Education for Life: The Subject of Math

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The Subject of Math – Click to Enlarge

This page is a free-shared non-linear educational subject outline for Math. It is purposed for use in community education environments, homeschool environments, traditional schooling environments, or as a supplemental and fun addition to any education program. As part of the complete Education for Life Program, this subject outline is specifically designed to work in conjunction with the other components: Foundations of Teaching, Curriculum, Lesson Plans for Life, Teaching Strategies, Learning Tools and Toys, Evaluation Model, and The Ultimate Classroom. If you’d like to learn how all these components work together, click here.

THESE LINKS JUMP DIRECTLY TO EACH COLOR ON THIS PAGE

MAXIMIZE BENEFITS FROM THIS PAGE WITH THESE KEY SECTIONS

Individualize learning math with the Lesson Plans Page
Explore and learn specific skills using the Online Resources Section
Maximize learning fun and involvement with the Teaching Strategies Page

Further integration specifically with the Khan Academy Math Program is in progress.

NOTE: The colors are provided as a possible linear progression (red/easiest to violet/most challenging) for people that might prefer a more linear structure. Our core philosophy is that through creativity every color can be made easy or challenging for any learning level.

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CLICK LINKS TO VISIT THE KHAN ACADEMY’S LEARNING ARCHIVE FOR SPECIFIC LESSONS FOR EACH BULLET-POINT. AN OVERVIEW OF ALL KHAN ACADEMY SECTIONS IS IN THE ONLINE RESOURCES SECTION AT THE BOTTOM OF THIS PAGE.

RED

	NOTE: The colors are provided as a possible linear progression (red/easiest to violet/most challenging) for people that might prefer a more linear structure. Our core philosophy is that through creativity every color can be made easy or challenging for any learning level.
	Compare numbers Know number names and the count sequence Count to tell the number of objects
	Understand subtraction as taking apart & taking from Subtracting within 20 Subtracting within 100
	Understand addition as putting together & adding to Classify objects and count the number of objects in different categories Adding within 20 Adding within 100
	Work with numbers 11″19 to gain foundations for place value
	Describe and compare measurable attributes using both the metric and the English measuring systems Measuring temperature, weight, volume, height, length, width, etc.
	Tell and write time
	Identify 2 dimensional shapes and reason with and recognize their attributes
	Identify different 3 dimensional objects and reason with and recognize their attributes

ORANGE

	NOTE: The colors are provided as a possible linear progression (red/easiest to violet/most challenging) for people that might prefer a more linear structure. Our core philosophy is that through creativity every color can be made easy or challenging for any learning level.
	Represent and solve problems involving addition and subtraction Add and subtract within 20
	Understand and apply units of measurement Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit
	Work with equal groups of objects to gain foundations for multiplication
	Measure and estimate lengths in standard units Relate addition and subtraction to length
	Use place value understanding and properties of operations to perform multi-digit arithmetic
$Develop understanding of fractions as numbers$	Develop understanding of fractions as numbers Extend understanding of fraction equivalence and ordering Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers Understand decimal notation for fractions, and compare decimal fractions
	Solve problems involving measurement & estimation of intervals of time, liquid volumes, & masses of objects Geometric measurement: concepts of area & relate area to multiplication & addition
	Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures Use the four operations with whole numbers to solve problems
	Gain familiarity with factors and multiples
	Understand place value Generalize place value understanding for multi-digit whole numbers Use place value understanding and properties of operations to add and subtract
	Geometric measurement: understand concepts of angle and measure angles
	Draw and identify lines and angles, and classify shapes by properties of their lines and angles
	Multiply and divide within 100 Represent and solve problems involving multiplication and division Solve problems involving the four operations; identify and explain patterns Understand properties of multiplication & the relationship between multiplication & division
	Generate and analyze patterns
	Begin to plot coordinates and understand the basics of a graph
	Begin calculating currency conversions and other complex problems with money Work with time and money

YELLOW

	NOTE: The colors are provided as a possible linear progression (red/easiest to violet/most challenging) for people that might prefer a more linear structure. Our core philosophy is that through creativity every color can be made easy or challenging for any learning level.
	Write and interpret numerical expressions
	Analyze patterns and relationships
	Perform operations with multi-digit whole numbers and with decimals to hundredths
$Use equivalent fractions as a strategy to add and subtract fractions.$	Use equivalent fractions as a strategy to add and subtract fractions
$Apply and extend previous understandings of multiplication and division to multiply and divide fractions.$	Apply and extend previous understandings of multiplication and division to multiply and divide fractions
	Measurement: understand concepts of volume & relate volume to multiplication & to addition
	Graph points on the coordinate plane to solve real-world and mathematical problems
	Classify two-dimensional figures into categories based on their properties
	Convert like measurement units within a given measurement system
	Understand ratio concepts and use ratio reasoning to solve problems
$Apply & extend understandings of multiplication & division to divide fractions by fractions.$	Apply & extend understandings of multiplication & division to divide fractions by fractions
	Compute fluently with multi-digit numbers and find common factors and multiples
	Apply and extend previous understandings of numbers to the system of rational numbers
	Reason about and solve one-variable equations and inequalities
	Represent and analyze quantitative relationships between dependent and independent variables
	Solve real-world and mathematical problems involving area, surface area, and volume
	Develop understanding of statistical variability
	Summarize and describe distributions
	Apply & extend understandings of multiplication & division to divide fractions by fractions within equations with variables
	Begin to understand and apply the relationship between fractions and decimals
	Begin to understand how to read formulas
	Apply and extend previous understandings of arithmetic to algebraic expressions

GREEN

	NOTE: The colors are provided as a possible linear progression (red/easiest to violet/most challenging) for people that might prefer a more linear structure. Our core philosophy is that through creativity every color can be made easy or challenging for any learning level.
	Analyze proportional relationships and use them to solve real-world and mathematical problems
	Use properties of operations to generate equivalent expressions
	Solve real-life and mathematical problems using numerical and algebraic equations
	Draw, construct & describe geometrical figures & describe relationships between them
	Use random sampling to draw inferences about a population
	Draw informal comparative inferences about two populations
	Investigate chance processes and develop, use, and evaluate probability models
	Know that there are numbers that are not rational & approximate them by rational numbers
	Work with radicals and integer exponents
	Understand the connection between proportional relationships, lines, & linear equations
	Analyze and solve linear equations and pairs of simultaneous linear equations
	Define, evaluate, and compare functions Use functions to model relationships between quantities
	Understand congruence & similarity using physical models, transparencies, or geometry software
	Understand and apply the Pythagorean Theorem
	Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres Investigate patterns of association in bivariate data
	Extend the properties of exponents to rational exponents
	Use properties of rational and irrational numbers
	Reason quantitatively and use units to solve problems Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers
	Interpret the structure of expressions Write expressions in equivalent forms to solve problems
	Perform arithmetic operations on polynomials
	Create equations that describe numbers or relationships Understand solving equations as a process of reasoning and explain the reasoning
	Solve equations and inequalities in one variable
	Solve systems of equations
	Represent and solve equations and inequalities graphically
	Represent & calculate simple probabilities with equations
	Calculate surface areas and volumes of 3d geometric shapes
	Begin working with and understanding irrational numbers
	Understand and use irrational numbers

BLUE

	NOTE: The colors are provided as a possible linear progression (red/easiest to violet/most challenging) for people that might prefer a more linear structure. Our core philosophy is that through creativity every color can be made easy or challenging for any learning level.
	Understand the concept of a function and use function notation Interpret functions that arise in applications in terms of the context Analyze functions using different representations Build a function that models a relationship between two quantities Build new functions from existing functions Interpret expressions for functions in terms of the situation they model
	Summarize, represent, and interpret data on a single count or measurement variable Summarize, represent, and interpret data on two categorical and quantitative variables
	Interpret linear models
	Perform arithmetic operations with complex numbers
	Use complex numbers in polynomial identities and equation
	Understand the r single count or measurement variable
	Use polynomial identities to solve problems
	Extend the domain of trigonometric functions using the unit circle
	Model periodic phenomena with trigonometric functions
	Prove and apply trigonometric identities
	Translate between the geometric description and the equation for a conic section
	Make inferences & justify conclusions from surveys, experiments, & observational studies
	Use probability to evaluate outcomes of decisions
	Summarize, represent, and interpret data on two categorical and quantitative variables
	Interpret linear models
	Experiment with transformations in the plane
	Understand congruence in terms of rigid motions
	Make geometric constructions
	Use coordinates to prove simple geometric theorems algebraically Prove geometric theorems
	Understand similarity in terms of similarity transformations
	Prove theorems involving similarity
	Define trigonometric ratios and solve problems involving right triangles
	Understand and apply theorems about circles
	Find arc lengths and areas of sectors of circles
	Understand the basic properties of waves
	Translate between the geometric description and the equation for a conic section
	Explain volume formulas and use them to solve problems
	Construct and compare linear, quadratic, and exponential models and solve problems
	Understand and evaluate random processes underlying statistical experiments
	Use irrational expressions in complex equations
	Rewrite rational expressions

INDIGO

	NOTE: The colors are provided as a possible linear progression (red/easiest to violet/most challenging) for people that might prefer a more linear structure. Our core philosophy is that through creativity every color can be made easy or challenging for any learning level.
	Understand independence and conditional probability and use them to interpret data
	Use rules of probability to compute probabilities of compound events in a uniform model
	Represent complex numbers and their operations on the complex plane
	Represent and model with vector quantities
	Represent and model derivative equations
	Perform operations on vectors
	Perform operations on matrices and use matrices in applications
	Apply trigonometry to general triangles
	Apply trigonometry to general circles
	Calculate varying types of mathematical series
	Understand and use the fundamental theorem of calculus
	Graph complex equations on the complex plane
	Translate between the geometric description and the equation for a conic section
	Graph trigonometric equations
	Visualize relationships between two-dimensional and three-dimensional objects
	Understand spherical trigonometry
	Apply geometric concepts in modeling situations
	Use the mean value theorem
	Calculating differentiation in derivatives
	Apply geometric concepts in Euclidian space
	Understand and graph integral calculus
	Solve and graph cubic polynomial functions
	Prove and use Rolle’s Theorum
	Understand parametric equations and polar graphs
	Understand basic functions
	Understand and calculate limits for functions
	Physics: Understand and calculate equations for basic physics and classical mechanics
	Understand and calculate basic equations in astronomy
	Use mathematics in project planning and project management
	Use mathematics to understand basic economics and globalization
	Use mathematics to understand the foundations of computer science
	Use mathematical equations in basic architecture blueprints and schematics
	Use mathematics in foundational biology applications
	Use mathematics in basic chemistry applications
	Understand and graph Riemann Sums
	Understand and use integrals and derivatives

VIOLET

	NOTE: The colors are provided as a possible linear progression (red/easiest to violet/most challenging) for people that might prefer a more linear structure. Our core philosophy is that through creativity every color can be made easy or challenging for any learning level.
	Graph trigonometric functions in Euclidean space
	Understand and graph differential geometry
	Understand and graph Symplectic Geometry
	Understand and apply contact geometry
	Understand and calculate differentiable and non-differentiable manifolds
	Understand and calculate intrinsic equations
	Calculate and understand mathematical equations for scalar fields
	Understand and use vector calculus
	Calculate vector fields
	Understand and use Topological Mathematics
$Design objects using fractal mathematical equations$	Design objects using fractal mathematical equations
	Calculate and use mathematical Measure and prove Measure Theory
	Use Chaos Theory Mathematics
	Use complex analysis and the theory of functions of a complex variable
	Understand and use Combinatorics
	Understand and use Combinatorial optimization
	Understand and use mathematical equations in cryptography and coding
	Understand and use applied mathematics within the fluid branch of mechanics
	Understand and use scientific computing
	Understand and use applied mathematics in advanced computer sciences and artificial intelligence
	Understand and use applied mathematics within economics and mathematical finance
	Understand and use applied mathematics within business
	Understand and use applied mathematics within engineering
	Understand and use applied mathematics within physics
	Understand and use applied mathematics within chemistry
	Understand and use applied mathematics within psychology
	Understand and use applied mathematics within biology
	Understand and use applied mathematics within scientific computation
	Understand and use mathematical finance
	Understand and use operational research and optimization
	Understand and use applied mathematics within quantum mechanics
	Understand and use quantum field theory applied mathematics within particle physics
	Understand light through quantum theory using applied mathematics
	Understand and use mathematics to understand atomic structures
	Understand and use the mathematics behind oscillations
	Understand and use applied mathematics within the statics branch of mechanics
	Understand and use applied mathematics within the kinematics branch of mechanics
	Understand and use applied mathematics within astronomy and the celestial branch of mechanics
	Understand and use applied mathematics within Statistical mechanics or statistical thermodynamics
	Understand and use applied mathematics within actuarial science and accounting
	Understand and use applied mathematics within software engineering
	Understand and use applied mathematics within advanced statistics
	Understand and use equations and diagrams within mathematical and computational sociology