Mathematics
Horizons Math + Pre-Calculus
Primary•Secondary•10 Levels•Ages 6–16
"Spiral Learning • Conceptual Mastery • Algebraic Thinking • University Readiness"
Programme Overview
The Mathematics curriculum begins with the Horizons Math Curriculum (HMC) in the primary years — a proven spiral-learning approach used widely in the United States.
From Grade 6 onwards, students advance through pre-algebra, Algebra I, Algebra II, and culminate in Pre-Calculus with an introduction to differentiation and integration by age 16.
This trajectory prepares students fully for A-Level or university entrance mathematics.
Core Progression
- Primary (Levels 1–5)Horizons Math Curriculum ensuring solid arithmetic, fractions, decimals and early geometry.
- Middle School (Levels 6–7)Pre-Algebra and Algebra I foundations, mastering proportional reasoning and linear equations.
- High School (Levels 8–9)Algebra I & II alongside formal geometry, quadratics, and trigonometry.
- Capstone (Level 10)Pre-Calculus and an introduction to limits, differentiation, and integration.
Mathematics at a Glance
| Lvl | Age | Primary Focus |
|---|---|---|
| 1 | 3-6 | Counting, basic addition/subtraction, shapes |
| 2 | 6-7 | Place value to 120, add/subtract to 20, measurement |
| 3 | 7-8 | Place value to 1000, 3-digit add/sub, time & money |
| 4 | 8-9 | Multiplication/division facts, basic fractions, area |
| 5 | 9-10 | Multi-digit ops, fraction equivalence, decimals |
| 6 | 10-11 | Decimal & fraction operations, volume, coordinate plane |
| 7 | 11-12 | Ratios, integers, basic equations, statistics |
| 8 | 12-13 | Proportional relationships, rational numbers, probability |
| 9 | 13-14 | Linear equations, functions, geometry, exponents |
| 10 | 14-15 | Algebra I, polynomials, quadratics, modeling |
Detailed Master Plans
LEVEL 1 - Kindergarten
Foundations of Number
Ages 3–6 | Early Years Foundation
Duration / Frequency: 36 Weeks | 4–5 Sessions/Week | 40 Min/Session
Aim: To build solid number sense, addition and subtraction fluency within 20, understand shapes, and develop early problem-solving and measurement skills based on standard Go Math pacing.
| Unit | Topic / Unit | Study Duration | Key Sub-topics & Skills |
|---|---|---|---|
| 1 | Numbers 1 to 5 | 3 Weeks | Count, write, represent and compare numbers up to 5 |
| 2 | Addition and Subtraction to 5 | 3 Weeks | Put together, take apart, addition & subtraction within 5 |
| 3 | Numbers 6 to 10 | 3 Weeks | Count, represent, order, and compare numbers up to 10 |
| 4 | Addition and Subtraction to 10 | 3 Weeks | Put together, take apart, addition & subtraction within 10 |
| 5 | Numbers to 15 | 2 Weeks | Count, represent, and compare numbers up to 15 |
| 6 | Numbers to 20 | 2 Weeks | Count, represent, order, and compare numbers up to 20 |
| 7 | Explore Addition & Subtraction to 20 | 2 Weeks | Use a ten to put together and take apart to 20 |
| 8 | Count to 100 | 3 Weeks | Count by ones and tens up to 100 forwards and backwards |
| 9 | Geometry: 2D & 3D Shapes | 4 Weeks | Identify, describe, compare, and create 2D and 3D shapes |
| 10 | Measurement and Data | 3 Weeks | Compare length, weight; Classify, sort, and count objects |
LEVEL 2 - Grade 1
Building Fluency
Ages 6–7 | Grade 1
Duration / Frequency: 36 Weeks | 4–5 Sessions/Week | 40 Min/Session
Aim: To master addition and subtraction to 1,000, introduce multiplication and division concepts, and strengthen fractions and measurement.
| Unit | Topic / Unit | Study Duration | Key Sub-topics & Skills |
|---|---|---|---|
| 1 | Counting and Number Sense (To 120) | 4 Weeks | Counting to 120, reading and writing numbers |
| 2 | Place Value: Tens and Ones | 3 Weeks | Tens and ones, expanded form |
| 3 | Comparing Numbers | 2 Weeks | Greater than, less than, ordering |
| 4 | Addition Concepts & Strategies | 4 Weeks | Addition within 20, properties of operations |
| 5 | Subtraction Concepts & Strategies | 4 Weeks | Subtraction within 20, unknown addends |
| 6 | Addition and Subtraction Relationships | 3 Weeks | Fact families, inverse operations |
| 7 | Two-Digit Addition and Subtraction | 3 Weeks | Adding and subtracting multiples of 10 |
| 8 | Measurement and Data (Graphing) | 3 Weeks | Picture graphs, tally charts, bar graphs |
| 9 | Time and Money | 3 Weeks | Telling time to hour/half-hour, coin values |
| 10 | Geometry and Fractions | 3 Weeks | Attributes of 2D/3D shapes, halves and fourths |
LEVEL 3 - Grade 2
Multiplication & Division Mastery
Ages 7–8 | Grade 2
Duration / Frequency: 36 Weeks | 4–5 Sessions/Week | 45 Min/Session
Aim: To achieve fluency in multiplication and division facts to 12, introduce fractions on a number line, and develop multi-step problem solving.
| Unit | Topic / Unit | Study Duration | Key Sub-topics & Skills |
|---|---|---|---|
| 1 | Understand Place Value | 3 Weeks | Hundreds, tens, ones, skip counting |
| 2 | Use Place Value to Count and Compare | 3 Weeks | Comparing 3-digit numbers using symbols |
| 3 | Basic Facts and Equal Groups | 4 Weeks | Addition/subtraction within 20, odd/even |
| 4 | 2-Digit Addition | 4 Weeks | Regrouping ones and tens, partial sums |
| 5 | 2-Digit Subtraction | 4 Weeks | Regrouping, taking apart to subtract |
| 6 | 3-Digit Addition and Subtraction | 4 Weeks | Adding and subtracting 3-digit numbers |
| 7 | Money | 2 Weeks | Counting coins and bills, word problems |
| 8 | Time | 2 Weeks | Time to 5 minutes, AM/PM |
| 9 | Length in Customary and Metric Units | 5 Weeks | Inches, centimeters, estimating lengths |
| 10 | Geometry, Fractions, and Data | 5 Weeks | Polygons, angles, measuring data |
LEVEL 4 - Grade 3
Multi-digit Operations & Fractions
Ages 8–9 | Grade 3
Duration / Frequency: 36 Weeks | 4–5 Sessions/Week | 45 Min/Session
Aim: To master multi-digit multiplication and division, build fraction arithmetic, and introduce algebraic thinking and geometry.
| Unit | Topic / Unit | Study Duration | Key Sub-topics & Skills |
|---|---|---|---|
| 1 | Addition and Subtraction Strategies | 2 Weeks | Mental math, rounding, properties |
| 2 | Understand Multiplication and Facts | 5 Weeks | Equal groups, arrays, properties of multiplication |
| 3 | Advanced Multiplication and Division Concepts | 4 Weeks | Multiply by multiples of 10 and 100 |
| 4 | Division Facts and Strategies | 4 Weeks | Quotients, remainders, relating to multiplication |
| 5 | Apply Multiplication and Division | 3 Weeks | Word problems, identifying patterns |
| 6 | Fractions: Understanding and Comparing | 5 Weeks | Unit fractions, equivalent fractions, comparing |
| 7 | Area and Perimeter | 4 Weeks | Finding unknown sides, area of rectangles |
| 8 | Time Measurement and Intervals | 2 Weeks | Time intervals, start and end times |
| 9 | Measurement (Capacity, Mass, Weight) | 3 Weeks | Liquid volume, mass, weight |
| 10 | Two-Dimensional Shapes and Data | 4 Weeks | Quadrilaterals, line plots, frequency tables |
LEVEL 5 - Grade 4
Ratios, Decimals & Pre-Algebra
Ages 9–10 | Grade 4
Duration / Frequency: 36 Weeks | 4–5 Sessions/Week | 50 Min/Session
Aim: To master fraction and decimal operations, introduce ratios, percentages, integers, and lay groundwork for algebra and coordinate geometry.
| Unit | Topic / Unit | Study Duration | Key Sub-topics & Skills |
|---|---|---|---|
| 1 | Whole Number Place Value, Addition and Subtraction | 3 Weeks | Place value to 1,000,000, multi-digit arithmetic |
| 2 | Multiplication by 1-Digit and 2-Digit Numbers | 5 Weeks | Area models, partial products, standard algorithm |
| 3 | Division Strategies and 1-Digit Divisors | 4 Weeks | Partial quotients, interpreting remainders |
| 4 | Factors, Multiples, and Patterns | 2 Weeks | Prime/composite numbers, divisibility rules |
| 5 | Fraction Equivalence and Comparison | 3 Weeks | Simplifying fractions, common denominators |
| 6 | Add, Subtract, and Multiply Fractions | 4 Weeks | Mixed numbers, like denominators |
| 7 | Relate Fractions and Decimals | 3 Weeks | Tenths and hundredths, money applications |
| 8 | Geometry: Angles and 2D Figures | 4 Weeks | Lines, rays, measuring angles with protractors |
| 9 | Measurement, Area, and Perimeter | 4 Weeks | Formulas for area/perimeter, metric conversions |
| 10 | Time, Temperature, and Data Representation | 3 Weeks | Elapsed time, measurement benchmarks, stem-and-leaf plots |
LEVEL 6 - Grade 5
Foundations of Algebra
Ages 10–11 | Grade 5
Duration / Frequency: 36 Weeks | 4–5 Sessions/Week | 50 Min/Session
Aim: To develop strong algebraic thinking, master ratio and proportional relationships, explore statistics, and transition confidently into formal algebra.
| Unit | Topic / Unit | Study Duration | Key Sub-topics & Skills |
|---|---|---|---|
| 1 | Whole Number Place Value, Multiplication, and Division | 4 Weeks | Powers of 10, multi-digit multiplication, long division |
| 2 | Decimal Place Value, Addition, and Subtraction | 4 Weeks | Read, write, compare, and round decimals |
| 3 | Multiply and Divide Decimals | 4 Weeks | Standard algorithms for decimal operations |
| 4 | Add and Subtract Fractions with Unlike Denominators | 4 Weeks | Least common multiple, equivalent fractions |
| 5 | Multiply and Divide Fractions | 4 Weeks | Area models, scaling, dividing unit fractions |
| 6 | Numerical Expressions and Patterns | 3 Weeks | Order of operations (PEMDAS), analyzing patterns |
| 7 | Measurement: Convert Units of Measure | 3 Weeks | Customary and metric conversions, line plots |
| 8 | Geometry: Perimeter, Area, and Volume | 4 Weeks | Volume formulas, composite solid figures |
| 9 | Classify 2D and 3D Figures | 3 Weeks | Attributes of polygons, hierarchy of shapes |
| 10 | Graphs and Data Interpretation | 3 Weeks | Coordinate plane, graphing relationships |
LEVEL 7 - Grade 6
Algebra I Foundations
Ages 11–12 | Grade 6
Duration / Frequency: 36 Weeks | 4–5 Sessions/Week | 55 Min/Session
Aim: To develop proportional reasoning, linear relationships, and foundational algebra skills including equations, inequalities, and geometry of two-dimensional figures.
| Unit | Topic / Unit | Study Duration | Key Sub-topics & Skills |
|---|---|---|---|
| 1 | Integers and Rational Numbers | 4 Weeks | Absolute value, ordering rational numbers |
| 2 | Operations with Fractions and Decimals | 4 Weeks | Dividing fractions, operations with multi-digit decimals |
| 3 | Ratios and Rates | 3 Weeks | Ratio language, unit rates, equivalent ratios |
| 4 | Percents and Proportions | 3 Weeks | Finding percent of a completely, real-world problems |
| 5 | Algebraic Expressions | 4 Weeks | Writing and evaluating expressions, combining like terms |
| 6 | Equations and Inequalities | 4 Weeks | One-step equations, writing and graphing inequalities |
| 7 | The Coordinate Plane | 3 Weeks | Graphing in 4 quadrants, distances, polygons on planes |
| 8 | Area of Polygons | 3 Weeks | Triangles, special quadrilaterals, composite figures |
| 9 | Surface Area and Volume | 4 Weeks | Nets, surface area, volume of right rectangular prisms |
| 10 | Data Displays and Statistical Measures | 4 Weeks | Mean, median, mode, mean absolute deviation, box plots |
LEVEL 8 - Grade 7
Algebra I & Geometry
Ages 12–13 | Grade 7
Duration / Frequency: 36 Weeks | 4–5 Sessions/Week | 55 Min/Session
Aim: To complete Algebra I, covering linear functions and systems of equations, and introduce geometric proofs, the Pythagorean theorem, and transformations.
| Unit | Topic / Unit | Study Duration | Key Sub-topics & Skills |
|---|---|---|---|
| 1 | Operations with Rational Numbers | 4 Weeks | Adding, subtracting, multiplying, dividing integers |
| 2 | Proportional Relationships | 4 Weeks | Unit rates with fractions, direct variation |
| 3 | Percent Problems and Applications | 3 Weeks | Markups, markdowns, interest, percent error |
| 4 | Equivalent Expressions | 3 Weeks | Expanding and factoring expressions |
| 5 | Solving Equations and Inequalities | 4 Weeks | Two-step equations, solving multi-step inequalities |
| 6 | Scale Drawings and Proportions | 3 Weeks | Scale factor, similar figures, missing measures |
| 7 | Circles: Area and Circumference | 4 Weeks | Radius, diameter, Pi, calculating area and perimeter |
| 8 | Surface Area and Volume of 3D Figures | 4 Weeks | Cross sections, surface area and volume of prisms/cylinders |
| 9 | Probability | 3 Weeks | Theoretical and experimental probability, tree diagrams |
| 10 | Sampling and Comparative Inferences | 4 Weeks | Populations, samples, inferences, comparing distributions |
LEVEL 9 - Grade 8
Algebra II & Trigonometry Foundations
Ages 13–14 | Grade 8
Duration / Frequency: 36 Weeks | 4–5 Sessions/Week | 55–60 Min/Session
Aim: To extend algebra to quadratic and exponential functions, introduce complex numbers, and lay foundations for trigonometry and advanced problem solving.
| Unit | Topic / Unit | Study Duration | Key Sub-topics & Skills |
|---|---|---|---|
| 1 | Real Numbers and Rational Approximations | 3 Weeks | Irrational numbers, approximating values |
| 2 | Exponents and Scientific Notation | 4 Weeks | Laws of exponents, operations with scientific notation |
| 3 | Solving Linear Equations | 4 Weeks | Multi-step equations, variables on both sides |
| 4 | Systems of Linear Equations | 4 Weeks | Graphing, substitution, and elimination methods |
| 5 | Introduction to Functions | 3 Weeks | Function notation, identifying linear vs non-linear |
| 6 | Linear Functions and Graphing | 4 Weeks | Slope, y-intercept, y=mx+b, rate of change |
| 7 | Transformations and Congruence | 4 Weeks | Translations, rotations, reflections, dilations |
| 8 | The Pythagorean Theorem | 3 Weeks | Right triangles, distance on coordinate planes |
| 9 | Volume of Cylinders, Cones, and Spheres | 3 Weeks | Formulas, solving for missing dimensions |
| 10 | Bivariate Data and Scatter Plots | 4 Weeks | Lines of best fit, two-way tables, frequencies |
LEVEL 10 - Grade 9
Pre-Calculus & Advanced Mathematics
Ages 14–15 | Grade 9
Duration / Frequency: 36 Weeks | 4–5 Sessions/Week | 60 Min/Session
Aim: To develop advanced mathematical reasoning through functions, conic sections, matrices, probability, and an introduction to calculus concepts.
| Unit | Topic / Unit | Study Duration | Key Sub-topics & Skills |
|---|---|---|---|
| 1 | Equations and Inequalities in One Variable | 3 Weeks | Literal equations, compound inequalities, word problems |
| 2 | Linear Equations and Graphs | 4 Weeks | Standard form, point-slope form, parallel/perpendicular |
| 3 | Systems of Linear Equations and Inequalities | 4 Weeks | Graphing systems, linear programming, optimization |
| 4 | Sequences and Exponential Functions | 4 Weeks | Arithmetic/geometric sequences, exponential growth/decay |
| 5 | Polynomials and Operations | 3 Weeks | Adding, subtracting, multiplying bi/trinomials |
| 6 | Factoring Polynomials | 4 Weeks | GCF, difference of squares, trinomial factoring |
| 7 | Quadratic Functions and Equations | 4 Weeks | Parabolas, vertex form, quadratic formula, roots |
| 8 | Radical Expressions and Equations | 3 Weeks | Simplifying roots, solving radical equations |
| 9 | Rational Expressions and Functions | 3 Weeks | Simplifying expressions, solving rational equations |
| 10 | Data Analysis and Statistical Models | 4 Weeks | Standard deviation, normal distribution, regressions |
Equip Your Child for Excellence
Build a bulletproof mathematical foundation that prepares them for global opportunities, critical thinking, and the highest levels of academia.