## Overview

The Math Syllabus at GEMS Wesgreen International Secondary School aims to support students to develop their ability to calculate fluently, to reason and solve problems through application of knowledge and transferable skills. Throughout the year we recover and extend objectives as the focus is on securing an understanding in the subject by developing a greater depth.

## 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

Unit 1 - 1 Representation of data

Approximate length: 4 weeks

In this unit the children will learn to compare and contrast sets of data draw and interpret back-to-back stem-and-leaf diagram.

Specific CIE Objectives Covered:

• select a suitable way of presenting raw statistical data, and Discuss advantages and/or disadvantages that particular representations may have.
• Draw and interpret stem-and-leaf diagrams, box-and-whisker plots, histograms and cumulative frequency graphs; including back-to-back stem-and-leaf diagrams.
• Understand and use different measures of central tendency (mean, median, mode) and variation (range, interquartile range, standard deviation), e.g. in comparing and contrasting sets of data.
• use a cumulative frequency graph, e.g. to estimate medians, quartiles, percentiles, the proportion of a distribution above (or below) a given value, or between two values
• Calculate and use the mean and standard deviation of a set of data (including grouped data) either from the data itself or from given totals, and use such totals in solving problems which may involve up to two data sets.

Unit 2 - 5.2 Permutations and combinations

Approximate length: 2 weeks

In this unit the children will build their understanding of permutations and combinations and about arrangements of objects.

Specific CIE Objectives Covered:

• understand the terms permutation and combination, and solve simple problems involving selections Notes and examples
• solve problems about arrangements of objects in a line, including those involving – repetition (e.g. the number of ways of arranging the letters of the word ‘NEEDLESS’) – restriction (e.g. the number of ways several people can stand in a line if two particular people must, or must not, stand next to each other).

Unit 3- Probability

Approximate length: 3 weeks

In this unit the children will analyse situations that can be represented by a sample space of equiprobable elementary events, or a tree diagram.

Specific CIE Objectives Covered:

• evaluate probabilities in simple cases by means of enumeration of equiprobable elementary events, or by calculation using permutations or
• use addition and multiplication of probabilities, as appropriate, in simple cases
• Understand the meaning of exclusive and independent events, including determination of whether events A and B are independent by comparing the values of P(AUB) AND P(A)XP(B).
• calculate and use conditional probabilities in simple cases

### Term 2

Unit 4- Discrete random variables

Approximate length: 2 weeks

In this unit the children will develop their understanding of probability distribution and apply formulae and notations related to these.

Specific CIE Objectives Covered:

• Draw up a probability distribution table relating to a given situation involving a discrete random variable X, and calculate E(X) and Var(X) Notes and examples.
• Use formulae for probabilities for the binomial and geometric distributions, and recognize practical situations where these distributions are suitable models.
• Use formulae for the expectation and variance of the binomial distribution and for the expectation of the geometric distribution.

Unit 5- The normal distribution

Approximate length: 3 weeks

In this unit the children will learn to use sketches of normal curves to illustrate distributions or probabilities.

Specific CIE Objectives Covered:

• Understand the use of a normal distribution to model a continuous random variable, and use normal distribution tables Notes and examples Sketches of normal curves to illustrate distributions or probabilities may be required.
• solve problems concerning a variable X, where
• Recall conditions under which the normal distribution can be used as an approximation to the binomial distribution, and use this approximation, with a continuity correction, in solving problems.

## 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 to access all the lessons and resources. Students will use Phoenix, Teams and myimaths. Each lesson begins with a set of clearly stated objectives and an explanation of its place in the overall CIE AS/A level 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. End of term 2 they have CIE format exam for S1. This is practice / preparation for their final CIE examinations. At the end of one year course, students appear for their final CIE examination for Syllabus - Cambridge CIE® Mathematics 9709.