Foundation module 5 scheme of work by nuhman10

VIEWS: 9 PAGES: 30

									AQA Mathematics for GCSE Chapter 1 – 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:
 Addition and subtraction of whole numbers
 Simple fractions such as quarter, half, third, etc.

                                                                                     Teacher’s book             Students’ book   Homework book
                       Learning objectives                              Grade
                                                                                       references                 references       references
   Express fractions of full turns in degrees and vice versa
   Recognise acute, obtuse and reflex angles, estimate angles
    and measure them accurately
                                                                          F
   Use properties of angles at a point and angles on a straight
                                                                                          pp. 1–8                  pp. 1–10         pp. 1–4
    line, understand the terms ‘perpendicular lines’ and ‘parallel
    lines’
   Recognise corresponding angles and alternate angles
                                                                          D
   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 – Angles (Foundation)
                             Chapter test grades F-D – Angles (Foundation)

Notes:
AQA Mathematics for GCSE Chapter 2 – 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:
 Properties of angles at a point and on a straight line
 Types of angles, including acute, obtuse, reflex and right angles
 Parallel lines, including opposite angles, corresponding angles and
    alternate angles

                                                                                      Teacher’s book             Students’ book       Homework book
                       Learning objectives                              Grade
                                                                                        references                 references           references
   Show that the angles of a triangle add up to 180° and use this
    to find angles
                                                                           E
   Show that an exterior angle of a triangle is equal to the sum of
    the interior opposite angles
                                                                                          pp. 9–16                  pp. 11–20            pp. 5–8
   Identify isosceles, equilateral and right-angled triangles
                                                                           G
   Use the word ‘congruent’ when triangles are identical
   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 – Properties of triangles (Foundation)
                             Chapter test grades G-E – Statistical measures (Foundation)

Notes:
AQA Mathematics for GCSE Chapter 3 – 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:
 Add, subtract and multiply integers
 Multiply a two-digit number by a single-digit number

                                                                                  Teacher’s book           Students’ book             Homework book
                      Learning objectives                            Grade
                                                                                    references               references                 references
   Simplify expressions with one variable such as a + 2a + 3a          F
   Simplify expressions with more than one variable such as
                                                                        E
    2a + 5b + a – 2b
                                                                                     pp. 17–24                pp. 21–30                    pp. 9–10
   Multiply out expressions with brackets                             D
   Expand (and simplify) harder expressions                           C
   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 – Use of symbols (Foundation)
                             Chapter test grades G-E – Use of symbols (Foundation)
                             Chapter test grades E-C – Use of symbols (Foundation)

Notes:
AQA Mathematics for GCSE Chapter 4 – 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 π in exact calculations without a calculator


Prior knowledge needed:                                                         Resources needed:
 Multiply and divide one- and two-digit numbers
 Find one half of a number

                                                                                   Teacher’s book            Students’ book             Homework book
                      Learning objectives                              Grade
                                                                                     references                references                 references
   Find the perimeter of a shape by counting sides of squares
                                                                        G
   Find the area of a square by counting squares
   Work out the area and perimeter of a simple rectangle, such
                                                                         F
    as 3 m by 8 m
   Work out the area and perimeter of a harder rectangle, such as
    3.6 m by 7.2 m                                                       E
   Find the area and perimeter of compound shapes
   Find the area of a triangle and a parallelogram                     D
   Estimate the area of an irregular shape by counting squares
                                                                        G
    and part squares                                                                  pp. 25–38                 pp. 31–54                   pp. 11–16
   Find the area and perimeter of compound shapes                      E
   Find the area of a kite and a trapezium                             D
   Name the parts of a circle                                          G
   Calculate the circumference of a circle, given the radius or
                                                                        D
    diameter, to an appropriate degree of accuracy
   Find the perimeter of a semicircle                                  C
   Calculate the area of a circle, given the radius or diameter, to
                                                                        D
    an appropriate degree of accuracy
   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 – Perimeter and area (Foundation)
                             Chapter test grades G-E – Perimeter and area (Foundation)
                             Chapter test grades E-C – Perimeter and area (Foundation)

Notes:
AQA Mathematics for GCSE Chapter 5 – 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:
 Recall and use properties of angles at a point, angles on a straight line,
    perpendicular lines, and opposite angles at a vertex
 Distinguish between acute, obtuse, reflex and right angles
 Use parallel lines, alternate angles and corresponding angles
 Prove that the angle sum of a triangle is 180°
 Prove that the exterior angle of a triangle is equal to the sum of the
    interior opposite angles
 Use angle properties of equilateral, isosceles and right-angled triangles
 Understand simple congruence

                                                                                    Teacher’s book             Students’ book             Homework book
                       Learning objectives                             Grade
                                                                                      references                 references                 references
   Recognise and name shapes, such as isosceles triangle,
                                                                          G
    parallelogram, rhombus, trapezium and hexagon
   Calculate interior and exterior angles of a quadrilateral
                                                                          E             pp. 39–48                 pp. 55–68                   pp. 17–20
   Investigate tessellations
   Classify a quadrilateral by geometric properties
                                                                          C
   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 – Properties of polygons (Foundation)
                             Chapter test grades G-E – Properties of polygons (Foundation)
                             Chapter test grades E-C – Properties of polygons (Foundation)
Notes:
AQA Mathematics for GCSE Chapter 6 – 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:
 Identify odd and even numbers

                                                                                 Teacher’s book          Students’ book   Homework book
                      Learning objectives                           Grade
                                                                                   references              references       references
   Continue a sequence of numbers or diagrams
                                                                       G
   Write down terms of a simple sequence
   Find a particular term in a sequence involving positive
    numbers
                                                                       F
   Write the term-to-term rule in a sequence involving positive
    numbers
   Find a particular term in a sequence involving negative or                      pp. 49–56              pp. 69–78        pp. 21–23
    fractional numbers
                                                                       E
   Write the term-to-term rule in a sequence involving negative
    or fractional numbers
   Write the terms of a sequence or a series of diagrams given
                                                                       D
    the nth term
   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 – Sequences (Foundation)
                             Chapter test grades G-E – Sequences (Foundation)
                             Chapter test grades E-C – Sequences (Foundation)

Notes:
AQA Mathematics for GCSE Chapter 7 – 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 ‘1-D’, ‘2-D’ and ‘3-D’; locate points with given coordinates; find the coordinates of points identified by geometrical information


Prior knowledge needed:                                                          Resources needed:
 Negative numbers and the number line

                                                                                    Teacher’s book            Students’ book              Homework book
                       Learning objectives                             Grade
                                                                                      references                references                  references
   Use coordinates in the first quadrant, such as plot the point
                                                                         G
    (3, 2)
   Use coordinates in all four quadrants, such as plot the points
                                                                          F
    (3, –2), (–2, 1) and (–4, –3)
   Draw lines such as x = 3 and y = x + 2                                E            pp. 57–66                  pp. 79–92                   pp. 24–29
   Solve problems involving straight lines
                                                                         D
   Draw lines such as y = 2x + 3
   Find the midpoint of a line segment
                                                                          C
   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 – Coordinates (Foundation)
                             Chapter test grades G-E – Coordinates (Foundation)
                             Chapter test grades E-C – Coordinates (Foundation)

Notes:
AQA Mathematics for GCSE Chapter 8 – 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:
 Find the areas of rectangles, triangles and parallelograms
 Draw nets of solids
 Multiply and divide two-digit numbers
 Multiply and divide by powers of 10

                                                                                 Teacher’s book            Students’ book            Homework book
                      Learning objectives                            Grade
                                                                                   references                references                references
   Find the volume of a solid by counting cubes and stating units     G
   Find the volume of a cube or cuboid
                                                                       E
   Find the height of a cuboid, given volume, length and breadth
   Calculate volumes of prisms and cylinders
                                                                                     pp. 67–76               pp. 93–106                  pp. 30–34
   Change between volume measures such as m3 to cm3 or cm3            C
    to litres
   Calculate surface areas of prisms and cylinders                    C
   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 – Area and volume (Foundation)
                             Chapter test grades G-E – Area and volume (Foundation)
                             Chapter test grades E-C – Area and volume (Foundation)

Notes:
    AQA Mathematics for GCSE Chapter 9 – 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:
     Collect like terms
     Substitution
     Multiply out brackets (by a number only, which may be negative)
     Cancel fractions
     Inequality signs
     Solve equations

                                                                                        Teacher’s book            Students’ book             Homework book
                           Learning objectives                             Grade
                                                                                          references                references                 references
       Solve equations such as 3x  12 or x  5  9 ,
                                                                             F
            x
        and  7 or 3x 1  9                                                 E
            2
       Solve equations such as 3x  4  5  x                               D
       Solve equations such as 2(5x  1)  28 ,                             D
        and 3x  12  2( x  5)                                              C             pp. 77–88                pp. 107–118                  pp. 35–39
                                  73          2x x
       Solve equations such as          2 or     5                       C
                                    x          3 4
       Solve inequalities such as 3x < 9 and 12 ≤ 3n < 20
       Solve linear inequalities such as 4x – 3 < 10 and 4x < 2x + 7        C
       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 – Equations and inequalities (Foundation)
                                 Chapter test grades F-D – Equations and inequalities (Foundation)
                                 Chapter test grades E-C – Equations and inequalities (Foundation)
Notes:
    AQA Mathematics for GCSE Chapter 10 – 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 = –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:
     Coordinates and equations of lines, such as x = 3, y = –2, y = x, y = –x
     Names of 2-D and 3-D shapes

                                                                                        Teacher’s book            Students’ book             Homework book
                           Learning objectives                             Grade
                                                                                          references                references                 references
       Draw the reflection of a shape in a mirror line                      G
       Reflect shapes in the axes of a graph                                E
       Reflect shapes in lines parallel to the axes such as x = 2 and
                                                                             D
        y = –1
       Reflect shapes in lines such as y = x and y = –x                     C
       Draw a line of symmetry on a 2-D shape                               G
       Draw all the lines of symmetry on a 2-D shape                        F
       Identify reflection symmetry in 3-D solids                           D
       Give the order of rotations symmetry of a 2-D shape
       Name, draw or complete 2-D shapes from information about             F             pp. 89–114               pp. 119–142                  pp. 40–56
        their symmetry
       Rotate shapes about any point                                        C
       Draw the line of reflection for two shapes                           F
       Describe fully reflections in a line and rotations about the
        origin
                                                                             D
       Describe fully reflections in any line and rotations about any
        point
       Find the centre of a rotation and describe it fully                  C
       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 – Reflections and rotations (Foundation)
                             Chapter test grades G-E – Reflections and rotations (Foundation)
                             Chapter test grades E-C – Reflections and rotations (Foundation)

Notes:
AQA Mathematics for GCSE Chapter 11 – 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:
 Substitute into algebraic expressions
 Use the bracket and power buttons on your calculator

                                                                                 Teacher’s book           Students’ book            Homework book
                      Learning objectives                           Grade
                                                                                   references               references                references
   Form and solve equations such as x 3  x  12 using trial and     C           pp. 115–118              pp. 143–150                  pp. 57–58
    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 – Trial and improvement (Foundation)
                             Chapter test grades E-C – Trial and improvement (Foundation)

Notes:
AQA Mathematics for GCSE Chapter 12 – 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:
 Plot positive and negative coordinates
 Add and subtract negative numbers
 Reflect shapes in a line of symmetry or mirror line
 Rotate shapes around a given centre
 Understand and use units of length
 Work out the area of rectangles and triangles
 Multiples of integers and decimals
 Understand the concept of ratio
 Find the HCF of two numbers

                                                                                    Teacher’s book            Students’ book             Homework book
                       Learning objectives                             Grade
                                                                                      references                references                 references
   Give a scale factor of an enlarged shape                              F
   Enlarge a shape by a positive scale factor                            E
   Compare the area of an enlarged shape with the original shape         D
   Enlarge a shape by a positive scale factor from a given centre        D
   Enlarge a shape by a fractional scale factor                          C
   Find the measurements of the dimensions of an enlarged
                                                                          E
    shape
   Translate a shape using a descriptiom such as 4 units right                       pp. 119–134              pp. 151–170                   pp. 59–64
                                                                          D
    and 3 units down
                                            4 
   Translate a shape by a vector such as                               C
                                            3
   Transform shapes by a combination of translation, rotation
                                                                          C
    and reflection
   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 – Translation and enlargement (Foundation)
                             Chapter test grades F-D – Translation and enlargement (Foundation)
                             Chapter test grades E-C – Translation and enlargement (Foundation)

Notes:
AQA Mathematics for GCSE Chapter 13 – 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:
 Calculate areas and volumes
 The circumference and area of circles
 Standard form
 Rounding numbers

                                                                                 Teacher’s book            Students’ book            Homework book
                      Learning objectives                           Grade
                                                                                   references                references                references
   Convert between imperial and metric units                          F
   Know rough metric equivalents of pounds, feet, miles, pints
                                                                       F
    and gallons
   Decide which metric unit to use for everyday measurements          G
   Make sensible estimates of a range of measures in everyday
                                                                       F
    settings
                                                                                   pp. 135–148              pp. 171–188                  pp. 65–77
   Solve simple speed problems                                        E
   Solve more difficult speed problems
   Understand and use compound measures such as speed and             C
    density
   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 – Measures (Foundation)
                             Chapter test grades G-E – Measures (Foundation)
                             Chapter test grades E-C – Measures (Foundation)
Notes:
AQA Mathematics for GCSE Chapter 14 – 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:
 Plot coordinates
 Plot and interpret a line graph
 Solve problems involving proportional reasoning

                                                                                    Teacher’s book            Students’ book             Homework book
                       Learning objectives                            Grade
                                                                                      references                references                 references
   Plot points of a conversion graph and read off positive values       F
   Read from a conversion graph for negative values                     E
   Interpret distance–time graphs                                       E           pp. 149–156               pp. 189–202                   pp. 66–70
   Calculate simple average speeds from distance–time graphs            D
   Calculate complex average speeds from distance–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 – Real-life graphs (Foundation)
                             Chapter test grades F-D – Real-life graphs (Foundation)
                             Chapter test grades E-C – Real-life graphs (Foundation)

Notes:
AQA Mathematics for GCSE Chapter 15 – 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:
 The four rules applied to negative numbers
 Calculate the squares, cubes and other powers of numbers
 Simplify expressions by collecting like terms
 Solve linear equations
 Know facts about angle properties, area, volume

                                                                                  Teacher’s book            Students’ book             Homework book
                      Learning objectives                            Grade
                                                                                    references                references                 references
   Use a formula written in words, such as
                                                                        G
    cost = 20  distance travelled
   Write an expression from a problem                                  E
   Find a solution to a problem by forming an equation and
                                                                        C
    solving it
   Use a simple formula such as P  2l  2w
                                                                        F
   Substitute positve numbers into a simple formula                                pp. 157–165               pp. 203–216                  pp. 71–75
   Substitute negative numbers into a simple formula
                                                                        E
   Use formulae from mathematics and other subjects
   Substitute numbers into more complicated formulae such as
         ( A  1) D                                                     D
    C
             9
   Rearrange linear formulae such as p  3q  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 – Formulae (Foundation)
                             Chapter test grades G-E – Formulae (Foundation)
                             Chapter test grades E-C – Formulae (Foundation)
Notes:
AQA Mathematics for GCSE Chapter 16 – 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:
 Use a protractor and a pair of compasses
 Different types of angles and triangles
 Use bearings
 Round decimals to the nearest whole number
 Use a scale on a map and scale drawing

                                                                                   Teacher’s book            Students’ book             Homework book
                       Learning objectives                            Grade
                                                                                     references                references                 references
   Measure a line accurately to the neaest millimetre                   G
   Measure or draw an angle accurately to the nearest degree            F
   Draw a triangle given three sides, or two angles and a side, or
                                                                         E
    two sides and the included angle
   Draw a quadrilateral such as a kite or a parallelogram with
    given measurements
                                                                         D
   Understand that giving the lengths of two sides and a non-
    included angle may not produce a unique triangle
   Construct the perpendicular bisector of a line                                   pp. 167–186               pp. 217–236                  pp. 76–80
                                                                         C
   Construct the bisector of an angle
   Construct the perpendicular from a point to a line
   Construct the perpendicular from a point on the line                 C
   Construct angles of 60° and 90°
   Recognise the net of a simple solid such as a cuboid                 G
   Draw the net of a simple solid such as a cuboid                      F
   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 – Construction (Foundation)
                             Chapter test grades G-E – Construction (Foundation)
                             Chapter test grades E-C – Construction (Foundation)

Notes:
AQA Mathematics for GCSE Chapter 17 – 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  mx  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:
 Plot coordinates in all four quadrants
 Discuss and interpret graphs of real-life situations

                                                                                     Teacher’s book            Students’ book              Homework book
                       Learning objectives                              Grade
                                                                                       references                references                  references
   Plot the graphs of straight lines such as x = 3 and y = 4
   Complete a table of values for equations such as y  2 x  3          E
    and draw the graph
   Solve problems involving graphs, such as finding where the
                                                                          D            pp. 187–196               pp. 237–246                   pp. 81–85
    line y  x  2 crosses the line y = 1
   Recognise the equations of straight-line graphs such as
    y  4x  2                                                           C
   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 – Graphs of linear functions (Foundation)
                             Chapter test grades E-C – Graphs of linear functions (Foundation)

Notes:
AQA Mathematics for GCSE Chapter 18 – Pythagoras’ theorem                   Time allocation:

AQA specification references:
F3.2h Understand, recall and use Pythagoras’ theorem


Prior knowledge needed:                                                     Resources needed:
 Squares of integers up to 15 and the corresponding square roots
 Round numbers with decimals to the nearest integer
 The properties of quadrilaterals and their diagonals
 Calculate areas and volumes

                                                                              Teacher’s book    Students’ book   Homework book
                      Learning objectives                           Grade
                                                                                references        references       references
   Use Pythagoras’ theorem to find the hypotenuse of a right-
                                                                     G
    angled triangle
   Use Pythagoras’ theorem to find any side of a right-angled
    triangle                                                                    pp. 197–204      pp. 247–258       pp. 86–89
   Use Pythagoras’ theorem to find the height of an isosceles       C
    triangle
   Use Pythagoras’ theorem in practical problems

Assessment:
E-Mathematics Module 5 CD-ROM: Pythagoras’ theorem (F): Prerequisite test
                                   Pythagoras’ theorem (F): Chapter test, grades E-C
Modular Test and Assessment: Prerequisite test – Pythagoras’ theorem (Foundation)
                             Chapter test grades E-C – Pythagoras’ theorem (Foundation)

Notes:
AQA Mathematics for GCSE Chapter 19 – 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:
 Substitute positive and negative values of x into expressions including
    squared terms
 Plot graphs from coordinates

                                                                                   Teacher’s book           Students’ book             Homework book
                      Learning objectives                            Grade
                                                                                     references               references                 references
   Draw graphs of simple quadratic functions such as y  3x 2
                                                                        D
    and y  x 2  4
   Draw graphs of harder quadratic functions such as
                                                                                    pp. 205–214               pp. 259–268                  pp. 90–96
     y  x 2  2x  1
   Find the points of intersection of quadratic graphs with lines      C
   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 – Quadratic graphs (Foundation)
                             Chapter test grades E-C – Quadratic graphs (Foundation)

Notes:
AQA Mathematics for GCSE Chapter 20 – 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:
 Measure a line accurately (within 2 millimetres)
 Measure and draw an angle accurately (within 2 millimetres)
 Construct the perpendicular bisector of a line
 Construct the bisector of an angle
 Construct and interpret a scale drawing

                                                                                  Teacher’s book   Students’ book   Homework book
                      Learning objectives                            Grade
                                                                                    references       references       references
   Understand the idea of a locus                                     D
   Construct accurate loci, such as those of points equidistant
    from two fixed points                                                          pp. 215–224      pp. 269–278       pp. 97–99
                                                                       C
   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 – Loci (Foundation)
                             Chapter test grades G-E – Loci (Foundation)
                             Chapter test grades E-C – Loci (Foundation)

Notes:
AQA Mathematics for GCSE Chapter 21 – 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:
 Find the surface area of simple shapes
 Calcualte the volume and surface area of cuboids, prisms, cylinders and
    shapes made from cubes and cuboids
 Draw the nets of 3-D solids

                                                                                 Teacher’s book           Students’ book            Homework book
                      Learning objectives                           Grade
                                                                                   references               references                references
   Recognise and name three-dimsensional (3-D) solids
                                                                      G
   Sketch three-dimsensional (3-D) solids
                                                                                   pp. 225–234              pp. 279–288                pp. 100–106
   Draw a cuboid on an isometric grid and mark its dimensions        E
   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 – 3-D solids (Foundation)
                             Chapter test grades G-E – 3-D solids (Foundation)
                             Chapter test grades F-D – 3-D solids (Foundation)

Notes:
AQA Mathematics for GCSE Chapter 22 – 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:
 Odd and even numbers
 Prime numbers
 Factors and multiples
 Square and cube numbers

                                                                                Teacher’s book           Students’ book            Homework book
                      Learning objectives                          Grade
                                                                                  references               references                references
   Decide with a reason whether a simple statement is true or
                                                                      E
    false
   Decide with a reason whether a harder statement is true or
    false                                                             D
   Identify a counter example                                                    pp. 235–242              pp. 289–296                pp. 107–109
   Understand the difference between a demonstration and a
    proof
                                                                      C
   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 – Algebraic proofs (Foundation)
                             Chapter test grades E-C – Algebraic proofs (Foundation)

Notes:

								
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