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 1
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Year 1

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.  

Quarter 1

  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.

 

Prime Numbers Page

Real Numbers Page

1.7 Square Roots

3 – 5 Days

 

Introduce square roots, what simplifying them means, and basic arithmetic, including rationalizing the denominator.

 

Square Roots Page

1.7 & 2.4 Exponents

3 – 5 Days

 

Exponent properties and “rules” not including fractional exponents. 

 

Exponents

       
       
1.7  and 1.8 

3 – 5 Days

 

Multiple ways to manipulate, think about, and simplify various rational and radical expressions.

 

Printable

Exponents Page 4

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.

 

Printable Scientific Notation

Printable Order of Operations

Scientific Notation Page

Order of Operations Page

 

Test Number One

 

1.3 LCM/GCF

1 – 2 Days

 

Connect LCM/GCF with

algebraic expressions. 

 

Printable

LCM/GCF Page

 

2.10 Alg. Fractions

2 – 3 Days

 

Introduction to reducing and adding/subtracting simple Algebraic Fractions.

 

Reducing Printable

Reduce Alg. Fractions Page

 

Add/Sbrct Printable

Add/Sbrct Page

 

 

1.6 Percentages, Profit, Interest

One Week

 

Writing equations is the key skill required for students to be successful with this unit.

 

Printable

 

Percentages Page

 

1.4 1.9, 1.10, 1.11
D = R×T, Units and Conversions

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.

 

Units Printable

Units Page

 

DRT Printable

DRT Page

Midterm Examination

Quarter 2

Please check back later ... under construction

Quarter 2

Unit/Week Time Notes Resources
1 1 Reading and Writing with Algebra Students should learn that Algebra is a written language that has meaning.  Often by verbalizing Algebra, solutions are presented clearly/. Quiz
1 2 Solving equations and inequalities in one variable Students should use problem solving strategies and inverse operations to solve problems. They will also learn that a graph is a, “picture of all solutions.”  They will learn that a solution is a value(s) that makes a statement true. Quiz
1 3 Coordinate Plane, Linear Equations and Linear Inequalities Students will solve problems involving graphs, use graphs to answer questions using function notation. Quiz
1 4 Simultaneous Equations (systems) Students will write and solve equations for problems involving systems of equations. Test
End Unit 1  
2 5 Graphs of other equations Students will use t-charts to create graphs of non-linear equations and answer questions given a graph. Quiz
2 6 Distance, Midpoint, Slope, Tangent lines Students will answer questions about distance rate and time from graphs.  Students will also write equations of lines given various pieces of information by using these formulas Quiz
2 7 Percentages and Algebra Students will learn that problems involving percentages, especially reverse percentages, are best tackled by writing mathematically first. Quiz
2 8 Variation Students will learn to write algebraic equations and solve them involving direction and inverse variation (proportion). Quiz
  9   Final Exam
End Unit 2 Review how the second set of SMART Goals went and write a new SMART Goal that addresses another limiting factor (personal) to success.
Quarter 3

  Unit # / Topic

Time

Notes

Resources

 

 

 

 

Quarter 4

  Unit # / Topic

Time

Notes

Resources

 

 

 

 

Year 2
Quarter 5
Quarter 6
Quarter 7
Quarter 8
Year 2

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.  

Quarter 5

  Unit # / Topic

Time

Notes

Resources

6.3, 6.6, 6.8

2 Days

 

Pizza Lesson

 

 

Sector Area and Arc Length

 

3 - 4 Days

This lesson is about compound volumes and the use of formulas. It begins with a great Dan Meyer lesson called Meatballs.

 

Volume and Formulas

6.2 & 6.5

2 Days

Perimeter and area of compound 2D shapes.  Trapezoid, semi-circles, parallelograms.  

 

 

Area and Perimeter w Compound Shapes

 

   

 

 

6.4 & 6.7

 

5 Days

Surface Area and Volume

Surface Area and Volume

 

4.7 & 6.1

 

2 - 3 Days

Scale Factors and Units

 

Quarter 6
Quarter 7
Quarter 8

Paper Preparation
Unit Quizzes
Unit Worksheets
Past Papers
Paper Preparation

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.  

Unit Quizzes
Unit Worksheets
Past Papers