# Mathematics Monster

## Welcome to Mathematics Monster

Hi, and welcome!Mathematics Monster has hundreds of step-by-step lessons (all with tests, games, or interactive widgets). There are also A-Z glossaries of mathematical terms and symbols. If you're looking to teach or master a specific topic, there is a topic-themed sitemap below. (There is also a handy search bar above.)

On Mathematics Monster (#MM), there is no log-in, and **everything is free!** There are a couple of ads, and that's how I fund the site. (There are no ads in the lesson content. None. Not one.)

This is the sister site of Grammar Monster.

## algebra curriculum

## Algebra Definitions

understanding equations understanding constants understanding variables understanding coefficients understanding exponents understanding operators understanding terms in algebra understanding expressions in algebra## Arithmetic with Letters

adding letters subtracting letters multiplying letters dividing letters## Arithmetic with Terms

adding terms subtracting terms multiplying terms dividing terms## Laws of Exponents in Algebra

understanding the laws of exponents understanding an exponent of −1 multiplying powers dividing powers finding a power of a power finding a power of a product finding a negative exponent## Like Terms

understanding like terms identifying like terms adding like terms subtracting like terms collecting like terms## Expanding Brackets

expanding brackets expanding brackets using the grid method expanding double brackets understanding the FOIL methods multiplying expressions in algebra expanding double brackets using the grid method## Solving Equations with Brackets

solving an equation with brackets solving an equation with two sets of brackets## Factoring

understanding factors in algebra finding factors in algebra understanding the greatest common factor in algebra finding the greatest common factor in algebra factoring an expression## Algebraic Fractions

understanding algebraic fractions adding algebraic fractions subtracting algebraic fractions multiplying algebraic fractions dividing algebraic fractions simplifying algebraic fractions finding the reciprocal of an algebraic fraction how to find a power of an algebraic fractionfamous mathematicians

Al-Khwarizmi Archimedes Rene Descartes Pythagoras Isaac Newton Euclid Fibonacci## linear equations curriculum

## Equations and Linear Equations

understanding linear equations## Lines, Slopes and Y-Intercepts

understanding linear equations in slope-intercept form understanding slope finding the slope of a line finding the slope from a linear equation understanding the y-intercept finding the y-intercept of a line finding the y-intercept from a linear equation finding the equation of a line## Slope-Point Form

understanding linear equations in slope-point form finding the slope from a linear equation in slope-point form finding the y-intercept from a linear equation in slope-point form## General Form

understanding linear equations in general form finding the slope from a linear equation in general form finding the y-intercept from a linear equation in general form converting a linear equation from general to slope-intercept form## Equation of a Line Between Two Points

finding the equation of a line between two points## quadratic equations curriculum

## Quadratic Equations

understanding quadratic equations## Solving Quadratic Equations

solving quadratic equations solving quadratic equations using factoring solving quadratic equations using factoring (a ≠ 1) solving quadratic equations using the quadratic formula solving quadratic equations using a graph## Difference of Squares

understanding a difference of squares solving quadratic equations using a difference of squares## Completing the Square

understanding perfect square trinomials understanding completing the square completing the square## simultaneous equations curriculum

## Solving Simultaneous Equations

solving simultaneous equations solving simultaneous equations using elimination solving simultaneous equations using elimination (where coefficients differ) solving simultaneous equations using substitution solving simultaneous equations using a graph## functions curriculum

## Functions

understanding functions evaluating functions## Plotting Functions

finding y-intercept of a function finding x-intercepts of a function## Composite Functions

understanding composite functions finding a composite function evaluating a composite function## Inverse Functions

understanding inverse functions finding the inverse of a function finding the inverse of a function using a graph## fractions curriculum

## Fractions

understanding fractions understanding the numerator understanding the denominator## Types of Fractions

understanding proper fractions understanding improper fractions understanding mixed fractions converting mixed to improper fractions converting improper to mixed fractions## Equivalent Fractions and Simplifying Fractions

understanding equivalent fractions and simplest form simplifying fractions## Arithmetic with Fractions

adding fractions subtracting fractions multiplying fractions dividing fractions finding the reciprocal of a fraction finding the power of a fraction## Using Fractions

finding a fraction of a number expressing a number as a fraction of another number## Converting Fractions

converting a fraction to a percentage converting a fraction to a decimal## percentages curriculum

## Percentages

understanding percentages finding a percentage of a number expressing a number as a percentage of another number## Percentage Changes

understanding percentage changes finding a percentage change## Converting Percentages

converting a percentage to a fraction converting a percentage to a decimal## geometry curriculum

here is an interactive widget to find the areas of plane shapes. here is an interactive widget to find the volumes of 3D shapes. here is an interactive widget to learn about circle geometry. here is an interactive widget to learn about triangle geometry. here is a game to learn about the different types of triangle. here is a game to learn about the 3 main types of angle. here is an interactive widget to learn about**parallelogram**geometry. here is an interactive widget to learn about

**trapezoid**geometry. here is an interactive widget to learn about

**rectangle**geometry. here is an interactive widget to learn about

**square**geometry. here is an interactive widget to learn about

**ellipse**geometry.

## Plane Shapes

understanding circles understanding ellipses understanding parallelograms understanding rectangles understanding squares understanding trapezoids understanding triangles## Areas

finding the area of a circle finding the area of an ellipse finding the area of a parallelogram finding the area of a rectangle finding the area of a square finding the area of a trapezoid finding the area of a triangle## Volumes

finding the volume of a cone finding the volume of a cube finding the volume of a cylinder finding the volume of a sphere## Circles

understanding the radius understanding the diameter understanding the circumference understanding pi finding the length of an arc (degrees) finding the length of an arc (radians) finding the area of a sector (degrees) finding the area of a sector (radians)## Radius of a Circle

finding the radius from the diameter finding the radius from the circumference finding the radius from the area## Diameter of a Circle

finding the diameter from the radius finding the diameter from the circumference finding the diameter from the area## Area of a Circle

finding the area of a circle using diameter## Circle Theorems

understanding the circle theorems tangent meets a radius at 90° two radii make an isosceles triangle perpendicular bisector of a chord angle at the center is twice the angle at the circumference angle in a semicircle is 90° angles in the same segment are equal angles in a cyclic quadrilateral tangents from the same point are the same length alternate segment theorem## Triangles

understanding the types of triangles understanding equilateral triangles understanding isosceles triangles understanding scalene triangles understanding the interior angles of a triangle finding a missing angle in a triangle finding a missing angle in an isosceles triangle## Angles

understanding angles understanding degrees understanding the types of angles understanding acute angles understanding right angles understanding obtuse angles understanding straight angles understanding reflex angles understanding full angles understanding radians## Angle Properties

understanding complementary angles understanding supplementary angles understanding explementary angles## Polygons

understanding polygons understanding the interior angles of a polygon finding the interior angle of a regular polygon finding the sum of the interior angles of a polygon understanding the exterior angles of a polygon finding the exterior angle of a regular polygon understanding the sum of an interior and exterior angle of a polygon is 180°## trigonometry curriculum

## Right Triangle

understanding right triangle understanding the adjacent understanding the opposite understanding the hypotenuse## Pythagoras' Theorem

understanding Pythagoras' theorem finding the hypotenuse using Pythagoras' theorem finding a shorter side using Pythagoras' theorem## Sine Function

understanding the sine function finding the angle using the sine function finding the opposite using the sine function finding the hypotenuse using the sine function## Cosine Function

understanding the cosine function finding the angle using the cosine function finding the adjacent using the cosine function finding the hypotenuse using the cosine function## Tangent Function

understanding the tangent function finding the angle using the tangent function finding the opposite using the adjacent function finding the adjacent using the tangent function## Area of a Triangle Using Trigonometry

finding the area of a triangle using trigonometry## transformations curriculum

## Transformations

understanding transformations## Translations

understanding translations translating a shape describing a translation## Rotations

understanding rotations understanding the common rotations rotating a shape describing a rotation## Reflections

understanding reflections understanding the common reflections reflecting a shape describing a reflection## Enlargements

understanding enlargements understanding the scale factor enlarging a shape enlarging a shape with a fractional scale factor enlarging a shape with a negative scale factor describing an enlargement describing an enlargement with a negative scale factor## graphs and coordinates curriculum

## Graphs

understanding the parts of a graph understanding the x-axis understanding the y-axis understanding the origin## Cartesian Coordinates

understanding Cartesian coordinates understanding the x-coordinate understanding the y-coordinate drawing a point from Cartesian coordinates reading off a point from Cartesian coordinates## Polar Coordinates

understanding polar coordinates understanding the radial coordinate understanding the angular coordinate drawing a point from Cartesian coordinates reading off a point from polar coordinates converting from Cartesian to polar coordinates converting from polar to Cartesian coordinates## Coordinate Geometry of Points and Lines

finding the distance between points finding the slope between points finding the midpoint between points## Transformations in Coordinate Geometry

translating shapes reflecting shapes in the x-axis reflecting shapes in the y-axis reflecting shapes in the line y = x reflecting shapes in the line y = −x## Equation of a Circle

understanding the basic equation of a circle understanding the equation of a circle finding the center and radius from the equation of a circle understanding the equation of a circle in general form converting an equation of a circle from general to standard form## numbers curriculum

## Types of Numbers

understanding the types of numbers understanding natural numbers understanding whole numbers understanding integers## Positive and Negative Numbers

understanding positive numbers understanding negative numbers arithmetic with negative numbers understanding absolute value## Even and Odd Numbers

understanding even numbers understanding odd numbers arithmetic with even and odd numbers## Prime Numbers

understanding prime numbers understanding composite numbers the fundamental theorem of arithmetic## Square Numbers and Square Roots

understanding square numbers understanding square roots## The Number Line

understanding the number line adding on the number line subtracting on the number line## arithmetic curriculum

## Operations and Their Order

understanding operations understanding inverse operations understanding the order of operations## Advanced Arithmetic

understanding place value understanding long addition understanding long subtraction understanding long multiplication understanding long multiplication with decimals understanding long division understanding long division with a remainder understanding long division with decimals## Factors

understanding factors finding factors understanding the greatest common factor finding the greatest common factor## Multiples

understanding multiples understanding the least common multiple finding the least common multiple## Powers

understanding powers understanding bases understanding exponents## Laws of Exponents

understanding the laws of exponents multiplying powers dividing powers finding a power of a power finding a negative exponent## Reciprocals

understanding reciprocals understanding an exponent of −1## probability curriculum

## Probability

understanding probability finding a probability## Combined Events

understanding independent events understanding the multiplication rule understanding dependent events understanding mutually exclusive events understanding the addition rule understanding complementary events## Tree Diagrams

understanding tree diagrams drawing a tree diagram multiplication rule on a tree diagram addition rule on a tree diagram understanding dependent events on a tree diagram## statistics curriculum

## Data

understanding data understanding the types of data understanding quantitative data understanding discrete data understanding continuous data understanding qualitative data## Averages

understanding averages understanding the mean finding the mean understanding the median finding the median understanding the mode finding the mode## Measures of Spread

understanding the range finding the range understanding the quartile understanding the lower quartile understanding the upper quartile finding the quartiles understanding the interquartile range finding the interquartile range## Frequency Tables

understanding frequency tables making a frequency table finding the mean from a frequency table finding the median from a frequency table finding the mode from a frequency table finding the range from a frequency table## Cumulative Frequency Tables

understanding cumulative frequency tables making a cumulative frequency table## Grouped Frequency Tables

understanding grouped frequency tables making a grouped frequency table finding the mean from a grouped frequency table finding the median group from a grouped frequency table finding the mode group from a grouped frequency table## Cumulative Grouped Frequency Tables

understanding cumulative grouped frequency tables making a cumulative grouped frequency table## Bar Charts

understanding bar charts reading from a bar chart creating a bar chart bar charts and the types of data## notation curriculum

## Scientific Notation

understanding powers of 10 understanding scientific notation converting a number to scientific notation converting a number less than 1 to scientific notation converting scientific notation to a number converting scientific notation with a negative exponent to a number## Engineering Notation

understanding engineering notation converting a number to engineering notation converting a number less than 1 to engineering notation converting engineering notation to a number converting engineering notation with a negative exponent to a number algebra with addition algebra with division methods of rounding numbers how to rearrange an equation circumference of a circle circumference of a circle using radius basics addition basics division basics multiplication basics subtraction algebra with multiplication algebra with subtraction find the areas of plane shapes interactive solving equations tetris test-on-linear-equations test-on-quadratic-equations whack a mole odd numbers whack a mole square numbers whack a mole prime numbers bubble pop composite numbers test bubble pop even numbers test bubble pop improper fractions test bubble pop mixed fractions test bubble pop odd numbers test bubble pop prime numbers test bubble pop proper fractions test bubble pop square numbers test read from bar chart sine function right triangle tangent function right triangle types of angles types of fractions types of triangles bar chart from frequency table widget basics multiplication times tables grid widget build a pie chart widget graphs basics interactive convert fractions decimals convert polar cartesian cosine function right triangle mean from frequency table mean from grouped frequency table median from frequency table median group from grouped frequency table mode from frequency table mode group from grouped frequency table pythagoras theorem## Are You Good at Mathematical Symbols?

Do you know, or can you guess, the technical mathematical symbols? Well, let's see!**Gold**

**Silver**

**Bronze**

- This test has questions.
- A correct answer is worth 5 points.
- You can get up to 5 bonus points for a speedy answer.
- Some questions demand more than one answer. You must get every part right.
**Beware!**Wrong answers score 0 points.- 🏆 If you beat one of the top 3 scores, you will be invited to apply for the Hall of Fame.

**Scoring System**

Guru (+)

Hero (+)

Captain (+)

Sergeant (+)

Recruit (+)

## Interactive Game on Prime Numbers

Here is an example of an interactive game. This one helps you to learn about prime numbers.- You are the fish.
- Pop the bubbles with prime numbers to collect red hearts. You need five to win.
- If a bubble with a prime number reaches the top, you will lose a red heart.
- Avoid the bubbles with composite numbers (i.e., non-prime numbers). If you pop one, you will lose one of your three lives.
- Good luck!
- The fish moves towards your clicks. (Hint: The farther the distance, the faster it moves.)