Unit 1: Number Sense and Arithmetic
Whole numbers and operations
Order of operationsEstimation and mental math
Place value and digit problems

Fractions, decimals, and percents
Operations and conversions
Comparing and ordering
Percent increase and decrease

Integers and exponents
Negative numbers
Powers and square roots
Scientific notation (basic)
Divisibility
Divisibility rules (2, 3, 4, 5, 6, 8, 9, 10, 11)Factors and multiples

Primes
Prime factorization
Counting divisors

GCD and LCM
Word problems with GCD and LCM

Remainders and modular thinking
Remainders and repeating cycles
Units digits and patterns

Perfect squares and cubes
Ratios and proportions
Scaling and unit conversion
Maps and scale drawings

Rates
Speed, distance, time
Work rates
Unit rates and best-buy problems

Percent applications
Discounts, tax, interest (simple)
Mixtures and concentrations
Expressions and equations
Simplifying expressions
Solving linear equations
Word problems and translating phrases

Inequalities (basic)Patterns and sequences
Arithmetic sequences
Finding the nth term
Sums of consecutive numbers

Systems and logic
Two-variable systems
Age and coin problems

Coordinate plane basics
Plotting points, slope intuition
Angles and lines
Angle relationships, parallel lines
Triangle angle sum, polygon angle sums

Triangles
Pythagorean Theorem and common triples
Special right triangles (45-45-90, 30-60-90)Area of triangles
Similar triangles

Quadrilaterals and polygons
Area and perimeter
Properties of parallelograms, trapezoids, rhombi

Circles
Circumference and area
Arcs and sectors (basic)

Area and perimeter strategies
Composite and shaded regions
Dissection and rearrangement

Solid geometry
Volume and surface area of cubes, prisms, cylindersV
isualizing 3D figures and nets

Transformations and symmetry

Reflections, rotations, translations
Line and rotational symmetry
Counting principles
Multiplication principle
Casework and organized lists
Arrangements and permutations (basic)
Combinations (basic)

Probability
Simple and compound events
Probability as a fraction and via counting
Geometric probability (areas)

Counting special structures
Handshake problems
Paths on grids
Venn diagrams and inclusion-exclusion (two sets)
Data analysis
Mean, median, mode, range
Reading tables, bar graphs, and line graphs
Effects of adding or removing data

Logic and reasoning
Truth-teller and liar puzzles
Elimination and grids
Working backward

Calendars, time, and clocks
Draw a diagram
Make an organized list or table
Look for a pattern
Work backward
Guess and check, then refine
Use symmetry and simplify
Try small cases
Use estimation to eliminate choices