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AQA Mathematics for GCSE Chapter 1 â€“ Angles Time allocation: AQA specification references: F3.4b Understand angle measure using the associated language F3.2b Distinguish between acute, obtuse, reflex and right angles F3.2b Estimate the size of an angle in degrees F3.2a Recall and use properties of angles at a point, angles on a straight line, perpendicular lines and opposite angles F3.2c Use parallel lines, alternate angles and corresponding angles F3.4b Use bearings to specify direction Prior knowledge needed: Resources needed: ï‚· Addition and subtraction of whole numbers ï‚· Simple fractions such as quarter, half, third, etc. Teacherâ€™s book Studentsâ€™ book Homework book Learning objectives Grade references references references ï‚· Express fractions of full turns in degrees and vice versa ï‚· Recognise acute, obtuse and reflex angles, estimate angles and measure them accurately F ï‚· Use properties of angles at a point and angles on a straight pp. 1â€“8 pp. 1â€“10 pp. 1â€“4 line, understand the terms â€˜perpendicular linesâ€™ and â€˜parallel linesâ€™ ï‚· Recognise corresponding angles and alternate angles D ï‚· Understand and use three-figure bearings Assessment: E-Mathematics Module 5 CD-ROM: Angles (F): Prerequisite test Angles (F): Chapter test, grades F-D Modular Test and Assessment: Prerequisite test â€“ Angles (Foundation) Chapter test grades F-D â€“ Angles (Foundation) Notes: AQA Mathematics for GCSE Chapter 2 â€“ Properties of triangles Time allocation: AQA specification references: F3.2c Understand a proof that the angle sum of a triangle is 180° F3.2c Understand a proof that the exterior angle of a triangle is equal to the sum of the interior angles at the other two vertices F3.2d Use angle properties of equilateral, isosceles and right-angled triangles. Understand congruence Prior knowledge needed: Resources needed: ï‚· Properties of angles at a point and on a straight line ï‚· Types of angles, including acute, obtuse, reflex and right angles ï‚· Parallel lines, including opposite angles, corresponding angles and alternate angles Teacherâ€™s book Studentsâ€™ book Homework book Learning objectives Grade references references references ï‚· Show that the angles of a triangle add up to 180° and use this to find angles E ï‚· Show that an exterior angle of a triangle is equal to the sum of the interior opposite angles pp. 9â€“16 pp. 11â€“20 pp. 5â€“8 ï‚· Identify isosceles, equilateral and right-angled triangles G ï‚· Use the word â€˜congruentâ€™ when triangles are identical ï‚· Use angle properties of isosceles, equilateral and right-angled E triangles Assessment: E-Mathematics Module 5 CD-ROM: Properties of triangles (F): Prerequisite test Properties of triangles (F): Chapter test, grades G-E Modular Test and Assessment: Prerequisite test â€“ Properties of triangles (Foundation) Chapter test grades G-E â€“ Statistical measures (Foundation) Notes: AQA Mathematics for GCSE Chapter 3 â€“ Use of symbols Time allocation: AQA specification references: F2.5b Expand the product of two linear expressions F2.5b Manipulate algebraic expressions by collecting like terms, by multiplying a single term over a bracket, and by taking out single term common factors Prior knowledge needed: Resources needed: ï‚· Add, subtract and multiply integers ï‚· Multiply a two-digit number by a single-digit number Teacherâ€™s book Studentsâ€™ book Homework book Learning objectives Grade references references references ï‚· Simplify expressions with one variable such as a + 2a + 3a F ï‚· Simplify expressions with more than one variable such as E 2a + 5b + a â€“ 2b pp. 17â€“24 pp. 21â€“30 pp. 9â€“10 ï‚· Multiply out expressions with brackets D ï‚· Expand (and simplify) harder expressions C ï‚· Factorise expressions D Assessment: E-Mathematics Module 5 CD-ROM: Use of symbols (F): Prerequisite test Use of symbols (F): Chapter test, grades G-E Use of symbols (F): Chapter test, grades E-C Modular Test and Assessment: Prerequisite test â€“ Use of symbols (Foundation) Chapter test grades G-E â€“ Use of symbols (Foundation) Chapter test grades E-C â€“ Use of symbols (Foundation) Notes: AQA Mathematics for GCSE Chapter 4 â€“ Perimeter and area Time allocation: AQA specification references: F3.4f Find areas of rectangles, recalling the formula, understanding the connection to counting squares and how it extends to this approach F3.2e Use their knowledge of rectangles, parallelograms and triangles to deduce formulae for the area of a parallelogram, and a triangle, from the formula for the area of a rectangle F3.4f Recall and use the formulae for the area of a parallelogram and a triangle F3.4f Find the surface area of simple shapes using the formulae for the areas of triangles and rectangles. Calculate perimeters and areas of shapes made from triangles and rectangles F3.2i Recall the definitions of a circle and the meaning of related terms F3.4h Find circumferences of circles and areas enclosed by circles, recalling relevant formulae (H2.3n) Use Ï€ in exact calculations without a calculator Prior knowledge needed: Resources needed: ï‚· Multiply and divide one- and two-digit numbers ï‚· Find one half of a number Teacherâ€™s book Studentsâ€™ book Homework book Learning objectives Grade references references references ï‚· Find the perimeter of a shape by counting sides of squares G ï‚· Find the area of a square by counting squares ï‚· Work out the area and perimeter of a simple rectangle, such F as 3 m by 8 m ï‚· Work out the area and perimeter of a harder rectangle, such as 3.6 m by 7.2 m E ï‚· Find the area and perimeter of compound shapes ï‚· Find the area of a triangle and a parallelogram D ï‚· Estimate the area of an irregular shape by counting squares G and part squares pp. 25â€“38 pp. 31â€“54 pp. 11â€“16 ï‚· Find the area and perimeter of compound shapes E ï‚· Find the area of a kite and a trapezium D ï‚· Name the parts of a circle G ï‚· Calculate the circumference of a circle, given the radius or D diameter, to an appropriate degree of accuracy ï‚· Find the perimeter of a semicircle C ï‚· Calculate the area of a circle, given the radius or diameter, to D an appropriate degree of accuracy ï‚· Find the area of a semicircle C Assessment: E-Mathematics Module 5 CD-ROM: Perimeter and area (F): Prerequisite test Perimeter and area (F): Chapter test, grades G-E Perimeter and area (F): Chapter test, grades E-C Modular Test and Assessment: Prerequisite test â€“ Perimeter and area (Foundation) Chapter test grades G-E â€“ Perimeter and area (Foundation) Chapter test grades E-C â€“ Perimeter and area (Foundation) Notes: AQA Mathematics for GCSE Chapter 5 â€“ Properties of polygons Time allocation: AQA specification references: F3.2d Explain why the angle sum of any quadrilateral is 360° F3.2g Calculate and use the sums of the interior and exterior angles of quadrilaterals F3.2f Recall the essential properties of special types of quadrilateral, including square, rectangle, parallelogram, trapezium and rhombus; classify quadrilaterals by their geometric properties F3.2g Calculate and use the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons F3.2g Calculate and use the angles of regular polygons F3.2i Understand that inscribed regular polygons can be constructed by equal division of a circle Prior knowledge needed: Resources needed: ï‚· Recall and use properties of angles at a point, angles on a straight line, perpendicular lines, and opposite angles at a vertex ï‚· Distinguish between acute, obtuse, reflex and right angles ï‚· Use parallel lines, alternate angles and corresponding angles ï‚· Prove that the angle sum of a triangle is 180° ï‚· Prove that the exterior angle of a triangle is equal to the sum of the interior opposite angles ï‚· Use angle properties of equilateral, isosceles and right-angled triangles ï‚· Understand simple congruence Teacherâ€™s book Studentsâ€™ book Homework book Learning objectives Grade references references references ï‚· Recognise and name shapes, such as isosceles triangle, G parallelogram, rhombus, trapezium and hexagon ï‚· Calculate interior and exterior angles of a quadrilateral E pp. 39â€“48 pp. 55â€“68 pp. 17â€“20 ï‚· Investigate tessellations ï‚· Classify a quadrilateral by geometric properties C ï‚· Calculate exterior and interior angles of a regular polygon Assessment: E-Mathematics Module 5 CD-ROM: Properties of polygons (F): Prerequisite test Properties of polygons (F): Chapter test, grades G-E Properties of polygons (F): Chapter test, grades E-C Modular Test and Assessment: Prerequisite test â€“ Properties of polygons (Foundation) Chapter test grades G-E â€“ Properties of polygons (Foundation) Chapter test grades E-C â€“ Properties of polygons (Foundation) Notes: AQA Mathematics for GCSE Chapter 6 â€“ Sequences Time allocation: AQA specification references: F2.6a Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence F2.6a Use linear expressions to describe the nth term of an arithmetic sequence Prior knowledge needed: Resources needed: ï‚· Identify odd and even numbers Teacherâ€™s book Studentsâ€™ book Homework book Learning objectives Grade references references references ï‚· Continue a sequence of numbers or diagrams G ï‚· Write down terms of a simple sequence ï‚· Find a particular term in a sequence involving positive numbers F ï‚· Write the term-to-term rule in a sequence involving positive numbers ï‚· Find a particular term in a sequence involving negative or pp. 49â€“56 pp. 69â€“78 pp. 21â€“23 fractional numbers E ï‚· Write the term-to-term rule in a sequence involving negative or fractional numbers ï‚· Write the terms of a sequence or a series of diagrams given D the nth term ï‚· Write the nth term of a sequence or a series of diagrams C Assessment: E-Mathematics Module 5 CD-ROM: Sequences (F): Prerequisite test Sequences (F): Chapter test, grades G-E Sequences (F): Chapter test, grades E-C Modular Test and Assessment: Prerequisite test â€“ Sequences (Foundation) Chapter test grades G-E â€“ Sequences (Foundation) Chapter test grades E-C â€“ Sequences (Foundation) Notes: AQA Mathematics for GCSE Chapter 7 â€“ Coordinates Time allocation: AQA specification references: F2.6b Use the conventions for coordinates in the plane. Plot points in all four quadrants F3.3e Use axes and coordinates to specify points in all four quadrants; locate points with given coordinates; find the coordinates of points identified by geometrical information F2.6b Plot graphs of functions in which y is given explicitly in terms of x or implicitly F3.3e Find the coordinates of the midpoint of the line segment AB, given points A and B F3.3e Understand that one coordinate identifies a point on a number line, two coordinates identify a point in a plane and three coordinates identify a point in space, using the terms â€˜1-Dâ€™, â€˜2-Dâ€™ and â€˜3-Dâ€™; locate points with given coordinates; find the coordinates of points identified by geometrical information Prior knowledge needed: Resources needed: ï‚· Negative numbers and the number line Teacherâ€™s book Studentsâ€™ book Homework book Learning objectives Grade references references references ï‚· Use coordinates in the first quadrant, such as plot the point G (3, 2) ï‚· Use coordinates in all four quadrants, such as plot the points F (3, â€“2), (â€“2, 1) and (â€“4, â€“3) ï‚· Draw lines such as x = 3 and y = x + 2 E pp. 57â€“66 pp. 79â€“92 pp. 24â€“29 ï‚· Solve problems involving straight lines D ï‚· Draw lines such as y = 2x + 3 ï‚· Find the midpoint of a line segment C ï‚· Use and understand coordinates in three dimensions Assessment: E-Mathematics Module 5 CD-ROM: Coordinates (F): Prerequisite test Coordinates (F): Chapter test, grades G-E Coordinates (F): Chapter test, grades E-C Modular Test and Assessment: Prerequisite test â€“ Coordinates (Foundation) Chapter test grades G-E â€“ Coordinates (Foundation) Chapter test grades E-C â€“ Coordinates (Foundation) Notes: AQA Mathematics for GCSE Chapter 8 â€“ Area and volume Time allocation: AQA specification references: F3.4g Find volumes of cuboids, recalling the formula and understanding the connection to counting cubes and how it extends this approach; calculate volumes of shapes made from cubes and cuboids F3.4g Calculate volumes of right prisms and of shapes made from cubes and cuboids (H2.3n) Use pi in exact calculations without a calculator F3.4i Convert between volume measures including cm3 and m3 F4.3f Find the surface area of simple shapes using the area formulae F4.3i Convert between area measures including cm2 and m2 Prior knowledge needed: Resources needed: ï‚· Find the areas of rectangles, triangles and parallelograms ï‚· Draw nets of solids ï‚· Multiply and divide two-digit numbers ï‚· Multiply and divide by powers of 10 Teacherâ€™s book Studentsâ€™ book Homework book Learning objectives Grade references references references ï‚· Find the volume of a solid by counting cubes and stating units G ï‚· Find the volume of a cube or cuboid E ï‚· Find the height of a cuboid, given volume, length and breadth ï‚· Calculate volumes of prisms and cylinders pp. 67â€“76 pp. 93â€“106 pp. 30â€“34 ï‚· Change between volume measures such as m3 to cm3 or cm3 C to litres ï‚· Calculate surface areas of prisms and cylinders C ï‚· Change between area measures such as m2 to cm2 D Assessment: E-Mathematics Module 5 CD-ROM: Area and volume (F): Prerequisite test Area and volume (F): Chapter test, grades G-E Area and volume (F): Chapter test, grades E-C Modular Test and Assessment: Prerequisite test â€“ Area and volume (Foundation) Chapter test grades G-E â€“ Area and volume (Foundation) Chapter test grades E-C â€“ Area and volume (Foundation) Notes: AQA Mathematics for GCSE Chapter 9 â€“ Equations and inequalities Time allocation: AQA specification references: F2.5e Solve linear equations, with integer 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 occuring anywhere in the equation, and those with a negative solution F2.5d Solve simple linear inequalities in one variable, and represent the solution set on a number line Prior knowledge needed: Resources needed: ï‚· Collect like terms ï‚· Substitution ï‚· Multiply out brackets (by a number only, which may be negative) ï‚· Cancel fractions ï‚· Inequality signs ï‚· Solve equations Teacherâ€™s book Studentsâ€™ book Homework book Learning objectives Grade references references references ï‚· Solve equations such as 3x ï€½ 12 or x ï€« 5 ï€½ 9 , F x and ï€½ 7 or 3x ï€1 ï€½ 9 E 2 ï‚· Solve equations such as 3x ï€ 4 ï€½ 5 ï€« x D ï‚· Solve equations such as 2(5x ï€« 1) ï€½ 28 , D and 3x ï€ 12 ï€½ 2( x ï€ 5) C pp. 77â€“88 pp. 107â€“118 pp. 35â€“39 7ï€3 2x x ï‚· Solve equations such as ï€½ 2 or ï€ ï€½5 C x 3 4 ï‚· Solve inequalities such as 3x < 9 and 12 â‰¤ 3n < 20 ï‚· Solve linear inequalities such as 4x â€“ 3 < 10 and 4x < 2x + 7 C ï‚· Represent sets of solutions on the number line Assessment: E-Mathematics Module 5 CD-ROM: Equations and inequalities (F): Prerequisite test Equations and inequalities (F): Chapter test, grades F-D Equations and inequalities (F): Chapter test, grades E-C Modular Test and Assessment: Prerequisite test â€“ Equations and inequalities (Foundation) Chapter test grades F-D â€“ Equations and inequalities (Foundation) Chapter test grades E-C â€“ Equations and inequalities (Foundation) Notes: AQA Mathematics for GCSE Chapter 10 â€“ Reflections and rotations Time allocation: AQA specification references: F3.3a Understand that reflections are specified by a mirror line, at first using a line parallel to an axis, then a mirror line such as y = x or y = â€“x F3.3b Recognise and visualise reflections including reflection symmetry of 2-D and 3-D shapes; transform triangles and other 2-D shapes by reflection and combinations of transformations, recognising that these tranformations preserve length and angle, so that any figure is congruent to its image F3.3b Recognise and visualise rotations including rotation symmetry of 2-D and 3-D shapes; transform triangles and other 2-D shapes by rotation and combinations of transformations, recognising that these tranformations preserve length and angle, so that any figure is congruent to its image F3.3a Understand that rotations are specified by a centre and an (anticlockwise) angle; rotate a shape about the origin or any other point; measure the angle of rotation using right angles, simple fractions or a turn or degrees Prior knowledge needed: Resources needed: ï‚· Coordinates and equations of lines, such as x = 3, y = â€“2, y = x, y = â€“x ï‚· Names of 2-D and 3-D shapes Teacherâ€™s book Studentsâ€™ book Homework book Learning objectives Grade references references references ï‚· Draw the reflection of a shape in a mirror line G ï‚· Reflect shapes in the axes of a graph E ï‚· Reflect shapes in lines parallel to the axes such as x = 2 and D y = â€“1 ï‚· Reflect shapes in lines such as y = x and y = â€“x C ï‚· Draw a line of symmetry on a 2-D shape G ï‚· Draw all the lines of symmetry on a 2-D shape F ï‚· Identify reflection symmetry in 3-D solids D ï‚· Give the order of rotations symmetry of a 2-D shape ï‚· Name, draw or complete 2-D shapes from information about F pp. 89â€“114 pp. 119â€“142 pp. 40â€“56 their symmetry ï‚· Rotate shapes about any point C ï‚· Draw the line of reflection for two shapes F ï‚· Describe fully reflections in a line and rotations about the origin D ï‚· Describe fully reflections in any line and rotations about any point ï‚· Find the centre of a rotation and describe it fully C ï‚· Combine reflections and rotations C Assessment: E-Mathematics Module 5 CD-ROM: Reflections and rotations (F): Prerequisite test Reflections and rotations (F): Chapter test, grades G-E Reflections and rotations (F): Chapter test, grades E-C Modular Test and Assessment: Prerequisite test â€“ Reflections and rotations (Foundation) Chapter test grades G-E â€“ Reflections and rotations (Foundation) Chapter test grades E-C â€“ Reflections and rotations (Foundation) Notes: AQA Mathematics for GCSE Chapter 11 â€“ Trial and improvement Time allocation: AQA specification references: F2.4b Select appropriate operations, methods and strategies to solve number problems, including trial and improvement (H2.5m) Use systematic trial and improvement to find approximate solutions of equations where there is no simple analytical method of solving them Prior knowledge needed: Resources needed: ï‚· Substitute into algebraic expressions ï‚· Use the bracket and power buttons on your calculator Teacherâ€™s book Studentsâ€™ book Homework book Learning objectives Grade references references references ï‚· Form and solve equations such as x 3 ï€« x ï€½ 12 using trial and C pp. 115â€“118 pp. 143â€“150 pp. 57â€“58 improvement methods Assessment: E-Mathematics Module 5 CD-ROM: Trial and improvement (F): Prerequisite test Trial and improvement (F): Chapter test, grades E-C Modular Test and Assessment: Prerequisite test â€“ Trial and improvement (Foundation) Chapter test grades E-C â€“ Trial and improvement (Foundation) Notes: AQA Mathematics for GCSE Chapter 12 â€“ Translation and enlargement Time allocation: AQA specification references: F3.3a Understand that enlargements are specified by a centre and positive scale factor F3.3c Recognise, visualise and construct enlargements of objects using positive scale factors greater than one, then positive scale factors less than one; understand from this that any two circles and any two squares are mathematically similar, while, in general, two rectangles are not F3.3a Understand that translations are specified by a distance and direction (or a vector) F3.3b Recognise and visualise tranlations; transform triangles and other 2-D shapes by translation and combinations of transformations, recognising that these transformations preserve length and angle, so that any figure is congruent to its image under any of these transformations F3.3f Understand and use vector notation for translations Prior knowledge needed: Resources needed: ï‚· Plot positive and negative coordinates ï‚· Add and subtract negative numbers ï‚· Reflect shapes in a line of symmetry or mirror line ï‚· Rotate shapes around a given centre ï‚· Understand and use units of length ï‚· Work out the area of rectangles and triangles ï‚· Multiples of integers and decimals ï‚· Understand the concept of ratio ï‚· Find the HCF of two numbers Teacherâ€™s book Studentsâ€™ book Homework book Learning objectives Grade references references references ï‚· Give a scale factor of an enlarged shape F ï‚· Enlarge a shape by a positive scale factor E ï‚· Compare the area of an enlarged shape with the original shape D ï‚· Enlarge a shape by a positive scale factor from a given centre D ï‚· Enlarge a shape by a fractional scale factor C ï‚· Find the measurements of the dimensions of an enlarged E shape ï‚· Translate a shape using a descriptiom such as 4 units right pp. 119â€“134 pp. 151â€“170 pp. 59â€“64 D and 3 units down ïƒ¦ 4 ïƒ¶ ï‚· Translate a shape by a vector such as ïƒ§ ïƒ· C ïƒ¨ ï€3ïƒ¸ ï‚· Transform shapes by a combination of translation, rotation C and reflection ï‚· Use map scales to find distance E Assessment: E-Mathematics Module 5 CD-ROM: Translation and enlargement (F): Prerequisite test Translation and enlargement (F): Chapter test, grades F-D Translation and enlargement (F): Chapter test, grades E-C Modular Test and Assessment: Prerequisite test â€“ Translation and enlargement (Foundation) Chapter test grades F-D â€“ Translation and enlargement (Foundation) Chapter test grades E-C â€“ Translation and enlargement (Foundation) Notes: AQA Mathematics for GCSE Chapter 13 â€“ Measures Time allocation: AQA specification references: F3.4a Convert measurements from one unit to another; know rough metric equivalents of pounds, feet, miles, pints and gallons; make sensible estimates of a range of measures in everyday settings F3.4c Understand and use compound measures, including speed and density F3.4a Recognise that measurements given to the nearest whole unit may be inaccurate by up to one half in either direction Prior knowledge needed: Resources needed: ï‚· Calculate areas and volumes ï‚· The circumference and area of circles ï‚· Standard form ï‚· Rounding numbers Teacherâ€™s book Studentsâ€™ book Homework book Learning objectives Grade references references references ï‚· Convert between imperial and metric units F ï‚· Know rough metric equivalents of pounds, feet, miles, pints F and gallons ï‚· Decide which metric unit to use for everyday measurements G ï‚· Make sensible estimates of a range of measures in everyday F settings pp. 135â€“148 pp. 171â€“188 pp. 65â€“77 ï‚· Solve simple speed problems E ï‚· Solve more difficult speed problems ï‚· Understand and use compound measures such as speed and C density ï‚· Recognise accuracy in measurements given to the nearest C whole unit Assessment: E-Mathematics Module 5 CD-ROM: Measures (F): Prerequisite test Measures (F): Chapter test, grades G-E Measures (F): Chapter test, grades E-C Modular Test and Assessment: Prerequisite test â€“ Measures (Foundation) Chapter test grades G-E â€“ Measures (Foundation) Chapter test grades E-C â€“ Measures (Foundation) Notes: AQA Mathematics for GCSE Chapter 14 â€“ Real-life graphs Time allocation: AQA specification references: F2.6c Construct linear functions from real-life problems and plot their corresponding graphs; discuss and interpret graphs modelling real situations F2.6e Interpret information presented in a range of linear and non-linear graphs Prior knowledge needed: Resources needed: ï‚· Plot coordinates ï‚· Plot and interpret a line graph ï‚· Solve problems involving proportional reasoning Teacherâ€™s book Studentsâ€™ book Homework book Learning objectives Grade references references references ï‚· Plot points of a conversion graph and read off positive values F ï‚· Read from a conversion graph for negative values E ï‚· Interpret distanceâ€“time graphs E pp. 149â€“156 pp. 189â€“202 pp. 66â€“70 ï‚· Calculate simple average speeds from distanceâ€“time graphs D ï‚· Calculate complex average speeds from distanceâ€“time graphs C Assessment: E-Mathematics Module 5 CD-ROM: Real-life graphs (F): Prerequisite test Real-life graphs (F): Chapter test, grades F-D Real-life graphs (F): Chapter test, grades E-C Modular Test and Assessment: Prerequisite test â€“ Real-life graphs (Foundation) Chapter test grades F-D â€“ Real-life graphs (Foundation) Chapter test grades E-C â€“ Real-life graphs (Foundation) Notes: AQA Mathematics for GCSE Chapter 15 â€“ Formulae Time allocation: AQA specification references: F2.5a Distinguish the different roles played by letter symbols in algebra, using the correct notational conventions for multiplying or dividing by a given number, and knowing that letter symbols represent definite known numbers F2.5f Use formulae from mathematics and other subjects expressed initially in words and then using letters and symbols substitute numbers into a formula; derive a formula and change its subject Prior knowledge needed: Resources needed: ï‚· The four rules applied to negative numbers ï‚· Calculate the squares, cubes and other powers of numbers ï‚· Simplify expressions by collecting like terms ï‚· Solve linear equations ï‚· Know facts about angle properties, area, volume Teacherâ€™s book Studentsâ€™ book Homework book Learning objectives Grade references references references ï‚· Use a formula written in words, such as G cost = 20 ï‚´ distance travelled ï‚· Write an expression from a problem E ï‚· Find a solution to a problem by forming an equation and C solving it ï‚· Use a simple formula such as P ï€½ 2l ï€« 2w F ï‚· Substitute positve numbers into a simple formula pp. 157â€“165 pp. 203â€“216 pp. 71â€“75 ï‚· Substitute negative numbers into a simple formula E ï‚· Use formulae from mathematics and other subjects ï‚· Substitute numbers into more complicated formulae such as ( A ï€« 1) D D Cï€½ 9 ï‚· Rearrange linear formulae such as p ï€½ 3q ï€« 5 C Assessment: E-Mathematics Module 5 CD-ROM: Formulae (F): Prerequisite test Formulae (F): Chapter test, grades G-E Formulae (F): Chapter test, grades E-C Modular Test and Assessment: Prerequisite test â€“ Formulae (Foundation) Chapter test grades G-E â€“ Formulae (Foundation) Chapter test grades E-C â€“ Formulae (Foundation) Notes: AQA Mathematics for GCSE Chapter 16 â€“ Construction Time allocation: AQA specification references: F3.4d Measure and drraw lines to the nearest millimetre, and angles to the nearest degree; draw triangles and other 2-D shapes using a ruler and protractor, given information about their side lengths and angles; understand, from their experience of constructing them, that triangles satisfying SSS, SAS, ASA and RHS are unique, but SSA triangles are not F3.4e Use straight edge and compasses to do standard constructions, including an equilateral triangle with a given side, the midpoint and perpendicular bisector of a line segment, the perpendicular from a point to a line, and the bisector of an angle F3.4d Construct cubes, regular tetrahedra, square-based pyramids and other 3-D shapes from given information Prior knowledge needed: Resources needed: ï‚· Use a protractor and a pair of compasses ï‚· Different types of angles and triangles ï‚· Use bearings ï‚· Round decimals to the nearest whole number ï‚· Use a scale on a map and scale drawing Teacherâ€™s book Studentsâ€™ book Homework book Learning objectives Grade references references references ï‚· Measure a line accurately to the neaest millimetre G ï‚· Measure or draw an angle accurately to the nearest degree F ï‚· Draw a triangle given three sides, or two angles and a side, or E two sides and the included angle ï‚· Draw a quadrilateral such as a kite or a parallelogram with given measurements D ï‚· Understand that giving the lengths of two sides and a non- included angle may not produce a unique triangle ï‚· Construct the perpendicular bisector of a line pp. 167â€“186 pp. 217â€“236 pp. 76â€“80 C ï‚· Construct the bisector of an angle ï‚· Construct the perpendicular from a point to a line ï‚· Construct the perpendicular from a point on the line C ï‚· Construct angles of 60° and 90° ï‚· Recognise the net of a simple solid such as a cuboid G ï‚· Draw the net of a simple solid such as a cuboid F ï‚· Construct and recognise the nets of 3-D solids such as D pyramids and triangular prisms Assessment: E-Mathematics Module 5 CD-ROM: Construction (F): Prerequisite test Construction (F): Chapter test, grades G-E Construction (F): Chapter test, grades E-C Modular Test and Assessment: Prerequisite test â€“ Construction (Foundation) Chapter test grades G-E â€“ Construction (Foundation) Chapter test grades E-C â€“ Construction (Foundation) Notes: AQA Mathematics for GCSE Chapter 17 â€“ Graphs of linear functions Time allocation: AQA specification references: F2.6b Use the conventions for coordinates in the plane; plot points in all four quadrants; recognise (when values are given for m and c) that equations of the form y ï€½ mx ï€« c correspond to straight-line graphs in the coordinates plane; plot graphs of functions in which y is given explicitly in terms of x, or implicitly Prior knowledge needed: Resources needed: ï‚· Plot coordinates in all four quadrants ï‚· Discuss and interpret graphs of real-life situations Teacherâ€™s book Studentsâ€™ book Homework book Learning objectives Grade references references references ï‚· Plot the graphs of straight lines such as x = 3 and y = 4 ï‚· Complete a table of values for equations such as y ï€½ 2 x ï€« 3 E and draw the graph ï‚· Solve problems involving graphs, such as finding where the D pp. 187â€“196 pp. 237â€“246 pp. 81â€“85 line y ï€½ x ï€« 2 crosses the line y = 1 ï‚· Recognise the equations of straight-line graphs such as y ï€½ ï€4x ï€« 2 C ï‚· Find the gradients of straight-line graphs Assessment: E-Mathematics Module 5 CD-ROM: Graphs of linear functions (F): Prerequisite test Graphs of linear functions (F): Chapter test, grades E-C Modular Test and Assessment: Prerequisite test â€“ Graphs of linear functions (Foundation) Chapter test grades E-C â€“ Graphs of linear functions (Foundation) Notes: AQA Mathematics for GCSE Chapter 18 â€“ Pythagorasâ€™ theorem Time allocation: AQA specification references: F3.2h Understand, recall and use Pythagorasâ€™ theorem Prior knowledge needed: Resources needed: ï‚· Squares of integers up to 15 and the corresponding square roots ï‚· Round numbers with decimals to the nearest integer ï‚· The properties of quadrilaterals and their diagonals ï‚· Calculate areas and volumes Teacherâ€™s book Studentsâ€™ book Homework book Learning objectives Grade references references references ï‚· Use Pythagorasâ€™ theorem to find the hypotenuse of a right- G angled triangle ï‚· Use Pythagorasâ€™ theorem to find any side of a right-angled triangle pp. 197â€“204 pp. 247â€“258 pp. 86â€“89 ï‚· Use Pythagorasâ€™ theorem to find the height of an isosceles C triangle ï‚· Use Pythagorasâ€™ theorem in practical problems Assessment: E-Mathematics Module 5 CD-ROM: Pythagorasâ€™ theorem (F): Prerequisite test Pythagorasâ€™ theorem (F): Chapter test, grades E-C Modular Test and Assessment: Prerequisite test â€“ Pythagorasâ€™ theorem (Foundation) Chapter test grades E-C â€“ Pythagorasâ€™ theorem (Foundation) Notes: AQA Mathematics for GCSE Chapter 19 â€“ Quadratic graphs Time allocation: AQA specification references: (H2.6e) Generate points and plot graphs of simple quadratic functions, then more general quadratic functions; find approximate solutions of a quadratic equation from the graph of the corresponding quadratic function Prior knowledge needed: Resources needed: ï‚· Substitute positive and negative values of x into expressions including squared terms ï‚· Plot graphs from coordinates Teacherâ€™s book Studentsâ€™ book Homework book Learning objectives Grade references references references ï‚· Draw graphs of simple quadratic functions such as y ï€½ 3x 2 D and y ï€½ x 2 ï€« 4 ï‚· Draw graphs of harder quadratic functions such as pp. 205â€“214 pp. 259â€“268 pp. 90â€“96 y ï€½ x 2 ï€ 2x ï€« 1 ï‚· Find the points of intersection of quadratic graphs with lines C ï‚· Use graphs to find the approximate solutions of quadratic equations Assessment: E-Mathematics Module 5 CD-ROM: Quadratic graphs (F): Prerequisite test Quadratic graphs (F): Chapter test, grades E-C Modular Test and Assessment: Prerequisite test â€“ Quadratic graphs (Foundation) Chapter test grades E-C â€“ Quadratic graphs (Foundation) Notes: AQA Mathematics for GCSE Chapter 20 â€“ Loci Time allocation: AQA specification references: F3.4j Find loci, both by reasoning and by using ICT to produce shapes and paths Prior knowledge needed: Resources needed: ï‚· Measure a line accurately (within 2 millimetres) ï‚· Measure and draw an angle accurately (within 2 millimetres) ï‚· Construct the perpendicular bisector of a line ï‚· Construct the bisector of an angle ï‚· Construct and interpret a scale drawing Teacherâ€™s book Studentsâ€™ book Homework book Learning objectives Grade references references references ï‚· Understand the idea of a locus D ï‚· Construct accurate loci, such as those of points equidistant from two fixed points pp. 215â€“224 pp. 269â€“278 pp. 97â€“99 C ï‚· Solve loci problems, such as identifying points less than 3 cm from a point P Assessment: E-Mathematics Module 5 CD-ROM: Loci (F): Prerequisite test Loci (F): Chapter test, grades G-E Loci (F): Chapter test, grades E-C Modular Test and Assessment: Prerequisite test â€“ Loci (Foundation) Chapter test grades G-E â€“ Loci (Foundation) Chapter test grades E-C â€“ Loci (Foundation) Notes: AQA Mathematics for GCSE Chapter 21 â€“ 3-D solids Time allocation: AQA specification references: F3.2j Explore the geometry of cuboids (including cubes), and shapes made from cuboids F3.2k Use 2-D representations of 3-D shapes and analyse 3-D shapes through 2-D projections and cross-sections, including plan and elevation Prior knowledge needed: Resources needed: ï‚· Find the surface area of simple shapes ï‚· Calcualte the volume and surface area of cuboids, prisms, cylinders and shapes made from cubes and cuboids ï‚· Draw the nets of 3-D solids Teacherâ€™s book Studentsâ€™ book Homework book Learning objectives Grade references references references ï‚· Recognise and name three-dimsensional (3-D) solids G ï‚· Sketch three-dimsensional (3-D) solids pp. 225â€“234 pp. 279â€“288 pp. 100â€“106 ï‚· Draw a cuboid on an isometric grid and mark its dimensions E ï‚· Draw plans and elevations of three-dimsensional (3-D) solids D Assessment: E-Mathematics Module 5 CD-ROM: 3-D solids (F): Prerequisite test 3-D solids (F): Chapter test, grades G-E 3-D solids (F): Chapter test, grades F-D Modular Test and Assessment: Prerequisite test â€“ 3-D solids (Foundation) Chapter test grades G-E â€“ 3-D solids (Foundation) Chapter test grades F-D â€“ 3-D solids (Foundation) Notes: AQA Mathematics for GCSE Chapter 22 â€“ Algebraic proofs Time allocation: AQA specification references: F2.1j Explore, identify, and use pattern and symmetry in algebraic contexts; investigating whether particular cases can be generalised further, and understanding the importance of a counter example, identifying exceptional cases when solving problems F2.1l Understand the difference between a practical demonstration and a proof F2.1k Show step-by-step deduction in solving a problem F2.1m Recognise the importance of making assumptions when deducing results; recognise the limitations of any assumptions that are made and the effect that varying the assumptions may have on the solution to a problem Prior knowledge needed: Resources needed: ï‚· Odd and even numbers ï‚· Prime numbers ï‚· Factors and multiples ï‚· Square and cube numbers Teacherâ€™s book Studentsâ€™ book Homework book Learning objectives Grade references references references ï‚· Decide with a reason whether a simple statement is true or E false ï‚· Decide with a reason whether a harder statement is true or false D ï‚· Identify a counter example pp. 235â€“242 pp. 289â€“296 pp. 107â€“109 ï‚· Understand the difference between a demonstration and a proof C ï‚· Show step-by-step deductions in providing a basic algebraic explanation Assessment: E-Mathematics Module 5 CD-ROM: Algebraic proofs (F): Prerequisite test Algebraic proofs (F): Chapter test, grades E-C Modular Test and Assessment: Prerequisite test â€“ Algebraic proofs (Foundation) Chapter test grades E-C â€“ Algebraic proofs (Foundation) Notes: