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Math Topics

Algebra

Absolute value

Absolute value equations

Absolute value graphs

Absolute value inequalities

Functions

Calculating input and output of a function

Domain and range of a function

Graphs of functions

Introduction to functions

Relations and functions

Working with table of values for a function

Inequalities

Graphing inequalities

Graphing linear inequalities in two variables

Solving and graphing inequalities in one variable

Solving inequalities using multiplication or division

Solving multi-step inequalities

Linear equations

Algebra fact families

Identifying solutions of an equation

Solution strategies for solving linear equations

Solving linear equations in one variable

Solving one-step equations

Solving simultaneous linear equations in three variables

Solving simultaneous linear equations in two variables by substitution or elimination

Solving simultaneous linear equations in two variables using determinants

Solving simultaneous linear equations in two variables using graphing

Solving two-step equations

Logarithms and exponentials

Exponentials and powers

Properties of exponential functions

Properties of logarithms

Simplifying expressions involving exponentials

Simplifying expressions involving logarithms

Solving equations involving exponentials

Solving equations involving logarithms

Working with exponential models for data

Monomials

Addition and subtraction of monomials

Multiplication and division of monomials

Multiplying polynomials by monomials

Using properties of exponents to simplify monomials

Polynomials

Addition and subtraction of polynomials

Dividing a polynomial by another polynomial

Dividing polynomials by monomials

Factoring polynomials

Factoring polynomials using a common monomial factor

Factoring polynomials using the Distributive property

Multiplication of polynomials

Multiplying binomials

Polynomial functions

Solving polynomial equations

Understanding and identifying polynomials

Quadratic Equations

Discriminant of a quadratic equation

Graphing quadratic equations and functions

Modeling data with quadratic functions

Solving quadratic equations by completing the square

Solving quadratic equations by factoring

Solving quadratic equations graphically

Solving quadratic equations using the Square Root Method

Solving quadratic equations using the quadratic formula

Radical Equations

Graphing radical equations

Multiplying and dividing radical expressions

Simplifying radical expressions

Solving equations containing radical expressions

Rational Expressions

Adding and subtracting rational expressions

Direct, inverse and joint variation

Multiplying and dividing rational expressions

Simplifying complex rational expressions

Simplifying rational expressions

Solving rational equations

Variables

Adding and subtracting variables

Learning about variables

Multiplying and dividing variables

Representing value of one variable in terms of another

Simplifying variable expressions

Solving equations with variables on both sides

Using variables to write equations

Using variables to write expressions

Computation

Complex Numbers

Correct order of operations on complex numbers

Simplifying expressions involving complex numbers

Decimal Addition

Adding decimals horizontally

Adding decimals vertically

Adding three or more decimals

Decimal Division

Dividing decimals by decimals and whole numbers

Decimal Multiplication

Multiplying decimals by powers of 10

Multiplying decimals using exponents

Multiplying two or more decimals

Decimal Subtraction

Subtracting decimals horizontally

Subtracting decimals vertically

Fraction Addition

Adding mixed numbers with like denominators

Adding mixed numbers with unlike denominators

Adding proper fractions with like denominators

Adding proper fractions with unlike denominators

Adding three or more fractions with like denominators

Adding three or more fractions with unlike denominators

Finding the Least Common Denominator

Fraction Division

Dividing fractions

Dividing two mixed numbers

Finding reciprocals

Fraction Multiplication

Changing mixed numbers into improper fractions and vice versa

Multiply mixed numbers with other mixed numbers or proper fractions

Multiplying fractions using exponents

Multiplying two fractions

Fraction Subtraction

Subtracting three or more fractions with like denominators

Subtracting three or more fractions with unlike denominators

Subtracting two fractions with like denominators

Subtracting two fractions with unlike denominators

Subtracting two mixed numbers with like denominators

Subtracting two mixed numbers with unlike denominators

Irrational Numbers

Calculating roots of real numbers that result in irrational numbers

Order of operations on irrational numbers

Rationalizing denominators to eliminate radicals in denominators

Matrices

Addition and subtraction of matrices

Matrices, determinants and inverses

Matrix multiplication

Scalar product

Order of Operations

Correct order for combination of operations in computations

Exponents and order of operations

Roots of Fractions and Decimals

Calculating square roots of fractions and decimals

Roots of Integers

Finding cubic and higher order roots of integers

Square roots

Whole Number Addition

Adding 2-digit numbers

Adding a single-digit number to a multi-digit number

Adding integers

Adding single-digit numbers

Adding three or more numbers

Adding two large numbers with 3 or more digits

Whole Number Division

Dividing by a single-digit divisor with a remainder

Dividing by a single-digit divisor with no remainder

Dividing with integers

Long division by a divisor with 2 or more digits

Long division by a single-digit divisor with a remainder

Long division by a single-digit divisor with no remainder

Whole Number Multiplication

Basic multiplication facts

Multiplying a multi-digit number by a single-digit number

Multiplying integers

Multiplying three or more numbers

Multiplying whole numbers using exponents

Multiplying with multi-digit numbers

Understanding multiplication as repeated addition

Using arrays to model multiplication

Whole Number Subtraction

Subtracting 2-digit numbers

Subtracting integers

Subtracting numbers with more than 2 digits

Subtracting single and multi-digit numbers

Subtracting single-digit numbers

Estimation

Estimating Measurement

Comparing and estimating measurement

Estimating by comparing to a known quantity

Estimating length and area

Estimating with percents

Using estimation strategies

Rounding

Estimating differences

Estimating products

Estimating quotients

Estimating sums

Estimating sums and differences

Rounding decimal to a tenth

Rounding decimals and fractions to a whole number

Rounding decimals to a hundredth or smaller order

Rounding whole numbers and decimals

Rounding whole numbers to a hundred

Rounding whole numbers to a ten

Rounding whole numbers to a thousand or greater order

Using Estimation to Solve Problems

Estimating answer by rounding numbers

Estimating answers to word problems

Estimating answers to word problems about money

Using estimatio to eliminate unreasonable answers

Geometry

Circles

Constructing circle on the XY-plane from an equation

Finding equations for circles from their graphs

Parts of a Circle

Properties of circle

Segments and angles on a circle

Coordinate Geometry

Finding the x or y intercept of a function in the XY coordinate plane

Graphing equations in the XY coordinate plane

Graphing ordered pairs

Lines in the XY coordinate plane

Moving objects on the XY coordinate plane

Plotting points on the XY coordinate plane

Proofs using coordinate geometry

Working with coordinates on the XY-plane

Working with shapes in the XY coordinate plane

Curves

Ellipses

Hyperbolas

Parabolas

Lines

Constructing lines by joining points on XY plane

Constructing lines from slope and y-intercept of a line

Determining equation of a line from coordinates of two points

Determining equation of a line from its slope and coordinates of one point

Determining equation of a line from its slope and y-intercept

Determining the equation of a line from given data

Determining the equation of a line from its graph

Graphical properties of parallel lines

Graphical properties of perpendicular lines

Identifying and distinguishing among planes, points, lines, line segments and rays

Numerical properties of parallel lines

Numerical properties of perpendicular lines

Numerical understanding of slope of a line

Plotting points on a line from its equation

Properties of parallel and perpendicular lines

Properties of tangent lines

Standard form of a linear equation

Understanding the affect of change in coefficients on the graph of an equation for a line

Using distance formula to find length of a line segment

Using the midpoint formula to find the mid-point of a line segment

Working with equations of lines and their graphs

Pythagorean Theorem

Introducing the Pythagoream Theorum

Pythagoream Theorum and its converse

Using Pythagorean Theorem to determine area and congruence of right triangles

Using Pythagorean Theorem to find side lengths of a right triangle

Sets

Determining intersection or overlap of two or more sets

Determining the union of two or more sets

Solid Figures

Classifying solid figures

Comparing solid figures

Decomposing solid figures

Drawing 2-D views of solid figures

Relating plane shapes to solid figures

Understanding solid figures

Spatial Relations

Analyzing the position of one figure in relation to another

Nets for solid figures

Theorems and Proofs

Logic statements

Theorems, Proofs, and Identities

Triangles

Characteristics of triangles

Classification of triangles

Congruence and similarity of triangles

Measuring and classifying angles

Special Right triangles

Sum of angles in a triangle

Visual Analysis and Symmetry

Congruent and similar figures

Determining congruence of shapes using geometric proof and numerical data

Determining number of edges on a 3-D shape

Dividing and combining shapes

Identifying Quadrilaterals

Identifying and naming polygons

Identifying shapes based on their vertices, edges, faces and angles

Lines of symmetry

Make and test generalizations about geometric figures

Reflections and symmetry

Rotations

Similarity

Tessellations

Transformations: rotations, translations, reflections, and dilations

Translations

Using symmetry to solve problems

Mathematical Modeling

Displays of data

Bar and line graphs

Circle or pie graphs

Interpreting box-and-whisker and stem-and-leaf plots

Interpreting data in tables

Interpreting graphs

Organize data using matrices

Organizing data into Venn diagrams

Organizing data into graphs and pictures

Reading graphs and charts

Using Venn diagrams

Using graphs and charts in calculations

Working with bar graphs

Working with scatter plots

Measurement

Angles

Addition of angles

Complementary and supplementary angles

Measuring angles in Degrees

Measuring angles in Radians

Properties of Acute, Obtuse, Straight and Right angles

Standard angles (45, 90, 180 and 360 degrees)

Using a protractor to measure angles

Vertical angles and angle pairs formed by parallel lines and a transversal

Linear

Converting from one unit of length to another

Customary units of length

Measuring length in non-standard units

Using American and Metric units of length

Liquids

Using American and Metric Units for liquid volume

Using containers to measure volume of liquids

Money

Determining the total cost of items and amount of money needed to purchase them

Making change with money

Multi-dimensional

Calculating area and perimeter of polygons

Calculating area of geometric shapes using formulas

Calculating volume of various three dimensional figures

Chords, arcs and circles

Circumference and area of circle

Surface area

Understanding perimeter

Temperature

Using Celsius and Fahrenheit scales to measure temperature

Using thermometers to measure temperature

Time

Addition and subtraction of units of time

Units of time

Using calendars

Using digital and analog clocks to measure time and elapsed time

Units

Addition and subtraction of common measurement units

American units

Conversions between Metric and American units using ratios and formulas

Metric units

Weight

Customery units of weight

Using Metric and American units of weight

Using scales to measure weight

Number Concepts

Absolute Value

Calculating absolute value

Integers and absolute value

Understanding absolute value

Complex Numbers

Graphing complex numbers

Simplifying expressions involving complex numbers

i: the imaginary number

Irrational Numbers

Arranging irrational numbers in order

Square roots and irrational numbers

Understanding irrational numbers

Number Theory

Common factors and Greatest Common Factor (GCF)

Common multiples and Least Common Multiple (LCM)

Factors and divisibility

Factors and multiples

Identifying and using the Associative property of addition

Identifying and using the Associative property of numbers

Identifying and using the Commutative property of numbers

Identifying and using the Distributive property of numbers

Identifying and using the Identity property of numbers

Identifying and using the Multiplicative identity of numbers

Identifying and using the zero property or additive identity of numbers

Number theory concepts

Ordinal numbers

Properties of exponents

Properties of numbers

Understanding systems of numbers

Understanding the concept of even and odd numbers

Using Number Theory concepts

Zero property of multiplication

Rational Numbers - Fractions and Decimals

Comparing and ordering decimals

Comparing and ordering fractions

Comparing and ordering fractions using graphics

Converting decimals to fractions and fractions to decimals

Converting percents to fractions and decimals

Decimal place value and order of magnitude

Equivalent fractions

Fractions on the Number Line

Locating decimals on the Number Line

Rational numbers

Reading and writing decimals

Reading and writing fractions

Understanding fractions using graphics

Using Scientific Notation

Working with fractions and decimals

Writing a fraction in its simplest form

Whole Numbers and Integers

Comparing and ordering integers

Comparing and ordering whole number expressions

Comparing and ordering whole numbers

Comparing and ordering whole numbers using greater than, less than or equal to

Comparing numbers through 12

Counting

Integers on the Number Line

Numbers in thousands

Numbers that are before, after or between other numbers

Place value

Prime factorization

Reading and writing integers

Reading and writing whole numbers

Representing numbers in expanded form

Skip counting

Understanding integers

Whole number sets

Whole numbers on the Number Line

Writing numbers in words

Patterns and Relationships

Arithmetic Sequences

Finding missing term in an arithmetic sequence

Finding the next term of an arithmetic sequence

Finding the relationship between terms of an arithmetic sequence

Understanding arithmetic sequences

Fibonacci Sequence

Understanding the Fibonacci sequence

Formulas and Functions

Creating a formula from a given set of (x, f(x)) pairs

Determining the rules of a pattern

Solving literal equations

Using formulas to solve problems

Writing and evaluating algebraic expressions

Geometric Sequences

Determining the convergence or divergence of a geometric sequence

Finding missing term in a geometric sequence

Finding the next term of a geometric sequence

Finding the relationship between terms of a geometric sequence

Understanding Geometric sequences

Geometric Shapes

Finding missing term in a sequence of geometric shapes

Using formulas to determing the affect of change in a dimension on the area, perimeter, volume or surface area of a geometric shape

Logic

Logic problems

Logic problems involving inequalities

Number and pattern sequences

Using logical reasoning to solve problems

Numerical

Calculating percent of change

Calculating simple and compound interest

Calculating with percents

Counting by multiples

Determining and using Rate of Change

Even and odd Numbers

Factorials

Prime and composite numbers

Ratios and proportions

Scale maps and scale drawings

Solving number puzzles

Solving problems using proportions

Understanding ratios

Using fact families

Using rates and unit rates

Series

Determining the convergence and divergence of a Series

Finding the sum of a series numerically

Finding the sum of a series using a formula

Sets

Finding relationships between objects of a set

Parts of a set

Probability and Statistics

Probability

Calculating probability of compound events

Determining number of possible combination of things

Determining probability from visual graphics

Determining probability of dependent events

Determining probability of independent events

Determining probability of simple Events and complements

Expressing probability as a fraction

Permutations: calculating the number of possible combinations in a specific order

Probability in games

Theoretical and experimental probability

Understanding probability

Using probability concepts to make predictions

Statistics

Central Tendency - Mode

Central Tendency - Range

Central tendency - Mean

Central tendency - Median

Collecting data using observations, surveys and experiments

Design of investigation to address a question

Determining data points from measures of Central Tendency

Determining the Line of Best Fit

Determining the significance of statistical results

Finding the Mean, Median, Mode, and Range

Outliers

Population data and sample data

Representative and random samplings

Sampling methods

Standard deviation

Understanding Normal Distribution

Problem Solving

Problem Solving Strategies

Choose the correct operation

Draw a picture and write a number sentence

Draw a picture and write an equation

Look for a pattern

Make a table to organize data

Make an organized list

Use objects to solve a problem

Work backwards

Write a number sentence

Write an equation

Writing multiplication stories

Writing to explain a problem

Word Problems

Counting strategies

Creating a word problem for a given equation

Creating equations and inequalities from information in a word problem

Determining missing or extra information when solving a problem

Determining solution strategies for a word problem

Determining which facts can be asserted from given information

Multiplication word problems using graphics

Organizing information in tables to solve a word problem

Place value word problems

Translating words into expressions in a word problem

Two-step word problems with multiple operations

Using variables to solve word problems

Word problems involving addition

Word problems involving addition of fractions

Word problems involving decimal addition

Word problems involving division

Word problems involving division of fractions

Word problems involving division with decimals

Word problems involving money

Word problems involving multiplication

Word problems involving multiplication of decimals

Word problems involving multiplication of fractions

Word problems involving subtraction

Word problems involving subtraction of decimals

Word problems involving subtraction of fractions

Trigonometry

Functions

Inverse trigonometric functions

Laws of Sines and Cosines

Sine and Cosine functions

Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent

Solving problems using trigonometric ratios

Solving trigonometric equations

Solving trigonometric identities

Trigonometric ratios