The course is based on the requirements of the National Curriculum and takes into account the demands of the Spanish system. In Years 7 and 8 the emphasis is on understanding and confidently using different forms of calculating with numbers while being introduced to algebra, shape and space. In Year 9 the basics are periodically checked but the course assumes the students are able to deal with any type of calculations allowing the correct use of calculators. We aim to try and balance the material in each term to always cover number, algebra, shape space and measures

Year 7 Key Objectives 

Numbers and the Number System

Number Calculations

Place value; multiply/divide by powers of 10; round to nearest 10/100/1000 and 1 decimal place;       Indices, squares, square roots, cubes, powers of 10; BIDMAS; four operations with whole numbers    including long multiplication and division; place directed numbers on the number line; order directed numbers; add/subtract directed numbers; factors and multiples; prime numbers; divisibility tests for 2, 3, 4, 5, 6, 9 and 10.

Fractions/Decimals/Percentages

Understanding fractions; simplifying fractions by cancelling; identify equivalent fractions; order          fractions; convert terminating decimals to fractions; add/subtract fractions and decimals; fractions of quantities; multiply fraction by an integer; understand a percentage as “number of parts per 100”; simple equivalence of percentages, fractions and decimals; simple percentages of amounts.

Shape and Space

Measures

Understand, use and measure units of distance, area, capacity, mass, time and angles; recognise acute, right, obtuse, straight and reflex angles; use ruler and protractor correctly.

Perimeter and Area

            Calculate area and perimeter of rectangles and compound shapes made of rectangles.

Triangles and Quadrilaterals

            Area of right-angled triangles; properties of sides, angles and symmetries; total interior angles in a   triangle; right-angled triangles; recognise squares, rectangles, rhombuses, parallelograms, kites, trapeziums; 2D symmetry.

Transformations

            Coordinates in 4 quadrants; reflections, rotations and translations.

Solids

2D representation of 3D solids; recognise cubes, cuboids, prisms, cones, pyramids, spheres; faces,            vertices and edges.

Algebra

Sequences and Functions

            Sequences and rules; function machines; functions and algebra; inverse functions

Expressions, Equations and Formulae

Using letter symbols to represent unknowns; basic rules of algebra; simplifying expressions; substitute positive integers into simple formulae; construct and solve simple linear equations with integer coefficients. 

Handling Data

Statistics

Mean mode, median and range for a small set of discrete data and simple frequency table of discrete data (not grouped); interpret pie charts; construct: - data sheet/questionnaire for survey, frequency table for discrete data grouped where appropriate in equal class intervals, pictograms, bar-charts with equal width for discrete data, bar-line graph for discrete data. 

Probability

Probability scale; find and justify probabilities from equally likely outcomes; identify all the possible outcomes of a single event; differentiate between experimental and theoretical data; collect data from a simple experiment and record in a frequency table.

Year 8 Key Objectives

Numbers and the Number System

Number Calculations

Revision of ordering directed numbers; four operations with directed numbers; indices with directed numbers; first and second rule of indices; revision of divisibility tests, factors, multiples and prime numbers; prime factors; HCF and LCM by prime factors; rounding using decimal places.

Fractions/Decimals/Percentages

Revision of four operations with fractions and decimals; revision of fractions of amounts using cancelling; changing between fractions, percentages and decimals, including fractional and decimal        percentages but not recurring decimals; percentages of amounts using fractional, decimal and mental methods; percentage increase and decrease.

Ratio and Proportion

Comparing ratio and proportion; simplifying a ratio; reducing a ratio to the form 1 : n;  comparing two ratios using 1 : n; division in a given ratio; direct and inverse proportion using unitary method; map scales and scale drawings.

Shape and Space

Measures

Revision of units of distance, area, capacity, mass, time and angles; convert between different units in same dimensions.

Triangles and Quadrilaterals

2D symmetry; calculate areas of triangles, squares, rectangles, rhombuses, parallelograms, kites and trapeziums; area of compound shapes; rearranging formulae of areas to find missing distances.

Circles

Understand centre, radius, diameter, circumference, area, semi–circle; definition and history of Pi; circumference and area formulae for circle; perimeter and area of semi-circle and quarter circle.

Solids

            Volume of cubes and cuboids; surface areas of cubes and cuboids; nets

Constructions

Constructions of triangles, polygons using ruler, compasses, protractor; angle/perpendicular bisectors.

Angles

Angles at a point; alternate/corresponding/interior angles in parallel lines; supplementary angles; angle properties of quadrilaterals. 

Algebra

Sequences

Generate and describe sequences using flow charts, term to term rule and position to term rule; recognise square, triangular, cubic and Fibonacci numbers; recognise arithmetic, quadratic and geometric sequences; find nth term of arithmetic and quadratic sequences.

Expressions, Equations and Formulae

Add/subtract and multiply expressions; multiply a single term over a bracket; simplify polynomials by multiplying out brackets and collecting like terms; substitute positive/negative integers; decimals and fractions into formulae; rearrange the subject of simple formulae; derive simple formulae; solve linear equations including set problems; understand the difference between expressions, equations and formulae.

Handling Data

Statistics

Understand difference between and discrete and continuous data; construct frequency table with equal class intervals for continuous data; construct stem-and-leaf diagrams; construct pie charts, bar-charts for continuous data with equal width, frequency polygons.

Probability

Experimental and theoretical probability; sample space diagrams; p (A) = 1 - p (A´); simulation.

Year 9 Key Objectives

Numbers and the Number System

Number Calculations

Revision of first and second rules of indices; third rule of indices; zero, negative and fractional indices; reciprocals; scientific notation; rounding using significant figures and decimal places.

Fractions/Decimals/Percentages

Revision of four operations with fractions and decimals; revision of fractions of amounts using           cancelling; revision of changing between fractions, percentages and decimals, including fractional, decimal percentages and recurring decimals; revision of percentages of amounts using fractional, decimal and mental methods; revision of percentage increase and decrease; combinations of percentage increases and decreases; simple and compound interest; reverse percentages.

Ratio and Proportion

Reducing a ratio to the form 1:n and its use in comparing two ratios; understand ratio and proportion; direct and inverse proportion using unitary method; division in a given ratio.

Shape and Space

Measures

Compound measures of speed and density; converting between different units of density and speed. Revision of area of triangles and quadrilaterals; Pythagoras’ Theorem.

Circles

Revision of Year 8 circles; chords, sectors and arcs; formulae for arc distance and sector area.

Solids

            Volume and surface area of prisms, pyramids, cones and spheres.

Angles

Interior and exterior angles of polygons; regular polygons; formulae for total of interior and exterior angles in polygons; formulae for each interior and exterior angles in regular polygons; tessellations;       bearings.

Similarity and Congruence

Congruent triangles; similar triangles; Tales theorem; finding missing distances in similar shapes; area and volume in similar shapes; enlargements with positive integer and fractional scale factors.

Algebra

Expressions, Equations and Formulae

Revision of Year 8 algebra; binomial expansion; change subject of formulae; simultaneous linear      equations; factorise linear and quadratic expressions; solving quadratic equations using factorisation and formulae; simplify expressions of algebraic fractions with numerical denominators; solve equations of algebraic fractions with numerical denominators; solve linear inequalities; understand difference between formulae, expressions, identities, equations and functions.

Graphs of Functions

Representation of linear functions using y = mx + c; solve simultaneous linear equations graphically; length and mid-point of a line; perpendicular and parallel lines; construct functions from real life situations and plot the corresponding graph; distance/time and speed/time graphs

Handling Data

Statistics

Primary and secondary sources; bias; poor graphs; construct scatter diagrams and use line of best fit to find if correlation is +ve, -ve, or zero; estimate mean, mode and identify modal class from frequency table of grouped continuous data; survey.

Probability

Dependent and independent events; mutually exclusive events; estimate probability from experimental data; understand relative frequency (experimental probability) as an estimate and use to compare outcome of a experiment; tree diagrams for combined events where the events are dependent or independent

Other Information

Calculators

            Practising mental arithmetic and learning tricks to improve a student’s ability to make those number connections is important. Therefore in Y7/8 and 9 we use a class set of basic calculators only when necessary in class and never to use calculators at home. We encourage students in class to share mental tricks and improve their level. 

Evaluations

            Students will receive a mark on their assessment profile every 3 weeks in Y7/8/9. This will reflect the progress made by the student over that time. Most of the time the evaluation will consist of a small assessment done in class. Students will always be clearly told beforehand on what they will be assessed. At the end of each term there is an end of term evaluation which tests the material learnt during the term. A student’s end of term mark is weighted so that the term’s mark are worth 70% and the end of term evaluation is worth 30%. Although a 5 ia a pass mark, a students should be aiming for at least a 6.5.

Competitions

            Every year, Y6 to Y11 students from St. Anne’s participate in the Concurso Primavera de matemáticas. This is a mathematical competition organised by the Comunidad de Madrid and takes place in Mathematics Faculty at the Complutense University in Madrid. It intends to encourage students to answer mathematics problems in a different way to problems seen in class and to stimulate a student’s interest in mathematics. Although it is not competitive, St Anne’s students achieve excellent results.

Homework

            Our students have a demanding day. They are in school until 5:00 pm and often will not return home until 6 pm. Important relaxation time means that there is little time left to do a lot homework. The emphasis on homework must be on quality rather than quantity. If students work hard in class then we do not set much homework. Often homework will consist of finishing off class work or a 10/15 min problem to do. Revision before evaluations should not be excessive.

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