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 ProTip. The big idea is a remote view of what students must understand. The key knowledge is prerequisite knowledge and relevant facts, and the ProTip 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.
 
1.7 Square Roots  3 – 5 Days 
Introduce square roots, what simplifying them means, and basic arithmetic, including rationalizing the denominator.
 
1.7 & 2.4 Exponents  3  4 Days 
Exponent properties and “rules” not including fractional exponents.
 
1.7 and 1.8  2 Days 
Multiple ways to manipulate, think about, and simplify various rational and radical expressions.
 
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.
 
Test Number One
 
1.3 LCM/GCF  1 – 2 Days 
Connect LCM/GCF with algebraic expressions.


2.10 Alg. Fractions  2 – 3 Days 
Introduction to reducing and adding/subtracting simple Algebraic Fractions.


1.6 Percentages, Profit, Interest  One Week 
Writing equations is the key skill required for students to be successful with this unit.


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.

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.


Unit 7  8 Days 
Linear Equations and Coordinate Geometry
Linear Inequalities


2.6 Systems of Linear Equations  2 Days 
Solving Systems of Equations algebraically.


2.14  2 Days 
Direct and Inverse Variation


Test 3
 
2.7 2.8 Polynomials  4 Days 
Polynomials Introduction, Combining Like Terms, Distributing


2.9 Factoring  6 – 8 Days 
Factoring


2.10 Algebraic Fractions  4 Days 
Algebaic Fractions


2.13 n^{th} term  2 – 3 Days 
Sequences and Series, n^{th} term


Semester 1 Final

The resources that populate this page are being uploaded daily.
Unit # / Topic  Time  Notes  Resources 
2.11 Graphing Quadratic Equations  16 Days 
Vertex Formula


Test 5
 
3.1 Function Notation  2 – 3 Days 
Function Notation, input/output, domain and range


3.2 3.3 Graphing Functions  2 Days 
Graphs of other functions


3.8 3.9 3.12 Interpreting Graphs  2 Days 
Graphs of other functions


3.10 Function Arithmetic  2 Days 
Composition of Functions and Arithmetic


3.11 Inverse Functions  2 Days 
Inverse Functions: Procedurally and conceptually


3.5 Function analysis  2 – 3 Days 
Recognition of types of functions


Midterm Examination

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


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.


Test 7
 
7.5 7.6 Linear Equations  2 Days 
Writing Linear Equations Review


2.10 Algebraic Fractions  2 Days 
Algebraic Fractions Review


2.11 Quadratic Equations  4 Days 
Quadratic Equations Review


3.11 Inverse Functions and Graphs  2 Days 
Graphing the composition of inverse functions


Paper 2 and 4 Review  6 – 8 Days 
Mixed Review of Topics Learned to Date


Semester 2 Final Examination

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
 
6.6 Volume Activity  2 Days 
Dan Meyers Meat Ball
 
4.1 Vocabulary  1 Day 
Vocabulary of Geometry
 
4.5 Constructions  2 Days 
Basic Geometry Constructions
 
4.3 Symmetry  1 Day 
Rotational Symmetry
 
4.3 Quadrilaterals  2 Days 
Hierarchy of Quadrilaterals and their Properties
 
4.4 Polygons  2 – 3 Days 
Polygons, Their Properties and Construction
 
4.6 Circles  4 Days 
Circles and Their Properties
 
Test 9
 
4.4 Angles around a Point  4 Days 
Finding Angles from Properties on a Diagram
 
4.7 4.8 Similarity and Congruence  2 Days 
Similarity and Congruence of Shapes
 
4.7 Scale Factors  4 Days 
Scale Factors and Proportion
 
6.2 & 6.5  2 Days 
Area and Perimeter of Compound Shapes
 
6.4 & 6.7  5 Days 
Surface Area and Volume
 
4.7 & 6.1  2  3 Days 
Scale Factors and Units
 
Midterm Examination

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


3.12 Transformations  1 Day 
Introducing Transformations


5.1 5.3 Vector Notation  2 Days 
Vector Notation, focus on magnitude


5.4 5.5 Vector Arithmetic  1 Days 
Add and subtract vectors. Multiply a vector by a scalar.


Test 11
 
8.1 Basic Trigonometry  3 – 4 Days 
Right Angle Trigonometry Function Input/Output Construct the Unit Circle


8.2 Calculator Trigonometry  3 – 4 Days 
Sine, Cosine and Tangent for angles between 0° and 360°.


8.3 8.4 8.5 Law of Sines, Law of Cosines, Area of a Triangle  4 Days 
Law of Sines, Law of Cosines,


Test 12
 
8.1 Bearings  1 Week 
Problems that summarize all applications of Trigonometry and Geometry


Review  1 Week 
Practice Paper 2 and Paper 4 style packets that review everything to date.


Review Number Unit 



Review Algebra Unit 



Midterm Examination

Unit # / Topic  Time  Notes  Resources 
9 Probability Unit  4 Weeks 
Notation, Expected Value, Combination of Outcomes, Tree Diagrams and Conditional Probability
 Probability Page 
Test 13  
10 Statistics Unit  4 Weeks 
Bar Graphs, Histograms, Estimated Mean, Cumulative Frequency, Interpretation of Graphs


Midterm

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 quarterlong 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.