Download Foundation – Unit 1

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Foundation – Unit 3
OVERVIEW for Foundation Tier
Notes:
1 hour 30 minutes calculator exam
80 marks – 40% (UMS 83 marks)
Topic
Yr 11 Autumn and Spring Term
18. Number skills
revisited
Teaching
hours
3
19. Angles
6
20. Measurement
1
21. Triangles and
constructions
22. Equations,
formulae and
proof
23. Quadrilaterals
and other
polygons
24. Perimeter,
area and volume
25. 3-D objects
26. Reflection,
translation and
rotation
5
3
3
5
4
4
6
30 -40% Functional Elements
15 marks Number, 15 marks Algebra, 50 marks Geometry
AQA Modular specification reference
Working with numbers and the number system: N1.3, N1.4,
N1.14
Fractions, decimals and Percentages: N2.1, N2.5, N2.6, N2.7
Ratio and Proportion: N3.1, N3.3
Properties of angles and shapes: G1.1, G1.2
Measures and Construction: G3.1, G3.6
Working with numbers and the number system: N1.3
Measures and Construction: G3.1, G3.3, G3.4, G3.5
Properties of angles and shapes: G1.1, G1.2, G1.8
Measures and Construction: G3.9, G3.10
The Language of Algebra: N4.1, N4.2
Expressions and Equations: N5.1, N5.4, N5.6, N5.8
Geometrical reasoning and calculation: G2.3
Expressions and Equations: N5.4
Sequences, Functions and Graphs: N6.3
Properties of angles and shapes: G1.2, G1.3, G1.4
Mensuration: G4.1, G4.4
Geometrical reasoning and calculation: G2.4
Properties of angles and shapes: G1.6, G1.7
Vectors: G5.1
Yr11 Summer
Term
27. Circles and
cylinders
6
28. Measurement
2
29. Enlargement
and similarity
30. Non-linear
graphs
31. Constructions
and loci
32. Pythagoras’
theorem
2
2
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Properties of angles and shapes: G1.5
Geometrical reasoning and calculation: G2.4
Mensuration: G4.1, G4.3, G4.4
Measures and Construction: G3.4, G3.7
3
Properties of angles and shapes: G1.7, G1.8
Measures and Construction: G3.2
Expressions and Equations:
Sequences, Functions and Graphs: N6.12, N6.13
Measures and Construction: G3.8, G3.10, G3.11
4
Geometrical reasoning and calculation: G2.1
2
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 18 Number skills revisited
Time: 3 hours
The number work will not be tested in isolation, but will be in contexts that tie in the other areas of the unit content.
N1.3 Understand and use number operations and the relationships between them, including inverse operations and hierarchy of operations.
N1.4 Approximate to a given power of 10, up to three decimal places and one significant figure.
N1.14 Use calculators effectively and efficiently.
N2.1 Understand equivalent fractions, simplifying a fraction by cancelling all common factors.
N2.5 Understand that ‘percentage’ means ‘number of parts per 100’ and use this to compare proportions.
N2.6 Interpret fractions, decimals, percentages as operators
N2.7 Calculate with fractions, decimals and percentages.
N3.1 Use ratio notation, including reduction to its simplest form and its various links to fraction notation.
N3.3 Solve problems involving ratio and proportion, including the unitary method of solution
AQA
Spec
ref
N1.3,
N1.4,
N1.14,
N2.1,
N2.5,
N2.6,
N2.7,
N3.1
N3.3
Learning objectives
Grade
Common mistakes and
misconceptions
Understand equivalent fractions
Simplify a fraction by cancelling all common factors
use fractions, decimals or percentages to compare proportions of shapes that are
shaded
use fractions, decimals or percentages to compare lengths, areas or volumes
recognise that questions may be linked to the assessment of scale factor
Recognise that each terminating decimal is a fraction
Convert simple fractions to percentages and vice versa
interpret the display, for example for money interpret 3.6 as £3.60 or for time
interpret 2.5 as 2 hours 30 minutes
Use percentages to compare proportions
work out percentage of shape that is shaded
shade a given percentage of a shape
Understand ‘reciprocal’ as multiplicative inverse
Use ratio notation
use ratios in the context of geometrical problems, for example similar shapes, scale
drawings and problem solving involving scales and measures
understand that a line divided in the ratio 1 : 3 means that the smaller part is onequarter of the whole
use direct proportion to solve geometrical problems
Use brackets and the hierarchy of operations
Add, subtract, multiply and divide integers
Use calculators effectively and efficiently; use function keys for squares
G-C
Forgetting to multiply/divide both the
numerator and denominator when finding
equivalent fractions and simplifying
fractions.
Applying an incorrect understanding of
‘reciprocal’.
Writing the ratio in the incorrect order.
Forgetting to use BIDMAS when using
calculators to perform calculations.
Not giving an answer in the context of the
problem.
Treating the digits each side of the
decimal point as separate whole numbers
, so that 0.95 rounded to 1 d.p. = 0.1.
Dropping zeros when rounding to a
number of significant figures (e.g. 5840 =
6 to 1 s.f.).
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Use inverse operations
Round to the nearest integer, to one significant figure and to one, two or three
decimal places
Give solutions in the context of the problem to an appropriate degree of accuracy
Resources:
AQA GCSE Maths Middle sets Book Sections 20
AQA Modular GCSE Mathematics Foundation Tier
 Chapter 9 Working with numbers P186
 Chapter 10 Powers and roots P213
 Chapter 11 Operations P222
 Chapter 13 Fractions, decimals and percentages P253
 Chapter 14 Calculating with fractions and decimals
 Chapter 15 Mental and written methods P298
 Chapter 16 Percentages P314
 Chapter 17 Ratio and proportion P331
 Chapter 20 Equivalent fractions P365
Foundation Practice Book sections 9, 10, 11, 13, 14, 15, 16, 17, 20
Resources
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Number, fractions and decimals/Teaching
Lesson plans/resource sheets/homework sheets/powerpoints
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Percentages & ratio/Teaching
Lesson plans/homework sheets/powerpoints
Functional skills activities Chapters 1, 3, 4, 12, 14, 15
Notes: Candidates should know not to round off values during the intermediate steps of a calculation.
Candidates should be able to use a calculator to apply the four rules to fractions and decimals in problems.
This is part of the core number work required across all units. The core number work will be assessed so that it is linked to other specification
references within this unit. In this unit candidates will be expected to use a calculator when solving problems. Questions requiring these number skills
could be set, for example, as a numerical part of a question testing fractions, decimals, percentages, ratio or proportion, interpreting graphs, using a
formula in words or substitution into an algebraic expression, using a calculator where appropriate.
Candidates should know that some answers are inappropriate without some form of rounding, for example 4.2 buses.
Candidates will not be required to calculate repeated percentage change, reverse percentage or compound interest in this unit. These are assessed
in Unit 1 only.
Candidates should note that division in a given ratio is assessed in Unit 2 only.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 19 Angles
Time: 6 hours
G1.1 Recall and use properties of angles at a point, angles at a point on a straight line (including right angles), perpendicular lines, and opposite angles at a
vertex.
G1.2 Understand and use the angle properties of parallel and intersecting lines, triangles and quadrilaterals.
G3.1 Use and interpret maps and scale drawings.
G3.6 Understand and use bearings.
AQA
Mod
spec
ref
G1.1
G1.2
Learning objectives
Grade
Common mistakes and misconceptions
Calculate angles around a point
Recognise vertically opposite angles
work out the size of missing angles at a point
work out the size of missing angles on a straight line
know that vertically opposite angles are equal
distinguish between acute, obtuse, reflex and right angles
name angles
estimate the size of an angle in degrees
justify an answer with explanations such as ‘angles on a straight line’, etc.
use one lower case letter or three upper case letters to represent an angle, for
example x or ABC
understand that two lines that are perpendicular are at 90º to each other
draw a perpendicular line in a diagram
identify lines that are perpendicular
use geometrical language
use letters to identify points, lines and angles
Calculate angles in diagrams with parallel lines
understand and use the angle properties of parallel lines
recall and use the terms, alternate angles, and corresponding angles
work out missing angles using properties of alternate angles and corresponding
angles
understand the consequent properties of parallelograms
understand the proof that the angle sum of a triangle is 180º
understand the proof that the exterior angle of a triangle is equal to the sum of the
interior angles at the other two vertices
use angle properties of equilateral, isosceles and right-angled triangles
use the angle sum of a quadrilateral is 360º
G, F, E
Measuring rather than calculating angles.
D
Confusing alternate and corresponding
angles.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
G3.6
G3.1
Use three-figure bearing notation
Measure the bearing from one place to another
Plot a bearing
Calculate bearings for return journeys
Draw and interpret scale diagrams to represent journeys
use bearings to specify direction
recall and use the eight points of the compass (N, NE, E, SE, S, SW, W, NW) and
their equivalent three-figure bearings
mark points on a diagram given the bearing from another point
draw a bearing between points on a map or scale drawing
measure a bearing of a point from another given point
work out a bearing of a point from another given point
work out the bearing to return to a point, given the bearing to leave that point
use and interpret maps and scale drawings
use a scale on a map to work out a length on a map
use a scale with an actual length to work out a length on a map
construct scale drawings
use scale to estimate a length, for example use the height of a man to estimate the
height of a building where both are shown in a scale drawing
work out a scale from a scale drawing given additional information
F, E, D,
C
Confusing which angles need to be found.
Not realising that some of the angles asked
for can simply be read off the diagram.
E, D, C
Scale could be given as a ratio, for example
1 : 500 000 or as a key, for example 1cm
represents 5km.
Missing out steps when converting between
(for example) km and cm.
Not making allowances when measurements
are given in a variety of units.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 21.1 – 21.3
AQA Modular GCSE Mathematics Foundation Tier
 Angles P370
 Angles and straight lines P375
 Angles in triangles P378
 Directions and bearings P585
 Maps and scale drawings P590
 Parallel lines P617
 Angles in quadrilaterals P622
Foundation Practice Book 21.1 -21.4, 32.1 – 32.2, 34.1 – 34.2
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Angles /Teaching Resources
Lesson plans and starters/questions/pictures/homework sheets/powerpoint
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Measures /Teaching Resources
Lesson plans/worksheets/homework sheets
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Bearings /Teaching Resources
Lesson plans/worksheets/homework sheets/powerpoints
Functional skills activities 11.2
Notes: Candidates should know the meaning and properties of alternate, corresponding, interior and vertically opposite angles. Colloquial terms such as F
or Z angles should not be used. Candidates should know the names and properties of isosceles, equilateral, right angled and scalene triangles.
Questions at Foundation tier will always be set so that the North direction is straight up the page.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 20 Measurement 1
Time: 5 hours
N1.3 Understand and use number operations and the relationships between them, including inverse operations and hierarchy of operations.
G3.3 Interpret scales on a range of measuring instruments and recognise the inaccuracy of measurements.
G3.4 Convert measurements from one unit to another.
G3.5 Make sensible estimates of a range of measures
AQA
Mod
spec ref
N1.3
Learning objectives
Grade
Common mistakes and
misconceptions
Solve problems involving times, dates and timetables
G,F, E
G3.4
Know and use approximate metric equivalents of pounds, feet, miles, pints and
gallons
convert between metric measures
recall and use conversions for metric measures for length, area, volume and
capacity
recall and use conversions between imperial units and metric units and vice versa
using common approximation
For example 5 miles ~ 8 kilometres, 4.5 litres ~1 gallon, 2.2 pounds ~ 1 kilogram,
1 inch ~ 2.5 centimetres.
Recognise that measurements given to the nearest whole unit may be inaccurate by
up to one half unit in either direction
interpret scales on a range of measuring instruments including those for time,
temperature and mass, reading from the scale or marking a point on a scale to show
a stated value
know that measurements using real numbers depend on the choice of unit
Make sensible estimates of measures
make sensible estimates of a range of measures in everyday settings
make sensible estimates of a range of measures in real-life situations, for example
estimate the height of a man
choose appropriate units for estimating measurements, for example a television
mast would be measured in metres
Estimate angle sizes by knowledge of acute, obtuse, reflex, right angles
E
Confusing the decimal parts of an hour
with hours and minutes (e.g. writing
1.25 hours as 1 hour 25 minutes) and
vice versa.
Not considering the relative size of units
when deciding whether to multiply or
divide.
G3.3
G3.5
D, C
Difficulty comprehending the definition
of the upper bound, since, for example,
146.5 rounds to 147.
F, E
Not using the guidance given to
compare – e.g the height of a man
compared to a bus
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 22.1 – 22.4
AQA Modular GCSE Mathematics Foundation Tier
 Reading information from a table P201
 Accuracy & measures P343
 Metric units P412
 Metric and imperial measures P416
 Everyday use of imperial and metric units P419
Foundation Practice Book 9.5, 18.1, 23.1 -23.3
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Number, fraction and decimals/Teaching Resources
lesson plans/resource sheets/homework sheet/powerpoint
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Measure/Teaching Resources
lesson plans/worksheets/homework sheet
Functional skills activities 8.1, 8.2, 8.3, 19.1, 19.3
Closely related –.
Notes: Metric conversions should be known. Imperial to metric conversions will be limited to 5 miles ~ 8 kilometres, 4.5 litres ~ 1 gallon, 2.2 pounds ~ 1
kilogram, 1 inch ~ 2.5 centimetres. Any imperial to metric conversions, other than those listed above, will be stated in the question.
Candidates will not be expected to recall conversions between capacity and volume.
For example 1ml = 1cm³
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 21 Triangles and constructions
Time: 3 hours
G1.1 Recall and use properties of angles at a point, angles at a point on a straight line (including right angles), perpendicular lines, and opposite angles at a
vertex.
G1.2 Understand and use the angle properties of parallel and intersecting lines, triangles and quadrilaterals.
G1.8 Understand congruence and similarity.
G3.9 Draw triangles and other 2D shapes using a ruler and protractor.
G3.10 Use straight edge and a pair of compasses to do constructions.
AQA
Mod
spec ref
G1.1,
G1.2
Learning objectives
Grade
Common mistakes and misconceptions
Solve angle problems in triangles
Solve angle problems in triangles involving algebra
F, E, D
G3.9,
G3.10
Draw triangles accurately when given the length of all three sides
make accurate drawings of triangles and other 2D shapes using a ruler and
protractor
make an accurate scale drawing from a sketch, a diagram or a description
Draw triangles accurately when at least one angle is given
use straight edge and a pair of compasses to do standard constructions
construct an equilateral triangle with a given side
draw parallel lines
draw circles or part circles given the radius or diameter
construct diagrams of 2D shapes
Recognise and explain how triangles are congruent
understand congruence
identify shapes that are congruent
recognise congruent shapes when rotated, reflected or in different orientations
understand similarity
identify shapes that are similar, including all squares, all circles or all regular
polygons with equal number of sides
recognise similar shapes when rotated, reflected or in different orientations
E, D
Not realising when a triangle is isosceles
and thinking that the problem cannot be
solved.
Trying to do too many steps in one go when
answering algebra-based questions.
Inaccurately using a protractor or
compasses.
Not completing the triangle by drawing the
third side.
Rubbing out construction lines.
G1.8
C
Thinking that two triangles are congruent
when they are not (due to the relative
positions of side lengths or angles being in
different positions).
Incorrectly assuming that by showing that
the three sets of angles are the same in
both triangles congruency is proved.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 23.1 -23.3
AQA Modular GCSE Mathematics Foundation Tier
 Angles in triangles P378
 Constructing triangles P382
Foundation Practice Book 21.3, 21.4
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Angle /Teaching Resources
lesson plans & starters/question sheets/pictures/homework sheets/powerpoints
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Transformations/Teaching Resources
lesson plans/worksheets/pdfs/homework sheets/powerpoints
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Shapes loci/Teaching Resources
lesson plans/notes/ homework sheets/powerpoints
Functional skills activities 11.2, 11.3
Notes:
Foundation tier will be restricted to perpendicular bisector and angle bisector.
Candidates will be expected to show clear evidence that a straight edge and compasses have been used to do constructions.
At Foundation tier candidates will not be asked to construct a perpendicular from a point to a line, a perpendicular at a point on a line or an
angle of 60º. When constructing triangles, compasses should be used to measure lengths rather than rulers. Construction arcs should be
shown.
Questions involving calculations of sides in similar shapes will not be set at Foundation tier.
Questions assessing the properties of similar shapes, including similar triangles, will not be set.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 22 Equations, formulae and proof
Time: 6 hours
N4.1 Distinguish the different roles played by letter symbols in algebra, using the correct notation
N4.2 Distinguish in meaning between the words ‘equation’, ‘formula’, and ‘expression’.
N5.1 Manipulate algebraic expressions by collecting like terms, by multiplying a single term over a bracket, and by taking out common factors.
N5.4 Set up and solve simple linear equations.
N5.6 Derive a formula, substitute numbers into a formula.
N5.8 Use systematic trail and improvement to find approximate solutions of equations where there is no simple analytical method of solving them.
G2.3 Justify simple geometrical properties.
AQA
Mod
spec ref
N5.4,
N5.6
G2.3,
N5.8
Learning objectives
Grade
Common mistakes and
misconceptions
Questions in this unit will include geometrical problems, problems set in a functional
context and questions requiring a graphical solution.
Write your own formulae and equations
Substitute into a formula to solve problems
Set up and solve equations
Change the subject of a formula
use formulae from mathematics and other subjects expressed initially in words and
then using letters and symbols; for example formula for area of a triangle, area of a
parallelogram, area of a circle, volume of a prism, conversions between measures
E, D, C
Failing to consider the different terms of
an expression when changing the
subject of a formula (e.g. W = 12 x + 3
Justify simple results from geometry
show step-by-step deduction in solving a geometrical problem
state constraints and give starting points when making deductions
Candidates should be able to explain reasons using words or diagrams
Use trial and improvement to find solutions to equations
use a calculator to identify integer values immediately above and below the solution,
progressing to identifying values to 1 d.p. above and immediately above and below
the solution
C
D, C
Algebra skills: expressions (N4.1, N4.2, N5.1); brackets (N5.1); solving equations (N5.4); formulae (N5.6)
 2W = x + 3).
Not using brackets or a clear division
(e.g. rewriting c = 2a + 5 as a = c − 5 ÷
2).
Not using the inverse operation (e.g. x +
y = z becomes x = z + y).
Not laying out answers in an organised
way.
Not providing reasons for each stage of
the working.
Not checking the mid-point to determine
which of two values is correct (e.g.
choosing between x = 3.3 and x = 3.4
based on the value of the function and
the desired output).
Using the value of the equation as the
answer rather than the value of the
variable.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 24.1 -24.3
AQA Modular GCSE Mathematics Foundation Tier
 Trial and improvement P695
 Chapter 22 Introducing algebra P390
 Chapter 24 Equations P426
 Chapter 26 Using a formula P457
 Chapter 33 More algebra skills P599
 Chapter 35 Using formulae P642
 Chapter 37 Equalities and inequalities P683
Foundation Practice Book 37.3, 22.1 -22.4, 24.1 – 24.2, 26.1 – 26.2, 33.1 – 33.3, 35.1 – 35.3, 37.1 -37.2
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Albegraic manipulation/Teaching Resources
lesson plans/worksheets/homework sheets
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Trial & Improvement/Teaching Resources
lesson plans/resource sheets/homework sheets/powerpoints
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Angles/Teaching Resources
lesson plans & starters/questions/pictures/homework sheets/powerpoints
Functional skills activities 10.1 -10.4
Notes: Candidates should also know the meaning of the word term.
Questions will include geometrical problems, problems set in a functional context and questions requiring a graphical solution.
Trial & improvement answers will be expected to 1 d.p. Candidates will be expected to test the mid-value of the 1 d.p. interval to establish which
1 d.p. value is nearest to the solution.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 23 Quadrilaterals and other polygons
Time: 5 hours
N5.4 Set up and solve simple linear equations
N6.3 Use the conventions for coordinates in the plane and plot points in all four quadrants, including geometric information.
G1.2 Understand and use the angle properties of parallel and intersecting lines, triangles and quadrilaterals.
G1.3 Calculate and use the sums of the interior and exterior angles of polygons.
G1.4 Recall the properties and definitions of special types of quadrilateral, including square, rectangle, parallelogram, trapezium, kite and rhombus.
AQA Mod
spec ref
G1.2, N5.4
Learning objectives
Grade
Common mistakes and misconceptions
Calculate the interior angles of quadrilaterals
Solve angle problems in quadrilaterals involving algebra
F, E, D
Working things out mentally without writing
down the calculations.
G1.2,
G1.4
Make quadrilaterals from two triangles
Use parallel lines and other angle properties in quadrilaterals
recall the properties and definitions of special types of quadrilateral
name a given shape
identify a shape given its properties
list the properties of a given shape
draw a sketch of a named shape
identify quadrilaterals that have common properties
classify quadrilaterals using common geometric properties
Use the exterior angles of polygons to solve problems
Solve more complex angle problems involving exterior and interior angles of a
polygon
recognise and name regular polygons; pentagons, hexagons, octagons and
decagons
use the angle sum of irregular polygons
calculate and use the angles of regular polygons
use the sum of the interior angles of an n-sided polygon
use the sum of the exterior angles of any polygon is 360º
use interior angle + exterior angle = 180
use tessellations of regular and irregular shapes
explain why some shapes tessellate and why other shapes do not tessellate
plot points in all four quadrants
find coordinates of points identified by geometrical information, for example the
fourth vertex of a rectangle given the other three vertices
find coordinates of a midpoint, for example on the diagonal of a rhombus
calculate the length of a line segment
G, F,
E, D
Giving correct answers but not explaining
the properties used.
F, E, D,
C
Incorrectly splitting the polygon into
triangles.
G, F, E
Plotting the numbers on the x- and y-axes
the wrong way round.
Not recognising, or be able to name, some
of the less common quadrilaterals (e.g. the
kite and trapezium).
G1.3, N5.4
N6.3
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
In this unit questions will be linked to geometrical situations, for example
transformations.
In this unit candidates will be expected to use graphs that model real situations
where a calculator may be required.
Resources:
Averaging only the x- or y-coordinate and
not both when finding the mid-point.
AQA GCSE Maths Middle sets Book Sections 25.1 – 25.4
AQA Modular GCSE Mathematics Foundation Tier
 Quadrilaterals P437
 Properties of polygons P626
 Angles in polygons P629
 2D and 3D coordinates P759
Foundation Practice Book 25.1, 34.3, 34.4, 41.1
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Algebraic Manipulation/Teaching Resources
lesson plans/worksheets/homework sheets
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Linear Graphs/Teaching Resources
lesson plans/problem sheets/homework sheets/resource sheet
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Polygons & circles/Teaching Resources
lesson plans/score sheets/homework sheets/work sheet/powerpoints
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Angles/Teaching Resources
lesson plans & starters/questions/pictures/homework sheets/powerpoints
Functional skills activities
Notes Candidates should be able to calculate the values of the interior angle, exterior angle and angle at the centre of regular polygons. At Foundation tier
these will be restricted to triangle, square, pentagon, hexagon, octagon, nonagon and decagon.
Candidates should know the side, angle and diagonal properties of quadrilaterals.
Questions involving tessellations will be clearly defined and could relate to real-life situations, for example tiling patterns.
Candidates should know how to work out the angle sum of polygons up to a hexagon.
It will not be assumed that candidates know the names heptagon or nonagon.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 24 Perimeter, area and volume
Time: 6 hours
G4.1 Calculate perimeters and areas of shapes made from triangles and rectangles.
G4.4 Calculate volumes of right prisms and of shapes made from cubes and cuboids.
AQA Mod
spec ref
G4.1
G4.1
G4.1,
G4.4
Learning objectives
Grade
Common mistakes and misconceptions
Find the perimeter and area of parallelograms and trapezia
work out the perimeter of a rectangle
work out the perimeter of a triangle
calculate the perimeter of shapes made from triangles and rectangles
calculate the perimeter of shapes drawn on a grid
calculate the perimeter of simple shapes
recall and use the formulae for area of a rectangle, triangle and parallelogram
work out the area of a rectangle
work out the area of a parallelogram
calculate the area of shapes made from triangles and rectangles
calculate the area of shapes drawn on a grid
calculate the area of simple shapes
calculate the area of shapes made from compound shapes made from two or more
rectangles, for example an L shape or T shape
calculate the perimeter of shapes made from compound shapes made from two or
more rectangles
Find the volume and surface area of a prism
work out the surface area of nets made up of rectangles and triangles
calculate the area of a trapezium
recall and use the formula for the volume of a cuboid
use the formula for the volume of a prism
work out the volume of a cube or cuboid
work out the volume of a prism using the given formula, for example a triangular
prism
G, F,
E, D
Not making rough estimates of areas as a
check to avoid arithmetical errors.
Incorrectly converting between units.
Using measurements in different units.
E, D
Incorrectly calculating missing lengths.
Adding areas instead of subtracting.
E, D, C
Confusing volume and surface area.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 26.1 -26.3
AQA Modular GCSE Mathematics Foundation Tier
 Perimeter of simple shapes P446
 Areas of simple shapes P449
 Volume of a cuboid P476
 Areas of parallelograms and triangles P658
 Composite shapes P674
 Surface area of prisms P709
 Volumes of prisms P716
Foundation Practice Book 25.4, 25.5, 27.2, 36.1, 36.4, 38.2, 38.3
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Perimeter, area and volume/Teaching Resources
lesson plans/worksheets/powerpoints/homework sheets
Functional skills activities 10.1 -10.4, 21.3
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 25 3-D objects
Time: 2 hours
G2.4 Use 2D representations of 3D shapes.
AQA Mod
spec ref
G2.4
Resources:
Learning objectives
Grade
Common mistakes and misconceptions
Make a drawing of a 3-D object on isometric paper
Identify planes of symmetry of 3-D objects
use 2D representations of 3D shapes
draw nets and show how they fold to make a 3D solid
know the terms face, edge and vertex (vertices)
identify and name common solids, for example cube, cuboid, prism, cylinder,
pyramid, sphere and cone
analyse 3D shapes through 2D projections and cross-sections, including plan and
elevation
understand and draw front and side elevations and plans of shapes made from
simple solids, for example a solid made from small cubes
understand and use isometric drawings
G, F,
E, D
Missing out hidden cubes when converting
from a 3-D view to a plan or elevation.
Using isometric paper in landscape not in
portrait.
AQA GCSE Maths Middle sets Book Sections 27.1
AQA Modular GCSE Mathematics Foundation Tier
 Three-dimensional shapes P472
 Plans and elevations P703
Foundation Practice Book 27.1, 38.1
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/3D shapes/Teaching Resources
lesson plans/handout/worksheets/homework sheets
Functional skills activities 22.1, 22.2
Notes:
It is not expected that Foundation candidates know the name of a tetrahedron.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 26 Reflection, translation and rotation
Time: 6 hours
G1.6 Recognise reflection and rotation symmetry of 2D shapes.
G1.7 Describe and transform 2D shapes using single or combined rotations, reflections, translations, or enlargements by a positive scale factor and
distinguish properties that are preserved under particular transformations.
G5.1 Understand and use vector notation for translations.
AQA Mod
spec ref
G5.1
Learning objectives
Grade
Common mistakes and misconceptions
Translate a shape on a grid
Use column vectors to describe translations
D, C
G1.6
recognise reflection symmetry of 2D shapes
identify lines of symmetry on a shape or diagram
draw lines of symmetry on a shape or diagram
understand line symmetry
draw or complete a diagram with a given number of lines of symmetry
recognise rotational symmetry of 2D shapes
identify the order of rotational symmetry on a shape or diagram
draw or complete a diagram with rotational symmetry
understand line symmetry
identify and draw lines of symmetry on a Cartesian grid
identify the order of rotational symmetry of shapes on a Cartesian grid
draw or complete a diagram with rotational symmetry on a Cartesian grid
Draw the position of a shape after rotation about a centre
Describe a rotation fully giving the size and direction of turn and the centre of rotation
describe and transform 2D shapes using single rotations
understand that rotations are specified by a centre and an (anticlockwise) angle
find a centre of rotation
rotate a shape about the origin or any other point
measure the angle of rotation using right angles
measure the angle of rotation using simple fractions of a turn or degrees
describe and transform 2D shapes using single reflections
understand that reflections are specified by a mirror line
identify the equation of a line of reflection
describe and transform 2D shapes using single transformations
G, F, E
Forgetting what the two values in the
column vector mean.
Using coordinate notation instead of vector
notation.
Confusing the terms ‘transformation’ and
‘translation’.
Not finding all lines of symmetry.
Confusing line symmetry with rotational
symmetry
Not ensuring that shapes reflected in a line
are drawn in the correct position
G1.7
G, F,
E, D, C
Working out the angle of rotation incorrectly.
Turning in the wrong direction.
Ignoring the centre of rotation when it is
outside the shape.
Drawing the image a different distance from
the mirror line than the object.
Incorrectly identifying mirror lines parallel to
the x- or y-axis
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
understand that translations are specified by a distance and direction (using a
vector)
translate a given shape by a vector
describe and transform 2D shapes using enlargements by a positive scale factor
distinguish properties that are preserved under particular transformations
understand that distances and angles are preserved under rotations, reflections and
translations, so that any figure is congruent under any of these transformations
describe a translation
Resources:
AQA GCSE Maths Middle sets Book Sections 28.1 -28.3
AQA Modular GCSE Mathematics Foundation Tier
 Reflection symmetry P440
 Rotation symmetry P443
 Reflections P523
 Rotations P536
 Translations P543
Foundation Practice Book 25.2, 25.3, 30.1, 30.3, 30.4
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Transformations /Teaching Resources
lesson plans /pdfs/homework sheets/worksheets/powerpoints
Functional skills activities 11.1
Notes: Single transformations only will be assessed in Foundation tier. Translations will be specified by a vector.
Lines of symmetry on a Cartesian grid will be restricted to x = a, y = a, y = x, y = –x
Foundation tier will be restricted to single transformations.
The direction of rotation will always be given.
Scale factors for enlargements will be restricted to positive integers at foundation tier.
Enlargements may be drawn on a grid, or on a Cartesian grid, where the centre of enlargement will always be at the intersection of two grid lines.
When describing transformations, the minimum requirement is:
Rotations described by centre, direction (unless half a turn) and an amount of turn (as a fraction of a whole or in degrees)
Reflection by a mirror line
Translations described by a vector or a clear description such as three squares to the right, five squares down.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 27 Circles and cylinders
Time: 6 hours
G1.5 Distinguish between centre, radius, chord, diameter, circumference, tangent, arc, sector and segment.
G2.4 Use 2D representations of 3D shapes.
G4.1 Calculate perimeters and areas of shapes made from triangles and rectangles.
G4.3 Calculate circumferences and areas of circles.
G4.4 Calculate volumes of right prisms and of shapes made from cubes and cuboids.
AQA Mod
spec ref
G1.5,
G4.1,
G4.3
G1.5,
G4.1,
G4.3
G2.4,
G4.1,
G4.3,
G4.4
Learning objectives
Grade
Common mistakes and misconceptions
recall the definition of a circle
identify and name these parts of a circle
draw these parts of a circle
understand related terms of a circle
draw a circle given the radius or diameter
Calculate the circumference of a circle
work out the radius or diameter given the circumference of a circle
use π = 3.14 or the π button on a calculator
work out the perimeter of semi-circles, quarter circles or other simple fractions of a
circle
recall and use the formula for the area of a circle
work out the area of a circle, given the radius or diameter
work out the radius or diameter given the area of a circle
work out the area of semi-circles, quarter circles or other simple fractions of a circle
recall and use the formula for the volume of a cylinder
Calculate the volume of a cylinder
G, F,
E, D, C
Not multiplying by 2 when the radius is
given and the diameter is needed.
D, C
Multiplying by  before squaring.
C
Multiplying by  before squaring.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 29.1 -29.3
AQA Modular GCSE Mathematics Foundation Tier
 Circle definitions and circumference P663
 Area of a circle P670
 Volume of prisms P716
Foundation Practice Book 36.2, 36.3, 38.3
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Polygons & circles/Teaching Resources
lesson plans/score sheets/work sheets/homework sheets/powerpoints
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/3D shapes/Teaching Resources
lesson plans/handout/work sheets/homework sheets
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Perimeter, Area, Volume/Teaching Resources
lesson plans/work sheets/homework sheets/powerpoints
Functional skills activities 21.1 – 21.3
Notes:
Knowledge of the terms ‘minor segment’ and ‘major segment’ is not required for Foundation tier.
Candidates will not be required to work out the surface area of a cylinder at Foundation tier.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 28 Measurement 2
Time: 2 hours
G3.4 Convert measurements from one unit to another.
G3.7 Understand and use compound measures
AQA Mod
spec ref
G3.4,
G3.7
G3.7
Resources:
Learning objectives
Grade
Common mistakes and misconceptions
Convert between different units of area
Convert between different units of volume
Calculate average speeds
D, C
Multiplying by 100 when converting from m3
to cm3.
Not remembering the formulae.
Confusing the decimal parts of an hour with
hours and minutes (e.g. using 1 hour 45
minutes as 1.45 hours).
E, D
AQA GCSE Maths Middle sets Book Sections 30.1 – 30.2
AQA Modular GCSE Mathematics Foundation Tier
 Speed P347
Foundation Practice Book 18.2
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Measures/Teaching Resources
lesson plans/worksheets/homework sheets
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Perimeter, area, volume/Teaching Resources
lesson plans/worksheets/homework sheets/powerpoints
Functional skills activities
Notes: Compound measures include area, volume and speed at Foundation tier.
Density will not be tested at Foundation tier.
Calculations involving distance and time will be restricted to ¼ hour, ⅓ hour, ½ hour, ⅔ hour or a whole number of hours.
Speed may be expressed in the form metres per second, (m/s). Candidates would be expected to understand these, and also units in common usage such as
miles per hour (mph) or kilometres per hour (km/h).
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 29 Enlargement and similarity
Time: 2 hours
G1.7 Describe and transform 2D shapes using single or combined rotations, reflections, translations, or enlargements by a positive scale factor and
distinguish properties that are preserved under particular transformations.
G1.8 Understand congruence and similarity.
G3.2 Understand the effect of enlargement for perimeter, area and volume of shapes and solids.
AQA Mod
spec ref
G1.7,
G1.8,
G3.2
Resources:
Learning objectives
Grade
Common mistakes and misconceptions
Enlarge a shape on a grid
Enlarge a shape using a centre of enlargement
understand that an enlargement is specified by a centre and a scale factor
enlarge a shape on a grid (centre not specified)
draw an enlargement
enlarge a shape using (0, 0) as the centre of enlargement
enlarge shapes with a centre other than (0, 0)
find the centre of enlargement
identify the scale factor of an enlargement of a shape as the ratio of the lengths of
two corresponding sides
understand the effect of enlargement on perimeter
understand the effect of enlargement on areas of shapes
understand the effect of enlargement on volumes of shapes and solids
F, E, D
Inaccurately counting squares.
Adding the scale factor instead of
multiplying by the scale factor.
Not using the centre of enlargement.
AQA GCSE Maths Middle sets Book Sections 31.1
AQA Modular GCSE Mathematics Foundation Tier
 Enlargement P529
Foundation Practice Book 30.2
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Transformations/Teaching Resources
lesson plans/pdfs/work sheets/homework sheets
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Perimeter, area & volume/Teaching Resources
lesson plans/work sheets/homework sheets/powerpoints
Functional skills activities
Notes: Foundation candidates will not be expected to use area or volume scale factors. Questions at Foundation tier will always include a diagram.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 30 Non-linear graphs
Time: 2 hours
.
N6.12 Discuss, plot and interpret graphs (which may be non-linear) modelling real situations
N6.13 Generate points and plot graphs of simple quadratic functions, and use these to find approximate solutions.
AQA Mod
spec ref
N6.12,
N6.13
N6.13
Resources:
Learning objectives
Grade
Common mistakes and misconceptions
Draw quadratic graphs
Identify the line of symmetry of a quadratic graph
Draw and interpret quadratic graphs in real-life contexts
interpret line graphs from real-life situations; for example conversion graphs
interpret graphs showing real-life situations in geometry, such as the depth of water
in containers as they are filled at a steady rate
interpret non-linear graphs showing real-life situations, such as the height of a ball
plotted against time
Use a graph to solve quadratic equations – restricted to finding the approximate
value of y for a given value of x or vice versa
D, C
Drawing the bottom of the graph flat when a
graph has its vertex between two plotted
points.
C
Forgetting to write down all the solutions.
AQA GCSE Maths Middle sets Book Sections 32.1 -32.2
AQA Modular GCSE Mathematics Foundation Tier
 Quadratic graphs P748
Foundation Practice Book 40.2
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Quadratic graphs/Teaching Resources
lesson plans/worksheets/homework sheets/powerpoints
Functional skills activities 19.2
Notes: Distance-time graphs will be assessed in Unit 2. Everyday graphs representing financial situations (e.g. gas, electric, water, mobile phone bills,
council tax) with or without fixed charges will be assessed in Unit 2. Linear graphs with or without a table of values will be assessed in Unit 2.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 31 Constructions and loci
Time: 3 hours
G3.8 Measure and draw lines and angles.
G3.10 Use straight edge and a pair of compasses to do constructions.
G3.11 Construct loci.
AQA Mod
spec ref
G3.8,
G3.10
G3.11
Resources:
Learning objectives
Grade
Common mistakes and misconceptions
measure and draw lines to the nearest mm
measure and draw angles to the nearest degree
Construct angles of 90°
Construct the bisector of an angle
construct a perpendicular bisector of a given line
construct an angle bisector
Solve locus problems, including the use of bearings
find loci, both by reasoning and by using ICT to produce shapes and paths
construct a region, for example, bounded by a circle and an intersecting line
construct loci, for example, given a fixed distance from a point and a fixed distance
from a given line
construct loci, for example, given equal distances from two points
construct loci, for example, given equal distances from two line segments
construct a region that is defined as, for example, less than a given distance or
greater than a given distance from a point or line segment
describe regions satisfying several conditions
C
Failing to keep the settings of compasses
constant.
Rubbing out construction lines.
Not using compasses.
C
Confusing a distance from a point with the
distance from a line.
Making inaccurate constructions.
Shading the wrong region.
AQA GCSE Maths Middle sets Book Sections 33.1 -33.2
AQA Modular GCSE Mathematics Foundation Tier
 Constructions and Loci P763
Foundation Practice Book 41.2
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Shapes, Loci/Teaching Resources
lesson plans/notes/homework sheets/powerpoints
Functional skills activities
Notes: Loci questions for Foundation tier will be restricted to at most two constraints. Loci questions will be restricted to 2D only.
Loci problems may be set in practical contexts such as finding the position of a radio transmitter.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 32 Pythagoras’ theorem
Time: 4 hours
G2.1 Use Pythagoras’ theorem
AQA Mod
spec ref
G2.1
G2.1
Learning objectives
Grade
Common mistakes and misconceptions
Understand Pythagoras’ theorem
Calculate the hypotenuse of a right-angled triangle
Solve problems using Pythagoras’ theorem
C
C
G2.1
Calculate the length of a shorter side in a right-angled triangle
Solve problems using Pythagoras’ theorem
C
G2.1
Calculate the length of a line segment AB
C
Forgetting that x2 means x × x, not x × 2.
Forgetting to take the square root to find the
final answer.
Not correctly identifying the hypotenuse.
Forgetting that Pythagoras’ theorem only
applies to right-angled triangles.
Not correctly identifying the hypotenuse.
Forgetting to take the square root to find the
final answer.
Forgetting that Pythagoras’ theorem only
applies to right-angled triangles.
Not identifying the appropriate information
when problems are set in context.
Not being able to identify the position of the
right angle.
Subtracting instead of adding the two pairs
of coordinates.
Resources:
AQA GCSE Maths Middle sets Book Sections 34.1 -34.4
AQA Modular GCSE Mathematics Foundation Tier
 Pythagoras Theorem P633
Foundation Practice Book 34.5
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 3/Pythagoras Theorem/Teaching Resources
lesson plans & starters/worksheet/powerpoints/homework sheets
Functional skills activities
Notes: Questions will be restricted to 2D at Foundation tier. Questions may be set in context, for example, a ladder against a wall, but questions will always
include a diagram of a right angled triangle with two sides marked and the third side to be found. Quoting the formula will not gain credit.