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 | 6–7 | Number sense, shapes, time |
| 2 | 7–8 | Place value, addition to 1,000 |
| 3 | 8–9 | Multiplication & division mastery |
| 4 | 9–10 | Multi-digit ops, fractions |
| 5 | 10–11 | Ratios, decimals, pre-algebra |
| 6 | 11–12 | Algebra foundations |
| 7 | 12–13 | Algebra I — linear equations |
| 8 | 13–14 | Algebra I/II + geometry |
| 9 | 14–15 | Algebra II + trigonometry |
| 10 | 15–16 | Pre-Calculus + intro to calculus |
Detailed Master Plans
LEVEL 1 — Grade 1
Foundations of Number
Ages 6–7 | HMC Grade 1
Duration / Frequency: 36 Weeks | 4–5 Sessions/Week | 40 Min/Session
Aim: To build solid addition and subtraction fluency to 20, introduce place value to 100, and develop early problem-solving and measurement skills.
| Unit | Unit / Topic | Key Skills / Outcomes |
|---|---|---|
| 1 | Number Sense & Counting to 120 | Count forward/backward, skip count |
| 2 | Place Value — Tens and Ones | Group, compare, expand numbers |
| 3 | Addition & Subtraction Fluency (to 20) | Mental math, fact families |
| 4 | Adding/Subtracting Multiples of 10 | Skip counting, number patterns |
| 5 | Measurement — Length (inches & cm) | Measure, estimate, compare |
| 6 | Time — Hour, Half Hour, Quarter Hour | Read analogue & digital clocks |
| 7 | Geometry — Shapes, Halves and Quarters | Identify, sort, describe, partition |
| 8 | Money — Coins and Values to $1 | Count coins, make amounts |
| 9 | Data — Picture Graphs and Tables | Read, create, interpret |
| 10 | Word Problems — One-step | Model, plan, solve, check |
LEVEL 2 — Grade 2
Building Fluency
Ages 7–8 | HMC Grade 2
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 | Unit / Topic | Key Skills / Outcomes |
|---|---|---|
| 1 | Place Value to 1,000 | Hundreds, tens, ones; expanded form |
| 2 | Addition & Subtraction to 1,000 (regrouping) | Multi-digit algorithms |
| 3 | Multiplication — Equal Groups & Arrays | Repeated addition, skip count |
| 4 | Division — Sharing Equally | Partition sets, basic facts |
| 5 | Fractions — Halves, Thirds, Fourths | Name, compare, order |
| 6 | Measurement — Length, Area, Perimeter | Estimate, measure, calculate |
| 7 | Time — Minutes and Elapsed Time | Tell time, calculate durations |
| 8 | Money — Making Change to $10 | Add, subtract, count change |
| 9 | Geometry — Perimeter and Basic Area | Count units, use formula |
| 10 | Data — Bar Graphs and Pictographs | Collect, display, analyse |
LEVEL 3 — Grade 3
Multiplication & Division Mastery
Ages 8–9 | HMC Grade 3
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 | Unit / Topic | Key Skills / Outcomes |
|---|---|---|
| 1 | Multiplication Facts 0–12 — Full Fluency | Times tables, mental recall |
| 2 | Division Facts | Fact families, missing factors |
| 3 | Multi-digit Multiplication (2-digit × 1-digit) | Partial products, algorithm |
| 4 | Division — 2-digit ÷ 1-digit | Estimate, divide, check |
| 5 | Fractions — Equivalence, Comparing, Line | Benchmark fractions, ordering |
| 6 | Decimals — Tenths and Hundredths | Place value, compare, order |
| 7 | Perimeter and Area of Rectangles | Formulas, real-world problems |
| 8 | Measurement — Mass, Volume | Convert units, estimate |
| 9 | Time — 12/24-hour, Elapsed Time | Word problems, timetables |
| 10 | Data & Probability — Scaled Graphs | Analyse, interpret, predict |
LEVEL 4 — Grade 4
Multi-digit Operations & Fractions
Ages 9–10 | HMC Grade 4
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 | Unit / Topic | Key Skills / Outcomes |
|---|---|---|
| 1 | Place Value to 1,000,000 | Read, Write, Compare, Round, order |
| 2 | Multi-digit Multiplication (3-digit × 2-digit) | Area model, standard algorithm |
| 3 | Long Division (4-digit ÷ 2-digit) | Estimate quotients, interpret remainders |
| 4 | Fraction Operations — Add & Subtract | LCM, equivalent fractions |
| 5 | Multiplying Fractions by Whole Numbers | Models, real-world application |
| 6 | Decimal Operations — Add and Subtract | Align decimal points, estimate |
| 7 | Geometry — Angles, Lines, Symmetry | Classify, measure with protractor |
| 8 | Order of Operations — PEMDAS | Evaluate multi-step expressions |
| 9 | Algebra — Variables and Simple Equations | Write and solve one-step equations |
| 10 | Statistics — Mean, Median, Mode, Range | Calculate and interpret data sets |
LEVEL 5 — Grade 5
Ratios, Decimals & Pre-Algebra
Ages 10–11 | HMC Grade 5
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 | Unit / Topic | Key Skills / Outcomes |
|---|---|---|
| 1 | Fraction Operations — Multiply and Divide | Algorithm, models, word problems |
| 2 | Decimal Operations — All Four Operations | Powers of 10, standard algorithm |
| 3 | Ratios and Proportional Reasoning | Equivalent ratios, unit rate, tables |
| 4 | Percentages — Conversions and Applications | Find % of quantity, discounts, tax |
| 5 | Integers — Positive and Negative Numbers | Number line, add, subtract |
| 6 | Coordinate Geometry — Four Quadrants | Plot ordered pairs, reflections |
| 7 | Geometry — Area, Volume, Surface Area | Prisms, pyramids, composite shapes |
| 8 | Algebra — Solving Two-step Equations | Balance, inverse operations |
| 9 | Advanced Order of Operations & Expressions | Simplify, expand, substitute |
| 10 | Probability — Theoretical and Experimental | Calculate, predict, compare |
LEVEL 6 — Grade 6
Foundations of Algebra
Ages 11–12 | Pre-Algebra / HMC Grade 6
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 | Unit / Topic | Key Skills / Outcomes |
|---|---|---|
| 1 | Ratios and Rates — Advanced Applications | Unit rate, ratio tables, tape diagrams |
| 2 | Proportional Relationships and Graphs | Identify, represent, interpret |
| 3 | Percentages — Increase/Decrease, Interest | Calculate change, real-world problems |
| 4 | Integers — All Four Operations | Rules for signs, absolute value |
| 5 | Rational Numbers — Fractions, Decimals, Negatives | Order, operate, convert |
| 6 | Expressions and Equations — Variables | Write, evaluate, simplify |
| 7 | Solving One- and Two-step Equations | Inverse operations, check solutions |
| 8 | Solving Inequalities — Introduction | Represent on number line, interpret |
| 9 | Geometry — Area of Complex Shapes, Volume | Decompose, calculate, apply |
| 10 | Statistics — Measures of Centre and Spread | Mean, MAD, box plots, histograms |
LEVEL 7 — Grade 7
Algebra I Foundations
Ages 12–13 | Algebra I Preparation
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 | Unit / Topic | Key Skills / Outcomes |
|---|---|---|
| 1 | Proportional Relationships | Constant of Proportionality, graphs, equations |
| 2 | Linear Equations — One Variable | Multi-step, distributive property |
| 3 | Linear Inequalities — Graphing Solutions | Compound inequalities, real-world |
| 4 | Operations with Rational Numbers | All operations, problem solving |
| 5 | Algebraic Expressions | Expand, factorise, simplify like terms |
| 6 | Geometry — Scale Drawings and Similar Figures | Calculate scale, find missing sides |
| 7 | Geometry — Angles, Triangles and Transversals | Angle relationships, proof introduction |
| 8 | Circles — Circumference and Area | Pi, formula, real-world applications |
| 9 | Statistics — Sampling and Inference | Random samples, draw conclusions |
| 10 | Probability — Compound Events | Tree diagrams, counting principle |
LEVEL 8 — Grade 8
Algebra I & Geometry
Ages 13–14 | Algebra I / Geometry
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 | Unit / Topic | Key Skills / Outcomes |
|---|---|---|
| 1 | Linear Functions — Slope and y-intercept | Graph, write equations, interpret |
| 2 | Systems of Linear Equations | Substitution, elimination, graphing |
| 3 | Exponents and Scientific Notation | Laws of exponents, convert, compute |
| 4 | Polynomials — Add, Subtract, Multiply | Standard form, FOIL, area model |
| 5 | Factoring Polynomials | GCF, difference of squares, trinomials |
| 6 | Pythagorean Theorem and Its Converse | Prove, apply, real-world problems |
| 7 | Geometry — Transformations | Translate, reflect, rotate, dilate |
| 8 | Geometry — Congruence and Similarity | Corresponding parts, scale factor |
| 9 | Volume of 3D Figures | Cylinders, cones, spheres formula |
| 10 | Bivariate Data — Scatter Plots | Lines of Best Fit, correlation |
LEVEL 9 — Grade 9
Algebra II & Trigonometry Foundations
Ages 14–15 | Algebra II
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 | Unit / Topic | Key Skills / Outcomes |
|---|---|---|
| 1 | Quadratic Functions | Graphs, vertex, axis of symmetry |
| 2 | Solving Quadratics | Factoring, formula, completing square |
| 3 | Complex Numbers — Introduction | i, add, subtract, multiply |
| 4 | Exponential Functions | Growth and decay, model real-world |
| 5 | Logarithms — Introduction and Properties | Convert between log and exponential |
| 6 | Radical Expressions and Equations | Simplify, solve, check extraneous |
| 7 | Rational Expressions and Equations | Simplify, add, multiply, solve |
| 8 | Sequences and Series | Arithmetic and Geometric, nth term |
| 9 | Introduction to Trigonometry (SOHCAHTOA) | Right triangles, sine, cosine, tangent |
| 10 | Trigonometry — Unit Circle | Special angles, exact values |
LEVEL 10 — Grade 10
Pre-Calculus & Advanced Mathematics
Ages 15–16 | Pre-Calculus
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 | Unit / Topic | Key Skills / Outcomes |
|---|---|---|
| 1 | Functions — Domain, Range, Composition | Analyse, transform, combine, inverses |
| 2 | Polynomial Functions — Higher Degree | Rational roots, end behaviour, zeros |
| 3 | Trigonometric Functions | Graphs, Amplitude, Period, transformations |
| 4 | Trigonometric Identities and Equations | Prove identities, solve equations |
| 5 | Conic Sections — Circle, Ellipse | Parabola, Hyperbola, standard form |
| 6 | Matrices — Operations, Determinants | Inverses, solve systems using matrices |
| 7 | Combinatorics and Probability | Permutations, combinations, Binomial |
| 8 | Limits — Introduction to Calculus | Concept of limit, continuity |
| 9 | Introduction to Differentiation | Derivative rules, tangent lines, rate of change |
| 10 | Introduction to Integration | Area under curve, Fundamental Theorem |
Equip Your Child for Excellence
Build a bulletproof mathematical foundation that prepares them for global opportunities, critical thinking, and the highest levels of academia.