Complete Elementary Mathematics Masterclass

📚 Topics Covered

• What are numbers? History and importance
• Counting 1-20: objects, fingers, visual aids
• Number recognition and writing practice
• Number words: spelling one to twenty
• Before, after, and between numbers
• Counting forward and backward
• Skip counting by 2s introduction
• Zero concept and its importance
• One-to-one correspondence
• Greater than, less than concepts

• Equal to understanding
• Number line introduction 0-20

📚 Topics Covered

• Counting 21-100 systematically
• Tens and ones concept introduction
• Place value understanding with blocks
• Writing numbers in expanded form
• Number patterns in 100 chart
• Skip counting by 2s, 5s, and 10s
• Even and odd numbers introduction
• Comparing two-digit numbers
• Ordering numbers from least to greatest
• Number bonds to 10

• Introduction to estimation
• Rounding to nearest 10

📚 Topics Covered

• Addition concept: combining sets
• Plus sign and equals sign meaning
• Addition sentences and vocabulary
• Adding with objects and pictures
• Addition on number line
• Addition facts 0-5
• Addition facts 6-10
• Doubles facts (1+1, 2+2, etc.)
• Near doubles strategy
• Making 10 strategy

• Commutative property (turn-around facts)
• Zero property of addition

📚 Topics Covered

• Subtraction as taking away
• Subtraction as finding difference
• Minus sign understanding
• Subtraction sentences
• Subtraction with objects and pictures
• Subtraction on number line
• Subtraction facts 0-10
• Fact families: addition and subtraction
• Related facts connection
• Counting back strategy

• Counting up strategy
• Think addition to subtract

📚 Topics Covered

• Adding multiples of 10
• Adding two-digit numbers without regrouping
• Vertical addition alignment
• Adding ones, then tens strategy
• Breaking apart numbers to add
• Addition with regrouping introduction
• Carrying concept explanation
• Using base-10 blocks for regrouping
• Addition with multiple addends
• Checking addition with subtraction

• Mental math strategies for addition
• Estimating sums

📚 Topics Covered

• Subtracting multiples of 10
• Two-digit subtraction without regrouping
• Vertical subtraction setup
• Subtract ones, then tens
• Subtraction with regrouping introduction
• Borrowing/regrouping concept
• Using manipulatives for regrouping
• Checking subtraction with addition
• Subtraction across zeros
• Mental math for subtraction

• Estimating differences
• Problem-solving with subtraction

📚 Topics Covered

• Multiplication as repeated addition
• Groups and arrays understanding
• Times sign and multiplication vocabulary
• Multiplication sentences
• Skip counting connection
• Multiplication by 0 and 1
• Multiplication by 2 and 5
• Multiplication by 10
• Doubles in multiplication
• Using arrays to multiply

• Commutative property of multiplication
• Building multiplication tables

📚 Topics Covered

• Circle: properties and examples
• Triangle: types and properties
• Square vs rectangle comparison
• Pentagon, hexagon, octagon
• Sides and vertices counting
• Straight vs curved lines
• Open vs closed shapes
• Symmetry introduction
• Lines of symmetry
• Creating patterns with shapes

• Combining shapes to make pictures
• Shape sorting and classification

📚 Topics Covered

• Operations review
• Problem-solving strategies review
• Mental math techniques
• Geometry concepts recap
• Real-world applications

📚 Topics Covered

• Clock reading: hour hand understanding
• Clock reading: minute hand understanding
• Reading time to the hour
• Reading time to the half hour
• Quarter past and quarter to
• Reading time to 5 minutes
• AM and PM understanding
• Days of the week sequence
• Months of the year
• Reading calendar dates

• Yesterday, today, tomorrow
• Elapsed time simple problems

📚 Topics Covered

• Coin identification and values
• Penny, nickel, dime, quarter
• Dollar bills introduction
• Counting coins same type
• Counting mixed coins
• Making change basics
• Dollar and cents notation
• Adding money amounts
• Subtracting money amounts
• Word problems with money

• Needs vs wants concept
• Simple budgeting introduction

📚 Topics Covered

• Non-standard units measurement
• Introduction to ruler use
• Inches and feet
• Centimeters and meters
• Measuring classroom objects
• Comparing lengths
• Ordering by length
• Estimating lengths
• Perimeter introduction
• Measuring curved lines

• Height measurement
• Distance concepts

📚 Topics Covered

• Heavy and light comparison
• Balance scale understanding
• Pounds and ounces introduction
• Kilograms and grams basics
• Weighing common objects
• Capacity: full, empty, half
• Cups, pints, quarts, gallons
• Liters and milliliters
• Comparing capacities
• Estimating weight and capacity

• Temperature introduction
• Reading thermometer

📚 Topics Covered

• Integration of all Phase 1 concepts
• Real-world problem solving
• Project presentation skills
• Mathematical communication
• Reflection on learning

📚 Topics Covered

• Multiplication facts 6-9
• Square numbers understanding
• Patterns in multiplication table
• Tricks for 9s facts
• Multiplication by 11 and 12
• Distributive property introduction
• Breaking apart to multiply
• Doubling and halving strategy
• Multiplication fact fluency drills
• Timed multiplication tests

• Multiplication games and competitions
• Real-world multiplication applications

📚 Topics Covered

• Multiplying by 10, 100, 1000
• Two-digit by one-digit multiplication
• Partial products method
• Standard algorithm introduction
• Area model for multiplication
• Lattice multiplication method
• Three-digit by one-digit
• Two-digit by two-digit basics
• Estimating products
• Checking multiplication with division

• Word problems with multiplication
• Multi-step problems

📚 Topics Covered

• Division as sharing equally
• Division as repeated subtraction
• Division symbol and vocabulary
• Dividend, divisor, quotient
• Division facts related to multiplication
• Dividing by 1 and itself
• Division by 2, 5, and 10
• Using multiplication to divide
• Fact families with multiplication/division
• Remainders introduction

• Division on number line
• Array model for division

📚 Topics Covered

• Long division setup
• Divide, multiply, subtract, bring down
• Two-digit divided by one-digit
• Handling remainders
• Checking division with multiplication
• Three-digit divided by one-digit
• Zeros in quotient
• Estimating quotients
• Division word problems
• Interpreting remainders in context

• Mental math division strategies
• Division patterns

📚 Topics Covered

• Choosing the correct operation
• Multi-step word problems
• Working backward strategy
• Guess and check method
• Drawing diagrams to solve
• Making tables strategy
• Finding patterns in problems
• Writing equations from words
• Checking reasonableness
• Problem-solving plan steps

• Creating own word problems
• Real-world applications

📚 Topics Covered

• Fraction as part of whole
• Numerator and denominator meaning
• Unit fractions understanding
• Halves, thirds, fourths
• Fifths, sixths, eighths
• Fractions on number line
• Comparing fractions same denominator
• Comparing fractions same numerator
• Equivalent fractions with models
• Simplest form introduction

• Mixed numbers introduction
• Improper fractions basics

📚 Topics Covered

• Adding fractions same denominator
• Subtracting fractions same denominator
• Adding mixed numbers simple
• Subtracting mixed numbers simple
• Finding common denominators
• Adding unlike fractions basics
• Subtracting unlike fractions basics
• Multiplying fraction by whole number
• Fraction of a set
• Word problems with fractions

• Estimating with fractions
• Fractions in measurement

📚 Topics Covered

• Decimal point meaning
• Tenths place understanding
• Hundredths place understanding
• Reading decimal numbers
• Writing decimals in words
• Decimals on number line
• Comparing decimals
• Ordering decimals
• Rounding decimals to whole
• Rounding to nearest tenth

• Fractions to decimals (tenths, hundredths)
• Money as decimals

📚 Topics Covered

• Adding decimals with same places
• Subtracting decimals same places
• Adding decimals different places
• Lining up decimal points
• Adding money with decimals
• Subtracting money with decimals
• Multiplying decimals by 10, 100
• Multiplying decimal by whole number
• Estimating with decimals
• Word problems with decimals

• Decimals in measurement
• Calculator use with decimals

📚 Topics Covered

• Collecting and organizing data
• Tally charts and frequency tables
• Pictographs reading and creating
• Bar graphs horizontal and vertical
• Line plots introduction
• Reading and interpreting graphs
• Finding range, mode, median
• Mean (average) introduction
• Creating surveys
• Double bar graphs

• Making predictions from data
• Data in real world

📚 Topics Covered

• Types of angles: acute, right, obtuse
• Measuring angles with protractor
• Drawing angles
• Parallel and perpendicular lines
• Types of triangles by sides
• Types of triangles by angles
• Quadrilaterals classification
• Properties of rectangles, squares
• Rhombus and parallelogram
• Trapezoid properties

• Congruent shapes
• Similar shapes basics

📚 Topics Covered

• 3D shapes: cube, rectangular prism
• Sphere, cylinder, cone
• Pyramid types
• Faces, edges, vertices counting
• Nets of 3D shapes
• Building 3D shapes from nets
• Volume as counting cubes
• Volume of rectangular prism
• Surface area introduction
• Real-world 3D shapes

• Cross-sections basics
• 3D shape sorting

📚 Topics Covered

• Perimeter of polygons
• Perimeter word problems
• Area by counting squares
• Area of rectangle formula
• Area of square
• Area of triangle introduction
• Area of parallelogram
• Composite figures area
• Perimeter of composite figures
• Area vs perimeter understanding

• Real-world area problems
• Estimating area and perimeter

📚 Topics Covered

• Coordinate plane introduction
• X-axis and y-axis
• Ordered pairs (x, y)
• Plotting points on grid
• Reading coordinates
• First quadrant focus
• Creating pictures with coordinates
• Distance between points (horizontal/vertical)
• Simple transformations: slides
• Reflections across axes

• Coordinate battleship game
• Real-world coordinate uses

📚 Topics Covered

• Integration of Phase 2 concepts
• Complex problem-solving
• Mathematical reasoning
• Project presentation
• Self-assessment and reflection

📚 Topics Covered

• Numbers to millions
• Place value to millions
• Reading and writing large numbers
• Expanded form to millions
• Comparing large numbers
• Ordering large numbers
• Rounding to any place value
• Scientific notation introduction
• Powers of 10 understanding
• Number patterns in large numbers

• Estimation with large numbers
• Real-world large numbers

📚 Topics Covered

• Factors definition and finding
• Factor pairs
• Prime and composite numbers
• Prime factorization
• Factor trees
• Greatest Common Factor (GCF)
• Multiples and common multiples
• Least Common Multiple (LCM)
• Using GCF and LCM
• Divisibility rules 2, 3, 5, 9, 10

• Perfect squares
• Square roots introduction

📚 Topics Covered

• Three-digit by two-digit multiplication
• Multiplication of decimals basics
• Multiplying by powers of 10
• Mental math multiplication tricks
• Distributive property applications
• Area model for larger numbers
• Partial products extended
• Estimation strategies for products
• Multiplication with variables introduction
• Order of operations with multiplication

• Complex word problems
• Real-world multiplication applications

📚 Topics Covered

• Three-digit by two-digit division
• Division with decimals in dividend
• Dividing by powers of 10
• Mental division strategies
• Interpreting remainders as fractions
• Interpreting remainders as decimals
• Division estimation techniques
• Compatible numbers for division
• Division with variables basics
• Order of operations with division

• Complex division word problems
• Division in real-world contexts

📚 Topics Covered

• Arithmetic sequences
• Finding the rule in patterns
• Extending number patterns
• Geometric sequences basics
• Fibonacci sequence introduction
• Triangular numbers
• Pattern rules with operations
• Input-output tables
• Function machines concept
• Growing patterns

• Decreasing patterns
• Complex pattern problems

📚 Topics Covered

• Adding mixed numbers with regrouping
• Subtracting mixed numbers with borrowing
• Finding least common denominator
• Adding three or more fractions
• Fraction multiplication understanding
• Multiplying fractions by fractions
• Multiplying mixed numbers
• Reciprocals introduction
• Division of fractions basics
• Dividing whole numbers by fractions

• Complex fraction word problems
• Fractions in recipes and scaling

📚 Topics Covered

• Multiplying decimals by decimals
• Division with decimals as divisor
• Repeating decimals introduction
• Terminating vs repeating
• Converting fractions to decimals
• Converting decimals to fractions
• Percent as special decimal
• Scientific notation with decimals
• Significant figures basics
• Decimal word problems complex

• Decimals in science contexts
• Calculator strategies with decimals

📚 Topics Covered

• Ratio concept and notation
• Writing ratios three ways
• Equivalent ratios
• Simplifying ratios
• Ratio tables
• Rates and unit rates
• Price per unit calculations
• Proportion definition
• Solving proportions
• Cross multiplication

• Scale drawings and maps
• Similar figures and ratios

📚 Topics Covered

• Percent meaning and symbol
• Percent as per hundred
• Converting percent to decimal
• Converting percent to fraction
• Finding percent of a number
• Mental math with percentages
• 10%, 25%, 50%, 75% shortcuts
• Percent increase introduction
• Percent decrease introduction
• Sales tax calculations

• Discount calculations
• Tips and gratuity

📚 Topics Covered

• Order of operations introduction
• PEMDAS/BODMAS rule
• Parentheses and brackets
• Exponents in order of operations
• Multiple operations problems
• Nested parentheses
• Writing expressions from words
• Evaluating expressions
• Creating equivalent expressions
• Properties of operations review

• Mental math with mixed operations
• Complex multi-step problems

📚 Topics Covered

• Complementary angles
• Supplementary angles
• Vertical angles
• Adjacent angles
• Angles in triangles sum to 180°
• Finding missing angles
• Angles in quadrilaterals
• Interior angles of polygons
• Exterior angles basics
• Angle bisectors

• Perpendicular bisectors
• Constructions with compass

📚 Topics Covered

• Translations (slides) in detail
• Reflections (flips) advanced
• Rotations (turns) 90°, 180°, 270°
• Combinations of transformations
• Line symmetry advanced
• Rotational symmetry
• Tessellations introduction
• Creating tessellation patterns
• Transformations on coordinate grid
• Enlargements and reductions

• Scale factor basics
• Symmetry in art and nature

📚 Topics Covered

• Circle vocabulary: radius, diameter
• Chord and arc definitions
• Center, circumference understanding
• Pi introduction and history
• Circumference formula C = πd
• Circumference formula C = 2πr
• Area of circle A = πr²
• Finding radius from circumference
• Finding radius from area
• Semicircles and quarter circles

• Composite figures with circles
• Real-world circle problems

📚 Topics Covered

• Metric system relationships
• Converting within metric system
• Imperial system relationships
• Converting within imperial system
• Metric to imperial conversions
• Area unit conversions
• Volume unit conversions
• Time conversions complex
• Speed, distance, time relationships
• Rate problems

• Dimensional analysis basics
• Real-world conversion problems

📚 Topics Covered

• Integration of advanced concepts
• Complex problem-solving showcase
• Mathematical modeling
• Project documentation
• Presentation preparation

📚 Topics Covered

• Variable as unknown number
• Writing algebraic expressions
• Translating words to algebra
• Evaluating expressions
• Substitution method
• Terms and coefficients
• Like terms identification
• Combining like terms
• Distributive property with variables
• Simplifying expressions

• Expression word problems
• Creating expressions from patterns

📚 Topics Covered

• Equation vs expression
• Solving one-step addition equations
• Solving one-step subtraction equations
• Solving one-step multiplication equations
• Solving one-step division equations
• Inverse operations concept
• Checking solutions
• Two-step equations introduction
• Equations with fractions basics
• Equations with decimals basics

• Word problems to equations
• Real-world equation applications

📚 Topics Covered

• Inequality symbols: <, >, ≤, ≥
• Graphing inequalities on number line
• Writing inequalities from words
• Solving one-step inequalities
• Checking inequality solutions
• Real-world inequality situations
• Compound inequalities basics
• And vs or in inequalities
• Graphing solution sets
• Inequality word problems

• Creating inequalities from data
• Systems thinking introduction

📚 Topics Covered

• Function concept introduction
• Input-output relationships
• Function tables
• Function rules and patterns
• Graphing points review
• Graphing linear patterns
• Slope concept basics
• Positive vs negative slope
• Y-intercept understanding
• Graphing from table of values

• Real-world linear relationships
• Non-linear patterns introduction

📚 Topics Covered

• Negative numbers in context
• Integers on number line
• Absolute value concept
• Adding integers with chips/number line
• Subtracting integers
• Multiplying integers
• Dividing integers
• Integer operation rules
• Order of operations with integers
• Integer word problems

• Temperature and elevation problems
• Financial contexts with integers

📚 Topics Covered

• Mean, median, mode review
• Range and outliers
• Quartiles introduction
• Box-and-whisker plots
• Stem-and-leaf plots
• Frequency distributions
• Histograms
• Circle graphs (pie charts)
• Choosing appropriate graphs
• Misleading graphs identification

• Data collection methods
• Surveys and sampling basics

📚 Topics Covered

• Probability as likelihood
• Probability scale 0 to 1
• Certain, likely, unlikely, impossible
• Experimental probability
• Theoretical probability
• Favorable outcomes
• Sample space
• Simple probability calculations
• Probability with dice
• Probability with cards

• Probability with spinners
• Compound events introduction

📚 Topics Covered

• Counting principle
• Tree diagrams for counting
• Organized lists
• Combinations introduction
• Permutations introduction
• Difference between combinations and permutations
• Factorial notation basics
• Simple combination problems
• Simple permutation problems
• Probability with combinations

• Real-world counting problems
• Problem-solving strategies

📚 Topics Covered

• Making predictions from data
• Interpolation and extrapolation
• Correlation vs causation
• Bias in data collection
• Random sampling importance
• Margin of error basics
• Confidence basics
• Using statistics to support arguments
• Critical analysis of statistics
• Statistics in media

• Creating statistical reports
• Presenting statistical findings

📚 Topics Covered

• Simple interest calculation
• Compound interest introduction
• Savings and investments basics
• Budget creation and management
• Profit and loss
• Markup and markdown
• Commission calculations
• Tax calculations advanced
• Unit price comparisons
• Best buy problems

• Currency exchange basics
• Financial planning introduction

📚 Topics Covered

• Logical thinking development
• If-then statements
• Converse and inverse
• Truth tables basics
• Venn diagrams advanced
• Set theory basics
• Union and intersection
• Logical puzzles
• Deductive reasoning
• Inductive reasoning

• Proof by example
• Counter-examples

📚 Topics Covered

• Polya's problem-solving method
• Understanding the problem
• Devising a plan
• Carrying out the plan
• Looking back and checking
• Multiple solution methods
• Working backwards mastery
• Guess and check refinement
• Make it simpler strategy
• Look for patterns advanced

• Use a model or diagram
• Eliminate possibilities

📚 Topics Covered

• Open-ended problem exploration
• Mathematical conjectures
• Testing hypotheses
• Finding counterexamples
• Generalizing patterns
• Mathematical communication
• Writing mathematical explanations
• Justifying solutions
• Peer review of solutions
• Mathematical debates

• Creating mathematical questions
• Research projects

📚 Topics Covered

• Math competition formats
• Time management strategies
• Mental math advanced techniques
• Estimation strategies advanced
• Number sense development
• Pattern recognition mastery
• Lateral thinking problems
• Multi-step problem strategies
• Competition problem types
• Practice competition rounds

• Analyzing solutions
• Learning from mistakes

📚 Topics Covered

• Mathematics in architecture
• Mathematics in art and design
• Mathematics in nature
• Mathematics in music
• Mathematics in sports
• Mathematics in cooking
• Mathematics in travel
• Mathematics in technology
• Mathematics in business
• Mathematics in science

• Career connections
• Future mathematics pathways

📚 Topics Covered

• Number and operations mastery review
• Algebraic thinking review
• Geometry and measurement review
• Data analysis review
• Problem-solving strategies review
• Making connections across topics
• Identifying strengths and gaps
• Creating personal math reference
• Reflection on learning journey
• Setting future goals

• Preparation for middle school math
• Celebration of achievements

📚 Topics Covered

• Preview of middle school mathematics
• Introduction to advanced algebra
• Geometry preview
• Advanced problem-solving
• Study skills for mathematics
• Using technology in math
• Online mathematics resources
• Mathematics communities
• Continuing education options
• Summer mathematics activities

• Maintaining skills
• Lifelong learning in mathematics