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Unit 3: Number, Algebra, Geometry 2 Number Use percentages in real-life situations Solve percentage problems, including increase and decrease in a variety of Functional contexts Calculate a given fraction of a quantity, expressing the answer as a fraction Understand ‘reciprocal’ as multiplicative inverse Multiply and divide a given fraction by an integer, by a unit fraction and by a general fraction Use a calculator to solve real-life problems involving fractions Algebra Simplify terms, products and sums Multiply a single term over a bracket Take out common factors Solve equations by using inverse operations or by transforming both sides in the same way Solve linear equations with integer or fractional coefficients, in which the unknown appears on either side or on both sides of the equation Solve linear equations that require prior simplification of brackets, including those that have negative signs occurring anywhere in the equation, and those with a negative solution Substitute numbers into formulae Use formulae from mathematics and other subjects that require prior simplification of brackets, including those that have negative signs occurring anywhere in the equation, and those with a negative solution Change the subject of a formula including where the subject occurs once Generate a formula in algebra or words Solve simple linear inequalities in one variable, and represent the solution set on a number line Use systematic trial and improvement to find approximate solutions of equations where there is no simple analytical method of solving them Interpret information presented in a range of linear and non-linear graphs modelling real situations Generate points and plotting graphs of quadratic functions Find approximate solutions of a quadratic equation from the graph of the corresponding quadratic function Geometry and Measures Use definitions and names of polygons Calculate and use the sums of the interior angles of quadrilaterals, pentagons and hexagons Calculate and use the angles of regular polygons Understand that inscribed regular polygons can be constructed by equal divisions of a circle Understand tessellations Understand similarity of triangles and of other plane figures. Recognise that enlargements preserve angle but not length Understand, recall and use Pythagoras’ theorem in 2-D Solve problems involving geometric figures (including triangles within circles) in which a right-angle triangle has to be extracted in order to solve it by Pythagoras. Calculate the length of a line segment between two coordinates Identify and name common solids Explore the geometry of cuboids (including cubes), and shapes from cuboids Transform triangles and other 2-D shapes by translation, rotation and reflection and combinations of these transformations Understand that translations are specified by a distance and direction (or a column vector), and enlarging by a centre and a scale factor Rotate a shape about the origin, or any other point Measure the angle of rotation using right angles, simple fractions of a turn or degrees Understand that rotations are specified by a centre and an (anticlockwise) angle Understand that reflections are specified by a mirror line, at first using a line parallel to any axis, then a mirror line such as y = x or y = –x Recognise, visualising and constructing enlargements of objects using a positive integer scale factor Use congruence to show that translations, rotations and reflections preserve length and angle, so that any figure is congruent to its image under any of these transformations Understand and using SSS, SAS, ASA and RHS conditions to prove the congruence of triangles using formal arguments, and to verify standard ruler and compass constructions Use and interpret maps and scale drawings Understand the effect of enlargement for perimeter, area and volume of shapes and solids Convert measurements from one unit to another (area and volume) Use and understand 3-figure bearings Draw accurate constructions of triangles and other 2-D shapes, using a ruler and protractor, given information about side lengths and angles Understand from their experience of constructing them, that triangles satisfying SSS, SAS, ASA and RHS are unique, but SSA are not Use straight edge and compasses to do standard constructions Find loci Find circumferences of circles and areas enclosed by circles, recalling relevant formulae Solve problems involving surface areas and volumes of prisms and cylinders Find the surface areas and volumes of compound solids constructed from; cubes, cuboids, cylinders and solve problems including examples of solids in everyday use