algebra ii ® curriculum guide

Algebra II ® Curriculum Guide

THIS HANDBOOK IS FOR THE IMPLEMENTATION OF THE NYS ALGEBRA II ® CURRICULUM IN MOUNT VERNON CITY SCHOOL

DISTRICT (MVCSD).

2016-17

MOUNT VERNON CITY SCHOOL DISTRICT

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Mount Vernon City School District

Board of Education Adriane Saunders

President

Adriane Saunders Vice President

Board Trustees Charmaine Fearon

Dr. Serigne Gningue Rosemarie Jarosz

Micah J.B. McOwen Omar McDowell

Darcy Miller Wanda White Lesly Zamor

Superintendent of Schools Dr. Kenneth 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

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. PHILOSOPHY OF MATHEMATICS CURRICULUM .............................................. 6

VII. MVCSD ALGEBRA II ® PACING GUIDE ................................................................... 9

VIII. WORD WALL ................................................................................................................. 16

IX. SETUP OF A MATHEMATICS CLASSROOM ......................................................... 17

X. SECONDARY GRADING POLICY ............................................................................. 18

XI. SAMPLE NOTEBOOK RUBRIC .................................................................................. 19

XII. CLASSROOM AESTHETICS ....................................................................................... 20

XIII. SYSTEMATIC DESIGN OF A MATHEMATICS LESSON ..................................... 21

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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 NYS Mathematics Core Curriculum.

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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Interpreting Functions F-IF Understand the concept of a function and use function notation. 1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). 2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1. Interpret functions that arise in applications in terms of the context. 4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity._ 5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function._ 6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph._ Analyze functions using different representations. 7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases._ a. Graph linear and quadratic functions and show intercepts, maxima, and minima. b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. d. (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. 8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay. 9. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

Building Functions F-BF Build a function that models a relationship between two quantities. 1. Write a function that describes a relationship between two quantities._ a. Determine an explicit expression, a recursive process, or steps for calculation from a context. b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. c. (+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time. 2. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms._ Build new functions from existing functions.

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3. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 4. Find inverse functions. a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x3 or f(x) = (x+1)/(x–1) for x ≠ 1. b. (+) Verify by composition that one function is the inverse of another. c. (+) Read values of an inverse function from a graph or a table, given that the function has an inverse. d. (+) Produce an invertible function from a non-invertible function by restricting the domain. 5. (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

Linear, Quadratic, & Exponential Models F-LE Construct and compare linear, quadratic, and exponential models and solve problems. 1. Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. 2. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 3. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 4. For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. Interpret expressions for functions in terms of the situation they model. 5. Interpret the parameters in a linear or exponential function in terms of a context.

Trigonometric Functions F-TF Extend the domain of trigonometric functions using the unit circle. 1. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. 2. Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. 3. (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosines, and tangent for x, π + x, and 2π – x in terms of their values for x, where x is any real number. 4. (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. Model periodic phenomena with trigonometric functions. 5. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline._ 6. (+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. 7. (+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context._ Prove and apply trigonometric identities. 8. Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle. 9. (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

ALGEBRA II ® PACING GUIDE This guide using Algebra II © 2015 was created to provide teachers with a time frame to complete the New York State Mathematics

Algebra 2 Curriculum.

CHAPTER / LESSONS PACING DATES

CHAPTER 1 EXPRESSIONS, EQUATIONS, AND INEQUALITIES 1-1 Patterns and Expressions Reviews A-SSE.B.3 1-2 Properties of Real Numbers Prepares for N-RN.B.3 1-3 Algebraic Expressions A-SSE.A.1a 1-4 Solving Equations A-CED.A.1, A-CED.A.4 1-5 Solving Inequalities A-CED.A.1 1-6 Absolute Value Equations and Inequalities A-SSE.A.1b, A-CED.A.1

9 Sept. 6 – Sept. 16

CHAPTER 2 FUNCTIONS, EQUATIONS, AND GRAPHS 2-1 Relations and Functions Reviews F-IF.A.1, F-IF.A.2 2-2 Direct Variation A-CED.A.2, F-IF.A.1, F-BF.A.1 2-3 Linear Functions and Slope-Intercept Form A-CED.A.2, F-IF.A.4, F-IF.C.7 2-4 More About Linear Equations A-CED.A.2, F-IF.B.4, F-IF.C.7, F-IF.C.8, F-IF.C.9 Concept Byte: Piecewise Functions F-IF.C.7b 2-5 Using Linear Models A-CED.A.2, F-IF.B.4, F-IF.B.6, F-BF.A.1 2-6 Families of Functions F-IF.C.7, F-BF.B.3 2-7 Absolute Value Functions and Graphs F-IF.C.7b, F-BF.B.3 2-8 Two-Variable Inequalities A-CED.A.2, F-IF.C.7b

10 Sept. 19 – Sept. 30

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CHAPTER 3 LINEAR SYSTEMS 3-1 Solving Systems Using Tables and Graphs A-CED.A.2, A-CED.A.3, A-REI.C.6, A-REI.D.11 3-2 Solving Systems Algebraically A-CED.A.2, A-CED.A.3, A-REI.C.5, A-REI.C.6 3-3 Systems of Inequalities A-CED.A.3, A-REI.C.6, A-REI.D.11 3-4 Linear Programming A-CED.A.3 Concept Byte: Linear Programming A-CED.A.3 Concept Byte: Graphs in Three Dimensions Extends A-REI.C.6 3-5 Systems With Three Variables Extends A-REI.C.6 3-6 Solving Systems Using Matrices A-REI.C.8

10 Oct. 5 – Oct. 21

CHAPTER 4 QUADRATIC FUNCTIONS AND EQUATIONS 4-1 Quadratic Functions and Transformations A-CED.A.1, F-IF.B.4, F-IF.B.6, F-IF.C.7, F-BF.B.3 4-2 Standard Form of a Quadratic Function A-CED.A.2, F-IF.B.4, F-IF.B.6, F-IF.C.9, F-BF.A.1 4-3 Modeling With Quadratic Functions F-IF.B.4, F-IF.B.5 Concept Byte: Identifying Quadratic Data F-IF.C.6 4-4 Factoring Quadratic Expressions A-SSE.A.2 Algebra Review: Square Roots and Radicals N-RN.A.2 4-5 Quadratic Equations A-SSE.A.1A, A-APR.B.3, A.CED.A.1 Concept Byte: Writing Equations From Roots A-CED.A.2 4-6 Completing the Square A-REI.B.4b 4-7 The Quadratic Formula A-REI.B.4b 4-8 Complex Numbers N-CN.A.1, N-CN.A.2, N-CN.C.7, N-CN.C.8 Concept Byte: Quadratic Inequalities A-CED.A.3 4-9 Quadratic Systems A-CED.A.3, A-REI.C.7 Concept Byte: Powers of Complex Numbers Extends N-CN.A.2

16 Oct. 24 – Nov. 16

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CHAPTER 5 POLYNOMIALS AND POLYNOMIAL FUNCTIONS 5-1 Polynomial Functions A-SSE.A.1c, F-IF.B.4, F-IF.C.7c 5-2 Polynomials, Linear Factors, and Zeros A-SSE.A.1, A-APR.B.3, F-IF.C.7c, F-BF.A.1 5-3 Solving Polynomial Equations A-SSE.A.2, A-REI.D.11 5-4 Dividing Polynomials A-APR.A.1, A-APR.A.2, A-APR.D.6 5-5 Theorems About Roots of Polynomial Equations N-CN.C.7, N-CN.C.8 Concept Byte: Solving Polynomial Inequalities A-APR.C.4 5-6 The Fundamental Theorem of Algebra N-CN.C.7, N-CN.C.8, N-CN.C.9, A-APR.B.3 Concept Byte: Graphing Polynomials Using Zeros A-APR.B.3 5-7 The Binomial Theorem A-APR.C.5 5-8 Polynomial Models in the Real World F-IF.B.4, F-IF.B.5, F-IF.B.6, F-IF.C.7 5-9 Transforming Polynomial Functions F-IF.C.7c, F-IF.C.9, F-BF.B.3

14 Nov. 17 – Dec. 8

CHAPTER 6 RADICAL FUNCTIONS AND RATIONAL EXPONENTS Algebra Review: Properties of Exponents Reviews N.RN.1 6-1 Roots and Radical Expressions A-SSE.A.2 6-2 Multiplying and Dividing Radical Expressions A-SSE.A.2 6-3 Binomial Radical Expressions A-SSE.A.2 6-4 Rational Exponents N-RN.A.1, N-RN.A.2 6-5 Solving Square Root and Other Radical Equations A-CED.A.4, A-REI.A.2 6-6 Function Operations F-BF.A.1b 6-7 Inverse Relations and Functions F-BF.B.4a, F-BF.B.4b Concept Byte: Graphing Inverses Extends F-BF.B.4a 6-8 Graphing Radical Functions F-IF.C.7b, F-IF.C.8

14 Dec. 9 – Jan. 6

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CHAPTER 7 EXPONENTIAL AND LOGARITHMIC FUNCTIONS 7-1 Exploring Exponential Models A-SSE.A.1b, A-CED.A.2, F-IF.C.7e 7-2 Properties of Exponential Functions A-SSE.A.1b, F-IF.C.7e, F-BF.A.1b 7-3 Logarithmic Functions as Inverses A-SSE.A.1b, F-IF.C.7e, F-IF.C.8, F-IF.C.9, F-BF.B.4a Concept Byte: Fitting Curves to Data F-IF.B.4 7-4 Properties of Logarithms Prepares for F-LE.A.4 7-5 Exponential and Logarithmic Equations A-REI.D.11, F-LE.A.4 Concept Byte: Using Logarithms for Exponential Models F-IF.C.7e, F-IF.C.8 7-6 Natural Logarithms F-LE.A.4 Concept Byte: Exponential and Logarithmic Inequalities A-CED.A.3, A-REI.D.11

12 Jan. 9 – Jan. 31

CHAPTER 8 RATIONAL FUNCTIONS 8-1 Inverse Variation A-CED.A.2, A-CED.A.4 Concept Byte: Graphing Rational Functions A-CED.A.1, F-IF.C.7d 8-2 The Reciprocal Function Family A-CED.A.2, F-BF.A.1, F-BF.A.2 8-3 Rational Functions and Their Graphs A-CED.A.2, F-IF.C.7, F-BF.A.1b Concept Byte: Oblique Asymptotes Extends F-IF.C.7d 8-4 Rational Expressions A-SSE.A.1a, A-SSE.A.1b, A-SSE.A.2 8-5 Adding and Subtracting Rational Expressions A-APR.C.7 8-6 Solving Rational Equations A-APR.C.6, A-APR.C.7, A-CED.A.1, A-REI.A.2, A-REI.D.11 Concept Byte: Systems With Rational Equations Extends A-REI.D.11 Concept Byte: Rational Inequalities Extends A-REI.D.11

14 Feb. 2 – Feb. 28

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CHAPTER 9 SEQUENCES AND SERIES 9-1 Mathematical Patterns Prepares for A-SSE.B.4 9-2 Arithmetic Sequences F-IF.A.3 Concept Byte: The Fibonacci Sequence F-IF.A.3 9-3 Geometric Sequences Prepares for A-SSE.B.4 9-4 Arithmetic Series Extends F-IF.A.3 Concept Byte: Geometry and Infinite Series A-SSE.B.4 9-5 Geometric Series A-SSE.B.4

8 Mar. 1 – Mar. 10

CHAPTER 10 QUADRATIC RELATIONS AND CONIC SECTIONS 10-1 Exploring Conic Sections Prepares for G-GPE.A.2 Concept Byte: Graphing Conic Sections Prepares for G-GPE.A.2 10-2 Parabolas G-GPE.A.2 10-3 Circles G-GPE.A.1 10-4 Ellipses G-GPE.A.3 10-5 Hyperbolas G-GPE.A.3 10-6 Translating Conic Sections G-GPE.A.2 Concept Byte: Solving Quadratic Systems Extends A-REI.C.7, A-REI.D.11

12 Mar. 13 – Mar. 29

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CHAPTER 11 PROBABILITY AND STATISTICS 11-1 Permutations and Combinations S-CP.B.9 11-2 Probability Prepares for S-IC.A.2 11-3 Probability of Multiple Events S-CP.A.2, S-CP.A.5, S-CP.B.7 Concept Byte: Probability Distributions S-IC.A.2 11-4 Conditional Probability S-CP.A.3, S-CP.A.4, S-CP.A.5, S-CP.B.6, S-CP.B.7 11-5 Probability Models S-MD.B.6, S-MD.B.7 11-6 Analyzing Data S-IC.B.6 11-7 Standard Deviation S-ID.A.4, S-IC.B.6 11-8 Samples and Surveys S-IC.A.1, S-IC.B.3, S-IC.S.B.4, S-IC.B.6 11-9 Binomial Distributions Extends S-CP.b.9 11-10 Normal Distributions S-ID.A.2, S-ID.A.4 Concept Byte: Margin of Error S-IC.B.4 Concept Byte: Drawing Conclusions from Samples S-IC.B.5

10 Mar. 30 – Apr. 20

CHAPTER 12 MATRICES 12-1 Adding and Subtracting Matrices N-VM.B.8, N.VM.B.9 Concept Byte: Working With Matrices N-VM.B.8 12-2 Matrix Multiplication N-VM.B.6, N-VM.B.7, N-VM.B.8, N.VM.B.9 Concept Byte: Networks N-VM.B.6 12-3 Determinants and Inverses N-VM.B.10, N.VM.B.12 12-4 Inverse Matrices and Systems N-VM.B.8 12-5 Geometric Transformations N-VM.B.6, N.VM.B.7, N-VM.B.8, G-CO.A.2, G-CO.B.5 12-6 Vectors N-VM.B.4a, N-VM.B.4b, N.VM.B.4c, N-VM.B.5a,

12 Apr. 21 – May 8

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CHAPTER 13 PERIODIC FUNCTIONS AND TRIGONOMETRY 13-1 Exploring Periodic Data F-IF.B.4, Prepares for F-TF.B.5 Geometry Review: Special Right Triangles Reviews G-SRT.C.6 13-2 Angles and the Unit Circle Prepares for F-TF.A.2 Concept Byte: Measuring Radians Prepares for F-TF.A.1 13-3 Radian Measure F-TF.A.1 13-4 The Sine Function F-IF.B.4, F-IF.C.7e, F-TF.A.2, F-TF.B.5 Concept Byte: Graphing Trigonometric Functions Prepares for F-TF.B.5 13-5 The Cosine Function F-IF.B.4, F-IF.C.7e, F-TF.A.2, F-TF.B.5 13-6 The Tangent Function F-IF.C.7e, F-TF.A.2, F-TF.B.5 13-7 Translating Sine and Cosine Functions F-IF.C.7e, F-TF.B.5 13-8 Reciprocal Trigonometric Functions F-IF.C.7e

12 May 9 – May 25

CHAPTER 14 TRIGONOMETRIC IDENTITIES AND EQUATIONS 14-1 Trigonometric Identities F-TF.C.8 14-2 Solving Trigonometric Equations Using Inverses F-TF.B.6, F-TF.B.7 14-3 Right Triangles and Trigonometric Ratios G-SRT.C.6, G-SRT.C.8 14-4 Area and the Law of Sines G-SRT.D.9, G-SRT.D.10, G-SRT.D.11 Concept Byte: The Ambiguous Case G-SRT.D.11 14-5 The Law of Cosines G-SRT.D.10, G-SRT.D.11 14-6 Angle Identities F-TF.C.9 14-7 Double-Angle and Half-Angle Identities F-TF.C.9

8 May 30 – June 8

MVCSD ALGEBRA II ® TEST JUNE 9, 2017

ALGEBRA II (COMMON CORE) REGENTS JUNE 16, 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.

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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. • The Suggested List of Mathematical Language for Algebra 2 &

Trigonometry ® level instruction must be incorporated into the Mathematics Word Wall.

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 Mathematics Standards • Power Performance Indicators - PPI (Grades 3 – 10) • 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 NYS Standard (Performance Indicator), Aim, Do Now and Homework. At the start of the class, students are to copy this information and immediately begin on the 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:

Aim #: NYS Performance Indicator: 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


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


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:

20

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 Standards

• Power Performance Indicators - PPI (Grades 3 - 10)

• 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:

21

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

22

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

algebra ii ® curriculum guide

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