# Mathematics

**Mathematics Objectives**

**Grade (1)**

**The students will begin to learn how to:**

* Add and subtract the numbers, using pictures to write the addition and subtraction sentences.

* Solve word problems.

* Adding and subtracting tens and ones.

* Order numbers from least to greatest and vice versa .

* Measure by using ruler.

* Recognize time –an hour or half an hour- by using the clock.

* Read and make picture graph and bar graph.

* Learn about fractions and 2&3D shapes.

**Grade (2)**

**The students will learn how to:**

* Differentiate between even and odd numbers.

* Decide the place values of digits.

* Write different forms and ways of numbers.

* Regroup of numbers- in addition or subtraction.

* Regroup tens and ones, hundreds and tens.

* Solve word problems about money and time.

* Measure with centimeter ruler.

* Read and make picture graph and bar graph, 2&3D shapes.

* Solve problems concerning timetables of 2,3,4,5.

**Grade (3)**

**The students will learn how to :**

* Round sums of addition or subtraction.

* Use place values to add and subtract.

* Apply multiplication and division rules to solve problems concerning timetables of 2 – 10 .

* Identify, compare , and order fractions.

* Measure liquids, volume and mass.

* Find perimeter and area.

* Describe and classify plain shapes.

**Grade (4)**

**Students are given much focus on learning:**

* The basic operations in math ( addition , subtraction , multiplication and division) for small and large whole numbers.

* An introduction of adding and subtracting fractions.

* Ways of applying these skills in their real lives.

**Grade (5)**

**Students are given much focus on learning:**

* The basic operations in math ( addition , subtraction , multiplication and division) for small and large whole, fraction, decimal and mixed numbers. –-ways of applying these skills on their real lives.

** Grade (6)**

** Students learn:**

* New sets of numbers which are integers and rational numbers.

* Use these sets to deal with other topics such as finding ratios and percents by using operations like (addition, subtraction, multiplication, division and exponent).

* Ways of applying these skills on their real lives.

**Grade (7)**

**Algebra1**

**Students will study:**

* Evaluating and simplifying expression, properties of the real number system, the order of operations, and patterns.

* Using inverse operations to solve equations containing variables, write equations to represent situations, and simplify equations before solving.

* Solving inequalities by using inverse operations.

* Solving inequalities with variables on both sides.

* Solving compound inequalities, relationships between variables.

* Determining whether a relation is a function, relationships in function notation, percent ,percent change, proportion ratio unit rate .

* Trending lines on scatter plots .

* Organizing data in tables, graphs, and plots.

**Geometry**

**Students will study:**

* Basic facts about points, lines, planes, segments, and angles, using formulas to find distance and the coordinates of a midpoint, inductive and deductive.

* Reasoning, writing two-column, parallel and perpendicular lines, angles formed by parallel, lines and a transversal, lines in a coordinate plane, classifying triangles, proving triangles congruent, using corresponding parts of congruent triangles in proofs.

* Proving theorems about isosceles and equilateral triangles.

**Grade (8)**

**Algebra1 **

**Students in 8th grade will study:**

* Writing and graphing linear functions.

* Identifying and interpreting the components of linear graphs, including the x-intercept, y-intercept, and slope.

* Graphing and analyzing families of functions, properties of exponents, powers of 10 and scientific notation.

* Adding, subtracting, and multiplying polynomials by using properties of exponents and combining like terms ,greatest common factors, how to factor polynomials .

* Factoring special products.

* Choosing a factoring method.

**Geometry**

**Students in 8th grade will study:**

* Properties of perpendicular bisectors and angle bisectors, special points, segments, and lines related to triangles ,inequalities in one triangle and in two triangles.

* Pythagorean inequalities and special right triangles, properties of polygons. properties of special quadrilaterals, showing that a polygon is a special quadrilateral, verifying that polygons are similar using corresponding angles and sides.

* Using properties of similar polygons, similarity of right triangles.

* Using ratios and proportions to find missing side lengths in right triangles.

**Grade (9)**

**Algebra 2**

**Students in 9th grade will study:**

* Graphing and transforming quadratic functions .

* Solving quadratic equations and inequalities .

* Fitting data to quadratic models .

* Using and performing operations with imaginary and other complex numbers .

* Dividing polynomials , exponential function , growth and decay .

* Solving problems with variation function .

* Simplifying rational and radical expressions , graphing rational and radical function , solving rational and radical equations and inequalities .

* Solving problems involving counting and arranging.

**Geometry**

**Students in 9th grade will study:**

* Using ratios and proportions to find missing side lengths in right triangles .

* Using trigonometric ratios to solve real-world problems, areas and perimeters of figures whose dimensions are found by using the Pythagorean Theorem .

* Areas and perimeters of figures in customary and metric units, proofs of formulas for area and perimeter, proofs of formulas for area and perimeter solve problems involving circles.

* The surface areas and volumes of three dimential figures ,the effect of changing dimension figures proportionally.

* Solving problems involving circles, finding lengths, angle measures, and a

reas associated with circles, applying circle theorems to solve a wide range of problems.

**Grade (10)**

**Algebra 2 **

**Students in 10th grade will study:**

* Using properties of equality to write and solve linear equations.

* Writing and graphing linear functions .

* Solving problems involving transformations of the linear parent function ,transformations of the absolute-value parent function .

* Graphing systems of linear equations, graphing systems of linear inequalities.

* Solving systems of linear equations ,organizing data into matrices ,operating with matrices, solving systems of equations several ways by using matrices.

* Using and performing operations with imaginary and other complex numbers, transforming piecewise functions .

* Performing operations on functions and function inverses the graphs of parabolas and other conic sections that are not functions, methods for solving systems of nonlinear functions .

* Finding theoretical , experimental , and binomial probabilities .

* Analyzing data to include expected value and standard devia

tion , patterns of numbers , called sequences , and their sums called series , patterns to determine whether the sequences arithmetic or geometric and how to write .

* Writing and evaluating sequences and series, using trigonometric functions and their inverses, and solving the triangles and , using angle of rotation and finding arc lengths of circles.

**Grade (11)**

**Pre Calculus**

**Students in 11th grade will study:**

* Analyzing and sketching graphs of quadratic functions .

* Analyzing and sketch graphs of polynomial functions of higher degree.

* Dividing polynomials .

* Performing operations with complex numbers and find complex solutions of quadratic equations .

* Finding zeros of polynomial functions,exponential functions and logarithmic functions.

**Grade (12)**

**Calculus**

**Students in 12th grade will study:**

**Limits and Continuity**

* Use graphical and numerical evidence to estimate limits, and to identify situations where limits fail to exist.

* Apply rules to calculate limits.

* Use the limit concept to determine where a function is continuous.

* Use the Intermediate Value Theorem to identify an interval where a continuous function has a root.

**Differentiation**

* Use the limit definition to calculate a derivative, or to determine when a derivative fails to exist.

* Calculate derivatives (of first and higher orders) with pencil and paper, without table or calculator or computer algebra software, using:

- Linearity of the derivative.

- Rules for products and quotients and the Chain Rule.

- Rules for constants, powers, and trigonometric and exponential functions.

- Rules for inverse functions, including logarithms and inverse trignometric functions.

- Use the derivative to find tangent lines to curves.

- Calculate derivatives of functions defined implicitly.

- Interpret the derivative as a rate of change.

- Solve problems involving rates of change of variables subject to a functional relationship.

- Calculate the linearization of a differentiable function at a point.

- Use differentials (linearization) to approximate the change in value of a function due to a small change in its argument.

**Applications of Derivatives**

* Find critical points, and use them to locate maxima and minima.

* Use critical points and signs of first and second derivatives to sketch graphs of functions:

- Use the first derivative to find intervals where a function is increasing or decreasing.

- Use the second derivative to determine concavity and find inflection points.

- Apply the first and second derivative tests to classify critical points.

- Use Differential Calculus to solve optimization problems.

**Integration**

- * Find antiderivatives of functions.
- * Use antiderivatives to solve.
- * First-order differential equations of the form dy/dx = f(x).
- * Separable first-order differential equations.
- * Use sigma notation to represent, manipulate and evaluate finite sums.
- * Use the definition to calculate a definite integral as a limit of approximating sums.
- * Apply the Fundamental Theorem of Calculus to evaluate definite integrals and to differentiate functions defined as integrals.
- * Calculate elementary integrals with pencil and paper, without calculator or computer algebra software, using : Linearity of the integral; Rules for powers (including exponent
*-1*) and exponentials, the six trigonometric functions and the inverse sine, tangent and secant;Simple substitution.

**Statistics**

**:Students in 12th grade will study**

* Learn how to pose conceptually focused problems in high school probability and statistics.

* Connect probability and statistics concepts vertically through middle school and high school.

.Examine ways to help students justify and explain the use of combinations, permutations, and the counting principle *

* Design thought-provoking high school tasks related to probability and statistics.

.Recognize how theoretical ideas from probability and statistics are connected to Indiana and NCTM Standard *

.Apply the addition and multiplication rules of probability to problems in context *

.Explore methods of data collection and analysis *

.Learn how to use various technologies effectively to analyze and summarize one-variable data *

.Develop conceptual and procedural understanding of the purpose and use of simulations *

.Develop conceptual and procedural understanding of the purpose and use of experimental probability *

.Develop conceptual and procedural understanding of the purpose and use of binomial probability *

.Investigate the application of probability in games and television shows *

* Graph a normal curve and summarize its important properties.

.Apply the empirical rule to solve real-world problems *

.Given µ and σ convert raw data to z scores *

.Given µ and σ, convert z scores to raw data *

.Graph the standard normal distribution, and find areas under the standard normal curve *