennessee’s Bridge Math StandardsCCSS Flip Book with Examples of each Standard

VideosBrightstormTeacher TubeThe Futures ChannelKhan AcademyMath TVLamar University TutorialShmoop - We Speak Students

Shelby County Schools 2016/2017Revised 11/28/16

16 of 17

Curriculum and Instruction – Mathematics

Quarter 3 Bridge Math

Additional SitesIlluminations (NCTM)Stem Resourcesht t p: / / j c - s c hools.n e t / d y n a m i c / m a th / math12.ht m l

Interactive ManipulativesNational Math ResourcesMARS Course 2NASA Space MathNational Math Resourcesht t p: / /ww w .i l ov e math.o r g / i nd e x .ph p ? opt i on =c om_docm a n http://www.mathopenref.comSMARTboard Lessons

CalculatorMath NspiredTexas Instrument ActivitiesCasio ActivitiesTasks/LessonsMathematics Assessment Project (MARS/ Math Shell Tasks)Dan Meyer's Three-Act Math TasksIllustrative Math TasksUT Dana CenterInside Math TasksLearnZillionMath Vision ProjectUT Dana CenterMars TasksBetter LessonSCS Tasks

LiteracyGlencoe- Reading and Writing in the Math ClassroomLiteracy Skills and Strategies for Content Area Teachers(Math, p. 22)Graphic Organizers (9-12) Graphic Organizers (dgelman)

ACTTN ACT Information & ResourcesACT College & Career Readiness Mathematics Standards

Shelby County Schools 2016/2017Revised 11/28/16

17 of 17