high school math objectives g10 - issosua.com viewidentify the domain and range of functions &...

Grade 10 Math Syllabus Algebra IICourse DescriptionGrade10 Algebra II has been developed taking into consideration the five standards (strands) of Mathematics defined by NCTM: the course develops student understanding and skills in Algebra II including numbers, operations, geometry, measurement, data analysis, probability and problem solving. The Algebra II course will focus on linear equations and inequalities, systems of equations and inequalities, factoring polynomials and trinomials, matrices, quadratics, relations, functions, graphs, roots, radicals, complex numbers and exponents and logarithms. In addition students learn different ways to represent math, to communicate their math understanding and to make connections to real world situations and other subject areas. Students are assessed in a variety of ways continuously throughout the program of study to ensure they are understanding content and are able to use and apply the knowledge and skills they are developing.

Curricular contentAPPENDIX A contains the standards. APPENDIX B contains the performance indicators for each standard for High School, APPENDIX C contains the Mathematics Focal Points for Grade 10 and APPENDIX D contains the Secondary Assessment Policy. Students use the Holt McDougal – Algebra 2 textbook.

Quarter 1

Unit 0: Numeracy Theory behind number Operations with intergers, fractions, decimals

Unit 1: Foundations for functions Classify and order real numbers (1.1) Simplify, add, subtract, multiply and divide square roots (1.3) Simplify and evaluate algebraic expressions (1.4) Simplify expressions involving exponents & use scientific notation (1.5) Identify the domain and range of functions & determine whether a relation is

a function (1.6) Graph functions (1.7)

Unit 2: Linear Equations and Inequalities in Two Variables Solving linear equations and inequalities (2.1) Proportional reasoning (2.2) Graphing linear equations on a coordinate plane (2.3)

- Graphing from slope-intercept form- Graphing using x and y intercepts

Writing equations of lines (2.4)

- Given slope and y-intercept- Given slope and a point- Given two points- Given a point and a parallel line- Given a point and a perpendicular line

Using linear equations and inequalities in two variables to solve real-world problems Linear Programming (2.4)

Graphing linear inequalities in two variables on a coordinate plane(2.5) Transforming linear functions (2.6) Solving absolute value equations and inequalities (2.8) Drawing absolute value functions and transforming them (2.9)

Unit 3: Systems of Linear Equations and Inequalities Solving systems of equations by graphing (3.1) Solving systems of equations with the substitution method (3.2) Solving systems of equations with the elimination (linear combination)

method (3.2) Determining number of solutions to a system of equations (3.2) Using systems of equations to solve real-world problems (3.2) Graphing systems of inequalities (3.3) Using systems of inequalities to solve real-world problems (3.3) Linear Programming (3.4)

- Finding the feasible region- Maximizing or minimizing the objective function- Linear problems in real world examples

Graph points and linear equations in 3 dimensions (3.5) Solve linear systems in 3 variables Linear Programming (3.6)

Quarter 2

Unit 4: Matrices Use Matrices to display real world data, Adding & subtracting (4.1) Multiplying matrices (4.2) Computing determinants of matrices (2x2 and 3x3 matrices only) (4.3) Using Cramer´s rule to solve systems of equations (4.3) Computing inverses of matrices (2x2 only) (4.5) Using inverse matrices to solve systems of equations (only systems of 2

equations) (4.5)

Unit 5: Quadratic Functions (Part 1) Graphing quadratic functions (5.1) Properties of quadratic functions in standard form (5.2) Solving quadratic equations by factoring (5.3)

- When leading coefficient is equal to 1- When leading coefficient is not equal to 1- Using special patterns (difference of squares, perfect square trinomial)

Using quadratic functions to solve real-world problems (5.3)

Semester Exam

Quarter 3

Unit 5: Quadratic Functions (Part 2) Solve quadratic equations by completing the square. (5.4) Write quadratic equations in vertex form. (5.4) Define and use imaginary and complex numbers. (5.5) Solve quadratic equations with complex roots. (5.5) Solve quadratic equations using the quadratic formula. (5.6) Classify roots using the discriminant. (5.6) Solve quadratic inequalities by using tables, graphs and algebra. (5.7) Perform operations with complex numbers. (5.9)

Unit 6: Polynomial Functions Identify, evaluate, add and subtract polynomials. (6.1) Classify and graph polynomials. (6.1) Multiply polynomials, use binomial expansion to expand binomial expressions that are

raised to positive integer powers. (6.2) Use long division and synthetic division to divide polynomials. (6.3) Use the factor theorem to determine factors of a polynomial. (6.4) Factor the sum and difference of two cubes. (6.4) Identify the multiplicity of roots. Solve polynomials with rational and irrational roots.

(6.5) Write a polynomial equation of least degree with given roots. (6.6) Identify all of the roots of a polynomial equation. (6.6) Use properties of end behavior to analyze, describe, and graph polynomial functions.

(6.7) Identify and use maxima and minima of polynomial functions to solve problems. (6.7) Transform polynomial functions. (6.8)

Unit 7: Exponential and Logarithmic Functions

Write and evaluate exponential expressions to model growth and decay situations. (7.1) Graph and recognize inverses of relations and functions. (7.2) Write equivalent forms for exponential and logarithmic functions. (7.3) Write, evaluate, and graph logarithmic functions. (7.3) Use properties to simplify logarithmic expressions. (7.4) Translate between logarithms in any base. (7.4) Solve exponential and logarithmic equations. Solve problems involving exponential and

logarithmic equations. (7.5) Use the number e to write and graph exponential functions representing real-world

situations. (7.6) Solve equations and problems involving e or natural logarithms. (7.6)

Quarter 4

Unit 8: Rational and Radical Functions Solve problems involving direct, inverse, joint, and combined variation. (8.1) Simplify rational expressions. (8.2) Multiply and divide rational expressions. (8.2) Add and subtract rational expressions. Simplify complex fractions. (8.3) Graph rational functions. Transform rational functions by changing parameters. (8.4) Solve rational equations. (8.5) Rewrite radical expressions by using rational exponents. (8.6) Simplify and evaluate radical expressions and expressions containing rational exponents.

(8.6) Solve radical equations. (8.8)

Unit 9: Probability and Statistics Solve problems involving the fundamental counting principle. (11.1) Solve problems involving permutations and combinations. (11.1) Find the theoretical probability of an event. (11.2) Find the experimental probability of an event. (11.2) Determine whether events are independent or dependent. (11.3) Find the probability of independent and dependent events. (11.3) Find the probability of mutually exclusive or inclusive events. (11.4) Find measures of central tendency and measures of variation for statistical data. (11.5) Examine the effect of outliers on statistical data. (11.5) Use the Binomial Theorem to expand a binomial raised to a power. (11.6) Find binomial probabilities and test hypotheses. (11.6) **Extension: Normal Distributions.

Final exams

Grading Policy

Effort: Classwork and Homework 15%Formative: Quizzes, projects, major HW, Accelerated Math 45%Summative: Quarter Tests and Major portfolio projects 40%

Semester grades are developed based upon the following formula for Math:

Quarterly Grades (average) - 80%Exam Grade or Semester Project - 20%

Final grades are accrued by averaging the two semester grades.

APPENDIX A: Mathematics Standards

1. Number and Operations

Instructional programs from prekindergarten through grade 12 should enable all students to--

understand numbers, ways of representing numbers, relationships among numbers, and number systems;

understand meanings of operations and how they relate to one another; compute fluently and make reasonable estimates

2. Algebra


understand patterns, relations, and functions; represent and analyze mathematical situations and structures using algebraic

symbols; use mathematical models to represent and understand quantitative relationships; analyze change in various contexts

3. Geometry


analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships;

specify locations and describe spatial relationships using coordinate geometry and other representational systems;

apply transformations and use symmetry to analyze mathematical situations; use visualization, spatial reasoning, and geometric modeling to solve problems.

4. Measurement


understand measurable attributes of objects and the units, systems, and processes of measurement;

apply appropriate techniques, tools, and formulas to determine measurements.

5. Data Analysis and Probability


formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them;

select and use appropriate statistical methods to analyze data; develop and evaluate inferences and predictions that are based on data; understand and apply basic concepts of probability

6. Problem Solving


build new mathematical knowledge through problem solving; solve problems that arise in mathematics and in other contexts; apply and adapt a variety of appropriate strategies to solve problems; monitor and reflect on the process of mathematical problem solving.

7. Reasoning and Proof


recognize reasoning and proof as fundamental aspects of mathematics; make and investigate mathematical conjectures; develop and evaluate mathematical arguments and proofs; select and use various types of reasoning and methods of proof.

8. Communication


organize and consolidate their mathematical thinking through communication; communicate their mathematical thinking coherently and clearly to peers,

teachers, and others; analyze and evaluate the mathematical thinking and strategies of others; use the language of mathematics to express mathematical ideas precisely.

9. Connections


recognize and use connections among mathematical ideas; understand how mathematical ideas interconnect and build on one another to

produce a coherent whole; recognize and apply mathematics in contexts outside of mathematics.

10. Representation


create and use representations to organize, record, and communicate mathematical ideas;

select, apply, and translate among mathematical representations to solve problems;

use representations to model and interpret physical, social, and mathematical phenomena.

APPENDIX B: Performance Indicators Grades 9-121. Numbers and Operations Standard

Instructional programs from prekindergarten through grade 12 should enable all students to

In grades 9 through 12 all students should—

1.1 Understand numbers, ways of representing numbers, relationships among numbers, and number systems

develop a deeper understanding of very large and very small numbers and of various representations of them;

compare and contrast the properties of numbers and number systems, including the rational and real numbers, and understand complex numbers as solutions to quadratic equations that do not have real solutions;

understand vectors and matrices as systems that have some of the properties of the real-number system;

use number-theory arguments to justify relationships involving whole numbers.

1.2 Understand meanings of operations and how they relate to one another

judge the effects of such operations as multiplication, division, and computing powers and roots on the magnitudes of quantities;

develop an understanding of properties of, and representations for, the addition and multiplication of vectors and matrices;

develop an understanding of permutations and combinations as counting techniques.

1.3 Compute fluently and make reasonable estimates

develop fluency in operations with real numbers, vectors, and matrices, using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases.

judge the reasonableness of numerical computations and their results.

2. Algebra StandardInstructional programs from prekindergarten through grade 12 should enable all students to—


2.1 Understand patterns, relations, and functions

generalize patterns using explicitly defined and recursively defined functions;

understand relations and functions and select, convert flexibly among, and use various representations for them;

analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior;

understand and perform transformations such as arithmetically combining, composing, and inverting commonly used functions, using technology to perform such operations on more-complicated symbolic expressions;

understand and compare the properties of classes of functions, including exponential, polynomial, rational,

logarithmic, and periodic functions; interpret representations of functions of two variables

2.2 Represent and analyze mathematical situations and structures using algebraic symbols

understand the meaning of equivalent forms of expressions, equations, inequalities, and relations;

write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency—mentally or with paper and pencil in simple cases and using technology in all cases;

use symbolic algebra to represent and explain mathematical relationships;

use a variety of symbolic representations, including recursive and parametric equations, for functions and relations;

judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology.

2.3 Use mathematical models to represent and understand quantitative relationships

identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships;

use symbolic expressions, including iterative and recursive forms, to represent relationships arising from various contexts;

draw reasonable conclusions about a situation being modeled.

2.4 Analyze change in various contexts

approximate and interpret rates of change from graphical and numerical data.

3. Geometry StandardInstructional programs from prekindergarten through grade 12 should enable all students to—


3.1 Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

analyze properties and determine attributes of two- and three-dimensional objects;

explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them;

establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others;

use trigonometric relationships to determine lengths and angle measures.

3.2 Specify locations and describe spatial relationships using coordinate geometry and other representational systems

use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze geometric situations;

investigate conjectures and solve problems involving two- and three-dimensional objects represented with Cartesian coordinates.

3.3 Apply transformations and use symmetry to analyze mathematical situations

understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices;

use various representations to help understand the effects of simple transformations and their compositions.

3.4 Use visualization, spatial reasoning, and geometric modeling to solve problems

draw and construct representations of two- and three-dimensional geometric objects using a variety of tools;

visualize three-dimensional objects and spaces from different perspectives and analyze their cross sections;

use vertex-edge graphs to model and solve problems; use geometric models to gain insights into, and answer

questions in, other areas of mathematics; use geometric ideas to solve problems in, and gain insights

into, other disciplines and other areas of interest such as art and architecture.

4. Measurement StandardInstructional programs from prekindergarten through grade 12 should enable all students to—

In grades 9 though 12 all students should—

4.1 Understand measurable attributes of objects and the units, systems, and processes of measurement

make decisions about units and scales that are appropriate for problem situations involving measurement.

4.2 Apply appropriate techniques, tools, and formulas to determine measurements

analyze precision, accuracy, and approximate error in measurement situations;

understand and use formulas for the area, surface area, and volume of geometric figures, including cones, spheres, and cylinders;

apply informal concepts of successive approximation, upper and lower bounds, and limit in measurement situations;

use unit analysis to check measurement computations

5. Data Analysis and Probability StandardInstructional programs from prekindergarten through grade 12 should enable all students to—


5.1 Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

understand the differences among various kinds of studies and which types of inferences can legitimately be drawn from each;

know the characteristics of well-designed studies, including the role of randomization in surveys and experiments;

understand the meaning of measurement data and categorical data, of univariate and bivariate data, and of the term variable;

understand histograms, parallel box plots, and scatterplots and use them to display data;

compute basic statistics and understand the distinction between a statistic and a parameter.

5.2 Select and use appropriate statistical methods to analyze data

for univariate measurement data, be able to display the distribution, describe its shape, and select and calculate summary statistics;

for bivariate measurement data, be able to display a scatterplot, describe its shape, and determine regression coefficients, regression equations, and correlation coefficients using technological tools;

display and discuss bivariate data where at least one variable is categorical;

recognize how linear transformations of univariate data affect shape, center, and spread;

identify trends in bivariate data and find functions that model the data or transform the data so that they can be modeled.

5.3 Develop and evaluate inferences and predictions that are based on data

use simulations to explore the variability of sample statistics from a known population and to construct sampling distributions;

understand how sample statistics reflect the values of population parameters and use sampling distributions as the basis for informal inference;

evaluate published reports that are based on data by examining the design of the study, the appropriateness of the data analysis, and the validity of conclusions;

understand how basic statistical techniques are used to monitor process characteristics in the workplace.

5.4 Understand and apply basic concepts of probability

understand the concepts of sample space and probability distribution and construct sample spaces and distributions in simple cases

use simulations to construct empirical probability distributions;

compute and interpret the expected value of random variables in simple cases;

understand the concepts of conditional probability and independent events;

understand how to compute the probability of a compound event.

APPENDIX C: Focal Points Grade 10 Algebra II

Students solve equations and inequalities involving absolute value.

Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices.

Students are adept at operations on polynomials, including long division.

Students factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes.

Students demonstrate knowledge of how real and complex numbers are related both arithmetically and graphically. In particular, they can plot complex numbers as points in the plane.

Students add, subtract, multiply, and divide complex numbers.

Students add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions, including those with negative exponents in the denominator.

Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula. Students apply these techniques in solving word problems. They also solve quadratic equations in the complex number system.

Students demonstrate and explain the effect that changing a coefficient has on the graph of quadratic functions; that is, students can determine how the graph of a parabola changes as a, b, and c vary in the equation y = a(x-b) 2+ c.

Students graph quadratic functions and determine the maxima, minima, and zeros of the function.

Students prove simple laws of logarithms.

o Students understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

o Students judge the validity of an argument according to whether the properties of real numbers, exponents, and logarithms have been applied correctly at each step.

Students know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay.

Students use the definition of logarithms to translate between logarithms in any base.

Students understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values.

Students determine whether a specific algebraic statement involving rational expressions, radical expressions, or logarithmic or exponential functions is sometimes true, always true, or never true.

Students demonstrate and explain how the geometry of the graph of a conic section (e.g., asymptotes, foci, eccentricity) depends on the coefficients of the quadratic equation representing it.

Given a quadratic equation of the form ax2 + by2 + cx + dy + e = 0, students can use the method for completing the square to put the equation into standard form and can recognize whether the graph of the equation is a circle, ellipse, parabola, or hyperbola. Students can then graph the equation.

Students use fundamental counting principles to compute combinations and permutations.

Students use combinations and permutations to compute probabilities.

Students know the binomial theorem and use it to expand binomial expressions that are raised to positive integer powers.

Students apply the method of mathematical induction to prove general statements about the positive integers.

Students find the general term and the sums of arithmetic series and of both finite and infinite geometric series.

Students derive the summation formulas for arithmetic series and for both finite and infinite geometric series.

Students solve problems involving functional concepts, such as composition, defining the inverse function and performing arithmetic operations on functions.

Students use properties from number systems to justify steps in combining and simplifying functions.

APPENDIX D: Secondary Assessment Policy

Assessment monitors the progress of student learning and produces feedback for students, teachers, parents and external institutions. The following policy outlines the general assessment procedures for the school. Teachers are responsible for communicating their individual assessment policies to the students and parents at the beginning of the school year.

Teachers are expected to communicate assessment expectations and criteria, including major assignments and projects clearly to students prior to a chunk of learning. Assessment should take into account the ISS diverse group of learners and learning styles. Feedback on assignments should be positive, constructive and prompt. Teachers should provide a wide variety of different assessment opportunities which are relevant and motivational to students. Formative assessments assist student in building understanding, knowledge and skills and summative assessments assess students’ acquired understanding, knowledge and skills.

External Summative FormativeDefinition External

assessments are assessments which are designed and marked externally

Summative assessments are those assessments given within a class at the end of a chunk of learning (such as a unit).

Formative assessments are those given regularly and continuously throughout the school year.

Primary Purpose

To measure growth and progress, to inform teaching, to identify needs, to collect data, to determine level of understanding, to determine reading or math levels against national norms, assessing student learning, providing a qualification for university or college entry.

To inform teaching, to identify needs, to determine level of understanding, to measure progress, to communicate with parents

To determine prior knowledge, to determine student interest, to modify teacher practice, measure understanding, ensuring short-term knowledge and understanding objectives and targets are being met, to ensure students are progressing

Policies Some external assessments are taken twice a year, some are once and some are on-going.

Assessments are aligned to curriculum, teachers model in advance, authentic assessments, differentiated if

Assessments are aligned to curriculum, differentiated if necessary.

necessary.Practices STAR Math,

NWEA, Accelerated Math, PSAT, SAT, AP

Essays, projects, test, RAFTS, portfolio, investigations, real-world examples, exams, oral presentation, reports, reflections, mid-trimester reports, mid-quarter reports

Observation, journal, quiz, exit cards, peer assessment or self-assessment (not graded on Gradequick), role play, conferencing, small group discussion, debate, create/present, note-taking, reflection, homework, classwork, effort, behavior, participation, Gradequick reporting,

Teachers will be asked to implement IEP's/ILP's in their classroom should it contain students receiving necessary support. Teachers will be provided with the document, as well as support in how to effectively implement the modifications in order to ensure student success. We strongly suggest that teachers consult with the learning specialist or principal during the design and implementation of all summative evaluations for students with IEPs.

high school math objectives g10 - issosua.com viewidentify the domain and range of functions &...

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