For Appointments Call (310) 993-2426

General Relations and Functions
Content:
The student will demonstrate understanding of:
        *    Distance and slope;
        *    Circle equations and graphs;
        *    Functions;
        *    Transformations;
        *    One-to-one and inverse functions;
        *    Using a graphing utility to solve equations, graph functions. 

Skills:
Student will develop/enhance skills in:
        *    Algebra;
        *    Use of graphing calculator.

Unit Circle and Trigonometric Functions
Content:
The student will develop an understanding of:
        *   The trigonometric functions and the exact values of these using the unit circle;
        *    The domain and range of the trigonometric functions;
        *    The even/odd properties of the trigonometric functions;
        *    Reference angles;
        *    The trigonometric identities including half and double-angle formulas;
        *    The process and algebra involved in establishing a trigonometric identity;
        *    The solution of exact value equations where the solution is one of the "special angles";
        *    The solution of trigonometric equations using a graphing utility;
        *    The relationship between the six trigonometric functions and their inverses.

Skills:
Student will develop/enhance skills in:
        *    Graphing
        *    Measurement

Right Triangle Trigonometric Applications
Content:
The student will be able to:
        *    Construct a drawing to express information given in narrative form;
        *    Use a scientific/graphic calculator to solve applied problems using the six trigonometric functions.

Skills:
Student will develop/enhance skills in:
        *    Measurement;
        *    Use of a clinometer
        *    Use of a scientific calculator;
        *    Solving real world problems.

Graphing Trigonometric Functions
Content:
The student will be able to:
        *    Determine the amplitude, period, phase shift of a trigonometric function;
         *    Graph all six trigonometric functions using transformations without the aid of a calculator;
         *    Graph trigonometric functions using a graphing utility, including the selection of an appropriate viewing window;
         *    Find a sinusoidal function from data.

Skills:
Student will develop/enhance skills in:
        *    Use of a graphing calculator;
        *    Critical thinking answering open-ended questions.

Uniform Circular Motion
Content:
The student will be able to:
        *    Find the arc length of a circle;
        *    Convert from degrees to radians, and vice versa;
        *    Determine the linear speed and angular velocity of an object traveling in circular motion.

Skills:
Student will develop/enhance skills in:
        *    Facility with algebraic concepts;
        *    Dimensional algebra.

Oblique Triangles (Law of Sines and Cosines)
Content:
The student will:
        *    Be able to interpret word problems by drawing an appropriately labeled triangle;
        *    Use to Law of Sines (including the ambiguous case) to solve triangles;
        *    Use the Law of Cosines to solve triangles;
        *    Find the area of a triangle by geometric formulas, Heron's Rule and A=1/2bcsinC.

Skills:
Student will develop/enhance skills in:
        *    Measurement;
        *    Use of clinometer;
        *    Solving real world problems.

Polar Coordinates
Content:
The student will be able to:
        *    Convert rectangular coordinates to polar coordinates;
        *    Convert polar coordinates to rectangular coordinates;
        *    Graph using polar coordinates.

Skills:
Student will develop/enhance skills in:
        *    Graphing;
        *    Algebra.

Trigonometry  - California State Standards Taught

Trigonometry uses the techniques that students have previously learned from the

study of algebra and geometry. The trigonometric functions studied are defined geometrically

rather than in terms of algebraic equations. Facility with these functions as

well as the ability to prove basic identities regarding them is especially important for

students intending to study calculus, more advanced mathematics, physics and other

sciences, and engineering in college.

1.0 Students understand the notion of angle and how to measure it, in both degrees

and radians. They can convert between degrees and radians.

2.0 Students know the definition of sine and cosine as y- and x-coordinates of points

on the unit circle and are familiar with the graphs of the sine and cosine functions.

3.0 Students know the identity cos2 (x) + sin2 (x) = 1:

3.1 Students prove that this identity is equivalent to the Pythagorean theorem

(i.e., students can prove this identity by using the Pythagorean theorem and, conversely,

they can prove the Pythagorean theorem as a consequence of this identity).

3.2 Students prove other trigonometric identities and simplify others by using the

identity cos2 (x) + sin2 (x) = 1. For example, students use this identity to prove that

sec2 (x) = tan 2 (x) + 1.

4.0 Students graph functions of the form f(t) = A sin (Bt + C) or f(t) = A cos (Bt + C)

and interpret A, B, and C in terms of amplitude, frequency, period, and phase

shift.

5.0 Students know the definitions of the tangent and cotangent functions and can

graph them.

6.0 Students know the definitions of the secant and cosecant functions and can graph

them.

7.0 Students know that the tangent of the angle that a line makes with the x-axis is

equal to the slope of the line.

8.0 Students know the definitions of the inverse trigonometric functions and can

graph the functions.

9.0 Students compute, by hand, the values of the trigonometric functions and the

inverse trigonometric functions at various standard points.

10.0 Students demonstrate an understanding of the addition formulas for sines and

cosines and their proofs and can use those formulas to prove and/or simplify

other trigonometric identities.

11.0 Students demonstrate an understanding of half-angle and double-angle formulas

for sines and cosines and can use those formulas to prove and/or simplify other

trigonometric identities.

12.0 Students use trigonometry to determine unknown sides or angles in right

triangles.

13.0 Students know the law of sines and the law of cosines and apply those laws to

solve problems.

14.0 Students determine the area of a triangle, given one angle and the two adjacent

sides.

15.0 Students are familiar with polar coordinates. In particular, they can determine

polar coordinates of a point given in rectangular coordinates and vice versa.

16.0 Students represent equations given in rectangular coordinates in terms of polar

coordinates.

17.0 Students are familiar with complex numbers. They can represent a complex

number in polar form and know how to multiply complex numbers in their polar

form.

18.0 Students know DeMoivre뭩 theorem and can give nth roots of a complex number

given in polar form.

19.0 Students are adept at using trigonometry in a variety of applications and word

problems.

For Appointments Call (310) 993-2426

attributes: a characteristic or distinctive feature—

bar graph: a graph that uses the height or length

classify numbers: to group a set of numbers

commonly used fractions: halves, thirds,

commutative property of addition: the sum

Example: 6 + 4 = 4 + 6.

composing or decomposing numbers:

congruent: objects that have the same shape and

develop fluency: developing the ability for

expression: a mathematical phrase that

identity property of addition: if you add a

line graph: a graph used to show change over

line plot: a diagram showing frequency of data on

model: to represent a mathematical situation with

number sentences: equations or comparisons.

pictorial (picture) graph: a graph that uses

quantitative: relating to number or quantity;

referent: a familiar object or place that a student

shape of data: An overview of numerical data—

By the end of grade three, students deepen their understanding of place value

and their understanding of and skill with addition, subtraction, multiplication,

and division of whole numbers. Students estimate, measure, and describe objects

in space. They use patterns to help solve problems. They represent number relationships

and conduct simple probability experiments.

Third Grade Math - California State Standards Taught

Number Sense

1.0 Students understand the place value of whole numbers:

1.1 Count, read, and write whole numbers to 10,000.

1.2 Compare and order whole numbers to 10,000.

1.3 Identify the place value for each digit in numbers to 10,000.

1.4 Round off numbers to 10,000 to the nearest ten, hundred, and thousand.

1.5 Use expanded notation to represent numbers (e.g., 3,206 = 3,000 + 200 + 6).

2.0 Students calculate and solve problems involving addition, subtraction, multi

plication, and division:

2.1 Find the sum or difference of two whole numbers between 0 and 10,000.

2.2 Memorize to automaticity the multiplication table for numbers between 1 and 10.

2.3 Use the inverse relationship of multiplication and division to compute and check

results.

2.4 Solve simple problems involving multiplication of multidigit numbers by one-digit

numbers (3,671 ?3 = __).

2.5 Solve division problems in which a multidigit number is evenly divided by a

one-digit number (135 ?5 = __).

2.6 Understand the special properties of 0 and 1 in multiplication and division.

2.7 Determine the unit cost when given the total cost and number of units.

2.8 Solve problems that require two or more of the skills mentioned above.

11

3.0 Students understand the relationship between whole numbers, simple fractions,

and decimals:

3.1 Compare fractions represented by drawings or concrete materials to show equivalency

and to add and subtract simple fractions in context (e.g., 1/2 of a pizza is the

same amount as 2/4 of another pizza that is the same size; show that 3/8 is larger than

1/4).

3.2 Add and subtract simple fractions (e.g., determine that 1/8 + 3/8 is the same as 1/2).

3.3 Solve problems involving addition, subtraction, multiplication, and division of

money amounts in decimal notation and multiply and divide money amounts in

decimal notation by using whole-number multipliers and divisors.

3.4 Know and understand that fractions and decimals are two different representations

of the same concept (e.g., 50 cents is 1/2 of a dollar, 75 cents is 3/4 of a dollar).

Algebra and Functions

1.0 Students select appropriate symbols, operations, and properties to represent,

describe, simplify, and solve simple number relationships:

1.1 Represent relationships of quantities in the form of mathematical expressions,

equations, or inequalities.

1.2 Solve problems involving numeric equations or inequalities.

1.3 Select appropriate operational and relational symbols to make an expression true

(e.g., if 4 __ 3 = 12, what operational symbol goes in the blank?).

1.4 Express simple unit conversions in symbolic form (e.g., __ inches = __ feet ?12).

1.5 Recognize and use the commutative and associative properties of multiplication

(e.g., if 5 ?7 = 35, then what is 7 ?5? and if 5 ?7 ?3 = 105, then what is

7 ?3 ?5?).

2.0 Students represent simple functional relationships:

2.1 Solve simple problems involving a functional relationship between two quantities

(e.g., find the total cost of multiple items given the cost per unit).

2.2 Extend and recognize a linear pattern by its rules (e.g., the number of legs on a

given number of horses may be calculated by counting by 4s or by multiplying the

number of horses by 4).

Measurement and Geometry

1.0 Students choose and use appropriate units and measurement tools to quantify

the properties of objects:

1.1 Choose the appropriate tools and units (metric and U.S.) and estimate and measure

the length, liquid volume, and weight/mass of given objects.

1.2 Estimate or determine the area and volume of solid figures by covering them with

squares or by counting the number of cubes that would fill them.

1.3 Find the perimeter of a polygon with integer sides.

1.4 Carry out simple unit conversions within a system of measurement (e.g., centimeters

and meters, hours and minutes).

2.0 Students describe and compare the attributes of plane and solid geometric

figures and use their understanding to show relationships and solve problems:

2.1 Identify, describe, and classify polygons (including pentagons, hexagons, and

octagons).

2.2 Identify attributes of triangles (e.g., two equal sides for the isosceles triangle, three

equal sides for the equilateral triangle, right angle for the right triangle).

2.3 Identify attributes of quadrilaterals (e.g., parallel sides for the parallelogram, right

angles for the rectangle, equal sides and right angles for the square).

2.4 Identify right angles in geometric figures or in appropriate objects and determine

whether other angles are greater or less than a right angle.

2.5 Identify, describe, and classify common three-dimensional geometric objects

(e.g., cube, rectangular solid, sphere, prism, pyramid, cone, cylinder).

2.6 Identify common solid objects that are the components needed to make a more

complex solid object.

Statistics, Data Analysis, and Probability

1.0 Students conduct simple probability experiments by determining the number

of possible outcomes and make simple predictions:

1.1 Identify whether common events are certain, likely, unlikely, or improbable.

1.2 Record the possible outcomes for a simple event (e.g., tossing a coin) and systemati

cally keep track of the outcomes when the event is repeated many times.

1.3 Summarize and display the results of probability experiments in a clear and orga

nized way (e.g., use a bar graph or a line plot).

1.4 Use the results of probability experiments to predict future events (e.g., use a line

plot to predict the temperature forecast for the next day).

Mathematical Reasoning

1.0 Students make decisions about how to approach problems:

1.1 Analyze problems by identifying relationships, distinguishing relevant from irrel

evant information, sequencing and prioritizing information, and observing patterns.

1.2 Determine when and how to break a problem into simpler parts.

2.0 Students use strategies, skills, and concepts in finding solutions:

2.1 Use estimation to verify the reasonableness of calculated results.

2.2 Apply strategies and results from simpler problems to more complex problems.

2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables,

diagrams, and models, to explain mathematical reasoning.

2.4 Express the solution clearly and logically by using the appropriate mathematical

notation and terms and clear language; support solutions with evidence in both

verbal and symbolic work.

2.5 Indicate the relative advantages of exact and approximate solutions to problems

and give answers to a specified degree of accuracy.

2.6 Make precise calculations and check the validity of the results from the context of

the problem.

3.0 Students move beyond a particular problem by generalizing to other situations:

3.1 Evaluate the reasonableness of the solution in the context of the original situation.

3.2 Note the method of deriving the solution and demonstrate a conceptual understand

ing of the derivation by solving similar problems.

3.3 Develop generalizations of the results obtained and apply them in other circum

stances.

For Appointments Call (310) 993-2426

Kindergarten   |    1st Grade   |     2nd Grade   |     3rd Grade   |    4th-6th Grade    |    Algebra 1    |    Geometry    |    Algebra 2    |    Pre Calculus    |    Trigonometry    |    Schedule Session

Looking for piano lessons?
Click Here to Learn Piano From a Real Concert Pianist