Geometry NR Curriculum Guide

THIS HANDBOOK IS FOR THE IMPLEMENTATION OF THE GEOMETRY NR CURRICULUM IN MOUNT VERNON CITY SCHOOL

DISTRICT (MVCSD).

2016-2017

MOUNT VERNON CITY SCHOOL DISTRICT

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Mount Vernon City School District

Board of Education Lesly Zamor

President

Adriane Saunders Vice President

Board Trustees Charmaine Fearon

Dr. Serigne Gningue Rosemarie Jarosz

Micah J.B. McOwen Omar McDowell

Darcy Miller Wanda White

Superintendent of Schools Dr. Kenneth R. Hamilton

Deputy Superintendent Dr. Jeff Gorman

Assistant Superintendent of Business Ken Silver

Assistant Superintendent of Human Resources Denise Gagne-Kurpiewski

Assistant Superintendent of School Improvement Dr. Waveline Bennett-Conroy

Associate Superintendent for Curriculum and Instruction Dr. Claytisha Walden

Administrator of Mathematics and Science (K-12) Dr. Satish Jagnandan

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TABLE OF CONTENTS I. COVER ............................................................................................................................... 1

II. MVCSD BOARD OF EDUCATION ............................................................................... 2

III. TABLE OF CONTENTS .................................................................................................. 3

IV. IMPORTANT DATES ...................................................................................................... 4

V. VISION STATEMENT ..................................................................................................... 5

VI. VII.

PHILOSOPHY OF MATHEMATICS CURRICULUM NYS P-12 COMMON CORE LEARNING STANDARDS

……………. 6

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VII. MVCSD CCLS GEOMTRY NR PACING GUIDE …………... 11

VIII. WORD WALL …………... 18

IX. SETUP OF A MATHEMATICS CLASSROOM …………... 19

X. SECONDARY GRADING POLICY …………... 20

XI. SAMPLE NOTEBOOK RUBRIC …………... 21

XII. CLASSROOM AESTHETICS …………... 22

XIII. SYSTEMATIC DESIGN OF A MATHEMATICS LESSON …………... 23

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IMPORTANT DATES 2016-17

REPORT CARD

MARKING PERIOD

MARKING PERIOD BEGINS

INTERIM PROGRESS REPORTS

MARKING PERIOD ENDS

DURATION OF INSTRUCTION

MP 1 September 6, 2016 October 7, 2016 November 10, 2016 10 weeks – 44 Days

MP 2 November 14, 2016 December 16, 2016 January 27, 2017 10 weeks – 46 Days

MP 3 January 30, 2017 March 10, 2017 April 21, 2017 10 weeks – 49 Days

MP 4 April 24, 2017 May 19, 2017 June 23, 2017 9 weeks – 43 Days

The Parent Notification Policy states “Parent(s) / guardian(s) or adult students are

to be notified, in writing, at any time during a grading period when it is apparent -

that the student may fail or is performing unsatisfactorily in any course or grade

level. Parent(s) / guardian(s) are also to be notified, in writing, at any time during

the grading period when it becomes evident that the student's conduct or effort

grades are unsatisfactory.”

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VISION STATEMENT

True success comes from co-accountability and co-responsibility. In a coherent instructional system, everyone is responsible for student learning and student achievement. The question we need to constantly ask ourselves is, "How are our students doing?"

The starting point for an accountability system is a set of standards and benchmarks for student achievement. Standards work best when they are well defined and clearly communicated to students, teachers, administrators, and parents. The focus of a standards-based education system is to provide common goals and a shared vision of what it means to be educated. The purposes of a periodic assessment system are to diagnose student learning needs, guide instruction and align professional development at all levels of the system.

The primary purpose of this Instructional Guide is to provide teachers and administrators with a tool for determining what to teach and assess. More specifically, the Instructional Guide provides a "road map" and timeline for teaching and assessing the Common Core Learning Standards.

I ask for your support in ensuring that this tool is utilized so students are able to benefit from a standards-based system where curriculum, instruction, and assessment are aligned. In this system, curriculum, instruction, and assessment are tightly interwoven to support student learning and ensure ALL students have equal access to a rigorous curriculum.

We must all accept responsibility for closing the achievement gap and improving student achievement for all of our students.

Dr. Satish Jagnandan

Administrator for Mathematics and Science (K-12)

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PHILOSOPHY OF MATHEMATICS CURRICULUM The Mount Vernon City School District recognizes that the understanding of mathematics is

necessary for students to compete in today’s technological society. A developmentally

appropriate mathematics curriculum will incorporate a strong conceptual knowledge of

mathematics through the use of concrete experiences. To assist students in the understanding and

application of mathematical concepts, the mathematics curriculum will provide learning

experiences which promote communication, reasoning, and problem solving skills. Students will

be better able to develop an understanding for the power of mathematics in our world today.

Students will only become successful in mathematics if they see mathematics as a whole, not as

isolated skills and facts. As we develop mathematics curriculum based upon the standards,

attention must be given to both content and process strands. Likewise, as teachers develop their

instructional plans and their assessment techniques, they also must give attention to the

integration of process and content. To do otherwise would produce students who have temporary

knowledge and who are unable to apply mathematics in realistic settings. Curriculum,

instruction, and assessment are intricately related and must be designed with this in mind. All

three domains must address conceptual understanding, procedural fluency, and problem solving.

If this is accomplished, school districts will produce students who will

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

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New York State P-12 Common Core Learning Standards for

Mathematics Mathematics - High School Geometry: Introduction

An understanding of the attributes and relationships of geometric objects can be applied in diverse contexts—interpreting a schematic drawing, estimating the amount of wood needed to frame a sloping roof, rendering computer graphics, or designing a sewing pattern for the most efficient use of material.

Although there are many types of geometry, school mathematics is devoted primarily to plane Euclidean geometry, studied both synthetically (without coordinates) and analytically (with coordinates). Euclidean geometry is characterized most importantly by the Parallel Postulate, that through a point not on a given line there is exactly one parallel line. (Spherical geometry, in contrast, has no parallel lines.)

During high school, students begin to formalize their geometry experiences from elementary and middle school, using more precise definitions and developing careful proofs. Later in college some students develop Euclidean and other geometries carefully from a small set of axioms.

The concepts of congruence, similarity, and symmetry can be understood from the perspective of geometric transformation. Fundamental are the rigid motions: translations, rotations, reflections, and combinations of these, all of which are here assumed to preserve distance and angles (and therefore shapes generally). Reflections and rotations each explain a particular type of symmetry, and the symmetries of an object offer insight into its attributes—as when the reflective symmetry of an isosceles triangle assures that its base angles are congruent.

In the approach taken here, two geometric figures are defined to be congruent if there is a sequence of rigid motions that carries one onto the other. This is the principle of superposition. For triangles, congruence means the equality of all corresponding pairs of sides and all corresponding pairs of angles. During the middle grades, through experiences drawing triangles from given conditions, students notice ways to specify enough measures in a triangle to ensure that all triangles drawn with those measures are congruent. Once these triangle congruence criteria (ASA, SAS, and SSS) are established using rigid motions, they can be used to prove theorems about triangles, quadrilaterals, and other geometric figures.

Similarity transformations (rigid motions followed by dilations) define similarity in the same way that rigid motions define congruence, thereby formalizing the similarity ideas of "same shape" and "scale factor" developed in the middle grades. These transformations lead to the criterion for triangle similarity that two pairs of corresponding angles are congruent.

The definitions of sine, cosine, and tangent for acute angles are founded on right triangles and similarity, and, with the Pythagorean Theorem, are fundamental in many real-world and theoretical situations. The Pythagorean Theorem is generalized to non-right triangles by the Law of Cosines. Together, the Laws of Sines and Cosines embody the triangle congruence criteria for

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the cases where three pieces of information suffice to completely solve a triangle. Furthermore, these laws yield two possible solutions in the ambiguous case, illustrating that Side-Side-Angle is not a congruence criterion.

Analytic geometry connects algebra and geometry, resulting in powerful methods of analysis and problem solving. Just as the number line associates numbers with locations in one dimension, a pair of perpendicular axes associates pairs of numbers with locations in two dimensions. This correspondence between numerical coordinates and geometric points allows methods from algebra to be applied to geometry and vice versa. The solution set of an equation becomes a geometric curve, making visualization a tool for doing and understanding algebra. Geometric shapes can be described by equations, making algebraic manipulation into a tool for geometric understanding, modeling, and proof. Geometric transformations of the graphs of equations correspond to algebraic changes in their equations.

Dynamic geometry environments provide students with experimental and modeling tools that allow them to investigate geometric phenomena in much the same way as computer algebra systems allow them to experiment with algebraic phenomena.

Connections to Equations. The correspondence between numerical coordinates and geometric points allows methods from algebra to be applied to geometry and vice versa. The solution set of an equation becomes a geometric curve, making visualization a tool for doing and understanding algebra. Geometric shapes can be described by equations, making algebraic manipulation into a tool for geometric understanding, modeling, and proof.

Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

Geometry Overview Congruence • Experiment with transformations in the plane • Understand congruence in terms of rigid motions • Prove geometric theorems • Make geometric constructions

Similarity, Right Triangles, and Trigonometry • Understand similarity in terms of similarity transformations • Prove theorems involving similarity • Define trigonometric ratios and solve problems involving right triangles • Apply trigonometry to general triangles

Circles • Understand and apply theorems about circles • Find arc lengths and areas of sectors of circles

Expressing Geometric Properties with Equations • Translate between the geometric description and the equation for a conic section • Use coordinates to prove simple geometric theorems algebraically

Geometric Measurement and Dimension • Explain volume formulas and use them to solve problems • Visualize relationships between twodimensional and three-dimensional objects

Modeling with Geometry • Apply geometric concepts in modeling situations

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Experiment with transformations in the plane 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. 2. Represent transformations in the plane using, e.g., transparencies and geometry software; describe

transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

5. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

Understand congruence in terms of rigid motions 6. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion

on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

7. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

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

Prove geometric theorems 9. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal

crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

10. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

11. Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

Make geometric constructions 12. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string,

reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

13. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

Understand similarity in terms of similarity transformations 1. Verify experimentally the properties of dilations given by a center and a scale factor:

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

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

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

Prove theorems involving similarity

Congruence G-CO

Similarity, Right Triangles, & Trigonometry G-SRT

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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.

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

Define trigonometric ratios and solve problems involving right triangles 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. 7. Explain and use the relationship between the sine and cosine of complementary angles. 8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.�

Apply trigonometry to general triangles 9. (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex

perpendicular to the opposite side. 10. (+) Prove the Laws of Sines and Cosines and use them to solve problems. 11. (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and

non-right triangles (e.g., surveying problems, resultant forces).

Understand and apply theorems about circles 1. Prove that all circles are similar. 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.

3. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

4. (+) Construct a tangent line from a point outside a given circle to the circle.

Find arc lengths and areas of sectors of circles 5. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius,

and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

Translate between the geometric description and the equation for a conic section 1. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square

to find the center and radius of a circle given by an equation. 2. Derive the equation of a parabola given a focus and directrix. 3. (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of

distances from the foci is constant.

Use coordinates to prove simple geometric theorems algebraically 4. Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure

defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).

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

6. Find the point on a directed line segment between two given points that partitions the segment in a given ratio. 7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance

formula.�

Explain volume formulas and use them to solve problems

Circles G-C

Expressing Geometric Properties with Equations G-GPE

Geometric Measurement & Dimension G-GMD

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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.

2. (+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.

3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.�

Visualize relationships between two-dimensional and three-dimensional objects 4. Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three- dimensional objects generated by rotations of two-dimensional objects.

Apply geometric concepts in modeling situations 1. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a

human torso as a cylinder).�

2. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).�

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).�

Modeling with Geometry G-MG

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CCLS GEOMETRY NR PACING GUIDE This guide using Geometry © 2015 was created to provide teachers with a time frame to complete the New York State Mathematics

Geometry Curriculum.

CHAPTER / LESSONS PACING DATES

CHAPTER 1 TOOLS OF GEOMETRY 1-1 Nets and Drawings for Visualizing Geometry Prepares for G-CO.A.1 1-2 Points, Lines, and Planes G-CO.A.1 1-3 Measuring Segments G-CO.A.1, G-GPE.B.6 1-4 Measuring Angles G-CO.A.1 1-5 Exploring Angle Pairs Prepares for G-CO.A.1

• Concept Byte: Compass Designs Prepares for G-CO.D.12 1-6 Basic Constructions G-CO.A.1, G-CO.D.12

• Concept Byte: Exploring Constructions Prepares for G-CO.D.12 1-7 Midpoint and Distance in the Coordinate Plane Prepares for G-GPE.B.4 and G-GPE.B.7; also G- GPE.B.6 Review: Classifying Polygons Prepares for G-MG.A.1 1-8 Perimeter, Circumference, and Area N-Q.A.1

• Concept Byte: Comparing Perimeters and Areas Prepares for G-MG.A.2

16 Sept. 6 – Sept. 27

CHAPTER 2 REASONING AND PROOF 2-1 Patterns and Inductive Reasoning Prepares for G-CO.C.9, G-CO.C.10, and G-CO.C.11 2-2 Conditional Statements Prepares for G-CO.C.9, G-CO.C.10, and G-CO.C.11

• Concept Byte: Logic and Truth Tables Prepares for G-CO.C.9, G-CO.C.10, and G-CO.C.11 2-3 Biconditionals and Definitions Prepares for G-CO.C.9, G-CO.C.10, and G-CO.C.11 2-4 Deductive Reasoning Prepares for G-CO.C.9, G-CO.C.10, and G-CO.C.11 2-5 Reasoning in Algebra and Geometry Prepares for G-CO.C.9, G-CO.C.10, and G-CO.C.11 2-6 Proving Angles Congruent G-CO.C.9

13 Sept. 28 – Oct. 21

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CHAPTER / LESSONS PACING DATES

CHAPTER 3 PARALLEL AND PERPENDICULAR LINES 3-1 Lines and Angles G-CO.A.1, Prepares for G-CO.D.12

• Concept Byte: Parallel Lines and Related Angles G-CO.D.12, Prepares for G-CO.C.9 3-2 Properties of Parallel Lines G-CO.C.9 3-3 Proving Lines Parallel Extends G-CO.C.9 3-4 Parallel and Perpendicular Lines G-MG.A.3

• Concept Byte: Perpendicular Lines and Planes Extends G-CO.A.1 3-5 Parallel Lines and Triangles G-CO.D.10

• Concept Byte: Exploring Spherical Geometry Extends G-CO.A.1 3-6 Constructing Parallel and Perpendicular Lines G-CO.D.12, G-CO.D.13 3-7 Equations of Lines in the Coordinate Plane Prepares for G-GPE.B.5 3-8 Slopes of Parallel and Perpendicular Lines G-GPE.B.5

13 Oct. 24 – Nov. 10

CHAPTER 4 CONGRUENT TRIANGLES 4-1 Congruent Figures Prepares for G-SRT.B.5

• Concept Byte: Building Congruent Triangles Prepares for G-SRT.B.5 4-2 Triangle Congruence by SSS and SAS G-SRT.B.5 4-3 Triangle Congruence by ASA and AAS G-SRT.B.5

• Concept Byte: Exploring AAA and SSA Extends G-SRT.B.5 4-4 Using Corresponding Parts of Congruent Triangles G-CO.D.12, G-SRT.B.5

• Concept Byte: Paper-Folding Conjectures G-CO.D.12 4-5 Isosceles and Equilateral Triangles G-CO.C.10, G-CO.D.13, G-SRT.B.5 Algebra Review: Systems of Linear Equations Reviews A-REI.C.6 4-6 Congruence in Right Triangles G-SRT.B.5 4-7 Congruence in Overlapping Triangles G-SRT.B.5

17 Nov. 14 – Dec. 8

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CHAPTER / LESSONS PACING DATES

CHAPTER 5 RELATIONSHIPS WITHIN TRIANGLES • Concept Byte: Investigating Midsegments Prepares for G-CO.C.10

5-1 Midsegments of Triangles G-CO.C.10, G-SRT.B.5 5-2 Perpendicular and Angle Bisectors G-CO.C.9, G-CO.D.12, G-SRT.B.5

• Concept Byte: Paper Folding Bisectors Prepares for G-C.A.3 5-3 Bisectors in Triangles G-C.A.3

• Concept Byte: Special Segments in Triangles Prepares for G-CO.C.10 5-4 Medians and Altitudes G-CO.C.10, G-SRT.B.5 5-5 Indirect Proof Extends G-CO.C.10 Algebra Review: Solving Inequalities Reviews A.CED.A.1 5-6 Inequalities in One Triangle Extends G-CO.C.10 5-7 Inequalities in Two Triangles Extends G-CO.C.10

17 Dec. 9 – Jan. 11

CHAPTER 6 POLYGONS AND QUADRILATERALS • Concept Byte: Exterior Angles of Polygons Prepares for G-SRT.B.5

6-1 The Polygon-Angle Sum Theorems G-SRT.B.5 6-2 Properties of Parallelograms G-CO.C.11, G-SRT.B.5 6-3 Proving That a Quadrilateral Is a Parallelogram G-CO.C.11, G-SRT.B.5 6-4 Properties of Rhombuses, Rectangles, and Squares G-CO.C.11, G-SRT.B.5 6-5 Conditions for Rhombuses, Rectangles, and Squares G-CO.C.11, G-SRT.B.5 6-6 Trapezoids and Kites G-SRT.B.5 6-7 Polygons in the Coordinate Plane G-GPE.B.7 6-8 Applying Coordinate Geometry Prepares for G-GPE.B.4

• Concept Byte: Quadrilaterals in Quadrilaterals G-CO.D12 6-9 Proofs Using Coordinate Geometry G-GPE.B.4

20 Jan. 12 – Feb. 17

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CHAPTER / LESSONS PACING DATES

CHAPTER 7 SIMILARITY 7-1 Ratios and Proportions Prepares for G-SRT.B.5 Algebra Review: Solving Quadratic Equations Reviews A-CED.A.1 7-2 Similar Polygons G-SRT.B.5

• Concept Byte: Fractals Extends G-SRT.B.5 7-3 Proving Triangles Similar G-SRT.B.5, G-GPE.B.5 7-4 Similarity in Right Triangles G-SRT.B.5, G-GPE.B.5

• Concept Byte: The Golden Ratio Extends G-SRT.B.5 • Concept Byte: Exploring Proportions in Triangles G-CO.D.12

7-5 Proportions in Triangles G-SRT.B.4

11 Feb. 27 – Mar. 13

CHAPTER 8 RIGHT TRIANGLES AND TRIGONOMETRY • Concept Byte: The Pythagorean Theorem Prepares for G-SRT.B.4

8-1 The Pythagorean Theorem and Its Converse G-SRT.4, G-SRT.C.8 8-2 Special Right Triangles G-SRT.C.8

• Concept Byte: Exploring Trigonometric Ratios G-SRT.C.6 8-3 Trigonometry G-SRT.C.7, G-SRT.C.8, G-MG.A.1

• Concept Byte: Measuring From Afar G-SRT.C.8 8-4 Angles of Elevation and Depression G-SRT.C.8 8-5 Law of Sines G-SRT.D.10, G-SRT.D.11 8-6 Law of Cosines G-SRT.D.10, G-SRT.D.11

11 Mar. 14 – Mar. 29

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CHAPTER / LESSONS PACING DATES

CHAPTER 9 TRANSFORMATIONS • Concept Byte: Tracing Paper Transformations G-CO.A.2

9-1 Translations G-CO.A.2, G-CO.A.4, G-CO.A.5, G-CO.B.6 • Concept Byte: Paper Folding and Reflections G-CO.A.5

9-2 Reflections G-CO.A.2, G-CO.A.4, G-CO.A.5, G-CO.B.6 9-3 Rotations G-CO.A.2, G-CO.A.4, G-CO.A.5, G-CO.B.6 Concept Byte: Tracing Paper Transformations G-CO.A.3 9-4 Compositions of Isometries G-CO.A.2, G-CO.A.5, G-CO.B.6 9-5 Triangle Congruence G-CO.B.6, G-CO.B.7, G-CO.B.8

• Concept Byte: Exploring Dilations G-SRT.A.1a, G-SRT.A.1b 9-6 Dilations G-CO.A.2 9-7 Similarity Transformations G-SRT.A.2, G-SRT.A.3

11 Mar. 30 – Apr. 21

CHAPTER 10 AREA • Concept Byte: Transforming to Find Area Prepares for G-GMD.A.3

10-1 Areas of Parallelograms and Triangles G-GPE.7, G-MG.A.1 10-2 Areas of Trapezoids, Rhombuses, and Kites G-MG.A.1 10-3 Areas of Regular Polygons G-CO.D.13, G-MG.A.1 10-4 Perimeters and Areas of Similar Figures Prepares for G-GMD.A.3 10-5 Trigonometry and Area G-SRT.C.9 10-6 Circles and Arcs G-CO.A.1, G-C.A.1, G-C.A.2, G-C.A.5

• Concept Byte: Circle Graphs G-C.A.2 • Concept Byte: Exploring the Area of a Circle G-GMD.A.1

10-7 Areas of Circles and Sectors G-C.B.5 • Concept Byte: Inscribed and Circumscribed Figures Extends G-GPE.B.7

10-8 Geometric Probability Prepares for S-CP.A.1

12 Apr. 24 – May 9

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CHAPTER / LESSONS PACING DATES

CHAPTER 12 CIRCLES 12-1 Tangent Lines Prepares for G-C.A.2

• Concept Byte: Paper Folding With Circles Prepares for G-C.A.2 12-2 Chords and Arcs G-C.A.2 12-3 Inscribed Angles G-C.A.2, G-C.A.3, G-C.A.4

• Concept Byte: Exploring Chords and Secants Extends G-C.A.2 12-4 Angle Measures and Segment Lengths Extends G-C.A.2 12-5 Circles in the Coordinate Plane G-GPE.A.1

• Concept Byte: Equation of a Parabola G-GPE.A.2 12-6 Locus: A Set of Points G-GMD.B.4

10 May 11 – May 24

CHAPTER 13 PROBABILITY 13-1 Experimental and Theoretical Probability S-CP.A.1, S-CP.A.4 13-2 Probability Distributions and Frequency Tables S-CP.A.4, S-CP.A.5 13-3 Permutations and Combinations Prepares for S-CP.B.9 13-4 Compound Probability and Probability of Multiple Events S-CP.B.7, S-CP.B.8, S-CP.B.9 13-5 Probability Models S-CP.A.4 13-6 Conditional Probability Formulas S-CP.A.2, S-CP.A.3, S-CP.A.5, S-CP.A.6 13-7 Modeling Randomness S-MD.B.6, S-MD.B.7

• Concept Byte: Probability and Decision Making S-MD.B.6, S-MD.B.7

9 May 25 – Jun. 8

MVCSD GEOMETRY NR TEST JUNE 9, 2017

Although pacing will vary somewhat in response to variations in school calendars, needs of students, your school's years of experience with the curriculum, and other local factors, following the suggested pacing and sequence will ensure that students benefit from the way mathematical ideas are introduced, developed, and revisited across the year.

WORD WALLS ARE DESIGNED …

• to promote group learning • support the teaching of important general • principles about words and how they work • Foster reading and writing in content area • Provide reference support for children during their reading and writing • Promote independence on the part of young students as they work with words • Provide a visual map to help children remember connections between words and the

characteristics that will help them form categories • Develop a growing core of words that become part of their vocabulary

Important Notice • A Mathematics Word Wall must be present in every mathematics classroom.

Math Word Wall

l Create a math word

wall l Place math words on

your current word wall but highlight them in some way.

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SETUP OF THE MATHEMATICS CLASSROOM

I. Prerequisites for a Mathematics Classroom • Teacher Schedule • Class List • Seating Chart • Code of Conduct / Discipline • Grade Level Common Core Learning Standards (CCLS) • Updated Mathematics Student Work • Mathematics Grading Policy • Mathematics Diagrams, Charts, Posters, etc. • Grade Level Number Line • Grade Level Mathematics Word Wall • Mathematics Portfolios • Mathematics Center with Manipulatives (Grades K - 12)

II. Updated Student Work

A section of the classroom must display recent student work. This can be of any type of assessment, graphic organizer, and writing activity. Teacher feedback must be included on student’s work.

III. Board Set-Up

Every day, teachers must display the Lesson # and Title, Objective(s), Common Core Learning Standard(s), Opening Exercise and Homework. At the start of the class, students are to copy this information and immediately begin on the Fluency Activity or Opening Exercise.

IV. Spiraling Homework Homework is used to reinforce daily learning objectives. The secondary purpose of homework is to reinforce objectives learned earlier in the year. The assessments are cumulative, spiraling homework requires students to review coursework throughout the year.

Student’s Name: Teacher’s Name:

School: Date:

Lesson # and Title: Objective(s) CCLS: Opening Exercise:

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SECONDARY MATHEMATICS GRADING POLICY This course of study includes different components, each of which are assigned the

following percentages to comprise a final grade. I want you--the student--to understand

that your grades are not something that I give you, but rather, a reflection of the work

that you give to me.

COMPONENTS

1. Common Assessments → 35%

2. Quizzes → 20%

3. Homework → 20%

4. Notebook and/or Journal → 10%

5. Classwork / Class Participation → 15%

o Class participation will play a significant part in the determination of your

grade. Class participation will include the following: attendance, punctuality

to class, contributions to the instructional process, effort, contributions during

small group activities and attentiveness in class.

Important Notice

As per MVCSD Board Resolution 06-71, the Parent Notification Policy states

“Parent(s) / guardian(s) or adult students are to be notified, in writing, at any time during

a grading period when it is apparent - that the student may fail or is performing

unsatisfactorily in any course or grade level. Parent(s) / guardian(s) are also to be

notified, in writing, at any time during the grading period when it becomes evident that

the student's conduct or effort grades are unsatisfactory.”

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SAMPLE NOTEBOOK SCORING RUBRIC

Student Name: Teacher Name:

Criteria 4 3 2 1 Points

Completion of Required Sections

All required sections are complete.

One required section is missing.

Two or three required sections

are missing.

More than three required sections

are missing.

Missing Sections No sections of

the notebook are missing.

One sections of the notebook is

missing.

Two sections of the notebook are

missing.

Three or more sections of the notebook are

missing.

Headers / Footers

No required header(s) and/or

footer(s) are missing within

notebook.

One or two required

header(s) and/or footer(s) are

missing within notebook.

Three or four required header(s) and/or footer(s) are

missing within notebook.

More than four required header(s) and/or footer(s) are

missing within notebook.

Organization

All assignment and/or notes are kept in a logical

or numerical sequence.

One or two assignments

and/or notes are not in a logical or

numerical sequence.

Three or Four assignments and/or notes are not in a

logical or numerical sequence.

More than four assignments and/or notes are not in a

logical or numerical sequence.

Neatness

Overall notebook is kept very neat.

Overall notebook is kept in a satisfactory condition.

Overall notebook is kept in a below

satisfactory condition.

Overall notebook is unkept and very

disorganized.

Total

Teacher’s Comments:

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CLASSROOM AESTHETICS

“PRINT–RICH” ENVIRONMENT CONDUCIVE TO LEARNING

TEACHER NAME:

COURSE / PERIOD:

ROOM:

CHECKLIST • Teacher Schedule

• Class List

• Seating Chart

• Code of Conduct / Discipline

• Grade Level Mathematics CCLS

• Mathematics Grading Policy

• Mathematics Diagrams, Posters, Displays, etc.

• Grade Level Number Line

• Updated Student Work (Projects, Assessments, Writing, etc.)

YES NO

• Updated Student Portfolios

• Updated Grade Level Mathematics Word-Wall

• Mathematics Centers with Manipulatives • Organization of Materials

• Cleanliness

Principal Signature: Date:

Asst. Pri. Signature: Date:

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SYSTEMATIC DESIGN OF A MATHEMATICS LESSON

What are the components of a Mathematics Block?

Component Fluency Practice • Information processing theory supports the view that automaticity in math facts is

fundamental to success in many areas of higher mathematics. Without the ability to retrieve facts directly or automatically, students are likely to experience a high cognitive load as they perform a range of complex tasks. The added processing demands resulting from inefficient methods such as counting (vs. direct retrieval) often lead to declarative and procedural errors. Accurate and efficient retrieval of basic math facts is critical to a student’s success in mathematics.

Opening Exercise - Whole Group • This can be considered the motivation or Do Now of the lesson • It should set the stage for the day's lesson • Introduction of a new concept, built on prior knowledge • Open-ended problems Conceptual Development - Whole Group (Teacher Directed, Student Centered) • Inform students of what they are going to do. Refer to Objectives. Refer to the Key Words

(Word Wall) • Define the expectations for the work to be done • Provide various demonstrations using modeling and multiple representations (i.e. model a

strategy and your thinking for problem solving, model how to use a ruler to measure items, model how to use inch graph paper to find the perimeter of a polygon,)

• Relate to previous work • Provide logical sequence and clear explanations • Provide medial summary Application Problems - Cooperative Groups, Pairs, Individuals, (Student Interaction & Engagement, Teacher Facilitated) • Students try out the skill or concept learned in the conceptual development • Teachers circulate the room, conferences with the students and assesses student work (i.e.

teacher asks questions to raise the level of student thinking) • Students construct knowledge around the key idea or content standard through the use of

problem solving strategies, manipulatives, accountable/quality talk, writing, modeling, technology applied learning

Student Debrief - Whole Group (Teacher Directed, Student Centered) • Students discuss their work and explain their thinking • Teacher asks questions to help students draw conclusions and make references • Determine if objective(s) were achieved • Students summarize what was learned • Allow students to reflect, share (i.e. read from journal) Homework/Enrichment - Whole Group (Teacher Directed, Student Centered) • Homework is a follow-up to the lesson which may involve skill practice, problem solving

and writing

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Remember: Assessments are on-going based on students’ responses.

Important Notice

• All lessons must be numbered with corresponding homework. For example, lesson #1 will corresponded to homework #1 and so on.

• Writing assignments at the end of the lesson (closure) bring great benefits. Not only do they

enhance students' general writing ability, but they also increase both the understanding of content while learning the specific vocabulary of the disciplines.

• Spiraling Homework o Homework is used to reinforce daily learning objectives. The secondary purpose of

homework is to reinforce objectives learned earlier in the year. The assessments are

cumulative, spiraling homework requires students to review coursework throughout the

year.

• Manipulative must be incorporated in all lessons. With students actively involved in

manipulating materials, interest in mathematics will be aroused. Using manipulative

materials in teaching mathematics will help students learn:

a. to relate real world situations to mathematics symbolism.

b. to work together cooperatively in solving problems.

c. to discuss mathematical ideas and concepts.

d. to verbalize their mathematics thinking.

e. to make presentations in front of a large group.

f. that there are many different ways to solve problems.

g. that mathematics problems can be symbolized in many different ways.

h. that they can solve mathematics problems without just following teachers' directions.

• Homework, projects or enrichment activities should be assigned on a daily basis. • SPIRALLING OF HOMEWORK - Teacher will also assign problems / questions pertaining

to lessons taught in the past

Assessment: Independent Practice (It is on-going! Provide formal assessment when necessary / appropriate) • Always write, use and allow students to generate Effective Questions for optimal learning • Based on assessment(s), Re-teach the skill, concept or content using alternative strategies

and approaches