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Pre-Math Skills/concepts

- Shape recognition
- Draw Shapes
- Money
- Same/different/opposite
- cardinal/ordinal numbers
- Number symbol/ number word correspondance/recognition
- How many?
- Mazes
- Direction (up, down, in front of, in back of, left, right)
- Placement (near, far, in, out, on, off, top, bottom, over, under, low, high, next to)
- number recognition

Shapes

Counting

- Cardinal Numbers
- Ordinal Numbers
- Skip counting
- Skip counting Games
- Greek numbers and prefixes

Addition

Subtraction

- Subtracting: Getting Started
- Borrowing Practice
- Subtraction from before subtraction
- Equal Additions Algorithm
- Decomposition Algorithm
- Complement Algorithm
- Austrian Algorithm

Multiplication

- Skip Counting Review
- Multiplication as repeated addition
- Multiplication as an array
- Multiplication by one
- Multiplication by two, doubling
- Multiplication by zero
- Commutative property of multiplication
- Multiplication by five
- Multiplication by ten
- Multiplication by three
- Multiplication by four
- Multiplication tables, to 5 x 5, Review
- Multiplication by nine
- Multiplication by eleven
- Multiplication by six
- Multiplication by seven
- Multiplication by eight
- Multiplication by twelve
- Mental Multiplication by using an expanded form, 12 = 10 + 2
- Multiplication tables, 1x1 to 12x12
- Multiplication by using guide numbers, 99 = 100 - 1
- Multiplication by powers of 10
- Multiplication by 25
- The Standard Algorithm
- Horizontal Multiplication
- The Box method
- The lattice method
- Halving and doubling method
- Russian peasent method
- German low stress method
- Using fingers
- Using an abacus
- Vedic methods
- Speed methods for single digit multipliers
- Checking your answers by casting out nines

Division

- Fact Families: p.1, p.2, p.3, p.4, p.5, p.6
- Division as repeated subtracting
- Divisibility Rules
- Scaffold Method
- Standard Algorithm
- Is the scaffold method efficient?

Fractions

- Fraction Pictures, manipulatives
- Equivalent fractions
- Comparing Fractions
- Compound fractions, reducing fractions
- Adding/subtracting fractions with like denominators
- Least common Multiple
- Greatest Common Factor
- Lowest Common denominator
- Adding/subtracting fractions with different denominators
- Multiplying/dividing frations
- Fraction families1,2
- Fractions to decimals to percents
- Ratios
- Aliquot Numbers
- Common Fractions (and decimal and percentage equivalents)

Decimals/Percents/Money

- Decimals

- Decimal Addition
- Decimal Subtraction
- Decimal Multiplication
- Decimal Division

- Percents
- Money

- Rounding
- Finding the Mode
- Finding the Median
- Averages
- Finding the Range of data
- Measures of central tendancy
- Quartiles
- Percentiles
- Box and whiskers graphs
- Possible Combinations? Using tree graphs
- What are the odds? Basic probabilities
- Reading bar graphs
- Reading circle/pie graphs
- Moving Averages
- Weighted Averages
- Line of best fit

Areas

- Areas 1-d to 2-d
- Areas of Squares
- Areas of Rectangles
- Areas of Triangles
- Areas of Circles
- Areas of Parallelograms
- Areas of Rhombus'
- Areas of trapezoids
- Areas of sectors
- Areas of similar figures
- Areas of regular polygons
- Composite areas
- Surface areas
- changing areas
- Word problems involving area
- In Summary: areas of various shapes

Angles

- Intro to Angles
- Measuring and Drawing Angles
- Acute, right obtuse angles, straight angles
- Angles of regular figures
- Solid angles, angles in higher dimensions

Variables

- Solving addition with unknowns
- Solving multiplication with unknowns
- Additive rule of equality
- Solving problems with both addition and multiplication with unknowns
- Set Theory, pt.1
- Dependant and independant variables
- Multiplicative rule of equality
- Distributive rule of equality
- Associative Law
- Commutative Law
- Foil Multiplication
- Sets 2
- Sets 3

Balancing Equations

- Balancing Equations 1
- Reciprocals
- Balancing Equations 2
- Multiplying Negative Numbers
- Multiplying Negatives and variables
- Multiplying equations by a negative number
- Balancing equations 3

Lines

- 0-D to 1-D
- Absolute Value
- Distance, Midpoint
- Straight line, line segments
- Parallel and Perpendicular lines
- Slope of a line
- Equations of a line: Standard form
- Equations of a line: Point-slope form
- Equations of a line: slope-intercept form
- non-straight lines - Euclid's 5th postulate
- lines in a 3-D or higher context

Powers

- Definitions, bases, exponents
- (a
^{m})^{n}= a^{mn} - (a/b)
^{m}= (a^{m})/(b^{m}) - (ab)
^{m}= a^{m}b^{m} - (a
^{m})/(A^{n}) = A^{m-n} - b
^{1/n} - b
^{m/n}

Functions

Time

SI Units/Unit Conversion/Measurements

- British Units
- SI Units
- Time Conversions
- Length Conversions
- temperature
- Area
- Volume
- Metric Prefixes
- Angles/ Radians/degrees
- Mass Conversions
- Weight Conversions
- Force
- Density
- Pressure
- Energy
- Power
- Acceleration
- Amount/moles

Solving Word Problems

- Clue words for word problems
- Worksheet 1
- Worksheet 2
- Worksheet 3
- Worksheet 4

Graphing

Number Theory

- Number map
- Prime numbers/composite numbers
- Create a prime number sieve
- Primes to 100, A different view of primes
- Factoring Startegies
- factor Trees
- Perfect squares
- Perfect Cubes
- Square Roots, Sq. roots up to root of 25
- Properties of powers
- Counting Systems
- Signed Numbers
- Factorials!
- Natural Numbers
- Integers
- Rational Numbers
- Real Numbers
- Complex Numbers
- Transcendental Numbers
- Perfects, Amicables

Geometry

- The pythagorean theorem
- Pythagorean Triples
- Definitions: Points, lines, planes, space, hyperspace
- Points (0-D)
- Lines, rays, line segments (1-D)
- Planes, angles, Areas (2-D)
- Intro to Logic
- Intro to Proof
- intersections, bisections
- Parallel and Perpendicular
- Polygons, perimeter
- diagonals, transversals
- triangles
- similarity
- congruence
- symmetry
- Basic constructions
- circles
- conic sections
- curves
- Space, dihedral angles, Volume (3-D)
- Pyramids & Cones
- Topology Basics
- Curves
- 4-D Space

Trigonometry

- Definitions
- Angle measurement, angle addition and subtraction
- Coordinate systems
- Basic planar Trig Ratios
- Reciprocal trig ratios
- Solution methods
- Trig functions
- Trig identities
- Vectors
- Application problems
- 3-D trig
- 4-d

Vectors

- Vector addition
- Vector subtraction
- Vector Multiplication

- Scalar Multiplication
- Dot Product
- Cross Product
- Wedge Product

- Vector calculus

Calculus

- The Derivative, the operator d/dx
- Separation of terms
- The Power Rule
- Pulling out coefficients
- Derivative of constants
- Initial Conditions
- Integration, Operator S
- Seperation of terms
- Pulling out coefficients
- Power Rule
- Integration of constants

Modelling

Symmetry/Tesselations/Group Theory

Topology

Matrices

Solving Simultaneous equations

Logarithms

Others