# Course Outline

## Overview

The Math Syllabus at GEMS Wesgreen International Secondary School aims to support students in building competency, confidence and fluency in their use of techniques and mathematical understanding. Throughout the year we recover and extend objectives as the focus is to develop in students their reasoning, problem-solving and analytical skills from a variety of abstract and real-life contexts.

## Learning Outcomes

The aims of all subjects state what a teacher may expect to teach and what a student may expect to experience and learn. These aims suggest how the student may be changed by the learning experience.

The aims of the Math Syllabus are to encourage and enable students to:

• become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
• reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
• can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

## Unit Overviews

### Term 1

Number - Chapter 1

Approximate length: 3 weeks

Syllabus - Cambridge IGCSE® Mathematics 0580 and Complete Mathematics for Cambridge IGCSE 5Th Edition-EXTENDED- David Rayner

In this unit the children will build on their understanding of Units of accuracy, ratio proportion, sequences, percentages, standard form, speed, distance and time.

Specific National Curriculum Objectives Covered:

• Use the four rules for calculations with whole numbers, decimals and fractions (including mixed numbers and improper fractions), including correct ordering of operations and use of brackets.
• Applies to positive and negative numbers.
• Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts.
• Recognise equivalence and convert between these forms.
• Includes the conversion of recurring decimals to fractions, e.g. change to a fraction. 0.7&
• Calculate with squares, square roots, cubes and cube roots and other powers and roots of numbers, e.g. work out 32 x 4 square root of 16
• Identify and use natural numbers, integers (positive, negative and zero), prime numbers, square numbers, common factors and common multiples, rational and irrational numbers (e.g. π, square root of 2), real numbers, reciprocals.
• Includes expressing numbers as a product of prime factors.
• Finding the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of two numbers.
• Continue a given number sequence.
• Recognise sequences of square, cube and triangular numbers.
• Recognise patterns in sequences including the term to term rule and relationships between different sequences; subscript notation might be used.
• Find and use the nth term of sequences in linear, simple quadratic and cubic sequences; for extended learners this is required for linear, quadratic, cubic and exponential sequences and simple combinations of these.
• Make estimates of numbers, quantities and lengths, give approximations to specified numbers of significant figures and decimal places and round off answers to reasonable accuracy in the context of a given problem.
• Give appropriate upper and lower bounds for data given to a specified accuracy, e.g. measured lengths.
• Obtain appropriate upper and lower bounds to solutions of simple problems given data to a specified accuracy, e.g. the calculation of the perimeter or the area of a rectangle.
• Understand the meaning of indices (fractional, negative and zero) and
• use the rule of indices 51/2= square root of 5
• Find the value of 51/2 , 1001/2 , 8-2/3
• Work out 2-3 x 24 , (23)2 , (2-3 / 24)
• Use the standard form A × 10n where n is a positive or negative integer, and 1 ≤ A < 10.
• Convert numbers into and out of standard form.
• Calculate with values in standard form.
• Use a calculator efficiently.
• Apply appropriate checks of accuracy.
• Demonstrate an understanding of ratio and proportion.
• To include numerical problems involving direct and inverse proportion. Use ratio and scales in practical situations. Formulae for other rates will be given in the question e.g. pressure and density.
• Increase and decrease a quantity by a given ratio.
• Calculate using money and convert from one currency to another.
• Use given data to solve problems on personal and household finance involving earnings, simple interest and compound interest.
• Includes discount, profit and loss.
• Extract data from tables and charts.
• Includes discount, profit and loss.
• Knowledge of compound interest formula is required.
• Calculate a given percentage of a quantity.
• Express one quantity as a percentage of another.
• Calculate percentage increase or decrease.
• Carry out calculations involving reverse percentages, e.g. finding the cost price given the selling price and the percentage profit.
• Calculate times in terms of the 24-hour and 12-hour clock.
• Read clocks, dials and timetables.
• Calculate average speed.
• Use common measures of rate.

Algebra 1 - Chapter 2

Approximate length: 2 weeks

Syllabus - Cambridge IGCSE® Mathematics 0580 and Complete Mathematics for Cambridge IGCSE 5Th Edition-EXTENDED- David Rayner

In this unit the children will build on their understanding of Directed numbers, Formulae, Brackets and simplifying , Solving linear equations, simultaneous equations (linear and quadratic) , quadratic equations and factorizing.

Specific National Curriculum Objectives Covered:

• Use directed numbers in practical situations, e.g. temperature changes, flood levels.
• Manipulate directed numbers.
• Use letters to express generalized numbers and express basic arithmetic processes algebraically.
• Substitute numbers for words and letters in complicated formulae.
• Use brackets and extract common factors, e.g. expand 3x(2x – 4y)
• Expand products of algebraic expressions (two brackets only), e.g. expand (x + 4)(x – 7); for extended include products of more than two brackets, e.g. (x + 4)(x – 7)(2x + 1)
• Derive and solve simple linear equations in one unknown.
• Derive and solve simultaneous linear equations in two unknowns.
• Factorise 9x2 + 15xy
• Factorise where possible expressions of the form: ax + bx + kay + kby ; a2x2 b2y2 ; a2 + 2ab + b2 ; ax2 + bx + c
• Derive and solve quadratic equations by factorisation, completing the square and by use of the formula.
• Derive and solve simultaneous equations, involving one linear and one quadratic.

Mensuration – Chapter 3

Approximate length: 2 weeks

Syllabus - Cambridge IGCSE® Mathematics 0580 and Complete Mathematics for Cambridge IGCSE 5Th Edition-EXTENDED- David Rayner

In this unit the children will build on their understanding of Area, Arc length, sector area, chord of a circle, Volume and Surface area.

Specific National Curriculum Objectives Covered:

• identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment
• calculate arc lengths, angles and areas of sectors of circles
• calculate surface areas and volumes of spheres, pyramids, cones and composite solids

Geometry – Chapter 4

Approximate length: 3 week

Syllabus - Cambridge IGCSE® Mathematics 0580 and Complete Mathematics for Cambridge IGCSE 5Th Edition-EXTENDED- David Rayner

In this unit the children will build on their understanding of Fundamental rules of angles, Pythagoras theorem and symmetry .

Specific National Curriculum Objectives Covered:

• apply Pythagoras’ Theorem and trigonometric ratios to find angles and lengths in right-angled triangles {and, where possible, general triangles} in two {and three} dimensional figures

Algebra 2 -Chapter 5 Approximate length: 4 week

Syllabus - Cambridge IGCSE® Mathematics 0580 and Complete Mathematics for Cambridge IGCSE 5Th Edition-EXTENDED- David Rayner

In this unit the children will build on their understanding of Algebraic fractions, changing subject of a formula, variation and indices.

Specific National Curriculum Objectives Covered:

• understand that X is inversely proportional to Y is equivalent to X is proportional to 1 Y construct and interpret equations that describe direct and inverse proportion

## Blended Learning

Throughout this year there will be blended learning and we are using multiple teaching methods in order to help our students learn more effectively. All students whether face to face or learning from home will have the opportunity access all the lessons and resources. Students will use Phoenix, Teams, myimaths and GCSE Pod. Each lesson begins with a set of clearly stated objectives and an explanation of its place in the overall IGCSE syllabus. Effective learning is encouraged through frequent activities and self-assessment questions.

Links for solving past papers and links related to concepts covered to reinforce classroom learning followed will be available to students. Students will have access to worksheets with progression of difficulty, online assessments, tasks/open ended questions and fun activities through online platforms.

## Assessment

Formative:

Throughout the units, the children will complete graded work, quizzes and problem- solving activities which allows the teacher to assess the students’ attainment and inform their planning.

For each unit the students complete written quizzes, online quizzes as well as Chapter- wise tests (Topic Tests). Quizzes are taken based on 1-chapter assessment, where Tests are combined as per the requirement i.e. 2 to 3 chapters/topics – sections. This allows us to see progress across the units and align our planning.

Summative:

At the end of each term we complete internal and standardized tests. This allows us to measure the students’ progress throughout the term and year. The tests will have IGCSE format combined questions from both papers and two separate exams for P-2 and P-4 for Mock Exam. This is practice / preparation for their final IGCSE examinations. At the end of the year students appear for their final IGCSE examination for Syllabus - Cambridge IGCSE® Mathematics 0580.