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.
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
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
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
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
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
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