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Jacari Tips: Key Stage Three Maths! These are some of the skills that pupils in Key Stage Three (ages 11 to 14) should be learning at school in Maths. Please note that you are not expected to teach your pupils all of the items on this list! However, it is useful to know what to aim for, and these may well help you to plan your lessons, make targets, and support your pupils to the best of their abilities. So, according to the National Curriculum for Maths, by the end of KS3 (ages 11 to 14), pupils should be able to... Numbers and the number system: Round large positive numbers to a given power of 10; understand and use negative numbers (e.g. on a number line and with multiplication); order integers; use vocabulary such as factor, multiple, common factor, least common multiple; prime number and prime factor composition. Use the terms square, positive and negative square root, cube, cube root Use index laws for multiplication and division of positive integer powers (e.g. 62 x 64 = 62+4 = 66) Use fraction notation; understand equivalent fractions; simplify fractions by cancelling out common factors; order fractions by writing them with common denominators Use decimal notation; order decimals; recognise that any finite decimal is a fraction Understand that percentage means "number of parts per 100" and use this to compare proportions Use ration notation (e.g. 1:4), including reduction to simplest form Calculations: Add, subtract, multiply and divide with integers and then any number Find the prime factor composition of any number (e.g. 8000 = 26 x 53) Use brackets and order of operations Calculate a fraction of a given number (e.g. 2/5 of 350), and express a given number as a fraction of another (e.g. what fraction of 30 is 14?) Add and subtract fractions by using a common denominator Perform division to convert a simple fraction into a decimal Understand and use unit fractions as the multiplication inverses (e.g. dividing by 5 is the same as multiplying by 1/5; multiplying by 6/7 is the same as dividing by 7 and then multiplying by 6) Convert fractions of a whole to percentages and vice versa Mental methods: Recall all positive addition facts to 100 (e.g. 63 + 27, 58 + 42); recall all multiplication facts up to 10x10; and use these to derive division facts quickly Recall the squares and cubes of 2, 3, 4, 5 and 10 Recall fraction-to-decimal conversions of 1/2, 1/4, 1/5, 1/10 Written methods: Use standard columns for addition and subtraction of integers, and for multiplication, remembering where to place the decimal point Solve a division problem involving a decimal by changing it into an integer (e.g. 524 2.4 = 5240 24) Solve simple percentage problems such as increase and decrease Calculator methods: Know how to enter complex calculations using brackets Use the keys for reciprocals, squares, square roots, powers, fractions Equations, formulae and identities: Distinguish the roles played by letter symbols in algebra, knowing that letter symbols can represent unknown but definite quantities in equations (e.g. n2 +1 = 65), or general, unspecified numbers in identities (e.g. A = l x h) Simplify algebraic expressions by collecting like terms; or expanding brackets; or taking out common factors Distinguish between vocabulary such as equation, formula, identity, expression Solve linear equations (e.g. with no powers), including those with negative numbers or in which the unknown appears on both sides of the equation Substitute numbers into a formula and rearrange a formula Solve simultaneous equations by elimination Sequences, functions and graphs: Generate common sequences such as odd numbers, square numbers, powers of 10, triangular numbers Find the first terms of a sequence given in a rule (e.g. multiply by 10, then add 4); express the rule for the nth term in the sequence (e.g. 10n + 4) Understand conventions for coordinates and plot points such as (-4, -3) Understand and plot linear equations such as y = 2x + 3 Find the gradient of lines and investigate the gradient of parallel and perpendicular lines Geometrical reasoning: Recall and use knowledge of angles around a point (360 degrees), angles on a straight line (180), perpendicular lines, and opposite angles Distinguish between acute, obtuse, reflex and right angles; estimate angles in degrees Use parallel lines, alternate angles, and corresponding angles Understand properties of a parallelogram and the proof of the angle sum of a triangle as 180 degrees Understand congruence Use knowledge of rectangles and triangles to deduce formulae for area of rectangles, parallelograms, and triangles Calculate sums of angles in quadrilaterals, pentagons, and hexagons Understand, recall and use Pythagoras' Theorem (a2+b2=c 2 for triangle sides) Recall definitions such as circle, centre, radius, chord, diameter, circumference, tangent, arc, sector, and segment Use 2-D representations of 3-D shapes Transformations and coordinates: Recognise and visualise rotations, reflections, translations and enlargements of 2-D shapes Understand that rotations are specified by a centre and an angle; reflections are specified by a mirror line; translations by distance and direction; enlargements by a centre and a scale factor Transform 2-D shapes by translation, rotation or reflection Recognise that enlargement preserves angle but not length; identify the scale factor of an enlargement as the ration of lengths of any two corresponding lines in the shape Understand that one coordinate identifies a point on a number line; two coordinates identify a point on a flat plane; three coordinates identify a point in space Find the coordinates of the midpoint of a line given the start and end points of the line, and calculate the length of the line Measures and construction: Interpret scales on a range of measurement instruments, including those for time and mass Convert measurements from one metric unit to another (e.g. cm to m, or ml to l) Recall rough equivalents from metric measurements to inches, feet, miles, pounds Measure and draw lines to nearest millimetre, and angles to nearest degree Draw accurate triangles and other shapes using a ruler and protractor Construct cubes and square-based pyramids from given dimensions Find areas of rectangles, parallelograms and triangles Calculate perimeters of simple shapes composed of triangles and rectangles Find circumference and area of circles, using relevant formulae Handling data: Specify a problem and plan for data to be collected Collect data from a variety of sources, including experiments and surveys Represent the data in charts or graphs (line graphs, pie charts, scatter graphs, frequency charts) Interpret and discuss the data; answer the initial questions Calculate mean, median, mode and range for small data sets Compare sets of data