Cambridge IGCSE
U N D E R C O N S T R U C T I O N
Scope and Sequence
Below you will find the IGCSE Mathematics 0444 syllabus sequenced and on a timeline. This sequence works, but is not the only sequence that does work. The syllabus is ordered by year and then by quarter. Each quarter outlines what is being taught and for how long. You'll find a Teacher Reference article that will help you understand what Cambridge expects of students with that particular topic. You'll also find a Lesson Guide and PowerPoint (or lesson). There will be a tab that contains quality practice problems for students and another that is a reference like a textbook, for students.
If you are looking for a particular item on the syllabus, please refer to the syllabus page.
On each “Teacher Reference,” page you will find a Big Idea, Key Knowledge, and Pro-Tip. The big idea is a remote view of what students must understand. The key knowledge is prerequisite knowledge and relevant facts, and the Pro-Tip is an idea that can either streamline student thinking or process. These are good to share with students.
This is a general overview of the sequence and pace that can work for a typical school in the United States. Keep in mind that Cambridge suggests students have 130 hours of guided learning per year. If on average, accounting for quiz and test time, holidays, standardized tests, district mandated summative assessments, assemblies and other class disruptions, that you have 3.5 hours a week with your students, for 36 weeks, that gives you 126 hours a year.
Also note that Cambridge refers to instruction as “guided learning.” This is not a difference of semantics, but a shift in ideology. Teachers cannot learn for students. Teachers can set up experiences for students through which they learn. Thus, through the design of our course we guide them through experiences that expose them to what it is they need to learn. The practice problems are aligned with this philosophy. There are very few problems that just practice a procedure. Instead, the problems seek to uncover common misconceptions.
The topics and lessons listed below are in sequence. One homework leads to the next lesson, and each lesson has time set aside for review of the previous day's homework. It is the feedback and guidance that is perhaps most important in teaching students math.
Keep in mind as students move through the program topics become increasingly integrated. To ease the difficulties that accompany this adjustment, there is a cyclic nature to how topics are introduced, then revisited and built upon.
Year One
The primary focus in year one is to develop mathematical literacy. The focus is served through applications of Algebra, both reading and writing.
| Unit # / Topic | Time | Notes | Resources |
| 1.1 Number Sense | 2 – 4 days |
Prime numbers: any whole number can be expressed as a unique product of primes. Real Numbers: arithmetic between rational and irrational numbers.
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| 1.7 Square Roots | 3 – 5 Days |
Introduce square roots, what simplifying them means, and basic arithmetic, including rationalizing the denominator.
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| 1.7 & 2.4 Exponents | 3 - 4 Days |
Exponent properties and “rules” not including fractional exponents.
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| 1.7 and 1.8 | 2 Days |
Multiple ways to manipulate, think about, and simplify various rational and radical expressions.
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| 1.2, 1.7, 3.1 | 2 – 3 Days |
The order of operations, reading mathematical structure and notation. Ex: Scientific notation is an application of the order of operations and properties of exponents. Ex: Introducing function notation as a way to practice the order of operations.
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Test Number One
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| 1.3 LCM/GCF | 1 – 2 Days |
Connect LCM/GCF with algebraic expressions.
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| 2.10 Alg. Fractions | 2 – 3 Days |
Introduction to reducing and adding/subtracting simple Algebraic Fractions.
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| 1.6 Percentages, Profit, Interest | One Week |
Writing equations is the key skill required for students to be successful with this unit.
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| 1.4 1.9, 1.10, 1.11 | One Week |
Students will learn to use rates to convert units while dealing with problems involving time (seconds to days), as well as distance, rate and time.
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DRT Page |
| Midterm Examination | |||
The resources linked in this page are being populated daily.
| Unit # / Topic | Time | Notes | Resources |
| 2.3 2.5 2.12 Equations and inequalities | 2 – 3 Days |
Reading and Writing with Algebra. Inequalities, solving simple equations.
| Solving Printable |
| 2.1 2.2 Inequalities | 2 Days |
Create and solve linear inequalities including compound and absolute value.
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| Unit 7 | 8 Days |
Linear Equations and Coordinate Geometry
Linear Inequalities
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| 2.6 Systems of Linear Equations | 2 Days |
Solving Systems of Equations algebraically.
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| 2.14 | 2 Days |
Direct and Inverse Variation
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Test 3
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| 2.7 2.8 Polynomials | 4 Days |
Polynomials Introduction, Combining Like Terms, Distributing
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| 2.9 Factoring | 6 – 8 Days |
Factoring
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| 2.10 Algebraic Fractions | 4 Days |
Algebaic Fractions
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| 2.13 nth term | 2 – 3 Days |
Sequences and Series, nth term
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Semester 1 Final
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The resources that populate this page are being uploaded daily.
| Unit # / Topic | Time | Notes | Resources |
| 2.11 Graphing Quadratic Equations | 16 Days |
Vertex Formula
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Test 5
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| 3.1 Function Notation | 2 – 3 Days |
Function Notation, input/output, domain and range
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| 3.2 3.3 Graphing Functions | 2 Days |
Graphs of other functions
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| 3.8 3.9 3.12 Interpreting Graphs | 2 Days |
Graphs of other functions
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| 3.10 Function Arithmetic | 2 Days |
Composition of Functions and Arithmetic
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| 3.11 Inverse Functions | 2 Days |
Inverse Functions: Procedurally and conceptually
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| 3.5 Function analysis | 2 – 3 Days |
Recognition of types of functions
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Midterm Examination
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This page is being populated with links to resources frequently.
| Unit # / Topic | Time | Notes | Resources |
| 4.4 Basics of Triangles | 3 – 4 Days |
Basics of Triangles, focusing on the 45 – 45 – 90 and 30 – 60 – 90 triangles
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| 8.1 Right Triangle Trigonometry | 12 Days |
Building the Unit Circle, defining trigonometry as a function with the domain being angles, the range being a ratio of sides.
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Test 7
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| 7.5 7.6 Linear Equations | 2 Days |
Writing Linear Equations Review
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| 2.10 Algebraic Fractions | 2 Days |
Algebraic Fractions Review
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| 2.11 Quadratic Equations | 4 Days |
Quadratic Equations Review
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| 3.11 Inverse Functions and Graphs | 2 Days |
Graphing the composition of inverse functions
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| Paper 2 and 4 Review | 6 – 8 Days |
Mixed Review of Topics Learned to Date
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Semester 2 Final Examination
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Year Two
In year two students use their mathematical literacy to acquire new concepts in Geometry, Trigonometry, Probability and Statistics. The goal is to have all new material learned by early March. The rest of the time will be devoted to test preparation.
This page is being populated with resources and links regularly.
| Unit # / Topic | Time | Notes | Resources |
| 6.3 Area Activity | 2 Days |
Dan Meyers Pizza Problem
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| 6.6 Volume Activity | 2 Days |
Dan Meyers Meat Ball
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| 4.1 Vocabulary | 1 Day |
Vocabulary of Geometry
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| 4.5 Constructions | 2 Days |
Basic Geometry Constructions
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| 4.3 Symmetry | 1 Day |
Rotational Symmetry
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| 4.3 Quadrilaterals | 2 Days |
Hierarchy of Quadrilaterals and their Properties
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| 4.4 Polygons | 2 – 3 Days |
Polygons, Their Properties and Construction
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| 4.6 Circles | 4 Days |
Circles and Their Properties
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Test 9
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| 4.4 Angles around a Point | 4 Days |
Finding Angles from Properties on a Diagram
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| 4.7 4.8 Similarity and Congruence | 2 Days |
Similarity and Congruence of Shapes
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| 4.7 Scale Factors | 4 Days |
Scale Factors and Proportion
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| 6.2 & 6.5 | 2 Days |
Area and Perimeter of Compound Shapes
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| 6.4 & 6.7 | 5 Days |
Surface Area and Volume
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| 4.7 & 6.1 | 2 - 3 Days |
Scale Factors and Units
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Midterm Examination
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Unit # / Topic | Time | Notes | Resources |
| 5.6 5.7 5.8 Transformations on a Coordinate Plane | 3 – 4 Days |
Translation, Reflection, Rotation, Dilation, Stretch, Colum Vector Notation
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| 3.12 Transformations | 1 Day |
Introducing Transformations
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| 5.1 5.3 Vector Notation | 2 Days |
Vector Notation, focus on magnitude
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| 5.4 5.5 Vector Arithmetic | 1 Days |
Add and subtract vectors. Multiply a vector by a scalar.
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Test 11
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| 8.1 Basic Trigonometry | 3 – 4 Days |
Right Angle Trigonometry Function Input/Output Construct the Unit Circle
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| 8.2 Calculator Trigonometry | 3 – 4 Days |
Sine, Cosine and Tangent for angles between 0° and 360°.
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| 8.3 8.4 8.5 Law of Sines, Law of Cosines, Area of a Triangle | 4 Days |
Law of Sines, Law of Cosines,
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Test 12
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| 8.1 Bearings | 1 Week |
Problems that summarize all applications of Trigonometry and Geometry
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| Review | 1 Week |
Practice Paper 2 and Paper 4 style packets that review everything to date.
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| Review Number Unit |
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| Review Algebra Unit |
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Midterm Examination
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Unit # / Topic | Time | Notes | Resources |
| 9 Probability Unit | 4 Weeks |
Notation, Expected Value, Combination of Outcomes, Tree Diagrams and Conditional Probability
| Probability Page |
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Test 13 | |||
| 10 Statistics Unit | 4 Weeks |
Bar Graphs, Histograms, Estimated Mean, Cumulative Frequency, Interpretation of Graphs
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Midterm
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Quarter 8
The last quarter is spent reviewing, taking practice tests, and practicing past Paper 2 and Paper 4 examinations. It has proven a good practice to create a quarter-long calendar for students leading up the examinations. On the calendar will be the sequence of quizzes, tests, and assignments that lead up to the Paper 2 and Paper 4 examinations.
Paper Preparation
To get students ready to take the examination two major things need to take place. First, students need to revisit all of the topics they've learned in the two year course. Second, students need to familiarize themselves with Paper 2 and Paper 4.
