Colin Foster teaches mathematics at a secondary school in Coventry, UK.

• Introduction.; 1 Decimal notation and place value.; 2 Comparing and ordering numbers and quantities.; 3 Negative numbers as positions on a number line.; 4 Multiples and factors.; 5 Highest common factor, lowest common multiple and primes.; 6 Prime factor decomposition of a number.; 7 Using fraction notation to describe parts of shapes.; 8 Equivalent fractions.; 9 Ordering fractions.; 10 Percentage as the OEnumber of parts per 1001.; 11 Equivalence of fractions, decimals and percentages. 12 Recurring decimals.; 13 Ratio and proportion.; 14 Reducing a ratio to its simplest form.; 15 Dividing a quantity into two or more parts in a given ratio.; 16 Comparing proportions; proportional change.; 17 Squares, positive and negative square roots, cubes and cube roots.; 18 Index notation for small positive integer powers, and numbers in standard form.; 19 Rounding numbers (Whole numbers to the nearest 10, 100, or 1000 decimals to the nearest whole number or to one dp).; 20 Rounding to n decimal places, significant figures, and upper and lower bounds.; 21 Order of operations including brackets.; 22 Multiplication and division facts to 10 X 10.; 23 Positive integer complements to 100.; 24 Add, subtract, multiply and divide integers.; 25 Add, subtract, multiply and divide numbers.; 26 Multiplying and dividing by numbers between 0 and 1.; 27 Adding and subtracting simple fractions.; 28 Calculate fractions of quantities.; 29 Dividing by fractions.; 30 +, -, X, / numbers raised to small positive integer powers.; 31 One number as a percentage of another.; 32 Estimating positions of numbers on a number line.; 33 Letter symbols representing unknown numbers or variables.; 34 Operating with and transforming linear expressions.; 35 Index laws.; 36 Transforming algebraic expressions.; 37 Construct and solve linear equations.; 38 Solving simultaneous linear equations.; 39 Representing and solving inequalities.; 40 Generating and describing simple integer sequences.; 41 Expression for general term of a sequence.; 42 Expressing simple functions in words and then symbols.; 43 Finding the inverse of a linear function.; 44 Graphs of linear functions.; 45 Substitute numbers into formulae and change the subject of a formula.; 46 Interpret graphs arising from real situations.; 47 Parallel and perpendicular lines.; 48 Alternate, corresponding, and vertically opposite angles.; 49 Angles on a line, at a point and in a triangle.; 50 Angle sum of triangle and quadrilateral.; 51 Exterior angle of triangle equals sum of opposite interior angles.; 52 Angle, side and symmetry properties of triangles and quadrilaterals.; 53 Interior and exterior angles of polygons.; 54 Reasoning and generalising about 2-D shapes.; 55 Coordinates in all four quadrants, length of line segment.; 56 2-D reflection in a mirror lines, and line symmetry.; 57 2-D rotation, and rotation symmetry.; 58 2-D translation.; 59 Combining 2-D transformations.; 60 Enlargement and similarity.; 61 2-D representations of 3-D shapes, plans and elevations.; 62 Estimating areas of 2-D shapes.; 63 Estimating angles.; 64 Area and perimeter of rectangles and shapes made from rectangles.; 65 Area of a triangle, parallelogram and trapezium.; 66 Volume and surface area of cuboids.; 67 Circumference and area of a circle, arcs and sectors of circles.; 68 Simple loci.; 69 Bearings.; 70 Sine, cosine and tangent.; 71 Statistics - the median.; 72 Statistics - the mean.; 73 Statistics - the range, median, mode and mean.; 74 Processing and representing data.; 75 Interpreting results.; 76 Frequency diagrams for grouped discrete data.; 77 Scatter graphs.; 78 Probabilities based on equally likely outcomes.; 79 Mutually exclusive outcomes for single and successive events.; 80 Comparing experimental and theoretical probabilities.

‘The problems in this book would enrich the mathematical learning of any class; they are clear and challenging whilst being easily differentiable. Colin Foster has produced a resource that will extend the mathematical learning of any student, helping them to engage with mathematics, instead of just doing mathematics.' James Robinson, Teacher of Mathematics, Ripley St Thomas School, UK