# Mathematics

Pre Primary

Teaching emphasis is on the development of numerical skills and the ability to use and apply mathematical skills in problem solving situation and in daily life as mathematics is an every day experiences . Our curriculum focuses on dedicated mathematics lesson each day direct teaching and interactive oral work with the whole class and in groups an emphasis on mental calculations Group work with all children doing work linked to common mathematical topics Pupils are trained to count, recognize and write numbers, understand the value of numbers know after, before, between and backward numbers. Recognize flat and solid shapes, do addition, subtraction and multiplication sums. Understand and solve simple problems using appropriate mathematical language. Organize and use simple data. Measure length, mass, capacity and time.

Primary

Mathematics is the foundation subject for all future education. Modern education has put even more emphasis on mathematical learning. To achieve that AMSB has designed the mathematics curriculum for the primary section in such a way that our students start to think mathematically. The details are as follows:

Level 1
Pupils discuss their work using mathematical language and are beginning to represent it using symbols and simple diagrams. They explain why an answer is correct. Pupils count sets of objects reliably, and use mental recall of addition and subtraction facts to 10. They begin to understand the place value of each digit in a number and use this to order numbers up to 100. They choose the appropriate operation when solving addition and subtraction problems. They use the knowledge that subtraction is the inverse of addition. They use mental calculation strategies to solve number problems involving money and measures. They recognise sequences of numbers, including odd and even numbers. Pupils count sets of objects reliably, and use mental recall of addition and subtraction facts to 10. They begin to understand the place value of each digit in a number and use this to order numbers up to 100. They choose the appropriate operation when solving addition and subtraction problems. They use the knowledge that subtraction is the inverse of addition. They use mental calculation strategies to solve number problems involving money and measures. They recognise sequences of numbers, including odd and even numbers. Pupils use mathematical names for common 3-D and 2-D shapes and describe their properties, including numbers of sides and corners. They distinguish between straight and turning movements, understand angle as a measurement of turn, and recognise right angles in turns. They begin to use everyday non-standard and standard units to measure length and mass. Pupils sort objects and classify them using more than one criterion. When they have gathered information, pupils record results in simple lists, tables and block graphs, in order to communicate their findings.

Level 2
Pupils try different approaches and find ways of overcoming difficulties that arise when they are solving problems. They are beginning to organise their work and check results. Pupils discuss their mathematical work and are beginning to explain their thinking. They use and interpret mathematical symbols and diagrams. Pupils show that they understand a general statement by finding particular examples that match it.Pupils show understanding of place value in numbers up to 1000 and use this to make approximations. They begin to use decimal notation and to recognise negative numbers, in contexts such as money and temperature. Pupils use mental recall of addition and subtraction facts to 20 in solving problems involving larger numbers. They add and subtract numbers with two digits mentally and numbers with three digits using written methods. They use mental recall of the 2, 3, 4, 5 and 10 multiplication tables and derive the associated division facts. They solve whole-number problems involving multiplication or division, including those that give rise to remainders. They use simple fractions that are several parts of a whole and recognise when two simple fractions are equivalent. Pupils classify 3-D and 2-D shapes in various ways using mathematical properties such as reflective symmetry for 2-D shapes. They use non-standard units, standard metric units of length, capacity and mass, and standard units of time, in a range of contexts. Pupils extract and interpret information presented in simple tables and lists. They construct bar charts and pictograms, where the symbol represents a group of units, to communicate information they have gathered, and they interpret information presented to them in these forms.

Level 3
Pupils develop their own strategies for solving problems and are using these strategies both in working within mathematics and in applying mathematics to practical contexts. They present information and results in a clear and organised way. They search for a solution by trying out ideas of their own. Pupils show understanding of place value in numbers up to 1000 and use this to make approximations. They begin to use decimal notation and to recognise negative numbers, in contexts such as money and temperature. Pupils use mental recall of addition and subtraction facts to 20 in solving problems involving larger numbers. They add and subtract numbers with two digits mentally and numbers with three digits using written methods. They use mental recall of the 2, 3, 4, 5 and 10 multiplication tables and derive the associated division facts. They solve whole-number problems involving multiplication or division, including those that give rise to remainders. They use simple fractions that are several parts of a whole and recognise when two simple fractions are equivalent. Pupils make 3-D mathematical models by linking given faces or edges, draw common 2-D shapes in different orientations on grids. They reflect simple shapes in a mirror line. They choose and use appropriate units and instruments, interpreting, with appropriate accuracy, numbers on a range of measuring instruments. They find perimeters of simple shapes and find areas by counting squares. Pupils extract and interpret information presented in simple tables and lists. They construct bar charts and pictograms, where the symbol represents a group of units, to communicate information they have gathered, and they interpret information presented to
them in these forms.

Level 4
In order to carry through tasks and solve mathematical problems, pupils identify and obtain necessary information. They check their results, considering whether these are sensible. Pupils show understanding of situations by describing them mathematically using symbols, words and diagrams. They draw simple conclusions of their own and give an explanation of their reasoning. Pupils use their understanding of place value to multiply and divide whole numbers by 10 or 100. In solving number problems, pupils use a range of mental methods of computation with the four operations, including mental recall of multiplication facts up to 10 x 10 and quick derivation of corresponding division facts. They use efficient written methods of addition and subtraction and of short multiplication and division. They add and subtract decimals to two places and order decimals to three places. In solving problems with or without a calculator, pupils check the reasonableness of their results by reference to their knowledge of the context or to the size of the numbers. They recognise approximate proportions of a whole and use simple fractions and percentages to describe these. Pupils recognise and describe number patterns, and relationships including multiple, factor and square. They begin to use simple formulae expressed in words. Pupils use and interpret coordinates in the first quadrant. When constructing models and when drawing or using shapes, pupils measure and draw angles to the nearest degree, and use language associated with angle. Pupils know the angle sum of a triangle and that of angles at a point. They identify all the symmetries of 2-D shapes. They make sensible estimates of a range of measures in relation to everyday situations. Pupils understand and use the formula for the area of a rectangle. Pupils extract and interpret information presented in simple tables and lists. They construct bar charts and pictograms, where the symbol represents a group of units, to communicate information they have gathered, and they interpret information presented to them in these forms.

Secondary

An ability to calculate mentally lies at the heart of numeracy. As a teacher, whether of mathematics or another subject,stresses the importance of mental calculation methods and give all pupils regular opportunities to develop the skills involved. The skills include an ability to:

• remember number facts and recall them without hesitation
• use known facts to figure out new facts: for example, knowing that half of 250 is 125 can be used to work out 250 – 123
• draw on a repertoire of mental strategies to work out calculations such as 326 – 81, 223 x 4 or 2.5% of £3000, with some thinking time
• understand and use the relationships between operations to work out answers and check results: for example, 900 ÷ 15 = 60, since 6 x 150 = 900
• approximate calculations to judge whether or not an answer is about the right size: for example, recognise that 1/4 of 57.9 is just under 1/4 of 60, or 15
• solve problems such as: ‘How many CDs at £3.99 each can I buy with £25?’ or: ‘Roughly how long will it take me to go 50 miles at 30 mph

As they progress to working with larger numbers they learn more sophisticated mental methods and tackle more complex problems. They develop some of these methods intuitively and some they are taught explicitly. Through a process of regular explanation and discussion of their own and other people’s methods they begin to acquire a repertoire of mental calculation strategies. It can be hard to hold all the intermediate steps of a calculation in the head and so informal pencil and paper notes, recording some or all of their solutions, become part of a mental strategy. These personal jottings may not be easy for someone else to follow but they are an important staging post to getting the right answer and acquiring fluency in mental calculation.

Algebra is generalized arithmetic. Its origins lie in arithmetic, in the art of manipulating sums, products and powers of numbers. The same rules are seen to hold true for all numbers, of whatever type, so it becomes possible to generalise the rules with letters in place of numbers. Indeed all numerical entities, coefficients as well as unknowns, can be represented by letters. This insight releases in due course the full power of algebra.

Algebra in Years 7 to 9 includes equations, formulae and identities, and sequences, functions and graphs. There is a need to stress the links between these topics and with arithmetic. Letters do not represent quantities like length or cost; they represent numbers. Pupils will have spent much time manipulating numbers in Key Stages 1 and 2, and they can build on their experience.

Shape, space and measures
Geometry in Key Stage 3 is the study of points, lines and planes and the shapes that they can make, together with a study of plane transformations. A key aspect is the use and development of deductive reasoning in geometric contexts. Geometrical activities can be linked to accurate drawing, construction and loci, and work on measures and mensuration. By ensuring that pupils have a range of suitable experiences you can develop their knowledge and understanding of shape and space and their appreciation of the ways that properties of shapes enrich our culture and environment.
Geometry cannot be learned successfully solely as a series of logical results. Pupils also need opportunities to use instruments accurately, draw shapes and appreciate how they can link together, for example, in tessellations. In Key Stage 3, it is vital to distinguish between the imprecision of constructions which involve protractors and rulers, and the ‘exactness in principle’ of standard constructions which use only compasses and a straight edge. Geometrical reasoning can show pupils why construction methods work, for example, the method to construct a perpendicular bisector of a line segment.
Practical work with transformations will produce interesting problems to solve as well as helping pupils to understand the topic more fully. Urging them to visualise solutions to problems such as: ‘When a triangle is rotated through 180° about the mid-point of one side, what shape do the original and final triangles form?’ Linking geometry to subjects such as art, through symmetry or tessellations, or religious education, perhaps through a study of the properties of Islamic patterns or cathedral rose windows, offers good opportunities to develop creativity. By encouraging pupils to speculate why the properties they have found hold true, can strengthen their reasoning skills.

Handling data
Data handling is best taught in a coherent way in the context of real statistical enquiries so that teaching objectives arise naturally from the whole cycle. As an enquiry develops, you will need to reinforce and develop certain skills by direct teaching of particular objectives.

Teaching strategies
The recommended approach to teaching is based on ensuring:

• Sufficient regular teaching time for mathematics, including extra support for pupils who need it to keep in step with the majority of their year group
• A high proportion of direct, interactive teaching
• Engagement by all pupils in tasks and activities which, even when differentiated, relate to a common theme
• Regular opportunities to develop oral, mental and visualization skills.

Pupils should

• have a sense of the size of a number and where it fits into the number system
• recall mathematical facts confidently
• calculate accurately and efficiently, both mentally and with pencil and paper, drawing on a range of calculation strategies
• use proportional reasoning to simplify and solve problems
• use calculators and other ICT resources appropriately and effectively to solve mathematical problems, and select from the display the number of figures appropriate to the context of a calculation
• use simple formulae and substitute numbers in them
• measure and estimate measurements, choosing suitable units, and reading numbers correctly from a range of meters, dials and scales
• calculate simple perimeters, areas and volumes, recognising the degree of accuracy that can be achieved
• understand and use measures of time and speed, and rates such as £ per hour or miles per litre
• draw plane figures to given specifications and appreciate the concept of scale in geometrical drawings and maps
• understand the difference between the mean, median and mode and the purpose for which each is used
• collect data, discrete and continuous, and draw, interpret and predict from graphs, diagrams, charts and tables
• have some understanding of the measurement of probability and risk; explain methods and justify reasoning and conclusions, using correct mathematical terms
• judge the reasonableness of solutions and check them when necessary
• give results to a degree of accuracy appropriate to the context
Pupils take increasing responsibility for planning and executing their work. They extend their calculating skills to fractions, percentages and decimals, and begin to understand the importance of proportional reasoning. They are beginning to use algebraic techniques and symbols with confidence. They generate and solve simple equations and study linear functions and their corresponding graphs. They begin to use deduction to manipulate algebraic expressions. Pupils progress from a simple understanding of the features of shape and space to using definitions and reasoning to understand geometrical objects. As they encounter simple algebraic and geometric proofs, they begin to understand reasoned arguments. They communicate mathematics in speech and a variety of written forms, explaining their reasoning to others. They study handling data through practical activities and are introduced to a quantitative approach to probability. Pupils work with increasing confidence and flexibility to solve unfamiliar problems. They develop positive attitudes towards mathematics and increasingly make connections between different aspects of mathematics.
• Understanding mathematical concepts is the first step in understanding mathematics. However, in order to solve problems, students also need basic skills. Teachers use a variety of approaches that include the use of concrete models and manipulative as well as algorithms and symbolic representations; presentations and mental arithmetic and estimation are also inculcated. A balanced and practical approach to mathematics learning that aims at more than just arithmetic;
• Since mathematics is best learned through active involvement in solving real problems, students engage in organized investigations of everyday situations, which emphasize both concepts and procedures. Students also apply the mathematics they know and develop skills, procedures, and concepts as they solve complex problems. Students become powerful mathematical thinkers who know how and when to apply, in a wide variety of contexts, the mathematics they have learned. Whole class instructions, small group activities, and individual work each have a place.

Our aim is to teach students to think mathematically.