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Grade 4
Term 1
Place Value
Introducing Place Value
Introduction to place value
Representing quantity using place value
Teens as sums with 10
Monkeys for a party
Place value example with 25
Place value
Place value 1
Place value 2
Place value 3
Representing numbers
Comparing place values
Understanding place value 1 exercise
Place value relationships example
Rounding whole numbers
Rounding whole numbers 1
Rounding whole numbers 2
Rounding whole numbers 3
Addition + Subtraction (3-digit)
Intro to addition and subtraction
Basic addition
Basic subtraction
Two digit addition and subtraction
Example: Adding two digit numbers (no carrying)
Subtraction 2
Example: 2-digit subtraction (no borrowing)
Level 2 addition
Addition with carrying
Carrying when adding three digit numbers
Why carrying works
Examples of regrouping when adding three digit numbers
Addition 4
Subtraction with borrowing (regrouping)
Basic regrouping when subtracting three digit numbers
Regrouping when subtracting three digit numbers
Regrouping twice when subtracting three digit numbers
Regrouping from 0 when subtracting three digit numbers
Borrowing once example 1
Borrowing once example 2
Regrouping (borrowing) twice example
Alternate mental subtraction method
Addition and subtraction word problems
Subtraction word problem
Number patterns
Figuring out days of the week
Math patterns example 1
Math patterns example 2
Relationships between patterns
Interpreting relationships between patterns
Interpreting and graphing relationships between patterns
Multiplication + Division (1-digit)
Concept of multiplication and division
Intro to multiplication
Multiplication as groups of objects
More on the concept of multiplication
The idea of division
Basic multiplication
Number line 1
Basic multiplication
Multiplication 2: The multiplication tables
Example: Ways to represent multiplication
Multiplication 3: 10,11,12 times tables
One-digit division
Division 1
Example: Expressing division in multiple ways
Starter multiplication and division word problems
Comparing with multiplication exercise
Comparing ages
Multiplication word problem example 1
Division word problem example 1
Comparing magic strength
Arithmetic properties
Commutative law of addition
Commutative property for addition
Commutative law of multiplication
Associative law of addition
Associative law of multiplication
Identity property of 1
Identity property of 1 (second example)
Identity property of 0
Inverse property of addition
Inverse property of multiplication
The distributive property
The distributive property 2
Distributive property example 1
Distributive property exercise
Time
Telling time exercise example 1
Telling time exercise example 2
Classifying shapes
Quadrilateral overview
Quadrilateral properties
Kites as a mathematical shape
Quadrilateral types exercise
Classifying shapes
Scalene, isosceles, equilateral, acute, right, and obtuse triangles
Categorizing triangles
Examples with perpendicular lines and right, obtuse, acute triangles
Language and notation of the circle
Data Handling
Reading tables 1
Reading tables 2
Reading pictographs
Reading bar graphs
Reading bar charts 1
Creating bar charts 1
Reading bar charts 2
Reading bar charts 3
Reading line graphs
Reading pie graphs (circle graphs)
Misleading line graphs
Histograms
Stem-and-leaf plots
Reading stem and leaf plots
Term 2
Place Value
Place value
Place value 1
Place value 2
Place value 3
Representing numbers
Comparing place values
Understanding place value 1 exercise
Place value relationships example
Rounding whole numbers
Rounding whole numbers 1
Rounding whole numbers 2
Rounding whole numbers 3
Addition with carrying
Carrying when adding three digit numbers
Why carrying works
Examples of regrouping when adding three digit numbers
Addition 4
Subtraction with borrowing
Basic regrouping when subtracting three digit numbers
Regrouping when subtracting three digit numbers
Regrouping twice when subtracting three digit numbers
Regrouping from 0 when subtracting three digit numbers
Borrowing once example 1
Borrowing once example 2
Regrouping (borrowing) twice example
Alternate mental subtraction method
Arithmetic properties
Commutative law of addition
Commutative property for addition
Commutative law of multiplication
Associative law of addition
Associative law of multiplication
Identity property of 1
Identity property of 1 (second example)
Identity property of 0
Inverse property of addition
Inverse property of multiplication
The distributive property
The distributive property 2
Distributive property example 1
Distributive property exercise
Common Fractions
Understanding fractions
Introduction to fractions
Identifying fraction parts
Recognizing fractions exercise
Numerator and denominator of a fraction
Plotting basic fractions on the number line
Fraction word problems 1 exercise
Visualizing equivalent fractions
Visualizing equivalent fractions
Equivalent fraction word problem example
Equivalent fraction word problem example 2
Equivalent fraction word problem example 3
Fractions cut and copy 1 exercise
Equivalent fractions and simplified form
Fractions in lowest terms
Equivalent fractions
Equivalent fractions example
Comparing fractions
Comparing fractions with greater than and less than symbols
Comparing fractions with like numerators and denominators
Adding and subtracting fractions
Adding fractions with like denominators
Subtracting fractions
What fraction of spider eyes are looking at me?
How much more piano practice?
How long is this lizard?
Multi-digit multiplication
Multiplying by multiples of 10
2 digit times 1 digit example (no carrying)
3 digit times 1 digit example (no carrying)
2 digit times 1 digit example
3 digit times 1 digit example
4 digit times 1 digit example
2-digit times a 2-digit number
Example: 2-digit times 2-digit
Multiplication estimation example
Long Division
Introduction to long division
Introduction to remainders
Long division with remainder example
More long division without and with remainders
Symmetry
Axis of symmetry
Rotating polygons 180 degrees about their center
Length
Unit conversion within the metric system
Converting within the metric system
Perimeter and unit conversion
Applying the metric system
Conversion between metric units
Term 3
Volume
How we measure volume
Measuring volume with unit cubes
Measuring volume as area times length
Volume of a rectangular prism or box examples
Volume word problem example
Common Fractions
Understanding fractions
Introduction to fractions
Identifying fraction parts
Recognizing fractions exercise
Numerator and denominator of a fraction
Plotting basic fractions on the number line
Fraction word problems 1 exercise
Visualizing equivalent fractions
Visualizing equivalent fractions
Equivalent fraction word problem example
Equivalent fraction word problem example 2
Equivalent fraction word problem example 3
Fractions cut and copy 1 exercise
Equivalent fractions and simplified form
Fractions in lowest terms
Equivalent fractions
Equivalent fractions example
Comparing fractions
Comparing fractions with greater than and less than symbols
Comparing fractions with like numerators and denominators
Adding and subtracting fractions
Adding fractions with like denominators
Subtracting fractions
What fraction of spider eyes are looking at me?
How much more piano practice?
How long is this lizard?
Addition with carrying
Carrying when adding three digit numbers
Why carrying works
Examples of regrouping when adding three digit numbers
Addition 4
Subtraction with borrowing
Basic regrouping when subtracting three digit numbers
Regrouping when subtracting three digit numbers
Regrouping twice when subtracting three digit numbers
Regrouping from 0 when subtracting three digit numbers
Borrowing once example 1
Borrowing once example 2
Regrouping (borrowing) twice example
Alternate mental subtraction method
Properties of 2D Shapes
Perimeter
Introduction to perimeter
Perimeter of a shape
Comparing areas and perimeters of rectangles
Area
Introduction to area and unit squares
Measuring the same rectangle with different unit squares
Rectangle area as product of dimensions same as counting unit squares
Area of rectangles and the distributive property
Comparing areas of plots of land
Table dimensions from perimeter and area
Finding width from perimeter and length
Comparing poster area
Data Handling
Reading tables 1
Reading tables 2
Reading pictographs
Reading bar graphs
Reading bar charts 1
Creating bar charts 1
Reading bar charts 2
Reading bar charts 3
Reading line graphs
Reading pie graphs (circle graphs)
Misleading line graphs
Histograms
Stem-and-leaf plots
Reading stem and leaf plots
Multi-digit multiplication
Multiplying by multiples of 10
2 digit times 1 digit example (no carrying)
3 digit times 1 digit example (no carrying)
2 digit times 1 digit example
3 digit times 1 digit example
4 digit times 1 digit example
2-digit times a 2-digit number
Example: 2-digit times 2-digit
Multiplication estimation example
Term 4
Addition with carrying
Carrying when adding three digit numbers
Why carrying works
Examples of regrouping when adding three digit numbers
Addition 4
Subtraction with borrowing
Basic regrouping when subtracting three digit numbers
Regrouping when subtracting three digit numbers
Regrouping twice when subtracting three digit numbers
Regrouping from 0 when subtracting three digit numbers
Borrowing once example 1
Borrowing once example 2
Regrouping (borrowing) twice example
Alternate mental subtraction method
Common Fractions
Understanding fractions
Introduction to fractions
Identifying fraction parts
Recognizing fractions exercise
Numerator and denominator of a fraction
Plotting basic fractions on the number line
Fraction word problems 1 exercise
Visualizing equivalent fractions
Visualizing equivalent fractions
Equivalent fraction word problem example
Equivalent fraction word problem example 2
Equivalent fraction word problem example 3
Fractions cut and copy 1 exercise
Equivalent fractions and simplified form
Fractions in lowest terms
Equivalent fractions
Equivalent fractions example
Comparing fractions
Comparing fractions with greater than and less than symbols
Comparing fractions with like numerators and denominators
Adding and subtracting fractions
Adding fractions with like denominators
Subtracting fractions
What fraction of spider eyes are looking at me?
How much more piano practice?
How long is this lizard?
Long Division
Introduction to long division
Introduction to remainders
Long division with remainder example
More long division without and with remainders
Measurement
Perimeter
Introduction to perimeter
Perimeter of a shape
Comparing areas and perimeters of rectangles
Area
Introduction to area and unit squares
Measuring the same rectangle with different unit squares
Rectangle area as product of dimensions same as counting unit squares
Area of rectangles and the distributive property
Comparing areas of plots of land
Table dimensions from perimeter and area
Finding width from perimeter and length
Comparing poster area
Volume
How we measure volume
Measuring volume with unit cubes
Measuring volume as area times length
Volume of a rectangular prism or box examples
Volume word problem example
Probability
Basic probability
Probability space exercise example
Example: Marbles from a bag
Example: Picking a non-blue marble
Example: Picking a yellow marble
Grade 5
Term 1
Place Value
Introducing Place Value
Introduction to place value
Representing quantity using place value
Teens as sums with 10
Monkeys for a party
Place value example with 25
Place value
Place value 1
Place value 2
Place value 3
Representing numbers
Comparing place values
Understanding place value 1 exercise
Place value relationships example
Rounding whole numbers
Rounding whole numbers 1
Rounding whole numbers 2
Rounding whole numbers 3
Addition and subtraction
Intro to addition and subtraction
Basic addition
Basic subtraction
Two digit addition and subtraction
Example: Adding two digit numbers (no carrying)
Subtraction 2
Example: 2-digit subtraction (no borrowing)
Level 2 addition
Addition with carrying
Carrying when adding three digit numbers
Why carrying works
Examples of regrouping when adding three digit numbers
Addition 4
Subtraction with borrowing (regrouping)
Basic regrouping when subtracting three digit numbers
Regrouping when subtracting three digit numbers
Regrouping twice when subtracting three digit numbers
Regrouping from 0 when subtracting three digit numbers
Borrowing once example 1
Borrowing once example 2
Regrouping (borrowing) twice example
Alternate mental subtraction method
Addition and subtraction word problems
Subtraction word problem
Multiplication and division
Concept of multiplication and division
Intro to multiplication
Multiplication as groups of objects
More on the concept of multiplication
The idea of division
Basic multiplication
Number line 1
Basic multiplication
Multiplication 2: The multiplication tables
Example: Ways to represent multiplication
Multiplication 3: 10,11,12 times tables
One-digit division
Division 1
Example: Expressing division in multiple ways
Starter multiplication and division word problems
Comparing with multiplication exercise
Comparing ages
Multiplication word problem example 1
Division word problem example 1
Comparing magic strength
Multi-digit multiplication
Multiplying by multiples of 10
2 digit times 1 digit example (no carrying)
3 digit times 1 digit example (no carrying)
2 digit times 1 digit example
3 digit times 1 digit example
4 digit times 1 digit example
2-digit times a 2-digit number
Example: 2-digit times 2-digit
Multiple digit numbers
Multiplication estimation example
Multiplication 7: Old video giving more examples
Area models and multiplication
Understanding multiplication through area models
Area model for multiplication
Arithmetic properties
Commutative law of addition
Commutative property for addition
Commutative law of multiplication
Associative law of addition
Associative law of multiplication
Identity property of 1
Identity property of 1 (second example)
Identity property of 0
Inverse property of addition
Inverse property of multiplication
The distributive property
The distributive property 2
Distributive property example 1
Distributive property exercise
Telling time
Telling time exercise example 1
Telling time exercise example 2
Data Handling
Reading tables 1
Reading tables 2
Reading pictographs
Reading bar graphs
Reading bar charts 1
Creating bar charts 1
Reading bar charts 2
Reading bar charts 3
Reading line graphs
Reading pie graphs (circle graphs)
Misleading line graphs
Histograms
Stem-and-leaf plots
Reading stem and leaf plots
Properies of 2D Shapes
Classifying shapes
Quadrilateral overview
Quadrilateral properties
Kites as a mathematical shape
Quadrilateral types exercise
Classifying shapes
Scalene, isosceles, equilateral, acute, right, and obtuse triangles
Categorizing triangles
Examples with perpendicular lines and right, obtuse, acute triangles
Language and notation of the circle
Angle basics and measurement
Angle basics
Measuring angles in degrees
Using a protractor
Measuring angles
Acute right and obtuse angles
Volume
How we measure volume
Measuring volume with unit cubes
Measuring volume as area times length
Volume of a rectangular prism or box examples
Volume word problem example
Term 2
Place Value
Place value
Place value 1
Place value 2
Place value 3
Representing numbers
Comparing place values
Understanding place value 1 exercise
Place value relationships example
Rounding whole numbers
Rounding whole numbers 1
Rounding whole numbers 2
Rounding whole numbers 3
Addition with carrying
Carrying when adding three digit numbers
Why carrying works
Examples of regrouping when adding three digit numbers
Addition 4
Subtraction with borrowing
Basic regrouping when subtracting three digit numbers
Regrouping when subtracting three digit numbers
Regrouping twice when subtracting three digit numbers
Regrouping from 0 when subtracting three digit numbers
Borrowing once example 1
Borrowing once example 2
Regrouping (borrowing) twice example
Alternate mental subtraction method
Common Fractions
Understanding fractions
Introduction to fractions
Identifying fraction parts
Recognizing fractions exercise
Numerator and denominator of a fraction
Plotting basic fractions on the number line
Fraction word problems 1 exercise
Visualizing equivalent fractions
Visualizing equivalent fractions
Equivalent fraction word problem example
Equivalent fraction word problem example 2
Equivalent fraction word problem example 3
Fractions cut and copy 1 exercise
Equivalent fractions and simplified form
Fractions in lowest terms
Equivalent fractions
Equivalent fractions example
Comparing fractions
Comparing fractions with greater than and less than symbols
Comparing fractions with like numerators and denominators
Adding and subtracting fractions
Adding fractions with like denominators
Subtracting fractions
What fraction of spider eyes are looking at me?
How much more piano practice?
How long is this lizard?
Mixed numbers and improper fractions
Comparing improper fractions and mixed numbers
Mixed numbers and improper fractions
Proper and improper fractions
Converting mixed numbers to improper fractions
Changing a mixed number to an improper fraction
Changing an improper fraction to a mixed number
Positive improper fractions on the number line
Fractions cut and copy 2 exercise example
Points on a number line
Mixed number addition and subtraction
Adding mixed numbers
Adding mixed numbers with unlike denominators
Adding mixed numbers word problem
Subtracting mixed numbers
Subtracting mixed numbers 2
Subtracting mixed numbers word problem
Adding mixed numbers with like denominators
Subtracting mixed numbers with like denominators
Adding and subtracting mixed numbers 1 (ex 1)
Adding and subtracting mixed numbers 1 (ex 2)
Length
Unit conversion within the metric system
Converting within the metric system
Perimeter and unit conversion
Applying the metric system
Conversion between metric units
Multi-digit multiplication
Multiplying by multiples of 10
2 digit times 1 digit example (no carrying)
3 digit times 1 digit example (no carrying)
2 digit times 1 digit example
3 digit times 1 digit example
4 digit times 1 digit example
2-digit times a 2-digit number
Example: 2-digit times 2-digit
Multiple digit numbers
Multiplication estimation example
Multiplication 7: Old video giving more examples
Understanding multiplication through area models
Area model for multiplication
Long Division
Introduction to long division
Introduction to remainders
Long division with remainder example
More long division without and with remainders
Arithmetic properties
Commutative law of addition
Commutative property for addition
Commutative law of multiplication
Associative law of addition
Associative law of multiplication
Identity property of 1
Identity property of 1 (second example)
Identity property of 0
Inverse property of addition
Inverse property of multiplication
The distributive property
The distributive property 2
Distributive property example 1
Distributive property exercise
Term 3
Common Fractions
Adding and subtracting fractions
Adding fractions with like denominators
Subtracting fractions
What fraction of spider eyes are looking at me?
How much more piano practice?
How long is this lizard?
Mixed numbers and improper fractions
Comparing improper fractions and mixed numbers
Mixed numbers and improper fractions
Proper and improper fractions
Converting mixed numbers to improper fractions
Changing a mixed number to an improper fraction
Changing an improper fraction to a mixed number
Positive improper fractions on the number line
Fractions cut and copy 2 exercise example
Points on a number line
Mixed number addition and subtraction
Adding mixed numbers
Adding mixed numbers with unlike denominators
Adding mixed numbers word problem
Subtracting mixed numbers
Subtracting mixed numbers 2
Subtracting mixed numbers word problem
Adding mixed numbers with like denominators
Subtracting mixed numbers with like denominators
Adding and subtracting mixed numbers 1 (ex 1)
Adding and subtracting mixed numbers 1 (ex 2)
Addition with carrying
Carrying when adding three digit numbers
Why carrying works
Examples of regrouping when adding three digit numbers
Addition 4
Subtraction with borrowing
Basic regrouping when subtracting three digit numbers
Regrouping when subtracting three digit numbers
Regrouping twice when subtracting three digit numbers
Regrouping from 0 when subtracting three digit numbers
Borrowing once example 1
Borrowing once example 2
Regrouping (borrowing) twice example
Alternate mental subtraction method
Properties of 2D Shapes
Classifying shapes
Quadrilateral overview
Quadrilateral properties
Kites as a mathematical shape
Quadrilateral types exercise
Classifying shapes
Scalene, isosceles, equilateral, acute, right, and obtuse triangles
Categorizing triangles
Examples with perpendicular lines and right, obtuse, acute triangles
Language and notation of the circle
Angle basics and measurement
Angle basics
Measuring angles in degrees
Using a protractor
Measuring angles
Acute right and obtuse angles
Symmetry
Axis of symmetry
Rotating polygons 180 degrees about their center
Transformations
Rotating segment about orgin example
Reflecting line across another line example
Translations of polygons
Determining a translation for a shape
Rotation of polygons example
Data Handling
Reading tables 1
Reading tables 2
Reading pictographs
Reading bar graphs
Reading bar charts 1
Creating bar charts 1
Reading bar charts 2
Reading bar charts 3
Reading line graphs
Reading pie graphs (circle graphs)
Misleading line graphs
Histograms
Stem-and-leaf plots
Reading stem and leaf plots
Multi-digit multiplication
Multiplying by multiples of 10
2 digit times 1 digit example (no carrying)
3 digit times 1 digit example (no carrying)
2 digit times 1 digit example
3 digit times 1 digit example
4 digit times 1 digit example
2-digit times a 2-digit number
Example: 2-digit times 2-digit
Multiple digit numbers
Multiplication estimation example
Multiplication 7: Old video giving more examples
Understanding multiplication through area models
Area model for multiplication
Term 4
Addition with carrying
Carrying when adding three digit numbers
Why carrying works
Examples of regrouping when adding three digit numbers
Addition 4
Subtraction with borrowing
Basic regrouping when subtracting three digit numbers
Regrouping when subtracting three digit numbers
Regrouping twice when subtracting three digit numbers
Regrouping from 0 when subtracting three digit numbers
Borrowing once example 1
Borrowing once example 2
Regrouping (borrowing) twice example
Alternate mental subtraction method
Common Fractions
Understanding fractions
Introduction to fractions
Identifying fraction parts
Recognizing fractions exercise
Numerator and denominator of a fraction
Plotting basic fractions on the number line
Fraction word problems 1 exercise
Visualizing equivalent fractions
Visualizing equivalent fractions
Equivalent fraction word problem example
Equivalent fraction word problem example 2
Equivalent fraction word problem example 3
Fractions cut and copy 1 exercise
Equivalent fractions and simplified form
Fractions in lowest terms
Equivalent fractions
Equivalent fractions example
Comparing fractions
Comparing fractions with greater than and less than symbols
Comparing fractions with like numerators and denominators
Adding and subtracting fractions
Adding fractions with like denominators
Subtracting fractions
What fraction of spider eyes are looking at me?
How much more piano practice?
How long is this lizard?
Mixed numbers and improper fractions
Comparing improper fractions and mixed numbers
Mixed numbers and improper fractions
Proper and improper fractions
Converting mixed numbers to improper fractions
Changing a mixed number to an improper fraction
Changing an improper fraction to a mixed number
Positive improper fractions on the number line
Fractions cut and copy 2 exercise example
Points on a number line
Mixed number addition and subtraction
Adding mixed numbers
Adding mixed numbers with unlike denominators
Adding mixed numbers word problem
Subtracting mixed numbers
Subtracting mixed numbers 2
Subtracting mixed numbers word problem
Adding mixed numbers with like denominators
Subtracting mixed numbers with like denominators
Adding and subtracting mixed numbers 1 (ex 1)
Adding and subtracting mixed numbers 1 (ex 2)
Loooong division!
Introduction to long division
Introduction to remainders
Long division with remainder example
More long division without and with remainders
Area, perimeter, volume
Area
Introduction to area and unit squares
Measuring the same rectangle with different unit squares
Rectangle area as product of dimensions same as counting unit squares
Area of rectangles and the distributive property
Comparing areas of plots of land
Table dimensions from perimeter and area
Finding width from perimeter and length
Comparing poster area
Perimeter
Introduction to perimeter
Perimeter of a shape
Comparing areas and perimeters of rectangles
Volume
How we measure volume
Measuring volume with unit cubes
Measuring volume as area times length
Volume of a rectangular prism or box examples
Volume word problem example
Transformations
Rotating segment about orgin example
Reflecting line across another line example
Translations of polygons
Determining a translation for a shape
Rotation of polygons example
Probability
Basic probability
Probability space exercise example
Example: Marbles from a bag
Example: Picking a non-blue marble
Example: Picking a yellow marble
Grade 6
Term 1
Place Value
Place value
Place value 1
Place value 2
Place value 3
Representing numbers
Comparing place values
Understanding place value 1 exercise
Place value relationships example
Rounding whole numbers
Rounding whole numbers 1
Rounding whole numbers 2
Rounding whole numbers 3
Addition with carrying
Carrying when adding three digit numbers
Why carrying works
Examples of regrouping when adding three digit numbers
Addition 4
Subtraction with borrowing
Basic regrouping when subtracting three digit numbers
Regrouping when subtracting three digit numbers
Regrouping twice when subtracting three digit numbers
Regrouping from 0 when subtracting three digit numbers
Borrowing once example 1
Borrowing once example 2
Regrouping (borrowing) twice example
Alternate mental subtraction method
Arithmetic properties
Commutative law of addition
Commutative property for addition
Commutative law of multiplication
Associative law of addition
Associative law of multiplication
Identity property of 1
Identity property of 1 (second example)
Identity property of 0
Inverse property of addition
Inverse property of multiplication
The distributive property
The distributive property 2
Distributive property example 1
Distributive property exercise
Order of operations
Introduction to order of operations
Order of operations
Order of operations with exponents
More complicated order of operations example
Common Fractions
Understanding fractions
Introduction to fractions
Identifying fraction parts
Recognizing fractions exercise
Numerator and denominator of a fraction
Plotting basic fractions on the number line
Fraction word problems 1 exercise
Visualizing equivalent fractions
Visualizing equivalent fractions
Equivalent fraction word problem example
Equivalent fraction word problem example 2
Equivalent fraction word problem example 3
Fractions cut and copy 1 exercise
Equivalent fractions and simplified form
Fractions in lowest terms
Equivalent fractions
Equivalent fractions example
Comparing fractions
Comparing fractions with greater than and less than symbols
Comparing fractions with like numerators and denominators
Adding and subtracting fractions
Adding fractions with like denominators
Subtracting fractions
What fraction of spider eyes are looking at me?
How much more piano practice?
How long is this lizard?
Adding and subtracting fractions with unlike denominators
Adding fractions with 10 and 100 as denominators
Adding and subtracting fractions
Adding fractions with unlike denominators
Adding fractions (ex 1)
Subtracting fractions with unlike denominators
Adding fractions with different signs
Adding fractions with unlike denominators word problem
Subtracting fractions with unlike denominators word problem
Mixed numbers and improper fractions
Comparing improper fractions and mixed numbers
Mixed numbers and improper fractions
Proper and improper fractions
Converting mixed numbers to improper fractions
Changing a mixed number to an improper fraction
Changing an improper fraction to a mixed number
Positive improper fractions on the number line
Fractions cut and copy 2 exercise example
Points on a number line
Mixed number addition and subtraction
Adding mixed numbers
Adding mixed numbers with unlike denominators
Adding mixed numbers word problem
Subtracting mixed numbers
Subtracting mixed numbers 2
Subtracting mixed numbers word problem
Adding mixed numbers with like denominators
Subtracting mixed numbers with like denominators
Adding and subtracting mixed numbers 1 (ex 1)
Adding and subtracting mixed numbers 1 (ex 2)
Time
Telling time exercise example 1
Telling time exercise example 2
Properties of 2D Shapes
Classifying shapes
Quadrilateral overview
Quadrilateral properties
Kites as a mathematical shape
Quadrilateral types exercise
Classifying shapes
Scalene, isosceles, equilateral, acute, right, and obtuse triangles
Categorizing triangles
Examples with perpendicular lines and right, obtuse, acute triangles
Language and notation of the circle
Angle basics and measurement
Angle basics
Measuring angles in degrees
Using a protractor
Measuring angles
Acute right and obtuse angles
Symmetry
Axis of symmetry
Rotating polygons 180 degrees about their center
Transformations
Rotating segment about orgin example
Reflecting line across another line example
Translations of polygons
Determining a translation for a shape
Rotation of polygons example
Data Handling
Analysing, interpreting and reporting data
Reading tables 1
Reading tables 2
Reading pictographs
Reading bar graphs
Reading bar charts 1
Creating bar charts 1
Reading bar charts 2
Reading bar charts 3
Reading line graphs
Reading pie graphs (circle graphs)
Misleading line graphs
Histograms
Stem-and-leaf plots
Reading stem and leaf plots
Measures of central tendency
Statistics intro: Mean, median and mode
Example: Finding mean, median and mode
Exploring mean and median module
Sample mean versus population mean
Term 2
Place Value
Place value
Place value 1
Place value 2
Place value 3
Representing numbers
Comparing place values
Understanding place value 1 exercise
Place value relationships example
Rounding whole numbers
Rounding whole numbers 1
Rounding whole numbers 2
Rounding whole numbers 3
Multiplication
Multiplying by multiples of 10
2 digit times 1 digit example (no carrying)
3 digit times 1 digit example (no carrying)
2 digit times 1 digit example
3 digit times 1 digit example
4 digit times 1 digit example
2-digit times a 2-digit number
Example: 2-digit times 2-digit
Multiple digit numbers
Multiplication estimation example
Understanding multiplication through area models
Area model for multiplication
Division
Introduction to long division
Introduction to remainders
Long division with remainder example
More long division without and with remainders
Dividing by a two digit number
Level 4 division
Arithmetic properties
Commutative law of addition
Commutative property for addition
Commutative law of multiplication
Associative law of addition
Associative law of multiplication
Identity property of 1
Identity property of 1 (second example)
Identity property of 0
Inverse property of addition
Inverse property of multiplication
The distributive property
The distributive property 2
Distributive property example 1
Distributive property exercise
Factors and multiples
Divisibility tests
Divisibility tests for 2, 3, 4, 5, 6, 9, 10
Recognizing divisibility
The why of the 3 divisibility rule
The why of the 9 divisibility rule
Divisibility and factors
Finding factors of a number
Finding factors and multiples
Divisibility intuition
Prime numbers
Prime numbers
Recognizing prime numbers
Prime factorization
Prime factorization
Prime factorization exercise
The fundamental theorem of arithmetic
Common divisibility examples
Order of operations
Introduction to order of operations
Order of operations
Order of operations with exponents
More complicated order of operations example
Decimal Fractions
Conceptualizing decimals and place notation
Decimal place value
Writing out a decimal in words
Writing out a decimal in words 2
Expanding out a decimal by place value
Writing a decimal to represent a quantity
Comparing place values in decimals
Using money to understand decimal place value
Decimals on a number line
Decimals on a number line
Points on a number line
Positive and negative decimals on a number line
Comparing decimals
Comparing decimals example 1
Comparing decimals example 2
Comparing decimals example 3
Comparing decimals example 4
Ordering decimals example
Another ordering decimals example
Adding and subtracting decimals
Adding decimals example 1
Adding decimals example 2
Adding decimals example 3
Subtracting decimals up to hundredths
Subtracting decimals
Adding decimals word problem
Subtracting decimals word problem
Subtracting decimals (old)
Moving the decimal to multiply and divide by 10
Multiplying a decimal by a power of 10
Dividing a decimal by a power of 10
Dividing a decimal by a power of 10 (part 2)
Decimals and fractions
Decimals and fractions
Converting fractions to decimals example
Converting fractions to decimals (ex1)
Converting fractions to decimals (ex2)
Converting fractions to decimals
Representing a number as a decimal, percent, and fraction 2
Representing a number as a decimal, percent, and fraction
Converting decimals to fractions 1 (ex 1)
Converting decimals to fractions 1 (ex 2)
Converting decimals to fractions 1 (ex 3)
Converting decimals to fractions 2 (ex 1)
Converting decimals to fractions 2 (ex 2)
Ordering numeric expressions
Converting a fraction to a repeating decimal
Representing a number as a decimal, percent, and fraction 2
Representing a number as a decimal, percent, and fraction 2
Intro to percentages
Describing the meaning of percent
Describing the meaning of percent 2
Representing a number as a decimal, percent, and fraction
Converting decimals to percents (ex 1)
Converting decimals to percents (ex 2)
Converting percents to decimals (ex 1)
Converting percents to decimals (ex 2)
Finding percentages example
Percent word problems
Taking a percentage example
Identifying percent amount and base
Representing a number as a decimal, percent, and fraction 2
Ordering numeric expressions
Taking a percentage example
Rewriting fraction as a decimal to the hundredths place
Rewriting a fraction as a decimal
Representing a number as a decimal, percent, and fraction 2
Volume
How we measure volume
Measuring volume with unit cubes
Measuring volume as area times length
Volume of a rectangular prism or box examples
Volume word problem example
Term 3
Addition with carrying
Carrying when adding three digit numbers
Why carrying works
Examples of regrouping when adding three digit numbers
Addition 4
Subtraction with borrowing
Basic regrouping when subtracting three digit numbers
Regrouping when subtracting three digit numbers
Regrouping twice when subtracting three digit numbers
Regrouping from 0 when subtracting three digit numbers
Borrowing once example 1
Borrowing once example 2
Regrouping (borrowing) twice example
Alternate mental subtraction method
Properties of 2D Shapes
Symmetry
Axis of symmetry
Rotating polygons 180 degrees about their center
Transformations
Rotating segment about orgin example
Reflecting line across another line example
Translations of polygons
Determining a translation for a shape
Rotation of polygons example
Percentages
Describing the meaning of percent
Describing the meaning of percent 2
Representing a number as a decimal, percent, and fraction
Converting decimals to percents (ex 1)
Converting decimals to percents (ex 2)
Converting percents to decimals (ex 1)
Converting percents to decimals (ex 2)
Finding percentages example
Percent word problems
Taking a percentage example
Identifying percent amount and base
Representing a number as a decimal, percent, and fraction 2
Ordering numeric expressions
Taking a percentage example
Rewriting fraction as a decimal to the hundredths place
Rewriting a fraction as a decimal
Representing a number as a decimal, percent, and fraction 2
Data Handling
Analysing, interpreting and reporting data
Reading tables 1
Reading tables 2
Reading pictographs
Reading bar graphs
Reading bar charts 1
Creating bar charts 1
Reading bar charts 2
Reading bar charts 3
Reading line graphs
Reading pie graphs (circle graphs)
Misleading line graphs
Histograms
Stem-and-leaf plots
Reading stem and leaf plots
Measures of central tendency
Statistics intro: Mean, median and mode
Example: Finding mean, median and mode
Exploring mean and median module
Sample mean versus population mean
Length
Unit conversion within the metric system
Converting within the metric system
Perimeter and unit conversion
Applying the metric system
Conversion between metric units
Term 4
Multi-digit multiplication
Multiplying by multiples of 10
2 digit times 1 digit example (no carrying)
3 digit times 1 digit example (no carrying)
2 digit times 1 digit example
3 digit times 1 digit example
4 digit times 1 digit example
2-digit times a 2-digit number
Example: 2-digit times 2-digit
Multiple digit numbers
Multiplication estimation example
Multiplication 7: Old video giving more examples
Common Fractions
Understanding fractions
Introduction to fractions
Identifying fraction parts
Recognizing fractions exercise
Numerator and denominator of a fraction
Plotting basic fractions on the number line
Fraction word problems 1 exercise
Visualizing equivalent fractions
Visualizing equivalent fractions
Equivalent fraction word problem example
Equivalent fraction word problem example 2
Equivalent fraction word problem example 3
Fractions cut and copy 1 exercise
Equivalent fractions and simplified form
Fractions in lowest terms
Equivalent fractions
Equivalent fractions example
Comparing fractions
Comparing fractions with greater than and less than symbols
Comparing fractions with like numerators and denominators
Adding and subtracting fractions
Adding fractions with like denominators
Subtracting fractions
What fraction of spider eyes are looking at me?
How much more piano practice?
How long is this lizard?
Adding and subtracting fractions with unlike denominators
Adding fractions with 10 and 100 as denominators
Adding and subtracting fractions
Adding fractions with unlike denominators
Adding fractions (ex 1)
Subtracting fractions with unlike denominators
Adding fractions with different signs
Adding fractions with unlike denominators word problem
Subtracting fractions with unlike denominators word problem
Mixed numbers and improper fractions
Comparing improper fractions and mixed numbers
Mixed numbers and improper fractions
Proper and improper fractions
Converting mixed numbers to improper fractions
Changing a mixed number to an improper fraction
Changing an improper fraction to a mixed number
Positive improper fractions on the number line
Fractions cut and copy 2 exercise example
Points on a number line
Mixed number addition and subtraction
Adding mixed numbers
Adding mixed numbers with unlike denominators
Adding mixed numbers word problem
Subtracting mixed numbers
Subtracting mixed numbers 2
Subtracting mixed numbers word problem
Adding mixed numbers with like denominators
Subtracting mixed numbers with like denominators
Adding and subtracting mixed numbers 1 (ex 1)
Adding and subtracting mixed numbers 1 (ex 2)
Area, Perimeter, Volume
Area
Introduction to area and unit squares
Measuring the same rectangle with different unit squares
Rectangle area as product of dimensions same as counting unit squares
Area of rectangles and the distributive property
Comparing areas of plots of land
Table dimensions from perimeter and area
Finding width from perimeter and length
Comparing poster area
Perimeter
Introduction to perimeter
Perimeter of a shape
Comparing areas and perimeters of rectangles
Volume
How we measure volume
Measuring volume with unit cubes
Measuring volume as area times length
Volume of a rectangular prism or box examples
Volume word problem example
Long Division
Introduction to long division
Introduction to remainders
Long division with remainder example
More long division without and with remainders
Dividing by a two digit number
Level 4 division
Factors and multiples
Divisibility tests
Divisibility tests for 2, 3, 4, 5, 6, 9, 10
Recognizing divisibility
The why of the 3 divisibility rule
The why of the 9 divisibility rule
Divisibility and factors
Finding factors of a number
Finding factors and multiples
Divisibility intuition
Prime numbers
Prime numbers
Recognizing prime numbers
Prime factorization
Prime factorization
Prime factorization exercise
The fundamental theorem of arithmetic
Common divisibility examples
Probability
Basic probability
Probability space exercise example
Example: Marbles from a bag
Example: Picking a non-blue marble
Example: Picking a yellow marble
Grade 7
Term 1
Whole Numbers
Properties of Numbers
Commutative law of addition
Commutative property for addition
Commutative law of multiplication
Associative law of addition
Associative law of multiplication
Properties of numbers 1
Number properties terminology 1
Identity property of 1
Identity property of 1 (second example)
Identity property of 0
Inverse property of addition
Inverse property of multiplication
Properties of numbers 2
The distributive property
The distributive property 2
Distributive property example 1
Distributive property exercise
Calculations using whole numbers
Addition with carrying
Carrying when adding three digit numbers
Why carrying works
Examples of regrouping when adding three digit numbers
Addition 4
Subtraction with borrowing
Basic regrouping when subtracting three digit numbers
Regrouping when subtracting three digit numbers
Regrouping twice when subtracting three digit numbers
Regrouping from 0 when subtracting three digit numbers
Borrowing once example 1
Borrowing once example 2
Regrouping (borrowing) twice example
Alternate mental subtraction method
Multi-digit multiplication
Multiplying by multiples of 10
2 digit times 1 digit example (no carrying)
3 digit times 1 digit example (no carrying)
2 digit times 1 digit example
3 digit times 1 digit example
4 digit times 1 digit example
2-digit times a 2-digit number
Example: 2-digit times 2-digit
Multiple digit numbers
Multiplication estimation example
Multiplication 7: Old video giving more examples
Loooong division!
Introduction to long division
Introduction to remainders
Long division with remainder example
More long division without and with remainders
Dividing by a two digit number
Level 4 division
Calculation Techniques
Rounding whole numbers
Rounding whole numbers 1
Rounding whole numbers 2
Rounding whole numbers 3
Multiples and Factors
Divisibility tests
Divisibility tests for 2, 3, 4, 5, 6, 9, 10
Recognizing divisibility
The why of the 3 divisibility rule
The why of the 9 divisibility rule
Divisibility and factors
Finding factors of a number
Finding factors and multiples
Divisibility intuition
Prime numbers
Prime numbers
Recognizing prime numbers
Prime factorization
Prime factorization
Prime factorization exercise
The fundamental theorem of arithmetic
Common divisibility examples
Least common multiple
Least common multiple exercise
Least common multiple exercise 2
Least common multiple (LCM)
Old least common multiple
Greatest common divisor
Greatest common divisor factor exercise
Greatest common divisor
LCM and GCF (greatest common factor) word problems
Solving problems
Ratios and proportions
Introduction to ratios
Ratios as fractions in simplest form
Simplifying rates and ratios
Ratio word problem exercise example 1
Ratio word problem exercise example 2
Proportion validity example
Solving ratio problems with tables exercise
Solving ratio problems with tables exercise 2
Solving ratio problems with tables exercise 3
Rates
Usain Bolt's average speed
Finding unit rates
Finding unit prices
Multiple rates word problem
Simple Interest
Introduction to interest
Interest (part 2)
Compound interest basics
Introduction to compound interest
The rule of 72 for compound interest
Exponents
Basic Exponents
Introduction to exponents
Exponent example 1
Exponent example 2
Raising a number to the 0th and 1st power
Powers of 1 and -1
Powers of fractions
Powers of zero
The square root
Understanding square roots
Approximating square roots
Simplifying square roots
Simplifying radicals
Square roots and real numbers
Adding and simplifying radicals
The cube root
Finding cube roots
Cube root of a non-perfect cube
Simplifying a cube root
Construction of Geometric Figures
No Videos Available
Geometry of 2D Shapes
Scalene, isosceles, equilateral, acute, right, and obtuse triangles
Categorizing triangles
Quadrilateral overview
Quadrilateral properties
Kites as a mathematical shape
Quadrilateral types exercise
Examples with perpendicular lines and right, obtuse, acute triangles
Language and notation of the circle
Circles: Radius, diameter, and circumference
Testing congruence by transformations example
Another congruence by transformation example
Example of rigid transformation and congruence
Another example of rigid transformations for congruence
Testing similarity through transformations
Quadrilateral similarity by showing congruent angles
Geometry of Straight Lines
Language and notation of basic geometry
Lines, line segments, and rays
Drawing lines exercise example
Identifying rays
Identifying parallel and perpendicular lines
Euclid as the father of geometry
Term 2
Common Fractions
Basic fractions review
Understanding fractions
Introduction to fractions
Identifying fraction parts
Recognizing fractions exercise
Numerator and denominator of a fraction
Plotting basic fractions on the number line
Fraction word problems 1 exercise
Visualizing equivalent fractions
Visualizing equivalent fractions
Equivalent fraction word problem example
Equivalent fraction word problem example 2
Equivalent fraction word problem example 3
Fractions cut and copy 1 exercise
Comparing fractions
Comparing fractions with greater than and less than symbols
Comparing fractions with like numerators and denominators
Comparing fractions
Comparing fractions 2
Ordering fractions
Equivalent fractions and simplified form
Fractions in lowest terms
Equivalent fractions
Equivalent fractions example
Finding common denominators
Adding and subtracting fractions
Adding fractions with like denominators
Subtracting fractions
Adding fractions with 10 and 100 as denominators
Adding and subtracting fractions
Adding fractions with unlike denominators
Adding fractions (ex 1)
Subtracting fractions with unlike denominators
Adding fractions with different signs
Multiplying fractions
Multiplying fractions and whole numbers
Multiplying a fraction by a fraction
Multiplying fractions
Multiplying negative and positive fractions
Multiplication as scaling
Mixed numbers and improper fractions
Comparing improper fractions and mixed numbers
Mixed numbers and improper fractions
Proper and improper fractions
Converting mixed numbers to improper fractions
Changing a mixed number to an improper fraction
Changing an improper fraction to a mixed number
Positive improper fractions on the number line
Fractions cut and copy 2 exercise example
Points on a number line
Percentages
Describing the meaning of percent
Describing the meaning of percent 2
Representing a number as a decimal, percent, and fraction
Converting decimals to percents (ex 1)
Converting decimals to percents (ex 2)
Converting percents to decimals (ex 1)
Converting percents to decimals (ex 2)
Finding percentages example
Percent word problems
Taking a percentage example
Identifying percent amount and base
Representing a number as a decimal, percent, and fraction 2
Ordering numeric expressions
Taking a percentage example
Rewriting fraction as a decimal to the hundredths place
Rewriting a fraction as a decimal
Representing a number as a decimal, percent, and fraction 2
Decimal Fractions
Decimals on a number line
Decimals on a number line
Points on a number line
Positive and negative decimals on a number line
Comparing decimals
Comparing decimals example 1
Comparing decimals example 2
Comparing decimals example 3
Comparing decimals example 4
Ordering decimals example
Another ordering decimals example
Estimating and rounding with decimals
Rounding decimals
Estimation with decimals
Adding and subtracting decimals
Adding decimals example 1
Adding decimals example 2
Adding decimals example 3
Subtracting decimals up to hundredths
Subtracting decimals
Adding decimals word problem
Subtracting decimals word problem
Subtracting decimals (old)
Multiplying decimals
Intro to multiplying decimals
Cost of filling tank
More intuition on multiplying decimals
Multiplying decimals
More involved multiplying decimals example
Dividing decimals
Dividing completely to get decimal answer
Dividing completely to get decimal answer example 2
Dividing a decimal by a whole number
Dividing a whole number by a decimal
Dividing decimals
Dividing decimal
Converting between fractions and decimals
Converting fractions to decimals (ex1)
Converting fractions to decimals (ex2)
Converting fractions to decimals
Converting fractions to decimals example
Decimals and fractions
Converting decimals to fractions 1 (ex 1)
Converting decimals to fractions 1 (ex 2)
Converting decimals to fractions 1 (ex 3)
Converting decimals to fractions 2 (ex 1)
Converting decimals to fractions 2 (ex 2)
Functions and relationships
No videos available
Area and perimeter of 2D shapes
Area basics
Introduction to area and unit squares
Measuring the same rectangle with different unit squares
Rectangle area as product of dimensions same as counting unit squares
Area of rectangles and the distributive property
Comparing areas of plots of land
Calculating the square footage of a house
Perimeter
Introduction to perimeter
Perimeter of a shape
Comparing areas and perimeters of rectangles
Surface area and volume of 3D objects
Volume
How we measure volume
Measuring volume with unit cubes
Measuring volume as area times length
Volume of a rectangular prism or box examples
Volume word problem example
Unit Conversion
Unit conversion within the metric system
Converting within the metric system
Perimeter and unit conversion
Applying the metric system
Conversion between metric units
U.S. customary and metric units
Term 3
Numeric and geometric patterns
No videos available
Functions and relationships
No videos available
Algebraic Expressions
Variables and expressions
What is a variable?
Why aren't we using the multiplication sign
Example: Evaluating an expression
Example: Evaluate a formula using substitution
Evaluating exponential expressions 2
Expressions with two variables
Example: Evaluating expressions with 2 variables
Examples of evaluating variable expressions
Example evaluating expressions in word problems
Writing and interpreting expressions
Writing expressions 1
Writing expressions 2
Writing expressions 2 exercise example
Interpreting linear expressions example
Interpreting linear expressions example 2
Writing expressions 3 exercise example 1
Writing expressions 3 exercise example 2
Writing expressions 3 exercise example 3
Algebraic Equations
Number Sentences
Writing expressions 1
Writing expressions 2
Writing expressions 2 exercise example
Interpreting linear expressions example
Interpreting linear expressions example 2
Writing expressions 3 exercise example 1
Writing expressions 3 exercise example 2
Writing expressions 3 exercise example 3
Transformation geometry
Rotation, Reflection, Translation
Translations of polygons
Determining a translation for a shape
Rotation of polygons example
Rotating segment about orgin example
Reflecting line across another line example
3D Shapes
Nets of polyhedra
Calculating surface area using net
Term 4
Integers
Counting, ordering, comparing integers
Negative numbers introduction
Number line 3 exercise examples
Ordering negative numbers
Adding and subtracting negative numbers
Example: Adding negative numbers
Example: Adding integers with different signs
Adding and subtracting negative number examples
Why subtracting a negative is equivalent to adding a positive
Negative number word problems 1
Adding decimals of different signs word problem
Adding/subtracting negative numbers
Numeric and geometric patterns
No videos available
Functions and relationships
No videos available
Algebraic Expressions
Variables and expressions
What is a variable?
Why aren't we using the multiplication sign
Example: Evaluating an expression
Example: Evaluate a formula using substitution
Evaluating exponential expressions 2
Expressions with two variables
Example: Evaluating expressions with 2 variables
Examples of evaluating variable expressions
Example evaluating expressions in word problems
Writing and interpreting expressions
Writing expressions 1
Writing expressions 2
Writing expressions 2 exercise example
Interpreting linear expressions example
Interpreting linear expressions example 2
Writing expressions 3 exercise example 1
Writing expressions 3 exercise example 2
Writing expressions 3 exercise example 3
Algebraic Equations
Number Sentences
Writing expressions 1
Writing expressions 2
Writing expressions 2 exercise example
Interpreting linear expressions example
Interpreting linear expressions example 2
Writing expressions 3 exercise example 1
Writing expressions 3 exercise example 2
Writing expressions 3 exercise example 3
Data Handling
Representing Data
Reading tables 1
Reading tables 2
Stem-and-leaf plots
Reading stem and leaf plots
Reading pictographs
Reading bar graphs
Histograms
Reading bar charts 1
Creating bar charts 1
Reading bar charts 2
Reading bar charts 3
Reading line graphs
Reading pie graphs (circle graphs)
Misleading line graphs
Mean, Median, Mode
Statistics intro: Mean, median and mode
Example: Finding mean, median and mode
Exploring mean and median module
Grade 8
Term 1
Whole Numbers
Properties of whole numbers
Commutative law of addition
Commutative property for addition
Commutative law of multiplication
Associative law of addition
Associative law of multiplication
Properties of numbers 1
Number properties terminology 1
Identity property of 1
Identity property of 1 (second example)
Identity property of 0
Inverse property of addition
Inverse property of multiplication
Properties of numbers 2
The distributive property
The distributive property 2
Distributive property example 1
Distributive property exercise
Calculations using whole numbers
Addition with carrying
Carrying when adding three digit numbers
Why carrying works
Examples of regrouping when adding three digit numbers
Addition 4
Subtraction with borrowing (regrouping)
Basic regrouping when subtracting three digit numbers
Regrouping when subtracting three digit numbers
Regrouping twice when subtracting three digit numbers
Regrouping from 0 when subtracting three digit numbers
Borrowing once example 1
Borrowing once example 2
Regrouping (borrowing) twice example
Alternate mental subtraction method
Multi-digit multiplication
Multiplying by multiples of 10
2 digit times 1 digit example (no carrying)
3 digit times 1 digit example (no carrying)
2 digit times 1 digit example
3 digit times 1 digit example
4 digit times 1 digit example
2-digit times a 2-digit number
Example: 2-digit times 2-digit
Multiple digit numbers
Multiplication estimation example
Multiplication 7: Old video giving more examples
Loooong division!
Introduction to long division
Introduction to remainders
Long division with remainder example
More long division without and with remainders
Dividing by a two digit number
Level 4 division
Calculation Techniques
Rounding whole numbers
Rounding whole numbers 1
Rounding whole numbers 2
Rounding whole numbers 3
Multiples and factors
Prime factorization
Prime factorization
Prime factorization exercise
The fundamental theorem of arithmetic
Common divisibility examples
Least common multiple
Least common multiple exercise
Least common multiple exercise 2
Least common multiple (LCM)
Old least common multiple
Greatest common divisor
Greatest common divisor factor exercise
Greatest common divisor
LCM and GCF (greatest common factor) word problems
Solving problems
Integers
Counting, ordering, comparing integers
Negative numbers introduction
Number line 3 exercise examples
Ordering negative numbers
Adding and subtracting negative numbers
Example: Adding negative numbers
Example: Adding integers with different signs
Adding and subtracting negative number examples
Why subtracting a negative is equivalent to adding a positive
Negative number word problems 1
Adding decimals of different signs word problem
Adding/subtracting negative numbers
Multiplying and dividing negative numbers
Multiplying positive and negative numbers
Why a negative times a negative is a positive
Why a negative times a negative makes intuitive sense
Dividing positive and negative numbers
Example: Multiplying numbers with different signs
Multiplying and dividing negative numbers
Exponents
Basic Exponents
Introduction to exponents
Exponent example 1
Exponent example 2
Raising a number to the 0th and 1st power
Powers of 1 and -1
Powers of fractions
Powers of zero
The square root
Understanding square roots
Approximating square roots
Simplifying square roots
Simplifying radicals
Square roots and real numbers
Adding and simplifying radicals
The cube root
Finding cube roots
Cube root of a non-perfect cube
Simplifying a cube root
Scientific notation
Introduction to scientific notation
Scientific notation
Scientific notation examples
Scientific notation I
Scientific notation example 2
Exponent properties
Exponent rules part 1
Exponent rules part 2
Exponent properties involving quotients
Numeric and geometric patterns
No videos available
Functions and relationships
No videos available
Algebraic Expressions
Grade 7 Review
Variables and expressions
What is a variable?
Why aren't we using the multiplication sign
Example: Evaluating an expression
Example: Evaluate a formula using substitution
Evaluating exponential expressions 2
Expressions with two variables
Example: Evaluating expressions with 2 variables
Examples of evaluating variable expressions
Example evaluating expressions in word problems
Writing and interpreting expressions
Writing expressions 1
Writing expressions 2
Writing expressions 2 exercise example
Interpreting linear expressions example
Interpreting linear expressions example 2
Writing expressions 3 exercise example 1
Writing expressions 3 exercise example 2
Writing expressions 3 exercise example 3
Manipulating expressions
Combining like terms
Adding like rational terms
Combining like terms 1
Combining like terms 2
Combining like terms 3
Combining like terms and the distributive property
Factoring a linear expression with rational terms
Distributive property with rational terms
Equivalent forms of expressions 1
Multiplying monomials
Multiplying monomials
Dividing monomials
Multiplying and dividing monomials 1
Multiplying and dividing monomials 2
Multiplying and dividing monomials 3
Monomial greatest common factor
Algebraic Equations
Number Sentences
Writing expressions 1
Writing expressions 2
Writing expressions 2 exercise example
Interpreting linear expressions example
Interpreting linear expressions example 2
Writing expressions 3 exercise example 1
Writing expressions 3 exercise example 2
Writing expressions 3 exercise example 3
Term 2
Algebraic Expressions
Grade 7 Review
Variables and expressions
What is a variable?
Why aren't we using the multiplication sign
Example: Evaluating an expression
Example: Evaluate a formula using substitution
Evaluating exponential expressions 2
Expressions with two variables
Example: Evaluating expressions with 2 variables
Examples of evaluating variable expressions
Example evaluating expressions in word problems
Writing and interpreting expressions
Writing expressions 1
Writing expressions 2
Writing expressions 2 exercise example
Interpreting linear expressions example
Interpreting linear expressions example 2
Writing expressions 3 exercise example 1
Writing expressions 3 exercise example 2
Writing expressions 3 exercise example 3
Manipulating expressions
Combining like terms
Adding like rational terms
Combining like terms 1
Combining like terms 2
Combining like terms 3
Combining like terms and the distributive property
Factoring a linear expression with rational terms
Distributive property with rational terms
Equivalent forms of expressions 1
Multiplying monomials
Multiplying monomials
Dividing monomials
Multiplying and dividing monomials 1
Multiplying and dividing monomials 2
Multiplying and dividing monomials 3
Monomial greatest common factor
Algebraic Equations
Basic Equations
Why we do the same thing to both sides: Simple equations
Representing a relationship with a simple equation
One-step equation intuition
One step equation intuition exercise intro
Adding and subtracting the same thing from both sides
Intuition why we divide both sides
Why we do the same thing to both sides: Two-step equations
Why we do the same thing to both sides: Multi-step equations
Why we do the same thing to both sides basic systems
Why all the letters in algebra?
One-step Equations
Super Yoga plans: Basic variables and equations
Super Yoga plans: Solving one-step equations
Super Yoga plans: Plotting points
Super Yoga plans: Solving systems by substitution
Super Yoga plans: Solving systems by elimination
One and two-step Equations
Simple equations of the form ax = b
Example solving x/3 = 14
Example solving x + 5 = 54
Examples of one-step equations like ax = b and x + a = b
Solving ax + b = c
Two-step equations
Example: Dimensions of a garden
Example: Two-step equation with x/4 term
Multistep Equations
Variables on both sides
Example 1: Variables on both sides
Example 2: Variables on both sides
Understanding steps when solving equations
Figuring out missing algebraic step
Geometry of 2D Shapes
2D Shapes (Classifying)
Scalene, isosceles, equilateral, acute, right, and obtuse triangles
Categorizing triangles
Quadrilateral overview
Quadrilateral properties
Kites as a mathematical shape
Quadrilateral types exercise
Examples with perpendicular lines and right, obtuse, acute triangles
Language and notation of the circle
Circles: Radius, diameter, and circumference
2D Shapes (Similarity + Congruence)
Testing congruence by transformations example
Another congruence by transformation example
Example of rigid transformation and congruence
Another example of rigid transformations for congruence
Testing similarity through transformations
Quadrilateral similarity by showing congruent angles
Geometry of Straight Lines
Lines
Language and notation of basic geometry
Lines, line segments, and rays
Drawing lines exercise example
Identifying rays
Identifying parallel and perpendicular lines
Euclid as the father of geometry
Angles
Angle basics
Measuring angles in degrees
Using a protractor
Measuring angles
Acute right and obtuse angles
Vertical, adjacent and linearly paired angles
Intersecting Lines
Introduction to vertical angles
Using algebra to find the measures of vertical angles
Proof: Vertical angles are equal
Angles formed by parallel lines and transversals
Identifying parallel and perpendicular lines
Figuring out angles between transversal and parallel lines
Using algebra to find measures of angles formed from transversal
Deducing angle measures
Term 3
Common Fractions
Basic fractions review
Understanding fractions
Introduction to fractions
Identifying fraction parts
Recognizing fractions exercise
Numerator and denominator of a fraction
Plotting basic fractions on the number line
Fraction word problems 1 exercise
Visualizing equivalent fractions
Visualizing equivalent fractions
Equivalent fraction word problem example
Equivalent fraction word problem example 2
Equivalent fraction word problem example 3
Fractions cut and copy 1 exercise
Comparing fractions
Comparing fractions with greater than and less than symbols
Comparing fractions with like numerators and denominators
Comparing fractions
Comparing fractions 2
Ordering fractions
Equivalent fractions and simplified form
Fractions in lowest terms
Equivalent fractions
Equivalent fractions example
Finding common denominators
Adding and subtracting fractions
Adding fractions with like denominators
Subtracting fractions
Adding fractions with 10 and 100 as denominators
Adding and subtracting fractions
Adding fractions with unlike denominators
Adding fractions (ex 1)
Subtracting fractions with unlike denominators
Adding fractions with different signs
Multiplying fractions
Multiplying fractions and whole numbers
Multiplying a fraction by a fraction
Multiplying fractions
Multiplying negative and positive fractions
Multiplication as scaling
Dividing fractions
Creating a fraction through division of whole numbers
My share of soap as a mixed number on a number line
Putting out bowls of potpurri
Spending the weekend studying
How many t-shirts can I make?
Dividing fractions by fractions
Conceptual understanding of dividing fractions by fractions
Another dividing fractions example
Dividing fractions example
Examples of dividing negative fractions
Mixed numbers and improper fractions
Comparing improper fractions and mixed numbers
Mixed numbers and improper fractions
Proper and improper fractions
Converting mixed numbers to improper fractions
Changing a mixed number to an improper fraction
Changing an improper fraction to a mixed number
Positive improper fractions on the number line
Fractions cut and copy 2 exercise example
Points on a number line
Percentages
Describing the meaning of percent
Describing the meaning of percent 2
Representing a number as a decimal, percent, and fraction
Converting decimals to percents (ex 1)
Converting decimals to percents (ex 2)
Converting percents to decimals (ex 1)
Converting percents to decimals (ex 2)
Finding percentages example
Percent word problems
Taking a percentage example
Identifying percent amount and base
Representing a number as a decimal, percent, and fraction 2
Ordering numeric expressions
Taking a percentage example
Rewriting fraction as a decimal to the hundredths place
Rewriting a fraction as a decimal
Representing a number as a decimal, percent, and fraction 2
Decimal Fractions
Decimals on a number line
Decimals on a number line
Points on a number line
Positive and negative decimals on a number line
Comparing decimals
Comparing decimals example 1
Comparing decimals example 2
Comparing decimals example 3
Comparing decimals example 4
Ordering decimals example
Another ordering decimals example
Estimating and rounding with decimals
Rounding decimals
Estimation with decimals
Adding and subtracting decimals
Adding decimals example 1
Adding decimals example 2
Adding decimals example 3
Subtracting decimals up to hundredths
Subtracting decimals
Adding decimals word problem
Subtracting decimals word problem
Subtracting decimals (old)
Multiplying decimals
Intro to multiplying decimals
Cost of filling tank
More intuition on multiplying decimals
Multiplying decimals
More involved multiplying decimals example
Dividing decimals
Dividing completely to get decimal answer
Dividing completely to get decimal answer example 2
Dividing a decimal by a whole number
Dividing a whole number by a decimal
Dividing decimals
Dividing decimal
Converting between fractions and decimals
Converting fractions to decimals (ex1)
Converting fractions to decimals (ex2)
Converting fractions to decimals
Converting fractions to decimals example
Decimals and fractions
Converting decimals to fractions 1 (ex 1)
Converting decimals to fractions 1 (ex 2)
Converting decimals to fractions 1 (ex 3)
Converting decimals to fractions 2 (ex 1)
Converting decimals to fractions 2 (ex 2)
Pythagoras
Pythagorean theorem
Pythagorean theorem
The Pythagorean theorem intro
Pythagorean theorem 1
Pythagorean theorem 2
Pythagorean theorem 3
Introduction to the Pythagorean theorem
Pythagorean theorem II
Pythagorean theorem proofs
Garfield's proof of the Pythagorean theorem
Bhaskara's proof of the Pythagorean theorem
Pythagorean theorem proof using similarity
Another Pythagorean theorem proof
Special right triangles
30-60-90 triangle side ratios proof
45-45-90 triangle side ratios
30-60-90 triangle example problem
Area of a regular hexagon
45-45-90 triangles
Intro to 30-60-90 triangles
30-60-90 triangles II
Sine, cosine and tangent trigonometric functions
Basic trigonometry
Example: Using soh cah toa
Basic trigonometry II
Example: Trig to solve the sides and angles of a right triangle
Trig ratios and similarity
Similarity to define sine, cosine, and tangent
Sine and cosine of complements example
Showing relationship between cosine and sine of complements
Example with trig functions and ratios
Example relating trig function to side ratios
Area and perimeter of shapes
Perimeter and area of triangles
Perimeter and area basics
Triangle area proofs
Interesting perimeter and area problems
Area of diagonal generated triangles of rectangle are equal
Area of an equilateral triangle
Area of shaded region made from equilateral triangles
Challenging perimeter problem
Circumference and area of circles
Circles: Radius, diameter, and circumference
Parts of a circle
Area of a circle
Perimeter and area of non-standard shapes
Quadrilateral overview
Quadrilateral properties
Area of a parallelogram
Area of a trapezoid
Area of a kite
Perimeter of a parallelogram
Perimeter and area of a non-standard polygon
Unit Conversion
Unit conversion within the metric system
Converting within the metric system
Perimeter and unit conversion
Applying the metric system
Conversion between metric units
U.S. customary and metric units
Data Handling
Representing Data
Reading tables 1
Reading tables 2
Stem-and-leaf plots
Reading stem and leaf plots
Reading pictographs
Reading bar graphs
Histograms
Reading bar charts 1
Creating bar charts 1
Reading bar charts 2
Reading bar charts 3
Reading line graphs
Reading pie graphs (circle graphs)
Misleading line graphs
Measures of central tendency
Statistics intro: Mean, median and mode
Example: Finding mean, median and mode
Exploring mean and median module
Comparing and sampling populations
Sample mean versus population mean
Reasonable samples
Comparing throws
Comparing swim times at the Olympics
Basic probability
Basic probability
Winning the lottery versus earning billions
Making sense of probabilities
Probability space exercise example
Example: Marbles from a bag
Example: Picking a non-blue marble
Example: Picking a yellow marble
Term 4
Functions and relationships
No videos available
Algebraic Equations
Basic Equations
Why we do the same thing to both sides: Simple equations
Representing a relationship with a simple equation
One-step equation intuition
One step equation intuition exercise intro
Adding and subtracting the same thing from both sides
Intuition why we divide both sides
Why we do the same thing to both sides: Two-step equations
Why we do the same thing to both sides: Multi-step equations
Why we do the same thing to both sides basic systems
Why all the letters in algebra?
One-step Equations
Super Yoga plans: Basic variables and equations
Super Yoga plans: Solving one-step equations
Super Yoga plans: Plotting points
Super Yoga plans: Solving systems by substitution
Super Yoga plans: Solving systems by elimination
One and two-step Equations
Simple equations of the form ax = b
Example solving x/3 = 14
Example solving x + 5 = 54
Examples of one-step equations like ax = b and x + a = b
Solving ax + b = c
Two-step equations
Example: Dimensions of a garden
Example: Two-step equation with x/4 term
Multistep Equations
Variables on both sides
Example 1: Variables on both sides
Example 2: Variables on both sides
Understanding steps when solving equations
Figuring out missing algebraic step
Graphs
Descartes and Cartesian coordinates
The coordinate plane
Plot ordered pairs
Graphing points exercise
Quadrants of coordinate plane
Graphing points and naming quadrants exercise
Points on the coordinate plane
Coordinate plane word problems exercise
Reflecting points exercise
Transformations
Rotating, Reflecting, Translating
Translations of polygons
Determining a translation for a shape
Rotation of polygons example
Rotating segment about orgin example
Reflecting line across another line example
Enlargement, Reduction
Dilating one line onto another
Comparing side lengths after dilation
Thinking about dilations
Dilating from an arbitrary point example
Transformations on the coordinate plane
Performing a rotation to match figures
Reflection and mapping points example
Scaling down a triangle by half
Possible transformations example
Determining the line of reflection
Determing a translation between points
Defining transformations to match polygons
Probability
Basic probability
Winning the lottery versus earning billions
Making sense of probabilities
Probability space exercise example
Example: Marbles from a bag
Example: Picking a non-blue marble
Example: Picking a yellow marble
Grade 9
Term 1
Whole Numbers
Properties of Numbers
Introduction to rational and irrational numbers
Recognizing irrational numbers
Approximating irrational number exercise example
Calculations using whole numbers
Addition with carrying
Carrying when adding three digit numbers
Why carrying works
Examples of regrouping when adding three digit numbers
Addition 4
Subtraction with borrowing (regrouping)
Basic regrouping when subtracting three digit numbers
Regrouping when subtracting three digit numbers
Regrouping twice when subtracting three digit numbers
Regrouping from 0 when subtracting three digit numbers
Borrowing once example 1
Borrowing once example 2
Regrouping (borrowing) twice example
Alternate mental subtraction method
Multi-digit multiplication
Multiplying by multiples of 10
2 digit times 1 digit example (no carrying)
3 digit times 1 digit example (no carrying)
2 digit times 1 digit example
3 digit times 1 digit example
4 digit times 1 digit example
2-digit times a 2-digit number
Example: 2-digit times 2-digit
Multiple digit numbers
Multiplication estimation example
Multiplication 7: Old video giving more examples
Loooong division!
Introduction to long division
Introduction to remainders
Long division with remainder example
More long division without and with remainders
Dividing by a two digit number
Level 4 division
Calculation techniques
Rounding whole numbers
Rounding whole numbers 1
Rounding whole numbers 2
Rounding whole numbers 3
Multiples and factors
Prime factorization
Prime factorization
Prime factorization exercise
The fundamental theorem of arithmetic
Common divisibility examples
Least common multiple
Least common multiple exercise
Least common multiple exercise 2
Least common multiple (LCM)
Old least common multiple
Greatest common divisor
Greatest common divisor factor exercise
Greatest common divisor
LCM and GCF (greatest common factor) word problems
Solving problems
Integers
Counting, ordering, comparing integers
Negative numbers introduction
Number line 3 exercise examples
Ordering negative numbers
Adding and subtracting negative numbers
Example: Adding negative numbers
Example: Adding integers with different signs
Adding and subtracting negative number examples
Why subtracting a negative is equivalent to adding a positive
Negative number word problems 1
Adding decimals of different signs word problem
Adding/subtracting negative numbers
Multiplying and dividing negative numbers
Multiplying positive and negative numbers
Why a negative times a negative is a positive
Why a negative times a negative makes intuitive sense
Dividing positive and negative numbers
Example: Multiplying numbers with different signs
Multiplying and dividing negative numbers
Common Fractions
Basic fractions review
Understanding fractions
Introduction to fractions
Identifying fraction parts
Recognizing fractions exercise
Numerator and denominator of a fraction
Plotting basic fractions on the number line
Fraction word problems 1 exercise
Visualizing equivalent fractions
Visualizing equivalent fractions
Equivalent fraction word problem example
Equivalent fraction word problem example 2
Equivalent fraction word problem example 3
Fractions cut and copy 1 exercise
Comparing fractions
Comparing fractions with greater than and less than symbols
Comparing fractions with like numerators and denominators
Comparing fractions
Comparing fractions 2
Ordering fractions
Equivalent fractions and simplified form
Fractions in lowest terms
Equivalent fractions
Equivalent fractions example
Finding common denominators
Adding and subtracting fractions
Adding fractions with like denominators
Subtracting fractions
Adding fractions with 10 and 100 as denominators
Adding and subtracting fractions
Adding fractions with unlike denominators
Adding fractions (ex 1)
Subtracting fractions with unlike denominators
Adding fractions with different signs
Multiplying fractions
Multiplying fractions and whole numbers
Multiplying a fraction by a fraction
Multiplying fractions
Multiplying negative and positive fractions
Multiplication as scaling
Dividing fractions
Creating a fraction through division of whole numbers
My share of soap as a mixed number on a number line
Putting out bowls of potpurri
Spending the weekend studying
How many t-shirts can I make?
Dividing fractions by fractions
Conceptual understanding of dividing fractions by fractions
Another dividing fractions example
Dividing fractions example
Examples of dividing negative fractions
Decimal Fractions
Decimals on a number line
Decimals on a number line
Points on a number line
Positive and negative decimals on a number line
Comparing decimals
Comparing decimals example 1
Comparing decimals example 2
Comparing decimals example 3
Comparing decimals example 4
Ordering decimals example
Another ordering decimals example
Estimating and rounding with decimals
Rounding decimals
Estimation with decimals
Adding and subtracting decimals
Adding decimals example 1
Adding decimals example 2
Adding decimals example 3
Subtracting decimals up to hundredths
Subtracting decimals
Adding decimals word problem
Subtracting decimals word problem
Subtracting decimals (old)
Multiplying decimals
Intro to multiplying decimals
Cost of filling tank
More intuition on multiplying decimals
Multiplying decimals
More involved multiplying decimals example
Dividing decimals
Dividing completely to get decimal answer
Dividing completely to get decimal answer example 2
Dividing a decimal by a whole number
Dividing a whole number by a decimal
Dividing decimals
Dividing decimal
Converting between fractions and decimals
Converting fractions to decimals (ex1)
Converting fractions to decimals (ex2)
Converting fractions to decimals
Converting fractions to decimals example
Decimals and fractions
Converting decimals to fractions 1 (ex 1)
Converting decimals to fractions 1 (ex 2)
Converting decimals to fractions 1 (ex 3)
Converting decimals to fractions 2 (ex 1)
Converting decimals to fractions 2 (ex 2)
Exponents
Basic Exponents
Introduction to exponents
Exponent example 1
Exponent example 2
Raising a number to the 0th and 1st power
Powers of 1 and -1
Powers of fractions
Powers of zero
The square root
Understanding square roots
Approximating square roots
Simplifying square roots
Simplifying radicals
Square roots and real numbers
Adding and simplifying radicals
The cube root
Finding cube roots
Cube root of a non-perfect cube
Simplifying a cube root
Scientific notation
Introduction to scientific notation
Scientific notation
Scientific notation examples
Scientific notation I
Scientific notation example 2
Negative and fractional exponents
Negative exponents
Negative exponent intuition
Zero, negative, and fractional exponents
Exponent properties
Exponent rules part 1
Exponent rules part 2
Exponent properties involving quotients
Functions and relationships
No videos available
Numeric and geometric patterns
No videos available
Algebraic Expressions
Grade 8 Review
Variables and expressions
What is a variable?
Why aren't we using the multiplication sign
Example: Evaluating an expression
Example: Evaluate a formula using substitution
Evaluating exponential expressions 2
Expressions with two variables
Example: Evaluating expressions with 2 variables
Examples of evaluating variable expressions
Example evaluating expressions in word problems
Manipulating expressions
Combining like terms
Adding like rational terms
Combining like terms 1
Combining like terms 2
Combining like terms 3
Combining like terms and the distributive property
Factoring a linear expression with rational terms
Distributive property with rational terms
Equivalent forms of expressions 1
Multiplying monomials
Multiplying monomials
Dividing monomials
Multiplying and dividing monomials 1
Multiplying and dividing monomials 2
Multiplying and dividing monomials 3
Monomial greatest common factor
Multiplying binomials
Multiplying binomials word problem
FOIL for multiplying binomials
Multiplying binomials with radicals
Multiplying binomials example 1
FOIL method for multiplying binomials example 2
Square a binomial
Special products of binomials
Multiplying binomials to get difference of squares
Squaring a binomial
Squaring a binomial example 2
Classic multiplying binomials video
Multiplying polynomials
Multiplying monomials by polynomials
Multiplying polynomials
Multiplying polynomials 3
More multiplying polynomials
Factoring simple expressions
Factoring and the distributive property 3
Factoring linear binomials
Factoring and the distributive property
Factoring and the distributive property 2
Factor expressions using the GCF
Factoring quadratic expressions
Factoring quadratic expressions
Examples: Factoring simple quadratics
Example 1: Factoring quadratic expressions
Example 1: Factoring trinomials with a common factor
Difference of two squares
Factoring special products
Example 1: Factoring difference of squares
Example 2: Factoring difference of squares
Factoring to produce difference of squares
Example: Factoring perfect square trinomials
Example: Factoring a fourth degree expression
Example: Factoring special products
Algebraic Equations
Basic Equations
Why we do the same thing to both sides: Simple equations
Representing a relationship with a simple equation
One-step equation intuition
One step equation intuition exercise intro
Adding and subtracting the same thing from both sides
Intuition why we divide both sides
Why we do the same thing to both sides: Two-step equations
Why we do the same thing to both sides: Multi-step equations
Why we do the same thing to both sides basic systems
Why all the letters in algebra?
One-step Equations
Super Yoga plans: Basic variables and equations
Super Yoga plans: Solving one-step equations
Super Yoga plans: Plotting points
Super Yoga plans: Solving systems by substitution
Super Yoga plans: Solving systems by elimination
One and two-step equations
Simple equations of the form ax = b
Example solving x/3 = 14
Example solving x + 5 = 54
Examples of one-step equations like ax = b and x + a = b
Solving ax + b = c
Two-step equations
Example: Dimensions of a garden
Example: Two-step equation with x/4 term
Multistep Equations
Variables on both sides
Example 1: Variables on both sides
Example 2: Variables on both sides
Understanding steps when solving equations
Figuring out missing algebraic step
Solving for a variable
Rearrange formulas to isolate specific variables
Solving for a variable
Solving for a variable 2
Example: Solving for a variable
Manipulating formula example
Solving quadratics by factoring
Solving a quadratic equation by factoring
Finding dimensions of triangle from area
Dimensions from volume of box
Recognizing a perfect square quadratic
Term 2
Construction of geometric figures
No videos available
Geometry of 2D shapes
Grade 8 Review
2D Shapes
Scalene, isosceles, equilateral, acute, right, and obtuse triangles
Categorizing triangles
Quadrilateral overview
Quadrilateral properties
Kites as a mathematical shape
Quadrilateral types exercise
Examples with perpendicular lines and right, obtuse, acute triangles
Language and notation of the circle
Circles: Radius, diameter, and circumference
3D Shapes
Nets of polyhedra
Lines
Language and notation of basic geometry
Lines, line segments, and rays
Drawing lines exercise example
Identifying rays
Euclid as the father of geometry
Angles
Angle basics
Measuring angles in degrees
Using a protractor
Measuring angles
Acute right and obtuse angles
Vertical, adjacent and linearly paired angles
Intersecting Lines
Introduction to vertical angles
Using algebra to find the measures of vertical angles
Proof: Vertical angles are equal
Angles formed by parallel lines and transversals
Identifying parallel and perpendicular lines
Figuring out angles between transversal and parallel lines
Using algebra to find measures of angles formed from transversal
Deducing angle measures
Congruent Triangles
Congruent triangles and SSS
Other triangle congruence postulates
Finding congruent triangles
More on why SSA is not a postulate
Congruent triangle proof example
Congruent triangle example 2
Proofs (Optional)
SSS to show a radius is perpendicular to a chord that it bisects
Two column proof showing segments are perpendicular
Perpendicular radius bisects chord
Similar Triangles
Similar triangle basics
Similarity postulates
Similar triangle example problems
Similarity example problems
Similarity example where same side plays different roles
Transformations
Rotating, Reflecting, Translating
Translations of polygons
Determining a translation for a shape
Rotation of polygons example
Rotating segment about orgin example
Reflecting line across another line example
Enlargement, Reduction
Dilating one line onto another
Comparing side lengths after dilation
Thinking about dilations
Dilating from an arbitrary point example
Transformations on the coordinate plane
Performing a rotation to match figures
Reflection and mapping points example
Scaling down a triangle by half
Possible transformations example
Determining the line of reflection
Determing a translation between points
Defining transformations to match polygons
Angles in a Polygon
Angles in a Triangle
Proof: Sum of measures of angles in a triangle are 180
Triangle angle example 1
Triangle angle example 2
Triangle angle example 3
Challenging triangle angle problem
Proof: Corresponding angle equivalence implies parallel lines
Finding more angles
Sum of interior angles of a polygon
Sum of the exterior angles of convex polygon
Angles in a Quadrilateral
Proof: Opposite sides of parallelogram congruent
Proof: Diagonals of a parallelogram bisect each other
Proof: Opposite angles of parallelogram congruent
Proof: Rhombus diagonals are perpendicular bisectors
Proof: Rhombus area half product of diagonal length
Area of a parallelogram
Whether a special quadrilateral can exist
Rhombus diagonals
Geometry of straight lines
Lines
Language and notation of basic geometry
Lines, line segments, and rays
Drawing lines exercise example
Identifying rays
Identifying parallel and perpendicular lines
Euclid as the father of geometry
Angles
Angle basics
Measuring angles in degrees
Using a protractor
Measuring angles
Acute right and obtuse angles
Vertical, adjacent and linearly paired angles
Intersecting Lines
Introduction to vertical angles
Using algebra to find the measures of vertical angles
Proof: Vertical angles are equal
Angles formed by parallel lines and transversals
Identifying parallel and perpendicular lines
Figuring out angles between transversal and parallel lines
Using algebra to find measures of angles formed from transversal
Deducing angle measures
Pythagoras
Pythagorean theorem
Pythagorean theorem
The Pythagorean theorem intro
Pythagorean theorem 1
Pythagorean theorem 2
Pythagorean theorem 3
Introduction to the Pythagorean theorem
Pythagorean theorem II
Pythagorean theorem proofs
Garfield's proof of the Pythagorean theorem
Bhaskara's proof of the Pythagorean theorem
Pythagorean theorem proof using similarity
Another Pythagorean theorem proof
Special right triangles
30-60-90 triangle side ratios proof
45-45-90 triangle side ratios
30-60-90 triangle example problem
Area of a regular hexagon
45-45-90 triangles
Intro to 30-60-90 triangles
30-60-90 triangles II
Sine, cosine and tangent trigonometric functions
Basic trigonometry
Example: Using soh cah toa
Basic trigonometry II
Example: Trig to solve the sides and angles of a right triangle
Trig ratios and similarity
Similarity to define sine, cosine, and tangent
Sine and cosine of complements example
Showing relationship between cosine and sine of complements
Example with trig functions and ratios
Example relating trig function to side ratios
Area and perimeter of 2D shapes
Perimeter and area of triangles
Perimeter and area basics
Triangle area proofs
Interesting perimeter and area problems
Area of diagonal generated triangles of rectangle are equal
Area of an equilateral triangle
Area of shaded region made from equilateral triangles
Challenging perimeter problem
Circumference and area of circles
Circles: Radius, diameter, and circumference
Parts of a circle
Area of a circle
Perimeter and area of non-standard shapes
Quadrilateral overview
Quadrilateral properties
Area of a parallelogram
Area of a trapezoid
Area of a kite
Perimeter of a parallelogram
Perimeter and area of a non-standard polygon
Unit Conversion
Unit conversion within the metric system
Converting within the metric system
Perimeter and unit conversion
Applying the metric system
Conversion between metric units
U.S. customary and metric units
Term 3
Functions ans relationships
No videos available
Algebraic Expressions
Grade 8 Review
Variables and expressions
What is a variable?
Why aren't we using the multiplication sign
Example: Evaluating an expression
Example: Evaluate a formula using substitution
Evaluating exponential expressions 2
Expressions with two variables
Example: Evaluating expressions with 2 variables
Examples of evaluating variable expressions
Example evaluating expressions in word problems
Manipulating expressions
Combining like terms
Adding like rational terms
Combining like terms 1
Combining like terms 2
Combining like terms 3
Combining like terms and the distributive property
Factoring a linear expression with rational terms
Distributive property with rational terms
Equivalent forms of expressions 1
Multiplying monomials
Multiplying monomials
Dividing monomials
Multiplying and dividing monomials 1
Multiplying and dividing monomials 2
Multiplying and dividing monomials 3
Monomial greatest common factor
Multiplying binomials
Multiplying binomials word problem
FOIL for multiplying binomials
Multiplying binomials with radicals
Multiplying binomials example 1
FOIL method for multiplying binomials example 2
Square a binomial
Special products of binomials
Multiplying binomials to get difference of squares
Squaring a binomial
Squaring a binomial example 2
Classic multiplying binomials video
Multiplying polynomials
Multiplying monomials by polynomials
Multiplying polynomials
Multiplying polynomials 3
More multiplying polynomials
Factoring simple expressions
Factoring and the distributive property 3
Factoring linear binomials
Factoring and the distributive property
Factoring and the distributive property 2
Factor expressions using the GCF
Factoring quadratic expressions
Factoring quadratic expressions
Examples: Factoring simple quadratics
Example 1: Factoring quadratic expressions
Example 1: Factoring trinomials with a common factor
Difference of two squares
Factoring special products
Example 1: Factoring difference of squares
Example 2: Factoring difference of squares
Factoring to produce difference of squares
Example: Factoring perfect square trinomials
Example: Factoring a fourth degree expression
Example: Factoring special products
Algebraic Equations
Basic Equations
Why we do the same thing to both sides: Simple equations
Representing a relationship with a simple equation
One-step equation intuition
One step equation intuition exercise intro
Adding and subtracting the same thing from both sides
Intuition why we divide both sides
Why we do the same thing to both sides: Two-step equations
Why we do the same thing to both sides: Multi-step equations
Why we do the same thing to both sides basic systems
Why all the letters in algebra?
One-step Equations
Super Yoga plans: Basic variables and equations
Super Yoga plans: Solving one-step equations
Super Yoga plans: Plotting points
Super Yoga plans: Solving systems by substitution
Super Yoga plans: Solving systems by elimination
One and two-step equations
Simple equations of the form ax = b
Example solving x/3 = 14
Example solving x + 5 = 54
Examples of one-step equations like ax = b and x + a = b
Solving ax + b = c
Two-step equations
Example: Dimensions of a garden
Example: Two-step equation with x/4 term
Multistep Equations
Variables on both sides
Example 1: Variables on both sides
Example 2: Variables on both sides
Understanding steps when solving equations
Figuring out missing algebraic step
Solving for a variable
Rearrange formulas to isolate specific variables
Solving for a variable
Solving for a variable 2
Example: Solving for a variable
Manipulating formula example
Solving quadratics by factoring
Solving a quadratic equation by factoring
Finding dimensions of triangle from area
Dimensions from volume of box
Recognizing a perfect square quadratic
Graphs
Coordinate plane
Descartes and Cartesian coordinates
The coordinate plane
Plot ordered pairs
Graphing points exercise
Quadrants of coordinate plane
Graphing points and naming quadrants exercise
Points on the coordinate plane
Coordinate plane word problems exercise
Reflecting points exercise
Graphing solutions to equations
Ordered pair solutions of equations
Ordered pair solutions of equations 2
Determining a linear equation by trying out values from a table
Plotting (x,y) relationships
Graphs of linear equations
Application problem with graph
Interpreting linear graphs
Exploring linear relationships
Recognizing linear functions
Graphing lines 1
x-intercepts and y-intercepts of linear functions
Graphing using x- and y-intercepts
Graphing using intercepts
x- and y-intercepts
x- and y-intercepts 2
Finding x intercept of a line
Finding intercepts for a linear function from a table
Interpreting intercepts of linear functions
Slope
Slope of a line
Slope of a line 2
Slope and rate of change
Graphical slope of a line
Slope of a line 3
Slope example
Slope and y-intercept intuition
Intuitive understanding of slope example
Graphing linear equations in slope-intercept form
Graphing a line in slope intercept form
Converting to slope-intercept form
Fitting a line to data
Constructing equations in slope-intercept form
Multiple examples of constructing linear equations in slope-intercept form
Constructing equations in slope-intercept form from graphs
Constructing linear equations to solve word problems
Linear equation from slope and a point
Finding a linear equation given a point and slope
Equation of a line from fractional slope and point
Constructing the equation of a line given two points
Finding y intercept given slope and point
Slope intercept form from table
Term 4
Transformations
Rotating, Reflecting, Translating
Translations of polygons
Determining a translation for a shape
Rotation of polygons example
Rotating segment about orgin example
Reflecting line across another line example
Enlargement, Reduction
Dilating one line onto another
Comparing side lengths after dilation
Thinking about dilations
Dilating from an arbitrary point example
Transformations on the coordinate plane
Performing a rotation to match figures
Reflection and mapping points example
Scaling down a triangle by half
Possible transformations example
Determining the line of reflection
Determing a translation between points
Defining transformations to match polygons
Data Handling
Representing Data
Reading tables 1
Reading tables 2
Stem-and-leaf plots
Reading stem and leaf plots
Reading pictographs
Reading bar graphs
Histograms
Reading bar charts 1
Creating bar charts 1
Reading bar charts 2
Reading bar charts 3
Reading line graphs
Reading pie graphs (circle graphs)
Misleading line graphs
Measures of central tendency
Statistics intro: Mean, median and mode
Example: Finding mean, median and mode
Exploring mean and median module
Scatter plots
Studying, shoe size, and test scores scatter plots
People smoking less over time scatter plot
Constructing a scatter plot
Constructing scatter plot exercise example
Probability
Basic probability
Basic probability
Winning the lottery versus earning billions
Making sense of probabilities
Probability space exercise example
Example: Marbles from a bag
Example: Picking a non-blue marble
Example: Picking a yellow marble
Compound events
Compound probability of independent events
Tree diagram to count outcomes
Water balloon outcomes
Fantasy game outcomes
Getting at least one head
Example: Probability of rolling doubles
LeBron asks: What are the chances of making 10 free throws in a row?
LeBron asks: What are the chances of three free throws versus one three pointer?
Frequency probability and unfair coins
Example: Getting two questions right on an exam
Example: Rolling even three times
Frequency stability
Grade 10
Term 1
Alegebraic Expressions
Multiplying and factoring expressions
Multiplying and dividing monomials
Multiplying monomials
Dividing monomials
Multiplying and dividing monomials 1
Multiplying and dividing monomials 2
Multiplying and dividing monomials 3
Monomial greatest common factor
Multiplying binomials
Multiplying binomials word problem
FOIL for multiplying binomials
Multiplying binomials with radicals
Multiplying binomials example 1
FOIL method for multiplying binomials example 2
Square a binomial
Special products of binomials
Multiplying binomials to get difference of squares
Squaring a binomial
Squaring a binomial example 2
Classic multiplying binomials video
Factoring simple expressions
Factoring and the distributive property 3
Factoring linear binomials
Factoring and the distributive property
Factoring and the distributive property 2
Factor expressions using the GCF
Factoring quadratic expressions
Factoring quadratic expressions
Examples: Factoring simple quadratics
Example 1: Factoring quadratic expressions
Example 1: Factoring trinomials with a common factor
Factoring special products
Factoring special products
Example 1: Factoring difference of squares
Example 2: Factoring difference of squares
Factoring to produce difference of squares
Example: Factoring perfect square trinomials
Example: Factoring a fourth degree expression
Example: Factoring special products
Factoring by grouping
Factor by grouping and factoring completely
Example: Basic grouping
Example 1: Factoring by grouping
Example 2: Factoring by grouping
Example 3: Factoring by grouping
Example 4: Factoring by grouping
Example 5: Factoring by grouping
Example 6: Factoring by grouping
Factoring quadratics in two variables
Factoring quadratics with two variables
Factoring quadratics with two variables example
Polynomial basics
Terms coefficients and exponents in a polynomial
Interesting polynomial coefficient problem
Polynomials 1
Polynomials 2
Evaluating a polynomial at a given value
Simplify a polynomial
Adding polynomials
Example: Adding polynomials with multiple variables
Addition and subtraction of polynomials
Adding and subtracting polynomials 1
Adding and subtracting polynomials 2
Adding and subtracting polynomials 3
Subtracting polynomials
Subtracting polynomials with multiple variables
Multiplying polynomials
Multiplying monomials by polynomials
Multiplying polynomials
Multiplying polynomials 3
More multiplying polynomials
Simplifying rational expressions
Simplifying rational expressions introduction
Simplifying rational expressions 1
Simplifying rational expressions 2
Simplifying rational expressions 3
Simplifying rational expressions example 2
Adding and subtracting rational expressions
Adding and subtracting rational expressions 2
Subtracting rational expressions
Simplifying first for subtracting rational expressions
Adding and subtracting rational expressions
Adding and subtracting rational expressions 3
Rationalizing denominators of expressions
Exponents
Exponent expressions and equations
Properties of integer exponents
Introduction to negative exponents
Thinking more about negative exponents
More negative exponent intuition
Products and exponents raised to an exponent properties
Negative bases and exponents classification example
Capstone exponent properties example
Exponent properties examples with variables
Negative and positive exponents
Evaluating exponential expressions 3
Exponent properties 1
Exponent properties 2
Exponent properties 3
Exponent properties 4
Exponent properties 5
Exponent properties 6
Exponent properties 7
More rational exponents and exponent laws
Simplifying expressions with exponents
Simplifying expressions with exponents 2
Simplifying expressions with exponents 3
Fractional exponents
Basic fractional exponents
Solving for a fractional exponent
Simplifying with exponent properties
Negative fractional exponent examples
Negative fractional exponent examples 2
Fractional exponents with numerators other than 1
Fractional exponent expressions 1
Fractional exponent expressions 2
Fractional exponent expressions 3
Rational exponents and exponent laws
More rational exponents and exponent laws
Simplifying radical expressions
Radical equivalent to rational exponents 2
Radical equivalent to rational exponents
Multiply and simplify a radical expression 1
Simplifying square roots
Simplifying square roots comment response
Radical expressions with higher roots
Subtracting and simplifying radicals
Adding and simplifying radicals
Multiply and simplify a radical expression 2
Simplifying cube roots
How to rationalize a denominator
Equations and Inequalities
Linear equations
The why of algebra
Why we do the same thing to both sides: Simple equations
Representing a relationship with a simple equation
One-step equation intuition
One step equation intuition exercise intro
Adding and subtracting the same thing from both sides
Intuition why we divide both sides
Why we do the same thing to both sides: Two-step equations
Why we do the same thing to both sides: Multi-step equations
Why we do the same thing to both sides basic systems
Super Yoga plans
Super Yoga plans: Basic variables and equations
Super Yoga plans: Solving one-step equations
Super Yoga plans: Plotting points
Super Yoga plans: Solving systems by substitution
Super Yoga plans: Solving systems by elimination
Constructing and solving equations in the real world 1 exercise
Equations for beginners
Simple equations of the form ax = b
Example solving x/3 = 14
Example solving x + 5 = 54
Examples of one-step equations like ax = b and x + a = b
Solving ax + b = c
Two-step equations
Example: Dimensions of a garden
Example: Two-step equation with x/4 term
Linear equation word problems
Basic linear equation word problem
Linear equation word problem example
More fancy equations for beginners
Variables on both sides
Example 1: Variables on both sides
Example 2: Variables on both sides
Understanding steps when solving equations
Figuring out missing algebraic step
Solutions to linear equations
Equation special cases
Number of solutions to linear equations
Number of solutions to linear equations ex 3
Number of solutions to linear equations ex 2
Solving for a variable
Rearrange formulas to isolate specific variables
Solving for a variable
Solving for a variable 2
Example: Solving for a variable
Manipulating formula example
Converting repeating decimals to fractions
Converting repeating decimals to fractions 1
Converting repeating decimals to fractions 2
Age word problems
Ex 1 age word problem
Ex 2 age word problem
Ex 3 age word problem
Absolute value equations
Absolute value equations
Absolute value equations example 1
Absolute value equation example 2
Absolute value equations
Absolute value equations 1
Absolute value equation example
Absolute value equation with no solution
Absolute value inequalities
Absolute value inequalities example 1
Absolute inequalities 2
Absolute value inequalities example 3
Simplifying complicated equations
Ex 2: Multi-step equation
Solving equations with the distributive property
Solving equations with the distributive property 2
Ex 2: Distributive property to simplify
Ex 1: Distributive property to simplify
Ex 3: Distributive property to simplify
Evaluating expressions with unknown variables
Evaluating expressions where individual variable values are unknown
Evaluating expressions with unknown variables 2
More equation practice
Mixture problems 2
Basic rate problem
Early train word problem
Patterns in sequences 1
Patterns in sequences 2
Equations of sequence patterns
Finding the 100th term in a sequence
Sum of consecutive odd integers
Challenge example: Sum of integers
2003 AIME II problem 1
Bunch of examples
Mixture problems 3
Old school equations with Sal
Order of operations examples
Algebra: Linear equations 1
Algebra: Linear equations 2
Algebra: Linear equations 3
Algebra: Linear equations 4
Averages
Taking percentages
Growing by a percentage
More percent problems
Age word problems 1
Age word problems 2
Age word problems 3
Linear inequalities
Thinking algebraically about inequalities
Inequalities using multiplication and division
One-step inequality with multiplication and division example
Constructing and solving one-step inequality
One-step inequality involving addition
Inequalities using addition and subtraction
Two-step inequality example
Multi-step inequalities
Multi-step inequalities 2
Multi-step inequalities 3
Interpreting inequalities
Writing and using inequalities 2
Writing and using inequalities 3
Compound and absolute value inequalities
Compound inequalities
Compound inequalities
Compound inequalities 2
Compound inequalities 3
Compound inequalities 4
Absolute value inequalities
Absolute value inequalities example 1
Absolute value inequalities example 2
Absolute value inequalities example 3
Writing and using inequalities
Structure in linear expressions
Dogs cats and bears in a pet store visual argument
Dogs cats and bears in a pet store analytic argument
Reasoning through inequality expressions
Using expressions to understand relationships
Systems of equations and inequalities
Solving systems of equations for the king
Trolls, tolls, and systems of equations
Solving the troll riddle visually
Solving systems graphically
King's cupcakes: Solving systems by elimination
Simple elimination practice
How many bags of potato chips do people eat?
Systems with elimination practice
Talking bird solves systems with substitution
Practice using substitution for systems
Inconsistent systems of equations
Infinite solutions to systems
Consistent and inconsistent systems
Independent and dependent systems
Practice thinking about number of solutions to systems
Systems of inequalities
Visualizing the solution set for a system of inequalities
Graphing systems of inequalities
Graphing systems of inequalities 2
Systems with three variables
Systems of three variables
Systems of three variables 2
Solutions to three variable system
Solutions to three variable system 2
Three equation application problem
Non-linear systems of equations
Intersecting functions example
Estimating a solution to nonlinear system with calculator
Estimating a solution to nonlinear system with calculator part 2
Non-linear systems of equations 1
Non-linear systems of equations 2
Non-linear systems of equations 3
Systems of nonlinear equations 1
Systems of nonlinear equations 2
Systems of nonlinear equations 3
Solving quadratics by factoring
Solving a quadratic equation by factoring
Finding dimensions of triangle from area
Dimensions from volume of box
Recognizing a perfect square quadratic
Trigonometry
Basic trigonometry
Basic trigonometric ratios
Basic trigonometry
Example: Using soh cah toa
Basic trigonometry II
Example: Trig to solve the sides and angles of a right triangle
Trigonometric ratios and similarity
Similarity to define sine, cosine, and tangent
Sine and cosine of complements example
Showing relationship between cosine and sine of complements
Example with trig functions and ratios
Example relating trig function to side ratios
Reciprocal trig functions
Secant (sec), cosecant (csc) and cotangent (cot) example
Example: Using trig to solve for missing information
Radians
Introduction to radians
Finding arc length from radian angle measure
Ratio between concentric arcs
Example: Radian measure and arc length
Radian and degree conversion practice
Example: Converting degrees to radians
Example: Converting radians to degrees
Radians and degrees
Unit circle definition of trigonometric functions
Unit circle definition of trig functions
Example: Unit circle definition of sin and cos
Example: Using the unit circle definition of trig functions
Example: Trig function values using unit circle definition
Example: The signs of sine and cosecant
Unit circle manipulative
Matching ratios to trig functions
Example: Calculator to evaluate a trig function
Trig functions of special angles
Solving triangle in unit circle
Finding trig functions of special angles example
Graphs of trig functions
Midline, amplitude and period of a function
Example: Amplitude and period
Example: Graph, domain, and range of sine function
Example: Graph of cosine
Example: Intersection of sine and cosine
Example: Amplitude and period transformations
Example: Amplitude and period cosine transformations
Determining the equation of a trig function
Example: Figure out the trig function
Plotting maxima, minima and midline intersections of trig function
Modeling with periodic functions
Modeling annual temperature variation with trigonometry
Applying inverse trig function with model
Modeling temperature through the day
Inverse trig functions
Inverse trig functions: arcsin
Inverse trig functions: arccos
Inverse trig functions: arctan
Example: Calculator to evaluate inverse trig function
Solution set to sin equation
Angle of sun with the ground based on shadow
Modeling annual temperature variation with trigonometry
Applying inverse trig function with model
Trig ratio application problems
How much of a pyramid is submerged
Angle to aim to get alien
Figuring out coordinate of bended figure using trig
Long live tau
Tau versus pi
Pi is (still) wrong.
Trig identities and examples
Symmetry and periodicity of trig functions
Symmetry of trig values
Unit circle symmetries for tan
Relating trig function through angle rotations
Periodicity of tan example
Pythagorean identity
Pythagorean trig identity from soh cah toa
Pythagorean trig identity from unit circle
Using the Pythagorean trig identity
Examples using pythagorean identities to simplify trigonometric expressions
Trigonometric identities
Trigonometry identity review/fun
Proof: sin(a + b) = (cos a)(sin b) + (sin a)(cos b)
Proof: cos(a + b) = (cos a)(cos b) - (sin a)(sin b)
Trig identities part 2 (part 4 if you watch the proofs)
Trig identies part 3 (part 5 if you watch the proofs)
Cosine addition identity example
Double angle formula for cosine example
More trig examples
Navigation word problem
Fun trig problem
IIT JEE trigonometry problem 1
IIT JEE trigonometric maximum
IIT JEE trigonometric constraints
Trigonometric system example
2003 AIME II problem 11
2003 AIME II problem 14
Trigonometry word problems (part 1)
Trigonometry word problems (part 2)
Ferris wheel trig problem
Ferris wheel trig problem (part 2)
Law of cosines and law of sines
Law of cosines
Law of cosines to determine grade
Law of cosines for star distance
Law of sines
Law of sines for missing angle
Proof of the law of cosines
Proof: Law of sines
Right triangles and trigonometry
Pythagorean theorem
Pythagorean theorem
The Pythagorean theorem intro
Pythagorean theorem 1
Pythagorean theorem 2
Pythagorean theorem 3
Introduction to the Pythagorean theorem
Pythagorean theorem II
Pythagorean theorem proofs
Garfield's proof of the Pythagorean theorem
Bhaskara's proof of the Pythagorean theorem
Pythagorean theorem proof using similarity
Another Pythagorean theorem proof
Special right triangles
30-60-90 triangle side ratios proof
45-45-90 triangle side ratios
30-60-90 triangle example problem
Area of a regular hexagon
45-45-90 triangles
Intro to 30-60-90 triangles
30-60-90 triangles II
Sine, cosine and tangent trigonometric functions
Basic trigonometry
Example: Using soh cah toa
Basic trigonometry II
Example: Trig to solve the sides and angles of a right triangle
Trig ratios and similarity
Similarity to define sine, cosine, and tangent
Sine and cosine of complements example
Showing relationship between cosine and sine of complements
Example with trig functions and ratios
Example relating trig function to side ratios
Number Patterns
Linear Patterns
Mixture problems 2
Basic rate problem
Early train word problem
Patterns in sequences 1
Patterns in sequences 2
Equations of sequence patterns
Finding the 100th term in a sequence
Sum of consecutive odd integers
Challenge example: Sum of integers
2003 AIME II problem 1
Bunch of examples
Mixture problems 3
Term 2
Functions
Functions and their graphs
Function introduction
What is a function?
Difference between equations and functions
Relations and functions
Evaluating with function notation
Understanding function notation (example 1)
Understanding function notation (example 2)
Understanding function notation (example 3)
Function expressions
Sum of functions
Difference of functions
Product of functions
Quotient of functions
Domain and range
Domain of a function
Domain and range of a relation
Domain and range of a function given a formula
Domain and range 1
Domain of a radical function
Domain and range 2
Domain and range of a function
Recognizing functions
Testing if a relationship is a function
Graphical relations and functions
Functions as graphs
Recognizing functions (example 1)
Recognizing functions (example 2)
Functional relationships 1
Recognizing functions (example 3)
Recognizing functions (example 4)
Recognizing functions (example 5)
Composing functions
Introduction to function composition
Creating new function from composition
Evaluating composite functions example
Modeling with function composition
Function inverses
Introduction to function inverses
Function inverse example 1
Function inverses example 2
Function inverses example 3
Shifting and reflecting functions
Shifting and reflecting functions
Shifting functions
Flipping and shifting radical functions
Equations for radical functions example
Matching radical functions with graphs exercise example
Properties and features of functions
When a function is positive or negative
Recognizing odd and even functions
Connection between even and odd numbers and functions
Recognizing features of functions (example 1)
Recognizing features of functions 2 (example 2)
Recognizing features of functions 2 (example 3)
Comparing and interpreting functions
Interpreting features of functions 2 (example 1)
Interpreting features of functions 2 (example 2)
Comparing features of functions 2 (example 1)
Comparing features of functions 2 (example 2)
Comparing features of functions 2 (example 3)
Undefined and indeterminate answers
Why dividing by zero is undefined
Why zero divided by zero is undefined/indeterminate
Undefined and indeterminate
More mathy functions
A more formal understanding of functions
Introduction to the inverse of a function
Linear Functions
Intercepts of linear functions
Graphing using x- and y-intercepts
Graphing using intercepts
x- and y-intercepts
x- and y-intercepts 2
Finding x intercept of a line
Finding intercepts for a linear function from a table
Interpreting intercepts of linear functions
Slope of a line
Slope of a line
Slope of a line 2
Slope and rate of change
Graphical slope of a line
Slope of a line 3
Slope example
Slope and y-intercept intuition
Recognizing linear functions
Analyzing linear functions
Comparing linear functions 1
Comparing linear functions 2
Comparing linear functions 3
Interpreting features of linear functions example
Interpreting features of linear functions example 2
Comparing linear functions applications 1
Comparing linear functions applications 2
Comparing linear functions applications 3
Constructing a linear function word problem
Constructing and interpreting a linear function
Constructing linear graphs
Graphing and analyzing linear functions
Coordinate plane
Descartes and Cartesian coordinates
The coordinate plane
Plot ordered pairs
Graphing points exercise
Quadrants of coordinate plane
Graphing points and naming quadrants exercise
Points on the coordinate plane
Coordinate plane word problems exercise
Reflecting points exercise
Graphing solutions to equations
Ordered pair solutions of equations
Ordered pair solutions of equations 2
Determining a linear equation by trying out values from a table
Plotting (x,y) relationships
Graphs of linear equations
Application problem with graph
Interpreting linear graphs
Exploring linear relationships
Recognizing linear functions
Graphing lines 1
x-intercepts and y-intercepts of linear functions
Graphing using x- and y-intercepts
Graphing using intercepts
x- and y-intercepts
x- and y-intercepts 2
Finding x intercept of a line
Finding intercepts for a linear function from a table
Interpreting intercepts of linear functions
Proportional relationships
Analyzing and identifying proportional relationships ex1
Analyzing and identifying proportional relationships ex2
Analyzing and identifying proportional relationships ex3
Comparing proportional relationships
Constructing an equation for a proportional relationship
Graphing proportional relationships example
Graphing proportional relationships example 2
Graphing proportional relationships example 3
Rates for proportional relationships
Comparing rates
Representing and comparing rates
Rate problem with fractions 1
Unit cost with fractions 1
Slope
Slope of a line
Slope of a line 2
Slope and rate of change
Graphical slope of a line
Slope of a line 3
Slope example
Slope and y-intercept intuition
Intuitive understanding of slope example
Graphing linear equations in slope-intercept form
Graphing a line in slope intercept form
Converting to slope-intercept form
Fitting a line to data
Constructing equations in slope-intercept form
Multiple examples of constructing linear equations in slope-intercept form
Constructing equations in slope-intercept form from graphs
Constructing linear equations to solve word problems
Linear equation from slope and a point
Finding a linear equation given a point and slope
Equation of a line from fractional slope and point
Constructing the equation of a line given two points
Finding y intercept given slope and point
Slope intercept form from table
Point-slope form and standard form
Idea behind point slope form
Linear equations in point slope form
Linear equations in standard form
Point-slope and standard form
Converting from point slope to slope intercept form
More analytic geometry
Midpoint formula
The Pythagorean theorem intro
Distance formula
Perpendicular line slope
Equations of parallel and perpendicular lines
Parallel line equation
Parallel lines
Parallel lines 2
Parallel lines 3
Perpendicular lines
Perpendicular lines 2
Distance between a point and a line
Algebra: Slope and y-intercept intuition
Algebra: Equation of a line
CA Algebra I: Slope and y-intercept
Graphing linear inequalities
Graphing inequalities
Solving and graphing linear inequalities in two variables 1
Graphing linear inequalities in two variables example 2
Graphing inequalities 2
Graphing linear inequalities in two variables 3
Graphing inequalities 1
CA Algebra I: Graphing inequalities
Triangle similarity and constant slope
Similar triangles to prove that the slope is constant for a line
Slope and triangle similarity 1
Slope and triangle similarity 2
Slope and triangle similarity 3
Slope and triangle similarity 4
Average rate of change
Average rate of change (example 1)
Average rate of change (example 2)
Average rate of change (example 3)
Average rate of change when function defined by equation
Modeling with graphs
Graphing relationship between rate and duration
Reasonable scale for plotting data
Thinking about slope and units
Exponential and logarithmic functions
Exponential growth and decay
Exponential growth functions
Graphing exponential functions
Understanding linear and exponential models
Comparing exponential and quadratic models
Constructing linear and exponential functions from data
Constructing linear and exponential functions from graph
Modeling with exponential functions
Exponential growth and decay word problems
Decay of cesium 137 example
Modeling ticket fines with exponential function
Solving exponential equation
Continuous compounding and e
Introduction to interest
Interest (part 2)
Introduction to compound interest and e
Compound interest and e (part 2)
Compound interest and e (part 3)
Compound interest and e (part 4)
Logarithmic functions
Comparing exponential and logarithmic functions
Graphing logarithmic functions
Matching functions to their graphs
Graphs of logarithmic functions
Vi and Sal explore how we think about scale
Parabolas
Parabola intuition example 1
Parabola focus and directrix 1
Focus and directrix of a parabola 2
Using the focus and directrix to find the equation of a parabola
Hyperbolas
Conic sections: Intro to hyperbolas
Conic sections: Hyperbolas 2
Conic sections: Hyperbolas 3
Foci of a hyperbola
Proof: Hyperbola foci
Trigonometric Functions
Graphs of trig functions
Midline, amplitude and period of a function
Example: Amplitude and period
Example: Graph, domain, and range of sine function
Example: Graph of cosine
Example: Intersection of sine and cosine
Example: Amplitude and period transformations
Example: Amplitude and period cosine transformations
Determining the equation of a trig function
Example: Figure out the trig function
Plotting maxima, minima and midline intersections of trig function
Euclidean Geometry
Introduction to Euclidean geometry
Euclid as the father of geometry
Language and notation of basic geometry
Lines, line segments, and rays
Drawing lines exercise example
Specifying planes in three dimensions
Language and notation of the circle
The golden ratio
Identifying rays
Congruence
Transformations and congruence
Testing congruence by transformations example
Another congruence by transformation example
Example of rigid transformation and congruence
Another example of rigid transformations for congruence
Congruence postulates
Congruent triangles and SSS
SSS to show a radius is perpendicular to a chord that it bisects
Other triangle congruence postulates
Two column proof showing segments are perpendicular
Finding congruent triangles
More on why SSA is not a postulate
Perpendicular radius bisects chord
Congruent triangle proof example
Congruent triangle example 2
Congruence and isosceles and equilateral triangles
Congruent legs and base angles of isosceles triangles
Equilateral triangle sides and angles congruent
Equilateral and isosceles example problems
Another isosceles example problem
Example involving an isosceles triangle and parallel lines
Figuring out all the angles for congruent triangles example
Problem involving angle derived from square and circle
Term 3
Analytical Geometry
Distances between points
Distance formula
Midpoint formula
Ratios of distances between colinear points
Finding a point part way between two points
Slope of a line
Slope of a line
Slope of a line 2
Slope and rate of change
Graphical slope of a line
Slope of a line 3
Slope example
Slope and y-intercept intuition
Circles
Radius and center for a circle equation in standard form
Completing the square to write equation in standard form of a circle
Special properties and parts of triangles
Perpendicular bisectors
Circumcenter of a triangle
Circumcenter of a right triangle
Three points defining a circle
Area circumradius formula proof
2003 AIME II problem 7
Angle bisectors
Point-line distance and angle bisectors
Incenter and incircles of a triangle
Inradius, perimeter, and area
Angle bisector theorem proof
Angle bisector theorem examples
Medians and centroids
Triangle medians and centroids
Triangle medians and centroids (2D proof)
Medians divide into smaller triangles of equal area
Exploring medial triangles
Proving that the centroid is 2-3rds along the median
Median centroid right triangle example
Altitudes
Proof: Triangle altitudes are concurrent (orthocenter)
Common orthocenter and centroid
Bringing it all together
Review of triangle properties
Euler line
Euler's line proof
Geometry problems on the coordinate plane
Recognizing points on a circle
Classifying a quadrilateral on the coordinate plane
Identifying similar triangles in the coordinate plane
Which minions can the wizard reach
Distances between points
Distance formula
Midpoint formula
Ratios of distances between colinear points
Finding a point part way between two points
Finance and Growth
Interest basics
Introduction to interest
Interest (part 2)
Statistics
Measures of central tendency
Statistics intro: Mean, median and mode
Example: Finding mean, median and mode
Exploring mean and median module
Sample mean versus population mean
Box-and-whisker plots
Reading box-and-whisker plots
Constructing a box-and-whisker plot
Box-and-whisker plots
Example: Range and mid-range
Trigonometry
Trigonometry
Basic trigonometry
Basic trigonometric ratios
Basic trigonometry
Example: Using soh cah toa
Basic trigonometry II
Example: Trig to solve the sides and angles of a right triangle
Trigonometric ratios and similarity
Similarity to define sine, cosine, and tangent
Sine and cosine of complements example
Showing relationship between cosine and sine of complements
Example with trig functions and ratios
Example relating trig function to side ratios
Reciprocal trig functions
Secant (sec), cosecant (csc) and cotangent (cot) example
Example: Using trig to solve for missing information
Radians
Introduction to radians
Finding arc length from radian angle measure
Ratio between concentric arcs
Example: Radian measure and arc length
Radian and degree conversion practice
Example: Converting degrees to radians
Example: Converting radians to degrees
Radians and degrees
Unit circle definition of trigonometric functions
Unit circle definition of trig functions
Example: Unit circle definition of sin and cos
Example: Using the unit circle definition of trig functions
Example: Trig function values using unit circle definition
Example: The signs of sine and cosecant
Unit circle manipulative
Matching ratios to trig functions
Example: Calculator to evaluate a trig function
Trig functions of special angles
Solving triangle in unit circle
Finding trig functions of special angles example
Graphs of trig functions
Midline, amplitude and period of a function
Example: Amplitude and period
Example: Graph, domain, and range of sine function
Example: Graph of cosine
Example: Intersection of sine and cosine
Example: Amplitude and period transformations
Example: Amplitude and period cosine transformations
Determining the equation of a trig function
Example: Figure out the trig function
Plotting maxima, minima and midline intersections of trig function
Modeling with periodic functions
Modeling annual temperature variation with trigonometry
Applying inverse trig function with model
Modeling temperature through the day
Inverse trig functions
Inverse trig functions: arcsin
Inverse trig functions: arccos
Inverse trig functions: arctan
Example: Calculator to evaluate inverse trig function
Solution set to sin equation
Angle of sun with the ground based on shadow
Modeling annual temperature variation with trigonometry
Applying inverse trig function with model
Trig ratio application problems
How much of a pyramid is submerged
Angle to aim to get alien
Figuring out coordinate of bended figure using trig
Long live tau
Tau versus pi
Pi is (still) wrong.
Trig identities and examples
Symmetry and periodicity of trig functions
Symmetry of trig values
Unit circle symmetries for tan
Relating trig function through angle rotations
Periodicity of tan example
Pythagorean identity
Pythagorean trig identity from soh cah toa
Pythagorean trig identity from unit circle
Using the Pythagorean trig identity
Examples using pythagorean identities to simplify trigonometric expressions
Trigonometric identities
Trigonometry identity review/fun
Proof: sin(a + b) = (cos a)(sin b) + (sin a)(cos b)
Proof: cos(a + b) = (cos a)(cos b) - (sin a)(sin b)
Trig identities part 2 (part 4 if you watch the proofs)
Trig identies part 3 (part 5 if you watch the proofs)
Cosine addition identity example
Double angle formula for cosine example
More trig examples
Navigation word problem
Fun trig problem
IIT JEE trigonometry problem 1
IIT JEE trigonometric maximum
IIT JEE trigonometric constraints
Trigonometric system example
2003 AIME II problem 11
2003 AIME II problem 14
Trigonometry word problems (part 1)
Trigonometry word problems (part 2)
Ferris wheel trig problem
Ferris wheel trig problem (part 2)
Law of cosines and law of sines
Law of cosines
Law of cosines to determine grade
Law of cosines for star distance
Law of sines
Law of sines for missing angle
Proof of the law of cosines
Proof: Law of sines
Euclidean Geometry
Geometry
Introduction to Euclidean geometry
Euclid as the father of geometry
Language and notation of basic geometry
Lines, line segments, and rays
Drawing lines exercise example
Specifying planes in three dimensions
Language and notation of the circle
The golden ratio
Identifying rays
Angles and intersecting lines
Angle basics and measurement
Angle basics
Measuring angles in degrees
Using a protractor
Measuring angles
Acute right and obtuse angles
Vertical, adjacent and linearly paired angles
Angles between intersecting and parallel lines
Introduction to vertical angles
Using algebra to find the measures of vertical angles
Proof: Vertical angles are equal
Angles formed by parallel lines and transversals
Identifying parallel and perpendicular lines
Figuring out angles between transversal and parallel lines
Using algebra to find measures of angles formed from transversal
CA Geometry: Deducing angle measures
Angles with triangles and polygons
Proof: Sum of measures of angles in a triangle are 180
Triangle angle example 1
Triangle angle example 2
Triangle angle example 3
Challenging triangle angle problem
Proof: Corresponding angle equivalence implies parallel lines
Finding more angles
Sum of interior angles of a polygon
Sum of the exterior angles of convex polygon
Sal's old angle videos
Introduction to angles (old)
Angles (part 2)
Angles (part 3)
Angles formed between transversals and parallel lines
Angles of parallel lines 2
The angle game
Angle game (part 2)
Acute right and obtuse angles
Complementary and supplementary angles
Complementary and supplementary angles
Example using algebra to find measure of complementary angles
Example using algebra to find measure of supplementary angles
Congruence
Transformations and congruence
Testing congruence by transformations example
Another congruence by transformation example
Example of rigid transformation and congruence
Another example of rigid transformations for congruence
Congruence postulates
Congruent triangles and SSS
SSS to show a radius is perpendicular to a chord that it bisects
Other triangle congruence postulates
Two column proof showing segments are perpendicular
Finding congruent triangles
More on why SSA is not a postulate
Perpendicular radius bisects chord
Congruent triangle proof example
Congruent triangle example 2
Congruence and isosceles and equilateral triangles
Congruent legs and base angles of isosceles triangles
Equilateral triangle sides and angles congruent
Equilateral and isosceles example problems
Another isosceles example problem
Example involving an isosceles triangle and parallel lines
Figuring out all the angles for congruent triangles example
Problem involving angle derived from square and circle
Similarity
Similarity and transformations
Testing similarity through transformations
Quadrilateral similarity by showing congruent angles
Triangle similarity
Similar triangle basics
Similarity postulates
Similar triangle example problems
Similarity example problems
Similarity example where same side plays different roles
Solving problems with similar and congruent triangles
Finding area using similarity and congruence
Golden ratio and Rembrandt's self portrait
Triangle similarity in pool
Golden ratio to find radius of moon
Challenging similarity problem
Old school similarity
Similar triangles
Similar triangles (part 2)
Right triangles and trigonometry
Pythagorean theorem
Pythagorean theorem
The Pythagorean theorem intro
Pythagorean theorem 1
Pythagorean theorem 2
Pythagorean theorem 3
Introduction to the Pythagorean theorem
Pythagorean theorem II
Pythagorean theorem proofs
Garfield's proof of the Pythagorean theorem
Bhaskara's proof of the Pythagorean theorem
Pythagorean theorem proof using similarity
Another Pythagorean theorem proof
Special right triangles
30-60-90 triangle side ratios proof
45-45-90 triangle side ratios
30-60-90 triangle example problem
Area of a regular hexagon
45-45-90 triangles
Intro to 30-60-90 triangles
30-60-90 triangles II
Sine, cosine and tangent trigonometric functions
Basic trigonometry
Example: Using soh cah toa
Basic trigonometry II
Example: Trig to solve the sides and angles of a right triangle
Trig ratios and similarity
Similarity to define sine, cosine, and tangent
Sine and cosine of complements example
Showing relationship between cosine and sine of complements
Example with trig functions and ratios
Example relating trig function to side ratios
Perimeter, area and volume
Perimeter and area of triangles
Perimeter and area basics
Triangle area proofs
Interesting perimeter and area problems
Area of diagonal generated triangles of rectangle are equal
Area of an equilateral triangle
Area of shaded region made from equilateral triangles
Challenging perimeter problem
Triangle inequality theorem
Triangle inequality theorem
Koch snowflake fractal
Koch snowflake fractal
Area of an equilateral triangle
Area of Koch snowflake (part 1) - advanced
Area of Koch snowflake (part 2) - advanced
Heron's formula
Heron's formula
Part 1 of proof of Heron's formula
Part 2 of proof of Heron's formula
Circumference and area of circles
Circles: Radius, diameter, and circumference
Parts of a circle
Area of a circle
Perimeter and area of non-standard shapes
Quadrilateral overview
Quadrilateral properties
Area of a parallelogram
Area of a trapezoid
Area of a kite
Perimeter of a parallelogram
Perimeter and area of a non-standard polygon
Volume and surface area
Solid geometry volume
Cylinder volume and surface area
Volume of a sphere
How many people can a blimp carry
How far can you see from a plane window
Circles
Circle arcs and sectors
Language and notation of the circle
Circles: Radius, diameter, and circumference
Length of an arc that subtends a central angle
Finding central angle measure given arc length
Area of a sector given a central angle
Central, inscribed and circumscribed angles
Inscribed and central angles
Measure of circumscribed angle
Example with tangent and radius
Hypotenuse of right triangle inscribed in circle
Equation of a circle
Equation for a circle using the Pythagorean Theorem
Completing the square to write equation in standard form of a circle
Pythagorean theorem and radii of circles
Area of inscribed triangle
SSS to show a radius is perpendicular to a chord that it bisects
Perpendicular radius bisects chord
Area of inscribed equilateral triangle (some basic trig used)
Geometric models
How far can you see from a plane window
Special properties and parts of triangles
Perpendicular bisectors
Circumcenter of a triangle
Circumcenter of a right triangle
Three points defining a circle
Area circumradius formula proof
2003 AIME II problem 7
Angle bisectors
Point-line distance and angle bisectors
Incenter and incircles of a triangle
Inradius, perimeter, and area
Angle bisector theorem proof
Angle bisector theorem examples
Medians and centroids
Triangle medians and centroids
Triangle medians and centroids (2D proof)
Medians divide into smaller triangles of equal area
Exploring medial triangles
Proving that the centroid is 2-3rds along the median
Median centroid right triangle example
Altitudes
Proof: Triangle altitudes are concurrent (orthocenter)
Common orthocenter and centroid
Bringing it all together
Review of triangle properties
Euler line
Euler's line proof
Quadrilaterals
Quadrilaterals
Quadrilateral overview
Quadrilateral properties
Kites as a mathematical shape
Quadrilateral types exercise
Proof: Opposite sides of parallelogram congruent
Proof: Diagonals of a parallelogram bisect each other
Proof: Opposite angles of parallelogram congruent
Proof: Rhombus diagonals are perpendicular bisectors
Proof: Rhombus area half product of diagonal length
Area of a parallelogram
Whether a special quadrilateral can exist
Rhombus diagonals
Logical reasoning
Logical reasoning
Conditional statements and deductive reasoning
Conditional statements exercise examples
Logical argument and deductive reasoning exercise example
Transformations
Symmetry
Axis of symmetry
Rotating polygons 180 degrees about their center
Constructing quadrilateral based on symmetry
Constructing a shape by reflecting over 2 lines
Exploring rigid transformations
Rotating segment about orgin example
Reflecting line across another line example
Translations of polygons
Determining a translation for a shape
Rotation of polygons example
Dilations or scaling around a point
Dilating one line onto another
Comparing side lengths after dilation
Thinking about dilations
Dilating from an arbitrary point example
Transformations on the coordinate plane
Performing a rotation to match figures
Reflection and mapping points example
Scaling down a triangle by half
Possible transformations example
Determining the line of reflection
Determing a translation between points
Defining transformations to match polygons
Analytic geometry
Geometry problems on the coordinate plane
Recognizing points on a circle
Classifying a quadrilateral on the coordinate plane
Identifying similar triangles in the coordinate plane
Which minions can the wizard reach
Distances between points
Distance formula
Midpoint formula
Ratios of distances between colinear points
Finding a point part way between two points
Geometric constructions
Constructing bisectors of lines and angles
Constructing a perpendicular bisector using a compass and straightedge
Constructing a perpendicular line using a compass and straightedge
Constructing an angle bisector using a compass and straightedge
Constructing regular polygons inscribed in circles
Constructing square inscribed in circle
Constructing equilateral triangle inscribed in circle
Constructing regular hexagon inscribed in circle
Constructing circumcircles and incircles
Constructing circle inscribing triangle
Constructing circumscribing circle
Worked examples
Interesting perimeter and area problems
Challenging perimeter problem
CA Geometry: Deductive reasoning
CA Geometry: Proof by contradiction
CA Geometry: More proofs
CA Geometry: Similar triangles 1
CA Geometry: Similar triangles 2
CA Geometry: More on congruent and similar triangles
CA Geometry: Triangles and parallelograms
CA Geometry: Area, pythagorean theorem
CA Geometry: Area, circumference, volume
CA Geometry: Pythagorean theorem, area
CA Geometry: Exterior angles
CA Geometry: Deducing angle measures
CA Geometry: Pythagorean theorem, compass constructions
CA Geometry: Compass construction
CA Geometry: Basic trigonometry
CA Geometry: More trig
CA Geometry: Circle area chords tangent
CA Geometry: Secants and translations
Ratios and proportions
Ratios and proportions
Ratio problem with basic algebra
Writing proportions
Find an unknown in a proportion
Find an unknown in a proportion 2
Proportions 2 exercise examples
Constructing proportions to solve application problems
Advanced ratios and proportions
The golden ratio
Advanced ratio problems
More advanced ratio problem with algebra
Another take on the rate problem
Alternate solution to ratio problem
Mountain height word problem
Rational and irrational numbers
Introduction to rational and irrational numbers
Sum and product of rational numbers
Proof that rational times irrational is irrational
Proof that sum of rational and irrational is irrational
Proof that square root of 2 is irrational
Proof that square root of prime number is irrational
Proof that there is an irrational number between any two rational numbers
Recognizing rational and irrational expressions example
Measurement
Volume
Cylinder volume and surface area
Solid geometry volume
Term 4
Probability
Independent and dependent events
Basic probability
Basic probability
Probability space exercise example
Example: Marbles from a bag
Example: Picking a non-blue marble
Example: Picking a yellow marble
Venn diagrams and adding probabilities
Probability with playing cards and Venn diagrams
Addition rule for probability
Compound, independent events
Compound probability of independent events
Getting at least one head
Example: Probability of rolling doubles
LeBron asks: What are the chances of making 10 free throws in a row?
LeBron asks: What are the chances of three free throws versus one three pointer?
Frequency probability and unfair coins
Example: Getting two questions right on an exam
Example: Rolling even three times
Frequency stability
Dependent probability
Introduction to dependent probability
Example: Dependent probability
Example: Bag of unfair coins
Example: Is an event independent or dependent?
Monty Hall problem
Basic set operations
Intersection and union of sets
Relative complement or difference between sets
Universal set and absolute complement
Subset, strict subset, and superset
Bringing the set operations together
Old school probability (very optional)
Probability (part 1)
Probability (part 2)
Probability (part 3)
Probability (part 4)
Probability (part 5)
Probability (part 6)
Probability (part 7)
Probability (part 8)
Introduction to random variables
Probability and combinatorics
Permutations and combinations
Permutations
Combinations
Example: Ways to arrange colors
Example: 9 card hands
Example: Ways to pick officers
Probability using combinatorics
Example: Probability through counting outcomes
Example: All the ways you can flip a coin
Getting exactly two heads (combinatorics)
Probability and combinations (part 2)
Probability using combinations
Exactly three heads in five flips
Example: Different ways to pick officers
Example: Combinatorics and probability
Example: Lottery probability
Mega millions jackpot probability
Generalizing with binomial coefficients (bit advanced)
Conditional probability and combinations
Conditional probability warmup
Birthday probability problem
Making decisions with probability
Simple hypothesis testing
Random variables and probability distributions
Random variables and probability distributions
Random variables
Discrete and continuous random variables
Constructing a probability distribution for random variable
Probability density functions
Expected value: E(X)
Law of large numbers
Term life insurance and death probability
Binomial distribution
Binomial distribution 1
Binomial distribution 2
Binomial distribution 3
Binomial distribution 4
Expected value of binomial distribution
Poisson process
Poisson process 1
Poisson process 2
Basic probability
Basic probability
Winning the lottery versus earning billions
Making sense of probabilities
Probability space exercise example
Example: Marbles from a bag
Example: Picking a non-blue marble
Example: Picking a yellow marble
Dependent probability
Introduction to dependent probability
Example: Dependent probability
Example: Is an event independent or dependent?
Example: Bag of unfair coins
Monty Hall problem
Estimating probability
Estimating the probability of rolling 7
Probability models examples
Grade 11
Term 1
Exponent expressions and equations
Properties of integer exponents
Introduction to negative exponents
Thinking more about negative exponents
More negative exponent intuition
Products and exponents raised to an exponent properties
Negative bases and exponents classification example
Capstone exponent properties example
Exponent properties examples with variables
Negative and positive exponents
Evaluating exponential expressions 3
Exponent properties 1
Exponent properties 2
Exponent properties 3
Exponent properties 4
Exponent properties 5
Exponent properties 6
Exponent properties 7
More rational exponents and exponent laws
Simplifying expressions with exponents
Simplifying expressions with exponents 2
Simplifying expressions with exponents 3
Fractional exponents
Basic fractional exponents
Solving for a fractional exponent
Simplifying with exponent properties
Negative fractional exponent examples
Negative fractional exponent examples 2
Fractional exponents with numerators other than 1
Fractional exponent expressions 1
Fractional exponent expressions 2
Fractional exponent expressions 3
Rational exponents and exponent laws
More rational exponents and exponent laws
Simplifying radical expressions
Radical equivalent to rational exponents 2
Radical equivalent to rational exponents
Multiply and simplify a radical expression 1
Simplifying square roots
Simplifying square roots comment response
Radical expressions with higher roots
Subtracting and simplifying radicals
Adding and simplifying radicals
Multiply and simplify a radical expression 2
Simplifying cube roots
How to rationalize a denominator
Equation and Inequalities
Linear equations
The why of algebra
Why we do the same thing to both sides: Simple equations
Representing a relationship with a simple equation
One-step equation intuition
One step equation intuition exercise intro
Adding and subtracting the same thing from both sides
Intuition why we divide both sides
Why we do the same thing to both sides: Two-step equations
Why we do the same thing to both sides: Multi-step equations
Why we do the same thing to both sides basic systems
Super Yoga plans
Super Yoga plans: Basic variables and equations
Super Yoga plans: Solving one-step equations
Super Yoga plans: Plotting points
Super Yoga plans: Solving systems by substitution
Super Yoga plans: Solving systems by elimination
Constructing and solving equations in the real world 1 exercise
Equations for beginners
Simple equations of the form ax = b
Example solving x/3 = 14
Example solving x + 5 = 54
Examples of one-step equations like ax = b and x + a = b
Solving ax + b = c
Two-step equations
Example: Dimensions of a garden
Example: Two-step equation with x/4 term
Linear equation word problems
Basic linear equation word problem
Linear equation word problem example
More fancy equations for beginners
Variables on both sides
Example 1: Variables on both sides
Example 2: Variables on both sides
Understanding steps when solving equations
Figuring out missing algebraic step
Solutions to linear equations
Equation special cases
Number of solutions to linear equations
Number of solutions to linear equations ex 3
Number of solutions to linear equations ex 2
Solving for a variable
Rearrange formulas to isolate specific variables
Solving for a variable
Solving for a variable 2
Example: Solving for a variable
Manipulating formula example
Converting repeating decimals to fractions
Converting repeating decimals to fractions 1
Converting repeating decimals to fractions 2
Age word problems
Ex 1 age word problem
Ex 2 age word problem
Ex 3 age word problem
Absolute value equations
Absolute value equations
Absolute value equations example 1
Absolute value equation example 2
Absolute value equations
Absolute value equations 1
Absolute value equation example
Absolute value equation with no solution
Absolute value inequalities
Absolute value inequalities example 1
Absolute inequalities 2
Absolute value inequalities example 3
Simplifying complicated equations
Ex 2: Multi-step equation
Solving equations with the distributive property
Solving equations with the distributive property 2
Ex 2: Distributive property to simplify
Ex 1: Distributive property to simplify
Ex 3: Distributive property to simplify
Evaluating expressions with unknown variables
Evaluating expressions where individual variable values are unknown
Evaluating expressions with unknown variables 2
More equation practice
Mixture problems 2
Basic rate problem
Early train word problem
Patterns in sequences 1
Patterns in sequences 2
Equations of sequence patterns
Finding the 100th term in a sequence
Sum of consecutive odd integers
Challenge example: Sum of integers
2003 AIME II problem 1
Bunch of examples
Mixture problems 3
Old school equations with Sal
Order of operations examples
Algebra: Linear equations 1
Algebra: Linear equations 2
Algebra: Linear equations 3
Algebra: Linear equations 4
Averages
Taking percentages
Growing by a percentage
More percent problems
Age word problems 1
Age word problems 2
Age word problems 3
Systems of equations and inequalities
Solving systems of equations for the king
Trolls, tolls, and systems of equations
Solving the troll riddle visually
Solving systems graphically
King's cupcakes: Solving systems by elimination
Simple elimination practice
How many bags of potato chips do people eat?
Systems with elimination practice
Talking bird solves systems with substitution
Practice using substitution for systems
Inconsistent systems of equations
Infinite solutions to systems
Consistent and inconsistent systems
Independent and dependent systems
Practice thinking about number of solutions to systems
Systems of inequalities
Visualizing the solution set for a system of inequalities
Graphing systems of inequalities
Graphing systems of inequalities 2
Systems with three variables
Systems of three variables
Systems of three variables 2
Solutions to three variable system
Solutions to three variable system 2
Three equation application problem
Non-linear systems of equations
Intersecting functions example
Estimating a solution to nonlinear system with calculator
Estimating a solution to nonlinear system with calculator part 2
Non-linear systems of equations 1
Non-linear systems of equations 2
Non-linear systems of equations 3
Systems of nonlinear equations 1
Systems of nonlinear equations 2
Systems of nonlinear equations 3
Radical equations
Solving radical equations
Extraneous solutions to radical equations
Solving radical equations 1
Solving radical equations 2
Solving radical equations 3
Applying radical equations 1
Applying radical equations 2
Applying radical equations 3
Quadratic equations
Solving quadratics by taking square root
Solving quadratic equations by square roots
Example: Solving simple quadratic
Order of steps exercise example
Determining mistakes in steps example
Solving quadratics by factoring
Solving a quadratic equation by factoring
Finding dimensions of triangle from area
Dimensions from volume of box
Recognizing a perfect square quadratic
Completing the square
Solving quadratic equations by completing the square
Example 1: Completing the square
Example 2: Completing the square
Example 3: Completing the square
Rewriting a quadratic function to find roots and vertex
Completing the square for vertex form
Completing the square for quadratic formula
The quadratic formula (quadratic equation)
How to use the quadratic formula
Example: Quadratics in standard form
Proof of quadratic formula
Example 1: Using the quadratic formula
Example 2: Using the quadratic formula
Example 3: Using the quadratic formula
Example 4: Applying the quadratic formula
Example 5: Using the quadratic formula
Graphing quadratics
Graphing a parabola with a table of values
Parabola vertex and axis of symmetry
Graphing a parabola by finding the roots and vertex
Finding the vertex of a parabola example
Multiple examples graphing parabolas using roots and vertices
Graphing a parabola using roots and vertex
Shifting and scaling parabolas
Parabola intuition example 1
Graphing a parabola in vertex form
Quadratic inequalities
Quadratic inequality example
Quadratic inequality example 2
Quadratic inequalities (visual explanation)
Quadratic odds and ends
Solving a quadratic by factoring
CA Algebra I: Factoring quadratics
Algebra II: Quadratics and shifts
Examples: Graphing and interpreting quadratics
CA Algebra I: Completing the square
Introduction to the quadratic equation
Quadratic equation part 2
Quadratic formula (proof)
CA Algebra I: Quadratic equation
CA Algebra I: Quadratic roots
Completing the square and the quadratic formula
Solving quadratic equations by square roots
Solving quadratic equations by completing the square
How to use the quadratic formula
Proof of quadratic formula
Example: Complex roots for a quadratic
Discriminant of quadratic equations
Discriminant for types of solutions for a quadratic
Fundamental theorem of algebra for quadratic
Number Patterns
Linear Patterns
Mixture problems 2
Basic rate problem
Early train word problem
Patterns in sequences 1
Patterns in sequences 2
Equations of sequence patterns
Finding the 100th term in a sequence
Sum of consecutive odd integers
Challenge example: Sum of integers
2003 AIME II problem 1
Bunch of examples
Mixture problems 3
Formula for arithmetic series
Analytical Geometry
Distances between points
Distance formula
Midpoint formula
Ratios of distances between colinear points
Finding a point part way between two points
Slope of a line
Slope of a line
Slope of a line 2
Slope and rate of change
Graphical slope of a line
Slope of a line 3
Slope example
Slope and y-intercept intuition
Dilations or scaling around a point
Dilating one line onto another
Comparing side lengths after dilation
Thinking about dilations
Dilating from an arbitrary point example
Term 2
Functions
Functions and their graphs
Function introduction
What is a function?
Difference between equations and functions
Relations and functions
Evaluating with function notation
Understanding function notation (example 1)
Understanding function notation (example 2)
Understanding function notation (example 3)
Function expressions
Sum of functions
Difference of functions
Product of functions
Quotient of functions
Domain and range
Domain of a function
Domain and range of a relation
Domain and range of a function given a formula
Domain and range 1
Domain of a radical function
Domain and range 2
Domain and range of a function
Recognizing functions
Testing if a relationship is a function
Graphical relations and functions
Functions as graphs
Recognizing functions (example 1)
Recognizing functions (example 2)
Functional relationships 1
Recognizing functions (example 3)
Recognizing functions (example 4)
Recognizing functions (example 5)
Composing functions
Introduction to function composition
Creating new function from composition
Evaluating composite functions example
Modeling with function composition
Function inverses
Introduction to function inverses
Function inverse example 1
Function inverses example 2
Function inverses example 3
Shifting and reflecting functions
Shifting and reflecting functions
Shifting functions
Flipping and shifting radical functions
Equations for radical functions example
Matching radical functions with graphs exercise example
Properties and features of functions
When a function is positive or negative
Recognizing odd and even functions
Connection between even and odd numbers and functions
Recognizing features of functions (example 1)
Recognizing features of functions 2 (example 2)
Recognizing features of functions 2 (example 3)
Comparing and interpreting functions
Interpreting features of functions 2 (example 1)
Interpreting features of functions 2 (example 2)
Comparing features of functions 2 (example 1)
Comparing features of functions 2 (example 2)
Comparing features of functions 2 (example 3)
Undefined and indeterminate answers
Why dividing by zero is undefined
Why zero divided by zero is undefined/indeterminate
Undefined and indeterminate
More mathy functions
A more formal understanding of functions
Introduction to the inverse of a function
Linear Functions
Intercepts of linear functions
Graphing using x- and y-intercepts
Graphing using intercepts
x- and y-intercepts
x- and y-intercepts 2
Finding x intercept of a line
Finding intercepts for a linear function from a table
Interpreting intercepts of linear functions
Slope of a line
Slope of a line
Slope of a line 2
Slope and rate of change
Graphical slope of a line
Slope of a line 3
Slope example
Slope and y-intercept intuition
Recognizing linear functions
Analyzing linear functions
Comparing linear functions 1
Comparing linear functions 2
Comparing linear functions 3
Interpreting features of linear functions example
Interpreting features of linear functions example 2
Comparing linear functions applications 1
Comparing linear functions applications 2
Comparing linear functions applications 3
Constructing a linear function word problem
Constructing and interpreting a linear function
Constructing linear graphs
Graphing and analyzing linear functions
Coordinate plane
Descartes and Cartesian coordinates
The coordinate plane
Plot ordered pairs
Graphing points exercise
Quadrants of coordinate plane
Graphing points and naming quadrants exercise
Points on the coordinate plane
Coordinate plane word problems exercise
Reflecting points exercise
Graphing solutions to equations
Ordered pair solutions of equations
Ordered pair solutions of equations 2
Determining a linear equation by trying out values from a table
Plotting (x,y) relationships
Graphs of linear equations
Application problem with graph
Interpreting linear graphs
Exploring linear relationships
Recognizing linear functions
Graphing lines 1
x-intercepts and y-intercepts of linear functions
Graphing using x- and y-intercepts
Graphing using intercepts
x- and y-intercepts
x- and y-intercepts 2
Finding x intercept of a line
Finding intercepts for a linear function from a table
Interpreting intercepts of linear functions
Proportional relationships
Analyzing and identifying proportional relationships ex1
Analyzing and identifying proportional relationships ex2
Analyzing and identifying proportional relationships ex3
Comparing proportional relationships
Constructing an equation for a proportional relationship
Graphing proportional relationships example
Graphing proportional relationships example 2
Graphing proportional relationships example 3
Rates for proportional relationships
Comparing rates
Representing and comparing rates
Rate problem with fractions 1
Unit cost with fractions 1
Slope
Slope of a line
Slope of a line 2
Slope and rate of change
Graphical slope of a line
Slope of a line 3
Slope example
Slope and y-intercept intuition
Intuitive understanding of slope example
Graphing linear equations in slope-intercept form
Graphing a line in slope intercept form
Converting to slope-intercept form
Fitting a line to data
Constructing equations in slope-intercept form
Multiple examples of constructing linear equations in slope-intercept form
Constructing equations in slope-intercept form from graphs
Constructing linear equations to solve word problems
Linear equation from slope and a point
Finding a linear equation given a point and slope
Equation of a line from fractional slope and point
Constructing the equation of a line given two points
Finding y intercept given slope and point
Slope intercept form from table
Point-slope form and standard form
Idea behind point slope form
Linear equations in point slope form
Linear equations in standard form
Point-slope and standard form
Converting from point slope to slope intercept form
More analytic geometry
Midpoint formula
The Pythagorean theorem intro
Distance formula
Perpendicular line slope
Equations of parallel and perpendicular lines
Parallel line equation
Parallel lines
Parallel lines 2
Parallel lines 3
Perpendicular lines
Perpendicular lines 2
Distance between a point and a line
Algebra: Slope and y-intercept intuition
Algebra: Equation of a line
CA Algebra I: Slope and y-intercept
Graphing linear inequalities
Graphing inequalities
Solving and graphing linear inequalities in two variables 1
Graphing linear inequalities in two variables example 2
Graphing inequalities 2
Graphing linear inequalities in two variables 3
Graphing inequalities 1
CA Algebra I: Graphing inequalities
Triangle similarity and constant slope
Similar triangles to prove that the slope is constant for a line
Slope and triangle similarity 1
Slope and triangle similarity 2
Slope and triangle similarity 3
Slope and triangle similarity 4
Average rate of change
Average rate of change (example 1)
Average rate of change (example 2)
Average rate of change (example 3)
Average rate of change when function defined by equation
Modeling with graphs
Graphing relationship between rate and duration
Reasonable scale for plotting data
Thinking about slope and units
Exponential and logarithmic functions
Exponential growth and decay
Exponential growth functions
Graphing exponential functions
Understanding linear and exponential models
Comparing exponential and quadratic models
Constructing linear and exponential functions from data
Constructing linear and exponential functions from graph
Modeling with exponential functions
Exponential growth and decay word problems
Decay of cesium 137 example
Modeling ticket fines with exponential function
Solving exponential equation
Continuous compounding and e
Introduction to interest
Interest (part 2)
Introduction to compound interest and e
Compound interest and e (part 2)
Compound interest and e (part 3)
Compound interest and e (part 4)
Logarithmic functions
Comparing exponential and logarithmic functions
Graphing logarithmic functions
Matching functions to their graphs
Graphs of logarithmic functions
Vi and Sal explore how we think about scale
Parabolas
Parabola intuition example 1
Parabola focus and directrix 1
Focus and directrix of a parabola 2
Using the focus and directrix to find the equation of a parabola
Hyperbolas
Conic sections: Intro to hyperbolas
Conic sections: Hyperbolas 2
Conic sections: Hyperbolas 3
Foci of a hyperbola
Proof: Hyperbola foci
Trigonometry
Basic trigonometry
Basic trigonometric ratios
Basic trigonometry
Example: Using soh cah toa
Basic trigonometry II
Example: Trig to solve the sides and angles of a right triangle
Trigonometric ratios and similarity
Similarity to define sine, cosine, and tangent
Sine and cosine of complements example
Showing relationship between cosine and sine of complements
Example with trig functions and ratios
Example relating trig function to side ratios
Reciprocal trig functions
Secant (sec), cosecant (csc) and cotangent (cot) example
Example: Using trig to solve for missing information
Radians
Introduction to radians
Finding arc length from radian angle measure
Ratio between concentric arcs
Example: Radian measure and arc length
Radian and degree conversion practice
Example: Converting degrees to radians
Example: Converting radians to degrees
Radians and degrees
Unit circle definition of trigonometric functions
Unit circle definition of trig functions
Example: Unit circle definition of sin and cos
Example: Using the unit circle definition of trig functions
Example: Trig function values using unit circle definition
Example: The signs of sine and cosecant
Unit circle manipulative
Matching ratios to trig functions
Example: Calculator to evaluate a trig function
Trig functions of special angles
Solving triangle in unit circle
Finding trig functions of special angles example
Graphs of trig functions
Midline, amplitude and period of a function
Example: Amplitude and period
Example: Graph, domain, and range of sine function
Example: Graph of cosine
Example: Intersection of sine and cosine
Example: Amplitude and period transformations
Example: Amplitude and period cosine transformations
Determining the equation of a trig function
Example: Figure out the trig function
Plotting maxima, minima and midline intersections of trig function
Modeling with periodic functions
Modeling annual temperature variation with trigonometry
Applying inverse trig function with model
Modeling temperature through the day
Inverse trig functions
Inverse trig functions: arcsin
Inverse trig functions: arccos
Inverse trig functions: arctan
Example: Calculator to evaluate inverse trig function
Solution set to sin equation
Angle of sun with the ground based on shadow
Modeling annual temperature variation with trigonometry
Applying inverse trig function with model
Trig ratio application problems
How much of a pyramid is submerged
Angle to aim to get alien
Figuring out coordinate of bended figure using trig
Long live tau
Tau versus pi
Pi is (still) wrong.
Special right triangles
30-60-90 triangle side ratios proof
45-45-90 triangle side ratios
30-60-90 triangle example problem
Area of a regular hexagon
45-45-90 triangles
Intro to 30-60-90 triangles
30-60-90 triangles II
Trig ratios and similarity
Similarity to define sine, cosine, and tangent
Sine and cosine of complements example
Showing relationship between cosine and sine of complements
Example with trig functions and ratios
Example relating trig function to side ratios
Trig identities and examples
Symmetry and periodicity of trig functions
Symmetry of trig values
Unit circle symmetries for tan
Relating trig function through angle rotations
Periodicity of tan example
Pythagorean identity
Pythagorean trig identity from soh cah toa
Pythagorean trig identity from unit circle
Using the Pythagorean trig identity
Examples using pythagorean identities to simplify trigonometric expressions
Trigonometric identities
Trigonometry identity review/fun
Proof: sin(a + b) = (cos a)(sin b) + (sin a)(cos b)
Proof: cos(a + b) = (cos a)(cos b) - (sin a)(sin b)
Trig identities part 2 (part 4 if you watch the proofs)
Trig identies part 3 (part 5 if you watch the proofs)
Cosine addition identity example
Double angle formula for cosine example
More trig examples
Navigation word problem
Fun trig problem
IIT JEE trigonometry problem 1
IIT JEE trigonometric maximum
IIT JEE trigonometric constraints
Trigonometric system example
2003 AIME II problem 11
2003 AIME II problem 14
Trigonometry word problems (part 1)
Trigonometry word problems (part 2)
Ferris wheel trig problem
Ferris wheel trig problem (part 2)
Law of cosines and law of sines
Law of cosines
Law of cosines to determine grade
Law of cosines for star distance
Law of sines
Law of sines for missing angle
Proof of the law of cosines
Proof: Law of sines
Term 3
Measurement
Volume
Cylinder volume and surface area
Volume of a sphere
Volume of a cone
Solid geometry volume
Perimeter, area and volume
Perimeter and area of triangles
Perimeter and area basics
Triangle area proofs
Interesting perimeter and area problems
Area of diagonal generated triangles of rectangle are equal
Area of an equilateral triangle
Area of shaded region made from equilateral triangles
Challenging perimeter problem
Triangle inequality theorem
Triangle inequality theorem
Koch snowflake fractal
Koch snowflake fractal
Area of an equilateral triangle
Area of Koch snowflake (part 1) - advanced
Area of Koch snowflake (part 2) - advanced
Heron's formula
Heron's formula
Part 1 of proof of Heron's formula
Part 2 of proof of Heron's formula
Circumference and area of circles
Circles: Radius, diameter, and circumference
Parts of a circle
Area of a circle
Perimeter and area of non-standard shapes
Quadrilateral overview
Quadrilateral properties
Area of a parallelogram
Area of a trapezoid
Area of a kite
Perimeter of a parallelogram
Perimeter and area of a non-standard polygon
Volume and surface area
Solid geometry volume
Cylinder volume and surface area
Volume of a sphere
How many people can a blimp carry
How far can you see from a plane window
Euclidean Geometry
Geometry
Introduction to Euclidean geometry
Euclid as the father of geometry
Language and notation of basic geometry
Lines, line segments, and rays
Drawing lines exercise example
Specifying planes in three dimensions
Language and notation of the circle
The golden ratio
Identifying rays
Logical reasoning
Logical reasoning
Conditional statements and deductive reasoning
Conditional statements exercise examples
Logical argument and deductive reasoning exercise example
Circles
Circle arcs and sectors
Language and notation of the circle
Circles: Radius, diameter, and circumference
Length of an arc that subtends a central angle
Finding central angle measure given arc length
Area of a sector given a central angle
Central, inscribed and circumscribed angles
Inscribed and central angles
Measure of circumscribed angle
Example with tangent and radius
Hypotenuse of right triangle inscribed in circle
Area of inscribed triangle
SSS to show a radius is perpendicular to a chord that it bisects
Perpendicular radius bisects chord
Area of inscribed equilateral triangle (some basic trig used)
Geometric models
How far can you see from a plane window
Quadrilaterals
Quadrilaterals
Quadrilateral overview
Quadrilateral properties
Kites as a mathematical shape
Quadrilateral types exercise
Proof: Opposite sides of parallelogram congruent
Proof: Diagonals of a parallelogram bisect each other
Proof: Opposite angles of parallelogram congruent
Proof: Rhombus diagonals are perpendicular bisectors
Proof: Rhombus area half product of diagonal length
Area of a parallelogram
Whether a special quadrilateral can exist
Rhombus diagonals
Analytic geometry
Geometry problems on the coordinate plane
Recognizing points on a circle
Classifying a quadrilateral on the coordinate plane
Identifying similar triangles in the coordinate plane
Which minions can the wizard reach
Distances between points
Distance formula
Midpoint formula
Ratios of distances between colinear points
Finding a point part way between two points
Geometric constructions
Constructing bisectors of lines and angles
Constructing a perpendicular bisector using a compass and straightedge
Constructing a perpendicular line using a compass and straightedge
Constructing an angle bisector using a compass and straightedge
Constructing regular polygons inscribed in circles
Constructing square inscribed in circle
Constructing equilateral triangle inscribed in circle
Constructing regular hexagon inscribed in circle
Constructing circumcircles and incircles
Constructing circle inscribing triangle
Constructing circumscribing circle
Worked examples
Interesting perimeter and area problems
Challenging perimeter problem
CA Geometry: Deductive reasoning
CA Geometry: Proof by contradiction
CA Geometry: More proofs
CA Geometry: Similar triangles 1
CA Geometry: Similar triangles 2
CA Geometry: More on congruent and similar triangles
CA Geometry: Triangles and parallelograms
CA Geometry: Area, pythagorean theorem
CA Geometry: Area, circumference, volume
CA Geometry: Pythagorean theorem, area
CA Geometry: Exterior angles
CA Geometry: Deducing angle measures
CA Geometry: Pythagorean theorem, compass constructions
CA Geometry: Compass construction
CA Geometry: Basic trigonometry
CA Geometry: More trig
CA Geometry: Circle area chords tangent
CA Geometry: Secants and translations
Ratios and proportions
Ratios and proportions
Ratio problem with basic algebra
Writing proportions
Find an unknown in a proportion
Find an unknown in a proportion 2
Proportions 2 exercise examples
Constructing proportions to solve application problems
Advanced ratios and proportions
The golden ratio
Advanced ratio problems
More advanced ratio problem with algebra
Another take on the rate problem
Alternate solution to ratio problem
Mountain height word problem
Rational and irrational numbers
Introduction to rational and irrational numbers
Sum and product of rational numbers
Proof that rational times irrational is irrational
Proof that sum of rational and irrational is irrational
Proof that square root of 2 is irrational
Proof that square root of prime number is irrational
Proof that there is an irrational number between any two rational numbers
Recognizing rational and irrational expressions example
Solution of Triangles
Right triangles and trigonometry
Pythagorean theorem
Pythagorean theorem
The Pythagorean theorem intro
Pythagorean theorem 1
Pythagorean theorem 2
Pythagorean theorem 3
Introduction to the Pythagorean theorem
Pythagorean theorem II
Pythagorean theorem proofs
Garfield's proof of the Pythagorean theorem
Bhaskara's proof of the Pythagorean theorem
Pythagorean theorem proof using similarity
Another Pythagorean theorem proof
Sine, cosine and tangent trigonometric functions
Basic trigonometry
Example: Using soh cah toa
Basic trigonometry II
Example: Trig to solve the sides and angles of a right triangle
Probability
Independent and dependent events
Basic probability
Basic probability
Probability space exercise example
Example: Marbles from a bag
Example: Picking a non-blue marble
Example: Picking a yellow marble
Venn diagrams and adding probabilities
Probability with playing cards and Venn diagrams
Addition rule for probability
Compound, independent events
Compound probability of independent events
Getting at least one head
Example: Probability of rolling doubles
LeBron asks: What are the chances of making 10 free throws in a row?
LeBron asks: What are the chances of three free throws versus one three pointer?
Frequency probability and unfair coins
Example: Getting two questions right on an exam
Example: Rolling even three times
Frequency stability
Dependent probability
Introduction to dependent probability
Example: Dependent probability
Example: Bag of unfair coins
Example: Is an event independent or dependent?
Monty Hall problem
Basic set operations
Intersection and union of sets
Relative complement or difference between sets
Universal set and absolute complement
Subset, strict subset, and superset
Bringing the set operations together
Old school probability (very optional)
Probability (part 1)
Probability (part 2)
Probability (part 3)
Probability (part 4)
Probability (part 5)
Probability (part 6)
Probability (part 7)
Probability (part 8)
Introduction to random variables
Probability and combinatorics
Permutations and combinations
Permutations
Combinations
Example: Ways to arrange colors
Example: 9 card hands
Example: Ways to pick officers
Probability using combinatorics
Example: Probability through counting outcomes
Example: All the ways you can flip a coin
Getting exactly two heads (combinatorics)
Probability and combinations (part 2)
Probability using combinations
Exactly three heads in five flips
Example: Different ways to pick officers
Example: Combinatorics and probability
Example: Lottery probability
Mega millions jackpot probability
Generalizing with binomial coefficients (bit advanced)
Conditional probability and combinations
Conditional probability warmup
Birthday probability problem
Making decisions with probability
Simple hypothesis testing
Random variables and probability distributions
Random variables and probability distributions
Random variables
Discrete and continuous random variables
Constructing a probability distribution for random variable
Probability density functions
Expected value: E(X)
Law of large numbers
Term life insurance and death probability
Binomial distribution
Binomial distribution 1
Binomial distribution 2
Binomial distribution 3
Binomial distribution 4
Expected value of binomial distribution
Poisson process
Poisson process 1
Poisson process 2
Basic probability
Basic probability
Winning the lottery versus earning billions
Making sense of probabilities
Probability space exercise example
Example: Marbles from a bag
Example: Picking a non-blue marble
Example: Picking a yellow marble
Dependent probability
Introduction to dependent probability
Example: Dependent probability
Example: Is an event independent or dependent?
Example: Bag of unfair coins
Monty Hall problem
Estimating probability
Estimating the probability of rolling 7
Probability models examples
Finance, Grwoth and Decay
Compound interest basics
Introduction to compound interest
The rule of 72 for compound interest
Term 4
Statistics
Statistical studies
Simple hypothesis testing
Descriptive statistics
Measures of central tendency
Statistics intro: Mean, median and mode
Example: Finding mean, median and mode
Exploring mean and median module
Sample mean versus population mean
Box-and-whisker plots
Reading box-and-whisker plots
Constructing a box-and-whisker plot
Box-and-whisker plots
Example: Range and mid-range
Variance and standard deviation
Range, variance and standard deviation as measures of dispersion
Variance of a population
Sample variance
Review and intuition why we divide by n-1 for the unbiased sample variance
Simulation showing bias in sample variance
Another simulation giving evidence that (n-1) gives us an unbiased estimate of variance
Simulation providing evidence that (n-1) gives us unbiased estimate
Population standard deviation
Sample standard deviation and bias
Statistics: Standard deviation
Exploring standard deviation 1 module
Statistics: Alternate variance formulas
Sal's old statistics videos
Statistics: The average
Statistics: Variance of a population
Statistics: Sample variance
Regression
Correlation and causality
Fitting a line to data
Estimating the line of best fit exercise
Squared error of regression line
Proof (part 1) minimizing squared error to regression line
Proof (part 2) minimizing squared error to regression line
Proof (part 3) minimizing squared error to regression line
Proof (part 4) minimizing squared error to regression line
Regression line example
Second regression example
R-squared or coefficient of determination
Calculating R-squared
Covariance and the regression line
Measures of central tendency
Statistics intro: Mean, median and mode
Example: Finding mean, median and mode
Exploring mean and median module
Comparing and sampling populations
Sample mean versus population mean
Reasonable samples
Comparing throws
Comparing swim times at the Olympics
Data and modeling
Estimating line of best fit
Estimating the line of best fit exercise
Scatter plots
Studying, shoe size, and test scores scatter plots
People smoking less over time scatter plot
Constructing a scatter plot
Constructing scatter plot exercise example
Patterns in data
Smoking in 1945
Interpreting a trend line
Video games and violence
Grade 12
Term 1
Number Patterns, Sequences and Series
Sequence convergence and divergence
Convergent and divergent sequences
Identifying sequence convergence and divergence
Definition of limit of a sequence and sequence convergence
Proving a sequence converges
Series
Sigma notation for sums
Series as sum of sequence
Writing a series in sigma notation
Explicitly defining a series
Formula for arithmetic series
Partial fraction decomposition to find sum of telescoping series
Leveraging properties of series to find sum
Finding the sum of n squares part 1
Finding the sum of n squares part 2
Alternate formula for sum of n squares
Geometric series
Geometric series
Formula for a finite geometric series
Sum of an infinite geometric series
Another derivation of the sum of an infinite geometric series
Geometric series convergence and divergence examples
Repeating decimal as infinite geometric series
Vertical distance of bouncing ball
Functions and Inverse Functions
Introduction to function inverses
Function inverses example 2
Function inverses example 3
A more formal understanding of functions
Function inverse example 1
Exponential and logarithmic functions
Exponential growth and decay
Exponential growth functions
Graphing exponential functions
Understanding linear and exponential models
Comparing exponential and quadratic models
Constructing linear and exponential functions from data
Constructing linear and exponential functions from graph
Modeling with exponential functions
Exponential growth and decay word problems
Decay of cesium 137 example
Modeling ticket fines with exponential function
Solving exponential equation
Continuous compounding and e
Introduction to interest
Interest (part 2)
Introduction to compound interest and e
Compound interest and e (part 2)
Compound interest and e (part 3)
Compound interest and e (part 4)
Finance, growth and decay
Interest and debt
Compound interest basics
Introduction to compound interest
The rule of 72 for compound interest
Interest basics
Introduction to interest
Interest (part 2)
Credit cards and loans
Annual percentage rate (APR) and effective APR
Institutional roles in issuing and processing credit cards
Payday loans
Continuous compound interest and e
e and compound interest
e as a limit
Formula for continuously compounding interest
Present value
Time value of money
Introduction to present value
Present value 2
Present value 3
Present value 4 (and discounted cash flow)
Personal bankruptcy
Personal bankruptcy: Chapters 7 and 13
Trigonometry- Compound angles
Trigonometric identities
Trigonometry identity review/fun
Proof: sin(a + b) = (cos a)(sin b) + (sin a)(cos b)
Proof: cos(a + b) = (cos a)(cos b) - (sin a)(sin b)
Trig identities part 2 (part 4 if you watch the proofs)
Trig identies part 3 (part 5 if you watch the proofs)
Cosine addition identity example
Double angle formula for cosine example
Term 2
Trigonometry 2D and 3D
Law of cosines and law of sines
Law of cosines
Law of cosines to determine grade
Law of cosines for star distance
Law of sines
Law of sines for missing angle
Proof of the law of cosines
Proof: Law of sines
Polynomial functions
Fundamental Theorem of Algebra
Fundamental theorem of algebra
Fundamental theorem of algebra for quadratic
Possible number of real roots
Dividing polynomials
Polynomial division
Polynomial divided by monomial
Dividing multivariable polynomial with monomial
Dividing polynomials 1
Dividing polynomials with remainders
Dividing polynomials with remainders example
Polynomial remainder theorem to determine coefficient example
Synthetic division
Synthetic division
Synthetic division example 2
Why synthetic division works
Factoring and roots of higher degree polynomials
Factoring sum of cubes
Difference of cubes factoring
Example: Factoring a fourth degree expression
Factoring 5th degree polynomial to find real zeros
Identifying graph based on roots
Differential Calculus
Differential calculus
Limits
Limits
Introduction to limits
Inferring limit from numerical data
Estimating limit numerically
Estimating limits from graphs
One-sided limits from graphs
Limit at a point of discontinuity
Determining which limit statements are true
2 sided limit from graph
Finding limits algebraically
Limit example 1
Limit properties
Limit by factoring cubic expression
Continuity using limits
Limits to define continuity
Limit and function defined at point of discontinuity
Fancy algebra to find a limit and make a function continuous
Defining a function at a point to make it continuous
Old limits tutorial
Introduction to limits
Limit examples (part 1)
Limit examples (part 2)
Limit examples (part 3)
Limit examples w/ brain malfunction on first prob (part 4)
More limits
Limits and infinity
Limits and infinity
Vertical asymptote of natural log
Visually determining vertical asymptotes
Limits at positive and negative infinity
More limits at infinity
Limits with two horizontal asymptotes
Limits at infinity using algebra
Squeeze theorem
Squeeze theorem or sandwich theorem
Squeeze theorem exercise example
Squeeze theorem (sandwich theorem)
Proof: lim (sin x)/x
Epsilon delta definition of limits
Limit intuition review
Building the idea of epsilon-delta definition
Epsilon-delta definition of limits
Proving a limit using epsilon-delta definition
Epsilon-delta limit definition 1
Epsilon-delta limit definition 2
Taking derivatives
Introduction to differential calculus
Newton, Leibniz, and Usain Bolt
Using secant line slopes to approximate tangent slope
Slope of a line secant to a curve
Slope of a secant line example 1
Slope of a secant line example 2
Slope of a secant line example 3
Approximating instantaneous rate of change word problem
Approximating equation of tangent line word problem
Introduction to derivatives
Derivative as slope of a tangent line
Tangent slope as limiting value of secant slope example 1
Tangent slope as limiting value of secant slope example 2
Tangent slope as limiting value of secant slope example 3
Calculating slope of tangent line using derivative definition
The derivative of f(x)=x^2 for any x
Formal and alternate form of the derivative
Formal and alternate form of the derivative for ln x
Formal and alternate form of the derivative example 1
Calculus: Derivatives 1
Calculus: Derivatives 2
Visualizing graphs of functions and their derivatives
Derivative intuition module
Interpreting slope of a curve exercise
Graphs of functions and their derivatives example 1
Where a function is not differentiable
Identifying a function's derivative example
Figuring out which function is the derivative
Intuitively drawing the derivative of a function
Intuitively drawing the antiderivative of a function
Visualizing derivatives exercise
Derivative properties and intuition
Using derivative properties
Power rule
Power rule
Is the power rule reasonable
Derivative properties and polynomial derivatives
Proof: d/dx(x^n)
Proof: d/dx(sqrt(x))
Power rule introduction
Chain rule
Derivatives of sin x, cos x, tan x, e^x and ln x
Chain rule introduction
Chain rule definition and example
Chain rule for derivative of 2^x
Derivative of log with arbitrary base
Chain rule example using visual function definitions
Chain rule example using visual information
Chain rule with triple composition
Derivative of triple composition
Extreme derivative word problem (advanced)
Product and quotient rules
Derivatives of sin x, cos x, tan x, e^x and ln x
Applying the product rule for derivatives
Product rule for more than two functions
Quotient rule from product rule
Quotient rule for derivative of tan x
Using the product rule and the chain rule
Product rule
Quotient rule and common derivatives
Equation of a tangent line
Implicit differentiation
Implicit differentiation
Showing explicit and implicit differentiation give same result
Implicit derivative of (x-y)^2 = x + y - 1
Implicit derivative of y = cos(5x - 3y)
Implicit derivative of (x^2+y^2)^3 = 5x^2y^2
Finding slope of tangent line with implicit differentiation
Implicit derivative of e^(xy^2) = x - y
Derivative of x^(x^x)
Derivative using log properties
Proofs of derivatives of common functions
Proof: d/dx(ln x) = 1/x
Proof: d/dx(e^x) = e^x
Proofs of derivatives of ln(x) and e^x
Derivative applications
Equations of normal and tangent lines
y-intercept of tangent line example
Equation of normal line
Equation of tangent line example 1
Motion along a line
Total distance traveled by a particle