Download AQA GCSE Maths Schemes of Work – writing brief D R A F T

NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Mathematics
GCSE Content and Overview
Higher Tier
(Outcomes U – 9)
1
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Key Information

This syllabus is to be taught over 2 years, starting 2015.

The first examination series for this syllabus will be Summer 2017.

Fully Linear course, no modules.

Re-sit is only available in November series immediately following the initial Summer exam (i.e. for Y12 students).

Assessment will be in the form of two written examinations in the Summer examination period of the second year (for Year 11
students). Comprising one calculator and one non-calculator paper. These will total a minimum of 3.5 hours.

Assessment results will be given as an outcome ranging between U – 9 (where 9 is the highest outcome achieved).

Passes will be considered as 9 - 3.

Fail will be considered as 2 – U.
2
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Assessment Objectives
The new curriculum has a greater focus on both problem solving and quality of written communication. This now comprises 25% of
the total marks.
The overall weighting of each of these objectives to be assessed through the final summer examination are as follows:
Assessment Objectives
AO1
AO2
AO3
Using and applying:
 Accurately recall facts and definitions.
 Use and interpret correct notation.
 Accurately carry out routine calculations or tasks requiring multistep solutions.
Reason, interpret and communicate mathematically:
 Make deductions and form conclusions from mathematical
information.
 Construct chains of reasoning to achieve a result.
 Interpret and communicate information accurately.
 Present arguments or proofs.
 Assess the validity of an argument.
Problem Solving:
 Translate problems in mathematical or non-mathematical
contexts into a series of mathematical processes.
 Make and use connections between different parts of
mathematics.
 Interpret results in the context of the given problem.
 Evaluate methods used and results obtained.
 Evaluate solutions.
3
Weighting
50%
25%
25%
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Formulae Guidance
1. Formulae included in the subject content. Candidates are expected to know these formulae; they must not be given in the
assessment.
The quadratic formula
The solutions of 𝑎𝑥2+𝑏𝑥+𝑐= 0 where 𝑎 ≠0
Circumference and area of a circle
Where r is the radius and d is the diameter:
Circumference of a circle= 2𝜋𝑟= 𝜋𝑑
Area of a circle= 𝜋𝑟2
4
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Pythagoras’s theorem
In any right-angled triangle where a, b and c are the length of the sides and c is the hypotenuse:
Trigonometry formulae
5
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Higher Tier
6
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
2. The following formulae are not specified in the content but should be derived or informally understood by candidates. These
formulae must not be given in the examination.
7
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
3. Formulae candidates should be able to use, but need not memorise. These can be given in the exam, either in the relevant
question, or in a list from which candidates select and apply as appropriate.
8
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Notes of Use
Teaching:

Content is to be taught to the highest achieving students in the cohort (i.e. set 1 pupils), dependent upon ability. Teachers are
responsible for differentiating all lessons appropriately for the pupils in their classes.
Resources:

Any resources listed can be found on the shared Maths drive, on staff laptops, or in the resource folders. All resource folders
are categorised by week and topic.

Suggested resources include:
Sumbooks worksheets
Ten Ticks worksheets
Abacus software
AQA Active Teach software (teacher examples, exercises, end of unit tests and mark schemes)
Interactive Essentials
www.mymaths.co.uk
www.worksheetworks.com
http://www.superteacherworksheets.com
http://www.tes.co.uk/maths-secondary-teaching-resources
9
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Assessment for Learning

Time has been built in to this scheme of work at the end of every Term so that revision of topics taught can be undertaken.

Formal assessments will be implemented at the end of every Term.

Regular homework must be set in line with the mathematics department policy for all Year 10 and Year 11 students. Teachers
may wish to use the GCSE homework sheets available on the shared maths drive or source a suitable alternative.
Topic colour codes
Number
Statistics
Algebra
Measures
Geometry
10
Number & Algebra
Revision/Exams
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Overview
Year 10
Week 1
Number 1
Mental & Written
Calculations
Week 2
Algebra 1
Simplifying &
Surds
Week 3
Geometry 1
Triangles,
Quadrilaterals &
Angles
Week 4
Geometry 2
Bearings
Week 5
Statistics 1
Data Collection
and Simple
Charts.
Week 9
Algebra 3
Using Equations
and Formulae
Week 17
Geometry 5
Circles
Week 10
Measures 1
Metric Measures
Week 11
Geometry 3
Circle Theorems
Week 12
Number 4
Percentages
Week 13
Algebra 4
Sequences
Week 14
Week 15
Revision & Unit Tests
Week 16
Geometry 4
Perimeter & Area
Week 18
Algebra 5
Real Life Graphs
Week 19
Number 5
Ratio and
Proportion
Week 20
Geometry 6
Polygons and
Angles
Week 21
Algebra 6
Expressions &
Equations
Week 24
Geometry 8
Transformations:
Rotation
Week 28
Statistics 2
Averages &
Probability
Week 36
Geometry 12
Loci
Week 22
Week 23
Algebra 7
Geometry 7
Equations:
Transformations:
Straight Lines &
Reflections &
Circles.
Translations
Week 30
Week 31
Algebra 8
Solving Quadratic Equations
Week 29
Statistics 3
Charts for
Grouped Data
Week 37
Week 38
Revision & Summer MOCK Exams
Week 25
Geometry 9
Congruence &
Similarity
Week 33
Number &
Algebra 1
Inequalities
Week 26
Week 27
Revision & Unit Tests
Week 34
Algebra 9
Plotting graphs
(Linear &
Quadratic)
Week 35
Geometry 11
Constructions
11
Week 6
Number 2
Laws of Indices &
Powers
Week 7
Algebra 2
Plotting
Coordinates &
Linear Graphs
Week 39
Number 6
FDP
Week 8
Number 3
Fractions,
Decimals &
Rounding
Week 32
Geometry 10
Representing 3D
shapes
Week 40
Measures 2
Using scales &
Compound
Measures
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AQA GCSE Linear
Higher Tier
Year 11
Week 1
Geometry 13
Surface Area
Week 2
Geometry 14
Volume
Week 9
Algebra 10
Solving Quadratic
Equations
Week 17
Statistics 5
Probability:
Experiments and
Charts.
Week 10
Algebra 11
Algebraic
Fractions
Week 18
Geometry 19
Sine and Cosine
Rule
Week 25
Revision
Week 33
Revision
Week 3
Number 9
Calculating with
Fractions
Week 4
Geometry 15
Enlargement
Week 5
Geometry 16
Vectors
Week 11
Week 12
Revision & MOCK Exams
Week 19
Geometry 20
Cylinders, Cones
and Spheres.
Week 26
Week 27
Revision
Revision
Week 34
Week 35
Summer Exams
Week 20
Algebra 13
More Real Life
Graphs
Week 13
Geometry 17
Pythagoras &
Trigonometry
Week 21
Algebra 14
Simultaneous
Equations
Week 28
Revision
Week 36
Week 29
Revision
Week 37
12
Week 6
Number &
Algebra 2
Direct & Indirect
Proportion
Week 14
Geometry 18
Pythagoras &
Trigonometry
Week 22
Geometry 21
Pyramids
Week 30
Revision
Week 38
Week 7
Number 10
Percentages &
Finance
Week 8
Number 10
Percentages &
Finance
Week 15
Algebra 12
Quadratic and
Other Graphs
Week 23
Statistics 6
Probability: Venn
Diagrams
Week 16
Statistics 4
Scatter Graphs &
Tree Diagrams
Week 24
Algebra 15
Inequalities:
Linear and
Quadratic
Week 31
Revision
Week 39
Week 32
Revision
Week 40
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Content: Year 10
Learning Objectives:
Autumn 1
Date:
Week 1
Resources:
Lesson:
1
Number 1
Mental and Written
Calculations
(Integers,
negatives, powers
and roots)
2
3
4
Week 2
Algebra 1
1
To be able to:

Recall the squares of integers up to
15 and the cubes of 2, 3, 4, 5 and 10
 Recall and use corresponding
squares, cubes and their roots.
 Recognise powers of 2, 3, 4, 5
 Evaluate expressions involving other
integer powers and roots (e.g. 23 +
42)
 Estimate powers and roots of any
given positive number.
 Calculate accurately with negative
numbers.
 Multiply and divide using whole and
decimal numbers.
 Solve numerical problems involving
decimals.
 Estimate and check answers to
calculations involving decimal and
negative numbers.
 Calculate sums using BIDMAS
involving negatives, powers and
decimals.
Common mistakes and
misconceptions
Outcome

Incorrectly thinking that ‘taking a
square’ means multiplying by 2 and
a cube as multiplying by 3.
 Not recognising that square roots
have 2 solutions (this will become
clearer when calculations with
negatives are studied)




Multiply together two algebraic
expressions with brackets.
 Argue mathematically to show
algebraic expressions are equivalent,
and use algebra to support and
construct arguments.
13


Adding and subtracting incorrectly.
 Mistakes made when using
negatives and powers (e.g. -33 = 27
instead of -27)
 Not considering context.
 Not rounding off numbers and
working accurately when asked to
estimate.
 Not showing all working
Forgetting to use the correct order.
Not writing down their working and
losing track of what they have done
previously in the calculation.
 Not multiplying all terms in one
bracket by the other.
Forgetting to simplify answers fully.
Students just square what they can
see
e.g. stating that (x + 3) = x2 + 9
NEW for Examination 2015
AQA GCSE Linear
Higher Tier

Simplifying &
Surds

2
3
4
Week 3
1
Geometry 1
Triangles,
Quadrilaterals &
Angles
2
3
Square a linear expression, e.g.
(x+1)2
 Expand products of two or more
binomials, e.g. (x+2)3 or (x+2)2 (x+3)3
 Use the addition and subtraction rule
of surds.
 Use the multiplication and division
rules of surds.
 Simplify surds fully (e.g. √12 = 2√3)
and rationalise denominators.
 Expand brackets involving surds
 Manipulate surds to rationalise
denominators.
 Simplify and manipulate algebraic
expressions (including those
involving surds)
 Solve angle problems algebraically
(straight lines, around a point,
opposite).
 Use and apply rules for parallel lines
to solve angles problems.
Pupils do not show working out as
proof (e.g. evidence of expanding
brackets)
 Pupils forget to answer the question
fully (e.g. forgetting to state Yes or
No when asked whether
expressions are equivalent)
 Thinking that (x+1)2 = x2 + 1
 Completing only some of the steps
to fully expanding.





Identify and derive properties of
special types of quadrilaterals,
14


Forgetting to multiply the entire
fraction by the same surd.
Not simplifying answers fully in more
complicated expressions.
Not using all the information in the
diagram.
 Confusing alternate and
corresponding angles.


Derive and understand that angles
inside a triangle sum to 180o
 Calculate missing angles inside
triangles.
 Solve angle problems in triangles
algebraically.
Adding the numbers underneath the
root signs, instead of collecting
together.
 Not simplifying answers where
possible, e.g. √4 is actually 2.
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
question.
Not recognising, or be able to name,
some of the less common
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
including square, rectangle,
parallelogram, trapezium, kite and
rhombus
 Draw diagrams from written
description
 Calculate missing angles inside
quadrilaterals
 Solve angle problems in
quadrilaterals involving algebra
4
Week 4
1
 Use three-figure bearing notation
 Measure the bearing from one place
to another.
 Plot 3-figure bearings.
 Plot bearings from worded problems.
2

Geometry 2
quadrilaterals (e.g. the kite and
trapezium).
 Not reading all of the information
before drawing / identifying the
shape being described.
 Not realising that some of the angles
asked for can simply be read off the
diagram.
 Trying to do too many steps in one
go when answering algebra-based
question.
 Confusing where to measure from
and to.
 Using the wrong scale on the
protractor
Bearings
Week 4

Draw and interpret scale diagrams to
represent journeys.
Not drawing bearings for all
information given.
 Measuring inaccurately and
intersections being in the wrong
places.
 Measuring the diagram instead of
realising that the angles can be
calculated.
 Confusing alternate and
corresponding angles.

Geometry 2
Bearings
3
Week 5

Calculate bearings in diagrams
(including return journeys)

Statistics 1
4
Data Collection
and Simple
Charts.
1
Consolidation:
Use and apply knowledge of angles
and bearings to complete exam
questions.
 To understand the data handling
cycle
NOTE: The above is not specifically tested
but is useful for pupil understanding
 Identify different types of data
(discreet, continuous, qualitative,
quantitative, primary, secondary)
15

Not appreciating that some data can
be treated as either discrete or
continuous depending on the
context (e.g. age – this is really
continuous, but is often treated as
discrete, such as when buying child
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AQA GCSE Linear
Higher Tier
or adult tickets).
Week 5
2


Work out methods for gathering data
efficiently
Work out methods for gathering data
that can take a wide range of values

 Sort data into class intervals
Interpret and use grouped frequency
tables Interpret a pie chart
Statistics 1
Data Collection
and Simple
Charts.
3
Week 6

Number 2
Laws of Indices
and Powers
4
Interpret and construct tables, charts
and diagrams, including frequency
tables, bar charts, pie charts and
pictograms for categorical data,
vertical line charts for ungrouped
discrete numerical data, tables and
line graphs for time series data and
know their appropriate use.
 Draw a pie chart
 Solve problems with pie charts.
16

Not realising that data collected by a
third party (even if the results of a
survey or experiment) is classed as
secondary data.

 Using overlapping class intervals.
Recording data which is on the boundary of
a class interval in the wrong class.


Looking at the angle in a pie chart
and ignoring the fact that the pie
chart can represent a different
number of people.
 Not drawing the angles in the pie
chart accurately or using the
appropriate scale on the protractor.
 Measuring each angle from the
same starting point.
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
1
Week 6
2
Number 2
3
Laws of Indices
and Powers
Week 7
4
Algebra 2
Plotting
Coordinates and
Linear Graphs
1
 Working out 27 as 2 × 7.
 Multiplying and dividing powers
instead of adding and subtracting.

Use laws of indices to multiply and
divide numbers written in index
notation. (e.g. x2 x x3 = x5)
 Calculate with roots, and with integer
and fractional indices.
Calculate a power of a power, e.g.
(23)4
 Simplify expressions involving
negative indices.
 Simplify expressions involving
fractional indices.
 Combine laws of indices to evaluate
more complicated expressions.
 Use proof to show equivalence in
expressions involving powers.
 Write numbers in standard form.
 Convert between standard form and
decimal numbers.
 Calculate using numbers written in
standard form.

Identify straight-line graphs that are
parallel to the x- or y- axis
 Identify and interpret gradients and yintercepts of lines in the form of y =
mx + c
 Use the form y = mx + c to identify
parallel and perpendicular lines.
 Find the equation of the line through
two given points, or through one point
with a given gradient.

17




Mixing up the rules.
Forgetting to write 1/
Not simplifying fully.
Simplifying and not evaluating fully
when asked to.
 Not showing all steps when
simplifying or showing equivalence.
 Forgetting to use a negative power
when working with very small
numbers.
 Working out only part of the
calculation, forgetting to simplify the
power.
 Ensuring final answers are in
standard form, e.g. 1.2 x104 and not
12 x103.
 Leaving answer as a decimal
number, if required.
 Confusing the x- and y- axis
 Mixing up the gradient and yintercept
 Not stating that the gradient is
negative.
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
2
Week 7


 Sketch straight line graphs
Match straight line graphs to their
equations
Forgetting that the bigger the
gradient, the steeper the graph
should look
 That gradients of 2 and -2 look the
same, but slope in opposite
directions
 Confusing the gradient and yintercept
 Incorrectly calculating with negative
numbers
 Ignoring BIDMAS.
 Confusing the x- and y- coordinates
 Not joining up all points.
 Only plotting 2 points and joining
these together, a 3rd should be used.
 Incorrectly dividing the change in xby change in y- values.
 Forgetting to check whether the
gradient should be positive or
negative once calculations have
been done.
 Mixing up the gradient and yintercept.

Algebra 2
Plotting
Coordinates and
Linear Graphs
3
4

Complete a table of values for linear
functions (for positive and negative
values of x)
 Plot graphs of linear functions using a
table of values.
 Plot linear functions with or without
being given a table of values.

Calculate the gradient of a straight
line (using change in y- / change in xvalues)
 Identify the equation of a line by
finding the gradient and using yintercept

Autumn 2
Date:
Week 8
Number 3
TT L5 P2 p33-34
Resourc
es:
1
Lesson:

Identify and understand equivalent
factions
Compare fractions with different
denominators using equivalence.
18
To be
able to:

Multiplying the denominator but not
the numerator when finding
equivalent fractions.
Stating that 1/3 is smaller than ¼ as the
denominator is smaller.
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Higher Tier
Fractions, Decimals
and Rounding
Week 8
Number 3
Sumbooks Higher
worksheet (11)page
19.
2
Fractions, Decimals
and Rounding
TT L9-10 p1 pg 3-5
TT L9-10 p1 pg 3-5
Week 9
Sumbooks Higher
worksheet (1), page
9.
3
4

Identify terminating and recurring
decimals
 Convert fractions into terminating
decimals
 Convert terminating decimals into
fractions
 Change recurring decimals into their
corresponding fractions and vice
versa
 Round decimals to a given number of
decimal places.
 Round numbers to a given number of
significant figures.
 Apply and identify limits of accuracy
when rounding. Including upper and
lower bounds.
 Estimate and approximate
calculations by rounding.
 Solve problems using estimation.
 Use inequality notation to specify
simple error intervals due to
truncation or rounding
19






1
Confusing 0.3 with 3.
Not understanding that recurring
decimals are a form of exact maths
and therefore rounding answers.
Giving the answer in the wrong form.
Treating the digits on each side of
the decimal point as separate whole
numbers
so giving 0.95 rounded to 1 d.p. as
0.1
Not considering context when giving
final answers to problems.
 Not rounding values to the same
degree of accuracy where
appropriate.
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Higher Tier
Algebra 3
1
Using Equations and
Formulae
2
Week 9
Algebra 3
 Form simple expressions
Form expressions involving powers
and brackets
 Form and solve linear equations to
solve problems.
 Substitute numbers to work out the
value of algebraic expressions
(including powers and indices)
 Substitute numerical values into more
complicated formulae.

Using Equations and
Formulae
Week 10
Measures 1
Metric Measures
Week 10
Measures 1
Sumbooks Higher
worksheet (55) page
63.
3

Find approximate solutions to
equations using trial and
improvement.
Sumbooks Higher
worksheet 41 (pg
49).
L5 p 3 pg 27-34
L5 p3 pg 35- 37
4

Find approximate solutions to
equations using iteration.
1

2
Change freely between related
standard units (time, length, area,
volume, mass, capacity, money)
 Change freely between metric units
of area and volume.

 Know and use approximate metric
equivalents of pounds, feet, miles,
pints and gallons
Note: This is no longer in the GCSE subject
content but still may be useful for students.
20


Not seeing the ‘general’ case.
Including brackets unnecessarily in
calculations.

Incorrectly substituting values into
expressions (e.g. substituting a = 6
into the expression 4a, writing 46
and assuming it is forty-six).
 Ignoring BIDMAS.
n
 Not realising that 10 means n ÷ 10,
1
1
or that 2 × 6 means 2 of 6 = 3.
 Giving answers irrespective of
context.
 Not showing all stages of working.
 Not understanding the concept of
rounding to get the final solution.


Not showing enough stages of
working out to show how the
answer tends to a given solution.

Ignoring the different units when
comparing measurements.
Not considering the relative size of
units when deciding whether to
multiply or divide.
 Forgetting the equivalent values.
 Multiplying instead for dividing.
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
L5 p 3 pg 29-33
3

Metric Measures
Week 11
Geometry 3
Circle Theorems
1
2
Week 11
Geometry 3
Circle Theorems
Week 12
Identify upper and lower limits of
numbers rounded to a given degree
of accuracy.
 Solve problems involving limits of
accuracy and measures.
Identify and:
Use the tangent / radius theorem.
 Use the two tangent theorem.
 Use the chord / bisector theorem.

Identify and:
Use the angle subtended by an arc
theorem.
 Use the semi-circle theorem.
 Use the same-segment theorem.


4
apply and prove
the standard
circle
theorems
3

 Estimate measures.
Solve problems involving measures
and conversion.

Identify and:
 Use the cyclic quadrilateral theorem.
 Use the alternate segment theorem.
Misinterpreting the rounding that has
taken place.
 Using the wrong limit when
performing calculations.

Forgetting that angles are equal
when using the two-tangent
theorem.
Forgetting that bi-sect means cut in
half.
Using the angle subtended by an arc
theorem the wrong way around, i.e.
the angle at the edge is twice the
one at the centre, instead of the
other way around.
 Doubling instead of halving.

Assuming that opposite angles in
cycling quadrilaterals are equal.
Not being able to spot the alternate
segment rule.
Students not able to see the bigger
picture.
Pupils forget to apply simple angles
rules to help prove more
complicated circle theorems.


Number 4
4
Percentages
 Apply combinations of circle
theorems concerning angles, radii,
tangents and chords, and use them
to prove related results.
 Prove the standard circle theorems
concerning angles, radii, tangents
and chords, and use them to prove
related results.
21


Ignoring context when estimating.
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AQA GCSE Linear
Higher Tier
1
Week 12
Number 4
3
Week 13
Algebra 4
Find a percentage of an amount
without using a calculator
 Find percentages of amounts in more
complex situations
 Compare two quantities using
percentages
 Find a percentage of an amount with
a calculator
 Write one quantity as a percentage of
another
4

1

Sequences
2
Convert between fractions, decimals
and percentages.
 Order fractions, decimals and
percentages.

2
Percentages

Calculate a percentage increase or
decrease
 Calculate percentage increase or
decrease using VAT
Recognise sequences of triangular,
square and cube numbers.
 Recognise and use sequences such
as Fibonacci, quadratic and involving
powers (e.g. 21, 22, 23, 24, 25…)
 Find any term in a sequence given
the nth term
 Show something is false using a
counter-example
 Find the nth term of a linear
sequence
22

Forgetting that fraction lines mean
‘divide’
 Multiplying by the wrong power of 10
to change between decimals and
percentages.
 Show their working out, forgetting to
order their final answer.
 Students divide by 10 to get 10%, so
therefore divide by 1 to find 1%.
 Treating a percentage such as
0.05% as though it were 5%.

Not using the original amount as the
denominator, when finding a
percentage difference.
 Working with quantities in different
units, forgetting to convert.
 Adding the percentage to the cost
when finding a percentage increase
(e.g. £315 + 15% VAT = £330).
 Thinking that percentages over
100% cannot exist.
 Giving the actual increase/decrease
as the answer, not the final total.
 Using the multiplier as 1.5 rather
than 1.05 for an increase of 5%.
 Writing 3 ‘ squared’ as 2 x 3
 Writing powers as 2x1, 2x2, 2x3…
 Not identifying an appropriate
counter-example.
 Not appreciating that a proof shows
something works for all values.


Not showing every step of working
out
NEW for Examination 2015
AQA GCSE Linear
Higher Tier

Week 13
Algebra 4
3
Sequences
Find the nth term for pattern
sequences
 Identify and use sequences involving
surds.
 Find the nth Term rule for a simple
quadratic sequence.
Not making the connection between the
structure of the physical pattern and the form
the nth term takes.


Week 14 / 15
4

Find the nth Term rule for any
quadratic sequence.
Week 16
Geometry 4
Perimeter and Area
Week 16
Geometry 4


Revision & Unit
Tests / Exam
Question focus?
Spring 1
Not showing all steps in working out.
Confusing whether they need to add
or subtract a value to get from one
part of a sequence to another.
 Missing out steps in working out.
 Mixing up n2 with 2n, for example.
Resourc
es:
Lesson:
10 ticks L5 P4 p3640
Abacus
Sumbooks (Y9
basics) p83
1
Calculate the perimeter of rectangles,
triangles, parallelograms and trapezia
10 ticks L5 P4 p3640
http://www.workshee
tworks.com/math/ge
ometry/measuring-
2
Apply angle facts, triangle congruence,
similarity and properties of quadrilaterals to
conjecture and derive results about angles
and sides, including Pythagoras’ Theorem
and the fact that the base angles of an
isosceles triangle are equal, and use known
results to obtain simple proofs.
 Identify missing measurements on
compound shapes.
 Calculate the perimeter of compound
shapes.
23
To be
able to:
Outcome

Counting squares instead of the
number of edges exposed around
the outside.
 Not adding all side lengths together
Assuming that everything is in ‘cm’ and not
checking the correct units

Stating a measurement because it
‘looks the same’ as another one
 Not converting lengths into the same
units before adding
 Only adding the measurements
given, ignoring unlabelled sides
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Perimeter and Area
Week 17
Geometry 5
Circles
figures.html
Abacus
Sumbooks
(Exercises in
Numeracy) p32
10 ticks L5 P4 p3640
Abacus
Sumbooks (Y9
basics) p83
10 ticks L5 P4 p3640
http://www.workshee
tworks.com/math/ge
ometry/measuringfigures.html
Abacus
Sumbooks
(Exercises in
Numeracy) p32
Abacus
Week 17
Geometry 5
10 ticks L6 P5 p3338
Abacus
Sumbooks
(Foundation book)
3

4


Writing ‘cm’ instead of ‘cm 2’
 For triangles, forgetting to halve
 Not using the vertical height
 Multiplying all measurements
together, instead of the ones they
need
Calculate the area of rectangles,
triangles, parallelograms and trapezia

Calculate the area of compound
shapes made from rectangles.
Calculate the area of compound
shapes involving triangles,
parallelograms and trapezia.

Forgetting to add all areas together
to get a total
 Not identifying the correct
measurements to use when there
are more than they need
Multiplying all given measurements
together

1
2

Recall the definition and properties of
circles (inc. symmetry)
 Know and label parts of a circle
(centre, radius, chord, diameter,
circumference, tangent, arc, sector
and segment)
 Draw circles accurately
 Calculate the circumference of a
circle using 2πr or πd
 Calculate the perimeters of
compound shapes involving circles or
parts of circles
 Leave answers in terms of π
24

Forgetting there are an infinite
number of lines of symmetry
 Confusing radius and diameter
 Confusing segment and sector
 Forgetting to divide by 2 when the
diameter is given and the radius is
needed.
 Not multiplying by 2 when the radius
is given and the diameter is needed.
 Forgetting to add all lengths to get
final answers.
 Adding measurements to the
perimeter that are inside the shape
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Circles
Week 18
Algebra 5
Real Life Graphs
Week 18
Algebra 5
Real Life Graphs
p54
10 ticks L6 P5 p3338
Abacus
Sumbooks
(Foundation book)
p61
Abacus

3

Calculate the area of a circle using
πr2
 Calculate the areas of compound
shapes involving circles or parts of
circles.
 Leave answers in terms of π.
4
 Calculate arc lengths .
 Calculate the area of a sector.
 Calculate angles inside sectors of
circles.
1

2
Read and interpret distance–time
graphs
 Draw distance-time graphs
 Read and interpret velocity-time
graphs
 Draw velocity-time graphs
 Solve problems involving speed,
distance and acceleration
 Read and interpret real-life graphs
 Sketch real-life graphs
 Read and interpret conversion graphs
 Plot conversion graphs
 Sketch and interpret reciprocal and
exponential graphs of real-life
functions.
Week 19
Number 5
Ratio and Proportion
25




Not leaving answers incorrect form.
Multiplying by  before squaring.
Using the diameter instead of radius.
Not leaving answers in correct form.
Using the angle for the major sector
when the minor is needed, and vice
versa.
 Not being able to rearrange
calculations to find the angle inside
the sector
 Drawing and labelling axes before
working out the axes range
appropriate to the problem.
 Confusing the formula for calculating
acceleration
 Forgetting that a positive slope is
acceleration and negative slope is
deceleration
 Not realising that the intercept
represents a fixed cost.
 Not recognising that a straight line
represents constant change, curves
show rates vary
 Inaccurately reading from one value
on a conversion graph to find
another value.
 Drawing out axes using an
unsuitable scale
 Not being able to use their graph to
work out a solution to a problem not
represented on the graph (e.g. axes
go up to 200g, need to use 800g)
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
3
4
1

Drawing a tangent to the curve
inaccurately.
 Dividing the change in x- by y Ignoring whether it should be a
positive or negative gradient.
 Drawing tangents to curves
inaccurately.

Calculate the gradients of chords and
tangents numerically and
algebraically.
 Write a ratio as a fraction.
 Interpret ratios in practical situations.
 Identify and work with fractions in
ratio problems.
 Divide a given quantity into a ratio.
 Use a ratio to find one quantity when
the other is known.
2
 Write a ratio in the form 1 : n or n : 1
 Use a ratio when comparing a scale
model to the real-life object
3
 Understand direct proportion
 Solve problems involving direct
proportion.
 Understand value for money.
 Work out which product is the better
buy.
Week 19

Interpret the gradient at a point on a
curve as the instantaneous rate of
change.

Turning a ratio into a fraction (e.g.
4
the ratio 4 : 5 becomes 5).
 Giving an answer without
considering the context.
 Dividing by 2 as there are two parts
to the ratio.
 Failing to find the value of the unit
fraction in more complex problems.
 Dividing by the wrong amount to find
the unit value.
 Writing the ratios the wrong way
around.
Number 5
Ratio and Proportion
Week 20
Geometry 6
Polygons and Angles
26



Giving an answer without
considering the context.
Not multiplying or dividing both sides
of the ratio by the same amount.
 Not finding the unit cost.
Dividing by the wrong amount to find
unit cost.
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Week 20
10 ticks L5 P3 p1921
Sumbooks (Y9
basics) p65
Sumbooks
(Intermediate book)
p42
10 ticks L6 P5 p2729
1
10 ticks L6 P5 p2729
3
10 ticks L6 P5 p2729
4
Geometry 6
Polygons and Angles
Angles re-cap:
Calculate angles inside a triangle
 Calculate angles inside quadrilaterals
 (including special quadrilaterals, and
algebraically)

2
Week 21

Use properties of triangles to find the
sum of interior angles inside
polygons.
Calculate interior angles of polygons.
 Understand that exterior angles on
polygons always sum to 360o
 Use exterior angles of polygons to
solve problems.
Algebra 6
Expressions and
Equations
1

 Understand indirect proportion.
 Solve problems involving indirect
proportion.
4

Solve more complex angle problems
involving exterior and interior angles
of polygons.

Know the difference between and
equation, expression and an identity
 Where appropriate interpret simple
expressions as functions with inputs
27

Not considering real-life context
before answering questions.
Incorrectly multiplying instead of
dividing.
 Not showing working.
Not stating the angles rule they have
used.
 Not remembering properties of
regular / irregular polygons and
other properties of shapes.
 Confusing the rule for triangles and
quadrilaterals.
 Incorrectly splitting the polygon into
triangles.
 Working things out mentally without
writing down the calculations.
 Thinking that exterior angles are
only 360o on quadrilaterals.
 Confusing the rules for interior and
exterior angles.
 Forgetting the formula for the
exterior angles of a polygon and
how to apply it.
 Failing to spot that all angles are
equal on a regular polygon when
only one angle is given.
 Forgetting that interior and exterior
sum to 180o
 Pupils do not use the correct
notation for angles (e.g. angle ABC
= angle DEF because…)
 Incorrectly combining number work
involving fractions and decimals with
equation solving.
 Getting the wrong signs when

NEW for Examination 2015
AQA GCSE Linear
Higher Tier
and outputs
Interpret the reverse process as the
‘inverse function’
 Interpret the succession of two
functions as a ‘composite function’.
 Solve two-step equations.
 Solve equations involving brackets.
 Solve equations with an unknown on
both sides.
 Solve equations with unknown on
both sides and brackets.


Week 21
Algebra 6
Expressions and
Equations
10 ticks L6 P1 p6-8
http://www.workshee
tworks.com/math/pre
-algebra.html
Sumbooks (Y9
basics) p5310 ticks
L6 P1 p6-8
http://www.workshee
tworks.com/math/pre
-algebra.html
Abacus
2
3

Solve equations involving fractions on
one side.
Solve equations involving fractions on
both sides.

4

1
 Argue mathematically to show
algebraic expressions are equivalent,
and use algebra to support and
construct arguments and proofs
 Find the equation of a straight line
Rearrange formulae to change the
subject.
 Rearrange formulae where the
subject appears twice.
28

multiplying negative numbers.
Incorrectly simplifying after
expanding the bracket.
Introducing errors when there are a
negative number of unknowns on
either side of the equation.

Not multiplying by the denominator
of the fraction.
 Not multiplying by the LCM of each
fraction when they appear o both
sides.
 Inaccurately multiplying so having
errors in final answer.
 Not using the inverse operation (e.g.
x + y = z becomes x = z + y).
 Not using brackets or a clear
division (e.g. rewriting c = 2a + 5 as
a = c − 5 ÷ 2).


Incorrectly working out the change in
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
through two points
Week 22
x- or y- values when finding the
gradient.
 Forgetting that they needs to
substitute in values for x- and yusing the coordinates given.
Not being able to solve the equation
to find the y-intercept.
Algebra 7

Equations: Straight
Lines & Circles.
2
Week 22
Algebra 7
3
Equations: Straight
Lines & Circles.
4
Spring 2
Geometry 7
Transformations:
Reflections and
Translations
Week 23
Find the equation of the line through
one point with a given gradient
 Solve problems involving equations
of straight lines.
 Recognise and use the equation of a
circle centre (0,0)


Abacus
Week 23



Find the equation of a tangent to a
circle at a given point.

Forgetting that when x=o, y is the
intercept.
Substituting in the wrong values into
the equation.
 Forgetting the formula.
Not square rooting to find the radius.

Learning
Objectiv
es:
Resourc
es:
10 ticks L4 P7 p2936
Sumbooks
(Foundation book)
p37
1
10 ticks L6 P2 p1112
2
Lesson:

Recognise and draw lines of
symmetry in plane shapes.
 Draw a reflection of a shape in a
mirror line (horizontal, vertical or
diagonal)
Draw reflections in the x- or y- axis on a
coordinate grid.

Identify lines that are parallel to the xor y- axes.
29
To be
able to:
Outcome

Only drawing on one line of
symmetry when there are several
Drawing the image a different distance from
the mirror line than the object.


Mixing up x = and y = lines
Confusing whether the line is
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Geometry 7
Transformations:
Reflections and
Translations

Reflect shapes on coordinate grids in
lines parallel to the x- or y- axis
 Reflect shapes in lines such as y = x
Sumbooks
(Foundation book)
p37
10 ticks L7-8 P4 p32
 Identify lines of reflection on a
coordinate grid by finding midpoints.
 Describe fully reflections on a
coordinate grid.
3




10 ticks L5 P4 p3132
10 ticks L6 P2 p3-10
Sumbooks
(Foundation book)
p48
4

Translate shapes according to a
given vector.
Describe translations fully using vectors.






Week 24
Geometry 8
Transformations:
Rotation
Week 24
Geometry 8
10 ticks L4 P7 p3738
Sumbooks (Y9
basics) p78
Sumbooks
(Foundation book)
p46
10 ticks L6 P2 p1316
Sumbooks
1
2
Describe the changes and invariance
achieved by combinations of
rotations, reflections and translations.
 Recognise rotational symmetry in
regular 2-D shapes.
 Recognise rotational symmetry in
other shapes.
 Complete images to give a given
order of rotational symmetry.

Use fractions of turns, angles and
compass directions (e.g. ¼ turn
clockwise, 90o anticlockwise, turn
through 180o)
30
horizontal or vertical when drawing
on the line of reflection.
Automatically reflecting in the x- or
y- axes.
Assuming the mirror line is either the
x- or y- axis.
Incorrectly identifying mirror lines
parallel to the x- or y-axis.
 Forgetting to give enough
information, i.e. ‘reflection in the
line…)
Only finding the new location of one
corner of the shape and then
drawing in the rest incorrectly.
Forgetting that negative numbers
mean left or down.
Confusing the left/right value for the
up/down value in column vectors.
Using coordinate notation instead of
vector notation.
Describing the translation of shape
A to shape B, when the opposite
was required.


Forgetting the definition of regular
polygons.
 Stating order 4 for shapes with 4
sides.
 Pupils make images symmetrical,
instead of giving order of rotational
symmetry.


Mixing up clockwise and
anticlockwise.
Not realising 180o turns end in the
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Transformations:
Rotation
Week 25

(Foundation book)
p47
10 ticks L6 P2 p1316
3
10 ticks L6 P2 p1316
4
10 ticks L7-8 P5
p11-14
Abacus
1
10 ticks L7-8 P5
p11-14
Abacus
Sumbooks
(Foundation book)
p77
10 ticks L7-8 P5
p23-24
2
Geometry 9
Congruence and
Similarity
Week 25
Geometry 9
Congruence and
Similarity
3
Rotate simple shapes on a grid
around a given point.

Draw the position of a shape after
rotation about the origin (0,0) on a
coordinate grid.
 Rotate a shape on a coordinate grid
given any centre of rotation.
 Identify the centre of rotation between
two shapes.
 Describe a rotation fully giving the
size and direction of turn and the
centre of rotation.

Understand the meaning of
congruence.
 Identify congruent shapes (squares,
circles, regular polygons)
 Identify congruent shapes on
coordinate grids (i.e. that have been
rotated, reflected, translated or
enlarged including fractional and
negative scale factors)

 Know the basic congruence criteria
for triangles (SSS, SAS, ASA, RHS)
 Recognise and explain how triangles
are congruent.
same position independent of
direction.
 Rotating the shape around the
wrong point.
 Working out the angle of rotation
incorrectly.
 Assuming that (0,0) is the centre of
rotation instead of reading the
question carefully.
 Not giving enough information, i.e.
centre, direction and angle.
If not using tracing paper:
 Not joining up corresponding
corners.
 Perpendicular lines not drawn
accurately, crossing in the wrong
place.
 Not realising that shapes are still
congruent even if they have been
rotated or reflected.



Understand the meaning of similar
shapes.
 Calculate scale factors in similar
shapes.
31
Mixing up the rules of congruence
(e.g. thinking that AAS = ASA)
 Stating congruence even when
corresponding sides / angles are not
equal.

Not checking that all lengths are
similar.
Dividing measurements that are not
corresponding.
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Week 26/27

Abacus
10 ticks L7-8 P5
p23-29
4
Abacus
Revision & Unit
Tests / Exam
Question focus?
(Easter)
Summer 1
Week 28
Identify similarity in simple shapes.




Describe and construct similar
shapes (e.g. circles, squares,
rectangles)
 Use similarity when working with area
Apply the concepts of congruence and
similarity to solve problems.

Resourc
es:
Lesson:
1
 Find MMR from a frequency table.
Find the modal class and median from a
grouped frequency table.
Statistics 2

Using the wrong scale factor.
Dividing lengths that are not
corresponding to check similarity.
Not using a squared scale factor
when working with area.

To be
able to:
Outcome

Adding up the total frequency
incorrectly.
Forgetting to divide by the total by the
number of data items.
Averages &
Probability
Week 28

2

Statistics 2
Find an estimate of the mean for
grouped data.
Compare a set of discreet data using
mode, range, median and mean.
Averages &
Probability
Week 29
3

Understand the meaning of
independent events.
32

Not using the midpoint of a class
interval.
 Adding the frequencies together
before multiplying by the midpoint.
 Selecting an inappropriate measure
for the data provided.
 Showing calculations without making
a conclusion or proving a
hypothesis.
 Working in a haphazard way when
giving possible combinations, thus
NEW for Examination 2015
AQA GCSE Linear
Higher Tier

Statistics 3
Charts for Grouped
Data
4
1
Week 29
2
Statistics 3
3
Charts for Grouped
Data
Week 30
Algebra 8
Systematically list all outcomes for
combined independent events (in a
list or table).
 Calculate the probability of combined
independent events.
 Construct theoretical possibility
spaces (sample space) combined
events.
 Calculate probabilities using
possibility spaces (sample space).
 Set up tree diagrams for combined
independent events.
 List outcomes using tree diagrams.
 NOTE: (you may wish to calculate
simple probabilities from a tree
diagram here)
 Construct and interpret diagrams for
grouped discrete data and continuous
data, i.e. histograms with equal and
unequal class intervals and
cumulative frequency graphs, and
know their appropriate use

Interpret and solve problems
involving histograms.

 Plot cumulative frequency curves.
 Interpret cumulative frequency
curves.

Interpret, analyse and compare the
distributions of data sets from
univariate empirical distributions
through
tendency (median, mean, mode and
33
missing one or more combinations.
Not simplifying fractions where
required.
 Not listing all outcomes of each
event.
 Miscounting the number of
possibilities in the sample space.


Not including enough ‘branches’ for
outcomes.
 Not reading across every possible
combination of branches and
therefore missing outcomes.

 Assuming that all column widths
should be equal.
 Forgetting that bar height represents
frequency density and not
frequency.
 Multiplying or dividing incorrectly
when trying to find missing values
needed.
 Using unsuitable scales on the axes.
 Not being able to identify the scale
that has been used.

 Forgetting to add frequencies
together.
 Plotting coordinates and joining
together like a frequency polygon.

NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Solving Quadratic
Equations
4
Week 30
Algebra 8
10 ticks L7-8 P3 p9
Sumbooks (Intermediate
book) p31
1
10 ticks L7-8 P3 p9
Sumbooks (Intermediate
book) p31
Sumbooks (Higher book)
p34
2
Week 31
3
Solving Quadratic

Expand and simplify expressions
involving brackets and surds.
 Factorise linear expressions.
 Factorise expressions involving
surds.

Factorise quadratic expressions.
Factorise using the difference of two
squares.
 Factorise quadratic expressions with
coefficients greater than 1 (e.g.
starting 2x2)
Factorise quadratic expressions of
the form ax2 + bx + c including the
difference of two squares.
 Plot graphs of quadratic functions (recap)
 Solve quadratic equations
graphically.
 Solve quadratic equations by
factorising algebraically (including

Solving Quadratic
Equations
Algebra 8
modal class) and spread (range,
including consideration of outliers,
quartiles and inter-quartile range)
 Draw box plots from cumulative
frequency curves.
 Interpret box blots.
 Understand and discuss the effect of
outliers.
34

Drawing the box inaccurately, so it
represents the lowest and highest
value instead of the interquartile
range.
 Placing the median in the middle of
the axes, instead of at the correct
value.
 Not finishing off whiskers.
 Not showing outliers where required.
 Errors made when working with
negative numbers.
 Not multiplying all terms in the
bracket by the number / term on the
outside.
 Forgetting basic rules of surds.
 Not taking out the highest common
factors.
 Forgetting that x2 is a factor of x3
 Forgetting that √2 is a factor of √10
and √12, for example.
 Errors made when multiplying out
brackets to check answers.

Forgetting to write the opposite sign
when writing the solution, e.g. (x +
1) gives solution of x= -1 not x=1.
 Not writing down both solutions.
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
those that need rearranging).
Equations
4

1
Week 31
2
Algebra 8
3
4
1
Solving Quadratic
Equations
Week 32
10 ticks L4 P8 p2228
Geometry 10
 Complete the square.
Solve quadratic equations by
completing the square.

Substitute into formulae (including
negatives and indices) (re-cap)
 Recognise and interpret the quadratic
formula.
 Substitute into the quadratic formula.
 Solve quadratic equations using the
quadratic formula, finding both
solutions.
 Consolidation
 Consolidation
 Identify 3D shapes: cubes, cuboids,
prisms, cylinders, pyramids, cones
and spheres.
 Describe 3D shapes by their
properties.
 Identify planes of symmetry of 3-D
objects.

Forgetting to halve the value in front
of the ‘x’
 Errors made when multiplying out
what is inside the bracket.
 Incorrectly writing add or subtract
after the bracket, when the opposite
is necessary.
 Forgetting there are always 2
solutions.
 Errors made when squaring or
multiplying with negatives.
 Forgetting to change the sign in from
of the ‘b’ value to a positive or
negative where required.
 Not writing both solutions on the
answer line.
 Miscalculating with negatives.



Giving correct answers but not
explaining the properties used.
Using incorrect terminology, e.g.
corners instead of vertices.
Representing 3D
shapes
Week 32
Geometry 10
Representing 3D
10 ticks L4 P8 p2228
10 ticks L6 P4 p3340
Sumbooks (Y9
basics) p71
2

Recognise the net of a 3-D object
 Draw the net of a 3-D object
35
Incorrectly visualising 3-D objects in 2-D.
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
shapes
Week 33
Number & Algebra 1
Inequalities
Sumbooks
(Foundation book)
p35
10 ticks L6 P2 p3742
Sumbooks (Y9
basics) p74
Sumbooks
(Foundation book)
p35
10 ticks L5 P6 p3034
10 ticks L6 P2 p3742
Sumbooks
(Foundation book)
p78
L 6 p 1 p9
Week 33
3
4

Make a drawing of a 3-D object on
isometric paper.
 Make isometric drawings of a 3-D
object when given certain criteria
(e.g. 24 cubes, draw a cube that has
125 cubes, draw a cuboid…)
 Set up linear equations.
 Solve linear equations.
2
Sumbooks higher p 245
3
Number & Algebra 1
Use the symbols <, >, ≤, ≥ to show
numerical inequalities.
 Write down integer values that satisfy
inequalities.
 Show inequalities on a number line.

Inequalities
Week 34
Algebra 9
Plotting graphs


Solve linear inequalities in one
variable.
Solve linear inequalities and show
solutions on a number line.
36
Using isometric paper in landscape
not in portrait.
 Not joining lines dot-to-dot.
Forgetting that there are cubes on
the inside of a shape (e.g. asked to
draw a cuboid that has 24 cubes)
and only considering the cubes you
can see.


Construct and interpret plans and elevations
of 3-D objects
1
L6 p 6 pg 7
L7-8 p 4 pg 13-15

Missing out hidden cubes when
converting from a 3-D view to a plan
or elevation.
 Confusing the different views.
 Misinterpreting the problem.
Not making links between one part
of the question and another.
 Correct equation formed but solved
incorrectly.
 Confusing the convention of an open
circle for a strict inequality and a
closed circle for an included
boundary.
 Not remembering how to use
inequality symbols.
 Not reversing the sign when
multiplying or dividing by a negative.
 Colouring in the circle when it is not
needed.
 Misinterpreting the symbols given in
the inequality.
 Not changing the symbols around

NEW for Examination 2015
AQA GCSE Linear
Higher Tier
(Linear and
Quadratic)
Week 34
Sumbooks higher p 245
4

L6 p 1 pg25
1

L6 p 1 pg27-29
L6 p 1 pg 35
L7-8 p 3 pg 29
2
AQA Higher book, Ex.
35D, page 551.
3
Solve linear inequalities in one or two
variables and represent solutions on
a number line.
Plot graphs of linear functions (with or
without a table of values)
 Plot graphs of two linear functions
and identify points of intersection.
 Solve linear equations graphically.
 Plot graphs of quadratic functions.
 Solve linear or quadratic equations
graphically.
Algebra 9
Plotting graphs
(Linear and
Quadratic)
4



Solving problems with quadratic
equations (graphically or
algebraically).
Plot graphs of other functions (e.g.
cubic, reciprocal, exponential for
positive values of k)
NOTE: This is not specifically tested,
but is useful for when students need
to sketch graphs of various functions.

Learning
Objectiv
es:
37

when multiplying or dividing by a
negative.
Writing x= on answer lines instead
of using the appropriate symbol.

Substituting incorrectly.
 Not using BIDMAS.
 Making mistakes when calculating
with negative numbers.
 Not using a third point as a check
when drawing a straight line.
 Not plotting enough points.
 Not joining points together.
 Joining coordinates with a straight
line instead of a smooth curve.
 Not visualising the problem.
 Incorrectly setting up equations.
 Students do not apply basic
knowledge of mathematics to help
solve problems (e.g. multiplying out
algebraic expressions given as
lengths, to find an expression or
equation for area).
 Joining non-linear graphs with
straight lines.
 Not checking ‘rogue’ coordinates
they have plotted (e.g. they can see
what the graph should look like, but
do not check working out when there
is a coordinate that does not fit with
the rest).

NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Summer 2
Week 35
Geometry 11
10 ticks L7-8 P5 p57
10 ticks L6 P4 p32
Resourc
es:
Lesson:

1
Construct acute, obtuse angles.
 Construct reflex angles.
Construct the bisector of an angle.
2

Constructions
Week 35
Geometry 11
Constructions
Week 36
Geometry 12
Loci
Week 36
Geometry 12
10 ticks L6 P4 p3132

10 ticks L6 P4 p3132
10 ticks L7-8 P5 p34
3
Sumbooks
(Intermediate book)
p87
Sumbooks (Year 9
basics) p69-70
4
Worksheet in resources
folder
1
Worksheet in resources
folder
2
Draw triangles accurately when at
least one angle is given.
Draw triangles accurately when given
the length of all three sides.

Know that the perpendicular bisector
of a line segment is the shortest route
between two points.
 Construct a perpendicular bisector of
a line.
 Construct a perpendicular to a given
line from/at a given point.
 Make an accurate drawing of given
shapes using constructions.
To be
able to:
Outcome

Labelling the wrong part of the angle
once drawn.
 Using the wrong scale on the
protractor.
Not keeping the arms of compasses an
equal distance apart when bisecting.

Not completing the triangle by
drawing the third side.
 Rubbing out construction lines.
 Not completing the triangle by
drawing the third side.
 Not opening the compasses so that
they are greater than the midpoint.
 Rubbing out construction lines.
 Not keeping a consistent distance
between the points of the compass
when drawing arcs.

Using the wrong type of
construction.
Not using compasses and drawing
‘freehand’
Not drawing according to all given
criteria.


 Construct a locus around a point.
 Construct a locus around a line of
points.
 Construct a locus that is equidistant
between two points.
 Construct a locus that is equidistant
between two lines.
38

Failing to keep the settings of
compasses constant.
 Rubbing out construction lines.
 Confusing a distance from a point
with the distance from a line.

NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Loci
Week 37/38
Sumbooks
(Intermediate book)
p57-58
10 ticks L7-8 P5 p710
Sumbooks
(Intermediate book)
p57-58
10 ticks L7-8 P5 p710
Sumbooks (Higher
book) p51 (including
bearings)
Revision &
Summer MOCK
Exams?

3
4

Solve problems involving
constructions and loci.
 Not using compasses.
Making inaccurate constructions.
Shading the wrong region.


Solve locus problems, including the
use of bearings and scale.

Forgetting that bearings use 3figures.
 Not using a North line.
Confusing clockwise and anticlockwise.


1
10 ticks L5 P3 p29-34
10 ticks L4 P3 p27-42
Week 39
Measures 2
Using scales &
Compound
measures (speed,
rates of pay, area)
2
Week 39
Measures 2
Using scales &
Compound
measures (speed,
10 ticks L6 P5 p9-12
Sumbooks
3

Calculate amounts such as daily or
weekly wages.
 Calculate rates of pay (including
overtime rates)
 Solve problems involving salaries and
pay.

Know the formula linking speed,
distance and time.
39

Assuming that rates of pay are the
same each day or time.
 Doubling rates of pay instead of
multiplying by 1.5, for example.
 Incomplete calculations, e.g.
working weekly pay but forgetting
the weekend hours worked.
 Not remembering the formula.
 Dividing instead of multiplying,
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
rates of pay, area)
Week 40

(Foundation book)
p58
Perform calculations involving speed,
distance and time.
Number 6
FDP
Week 40
Number 6
FDP
10 ticks L4 P3 p2742
4
10 ticks L6 P3 p3-12
http://www.workshee
tworks.com/math/per
cent.html
Abacus
Sumbooks (Y9
basics) p2910 ticks L6 P3 p1316
Abacus
Sumbooks (Y9
basics) p32
Sumbooks
(Foundation book)
p9-11
10 ticks L6 P3 p1316
Abacus
1
2
3

Change freely between related
standard units and compound units
(e.g. speed, rates of pay, prices,
density, pressure) in numerical and
algebraic contexts.
 Convert metric units of measurement
(re-cap)
 Convert between units of compound
measures such as area, rates of pay
and speed.
 Use compound measures such as
area, rates of pay and speed.
 Calculate percentages of amounts.
 Calculate with percentages in real-life
contexts.
 Calculate percentage increase and
decrease.
where appropriate.
Not checking that measurements
are using the same units (e.g.
distance in Km but time in metres
per hour)
 Multiplying or dividing by the wrong
power of 10.
 Assuming that area in m2 need to be
x100 to convert into cm 2.
 Forgetting to convert both sets of
units, e.g. when converting km per
hour into metres per minute.





Use decimals as multipliers and to
calculate quantities (with or without a
calculator)
 Convert between decimals and
percentages.
40

Forgetting to put decimal places
back in when performing without
calculator.
Multiplying or dividing by the wrong
power of 10.


Not realising that 1/10 = 10/100.
Writing 0.1 as 1%, for example.
Forgetting to convert into the same


Convert between fractions and
terminating decimals.
 Order fractions, decimals and
Dividing by the wrong power of 10.
Mistaking 0.3 for 3%, for example.
Calculating the increase / decrease
but forgetting to add it to original
amount to get a total.

NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Sumbooks (Y9
basics) p32
Sumbooks
(Exercises in
Numeracy) p24
Sumbooks
(Foundation book)
p9-11
10 ticks L5 P2 p3
10 ticks L6 P3 p1316
Abacus
Sumbooks
(Foundation book)
p9-11
percentages.
4
 Recognise fractions as multipliers.
 Calculate fractions of amounts.
 Compare quantities using fractions,
decimals and percentages.

41
type of number before trying to
compare.

Not spotting that ½ = 0.5, so
multiplying by 0.5 is the same as
multiplying by ½
 Multiplying by the denominator
instead of the numerator, and vice
versa.
 Multiplication or division errors made
but method correct.

NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Content: Year 11
Learning Objectives:
Autumn 1
Date:
Week 1
Geometry 13
Surface Area
(Cubes, cuboids,
other prisms)
Resources:
Lesson:
Geometry 14

Sumbooks Higher
worksheet (92-93)
page 100-101.
(includes parts of
circles)
L7-8 p 6 p3-11
1
L5 p 6 pg 36
3
Whiteboard maths
mensuration 93
4

L5 p 3 pg 31-3
1

2
NOTE: Not cylinders
Week 2
To be able to:
Calculate the areas of compound
shapes.

Calculate the surface area of a cube.
 Calculate the surface area of a
cuboid.
 Calculate the surface area of
triangular prisms.
 Calculate the surface area of other
prisms.
 Convert between metric units of area.
 Solve problems involving surface
area.
Apply properties of similarity and
congruence when working with area.
Calculate the volume of a cube or
cuboid.
 Calculate the volume of a triangular
prism.
 Calculate the volume of other prisms.
42
Common mistakes and
misconceptions
Outcome

Not being able to visualise how to
split shapes up into smaller
components.
 Using the incorrect units or
measurements.
Not accounting for every side of the
shape.
 Forgetting to divide by 2 for
triangles, or dividing the area of the
whole shape by 2 to get final
answers.


Not giving answers in the units
required.
 Not being able to rearrange a
formula or calculation to find missing
measurements.
 Working with a mixture of units
instead of converting them to the
same type.
 Not comparing corresponding sides
of shapes to check similar lengths.


Confusing volume and surface area.
Not splitting shapes up into smaller
parts to find cross-sectional area.
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Volume
(Cubes, cuboids,
other prisms)
Sumbooks Higher
worksheet (94)
page 102.
2

3

NOTE: Not cylinders
Solve problems involving volume and
capacity.
Convert between units when working
with area and volume.
 Compare lengths, areas and volumes
using ratio notation.
 Make links to similarity (including
trigonometric ratios) and scale factors

4
Week 3
1
Number 9
Calculating with
Fractions
2
Calculate exactly
with fractions, surds
and multiples of π
3
calculate exactly with
fractions, surds ) and
rationalise
denominators and
multiples of π
simplify surd
expressions involving
squares (e.g. 12 = 4×3
= 4× 3 = 2 3


Writing ratios in the wrong order.
 Not simplifying ratios.
Using linear ratios when they should
be squared or cubed.
Consolidation


Write amounts as one fraction of
another (e.g. 2/5 shaded, 3/5 not
shaded)
 Add and subtract fractions with the
same denominator.
 Add and subtract mixed numbers.
 Write two or more fractions with the
same denominator.
 Add and subtract fractions when one
or more denominators need to be
changed.
 Multiply a fraction by a fraction
 Multiply a fraction by a whole
number.
 Multiply a fraction by a mixed
number, or a mixed number by a
mixed number.


Incorrectly converting a mixed
number to an improper fraction.
Not converting the final answer back to a
mixed number where required.
Not multiplying numerator and
denominators by the same thing.

Multiplying diagonally as though ‘crossmultiplying’ is being done,
2 5 12
e.g. 3 × 6 = 15

Multiplying the numerator and the
denominator by the whole number
e.g.
4

Divide a whole number or a fraction
by a fraction
 Divide mixed numbers by whole
numbers.
 Find the reciprocal of a whole
number, a decimal or a fraction
43

1
20
× 20 =
.
4
80

Leaving denominators as decimal
numbers.
Not simplifying answers when asked to
do so.

Finding the reciprocal of the wrong
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
fraction, or finding the reciprocal of
both fractions.
Week 4
L6 p 2 pg 19-21
 Identify the scale factor of an
enlargement (including fractional /
decimal)
 Enlarge a shape on a grid
Enlarge a shape by a fractional scale
factor.
1
L7-8 p 4 pg 34-37
Geometry 15

Enlargement
L7-8 p 4 pg 34-37
2
L9-10 p 3 pg 3-5
L7-8 p 4 pg 34-37
3
L9-10 p 3 pg 3-5
L9-10 p 3 p6-18
Week 5
4
1
Geometry 16
Vectors
2
3

Enlarge a shape using a centre of
enlargement.
 Enlarge a shape on a coordinate grid,
using a centre of enlargement as
(0,0) or another coordinate.
(as above, including fractional scale factors)
 Find a centre of enlargement.
 Describe enlargements fully, giving
scale factor and centre.

Dividing the measurements of the
original by the image, instead of
image by original.
 Inaccurately counting squares.
 Adding the scale factor instead of
multiplying by the scale factor.
 Not using the centre of enlargement.
 Not enlarging all sides of the shape
by the same scale factor.
 Using the wrong centre of
enlargement.


Construct similar or congruent
shapes on a coordinate grid using
rotation, reflection, translation or
enlargement.
 Understand and describe the effects
of enlargement on perimeter, area
and volume of shapes.
 Understand vector notation.
 Represent column vectors pictorially.
 Describe vectors using column
notation.

Apply addition and subtraction of
column vectors.
 Draw the result vector after an
addition or subtraction of vectors.
 Use multiplication of vectors by a
scalar.
44
Not joining corresponding corners of
shapes.
 Giving only part of the information
required.
 Assuming that a scale factor of 2
doubles the area of the shape.
 Not carrying out multiple
transformations where required.

Writing vectors as coordinates.
Mixing up the left right direction with
the up / down.
 Not writing left / down as a negative
value.
 Mistakes made when adding or
subtracting with negative numbers.
 Not drawing the resultant vector to
show final answer.
 Not multiplying both values by the
scalar multiple.

NEW for Examination 2015
AQA GCSE Linear
Higher Tier


4
Week 6
L 7-8 p 1 pg 35
Number & Algebra 2
Sumbook higher
17
1
Direct and Indirect
Proportion
Sumbook higher
17
2
3
L9-10 p 1 pg 11
4
Use diagrammatic and column
representations of vectors.
 Identify parallel vectors from column
vectors or diagrams.
Consolidation:
 Solve simple problems involving
vectors.
 Use vectors to construct geometric
arguments and proofs.
 Know that when y is directly
proportional to x, y α x and y = k x
 Interpret the gradient of a straight line
graph as a rate of change.
 Calculate the constant of
proportionality (k) given values for x
and y.
 Write a formula in terms of x and y for
direct proportion problems.
 Know that when y is inversely
proportional to x, y α 1/x and y = k/x
 Calculate the constant of
proportionality (k) given values for x
and y when they are inversely
proportional.
 Write a formula in terms of x and y for
inverse proportion problems.
 Recognise and sketch graphs of
direct and indirect proportion.
 Construct and interpret equations that
describe direct and inverse
proportion.
 Solve problems involving direct and
indirect proportion algebraically and
graphically.
45





Not sketching the vectors to help
identify which ones are parallel.
Failing to identify common factors of
vectors written in column notation.
 Mixing up the rules of adding /
subtracting or using multiples of
vectors.
Not understanding that if we travel
the wrong way across a vector, it
changes it into a negative, for
example.
 Forgetting the formula.
Multiplying instead of dividing to find
‘k’.
Mixing up the value of x and y when
substituting.
Not substituting the value of ‘k’ back
in to original formula.

Using the formula for direct instead
of indirect (inverse) proportion.
Dividing instead of multiplying to find
‘k’.
Not substituting the value of ‘k’ back
in to original formula.




Confusing graphs of direct and
inverse proportion.
 Not substituting values into
equations to check the effect on the
shape of the graph.
Misinterpreting a problem as direct
proportion, when it is inverse.
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
?
?
Week 7
1
Number 10
Percentages &
Finance
2
3
4
Week 8
1


interpret the gradient at a point on a
curve as the instantaneous rate of
change; apply the concepts of
average and instantaneous rate of
change (gradients of chords and
tangents) in numerical, algebraic and
graphical contexts
 Set up, solve and interpret the
answers in growth and decay
problems, including compound
interest and work with general
iterative processes.
 Calculate percentages of amounts.
(re-cap)
 Calculate percentage increase and
decrease. (re-cap)
 Find the original value after a
percentage increase or decrease.

Solve problems involving percentage
increase / decrease or overall
percentage change.
 Calculate using simple interest.
 Solve problems involving credit.








Calculate repeated percentage
change.
 Solve problems involving repeated
percentage change / compound
interest.
 Calculate a percentage profit or loss
 Calculate original values using profit
or loss.
Number 10


46
Dividing by the wrong power of 10.
Forgetting to add on the increase or
deduct the decrease.
Using the wrong multiplier, i.e. 1.2
for 2% increase.
Not understanding that it is possible
to have more than 100% when using
percentages in context.
Assuming that an increase of 30%,
then a decrease of 10% is equal to
an increase of 20%.
Not seeing that 17.5% = 10% + 5%
+ 2.5%.
 Forgetting to add on the initial
deposit in credit calculations.
 Incorrectly calculating 1.5 x 2
instead of 1.52.
 Not checking whether it is a
repeated increase or decrease.
Writing the profit or loss in a
monetary value instead of a final
percentage.
Dividing by the selling price instead
of the original cost price.
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Percentages &
Finance
2
3
4
Week 9
1
Understand the Retail Price Index
and its use in real-life context.
 Interpret changes in the retail price
index in terms of the base year (i.e.
+5%, -10%, +23%).
 Interpret and make comparisons in
the changes in the value of goods
using the Retail Price Index (e.g.
price of food has increased by 10%,
but this is below the expected
increase for that year).
 Calculate simple price changes using
the Retail Price Index (increase or
decrease)
 Calculate base year prices given the
relevant price index.
 Solve more complex problems
involving the Retail Price Index.
Re-cap:
Solve equations with unknowns on
both sides.
 Solve equations involving brackets or
fractions.
 Factorise quadratic expressions.
 Solve quadratic equations by
factorising (including coefficients
greater than 1).

Algebra 10
Solving Quadratic
Equations (recap)

2
3

 Complete the square.
Solve equations by completing the
square.

4

Solve quadratic equations
graphically.
Solve quadratic equations using the
47

Forgetting that the base year always
has an index of 100 (100%)
 105 means an increase of 5%, not
105% from the base year.
 An index less than 100 means a
decrease in value.
 Using the last price in the table to
calculate an increase, instead of the
base year price.
 Not understanding when the
multiplier should be greater than or
less than 1.
 Using the multiplier as 1.5 rather
than 1.05 for an increase of 5%.
 Misinterpreting the problem.
 Not showing all stages or working
out, or missing stages of working out
not believing they are relevant.
 Errors made when working with
negative numbers.
 Not multiplying all terms in the
bracket by the number / term on the
outside.
 Forgetting that x2 is a factor of x3
 Forgetting to change the sign
around when giving solutions.
 Not multiplying out brackets to check
factorisation has been done
correctly.
 Not halving the coefficient in front of
the ‘x’.
 Incorrectly rearranging.
 Not writing down both solutions.
 Forgetting to write the opposite sign
when writing the solution, e.g. (x +
1) gives solution of x= -1 not x=1.
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
formula.
Week 10

TT L 9 to 10, Pack
4, Page 28.
1
TT L 9 to 10, Pack
4, Page 29.
2
Sumbooks Higher
worksheet (10)
page 18.
TT L 9 to 10, Pack
4, Page 30.
TT L 9 to 10, Pack
4, Page 31.
3

Add or subtract algebraic fractions,
simplifying answers fully
4

Solve equations involving algebraic
fractions.

Use basic laws of indices (re-cap)
 Simplify algebraic fractions
Algebra 11
Algebraic Fractions
Week 11/12
Week 13
Geometry 17
Pythagoras &
Trigonometry

Multiply and divide algebraic
fractions, simplifying fully
Incorrectly substituting in values for
a, b and c.
 Not changing the sign of the ‘b’
value where necessary.
 Mixing up the multiplication and
division laws of indices.
 Not simplifying fully.

Forgetting the rules of multiplying
with simple fractions.
 Not switching the second fraction
upside down when dividing.
 Not making denominators match
before trying to add or subtract.
 Forgetting to simplify answers where
possible.

Mixing up the rules for adding,
subtracting, multiplying and dividing.
Revision & MOCK Exams?
L7-8 p 2 pg 3
L7-8 p 2 pg 5-7
1
Know and understand Pythagoras’
theorem a2 + b2 = c2
 Calculate the length of the
hypotenuse of a right-angled triangle.
 Calculate the length of shorter sides
in a right-angled triangle.
 Use Pythagoras’ Theorem to solve
problems in real-life context.

48

Forgetting to take the square root to
find the final answer.
 Not correctly identifying the
hypotenuse.
 Drawing a scale diagram to
‘calculate’ the length of a
hypotenuse.
 Adding instead of subtracting to find
the shorter sides.
 Thinking that square root is not
needed when finding shorter sides.
 Failing to identify whether they are
finding the longer or shorter side
when problem solving.
 Students do not sketch out the
problem to help them visualise it.
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
2
TT L7-8 p5 pg 2831.
TT L7-8 p 5 pg
33-35.
Sumbooks Higher
worksheet (101)
page 109.
3
Calculate the length of a line segment
AB (e.g. on a coordinate grid) using
Pythagoras’ Theorem.
 Calculate lengths in other geometrical
figures using Pythagoras’ Theorem.
 Identify and label sides of triangles in
terms of Trigonometric ratios (i.e.
opposite, adjacent and hypotenuse)
 Know and use the trigonometric
ratios. (SOHCAHTOA) to find missing
lengths.
4

TT L7-8 p 5 pg
36-37.
Sumbooks Higher
worksheet (102)
page 110.
Week 14

Sumbooks Higher
worksheet (100)
page 108.
1
Calculate missing angles inside rightangled triangles using Trigonometry.
 Solve problems involving
trigonometry.
 Know the formulae for Pythagoras
and trigonometry ratios and apply
them to find angles and lengths in
right-angled triangles and, where
possible, general triangles in two and
three dimensional figures
 Solve problems involving Pythagoras
and Trigonometry.
Geometry 17
2
 Use and apply the rules of
Pythagoras and Trigonometry in 3D
problems.
3
Know the exact values of sinθ and
cosθ for θ = 00, 300, 450 , 600 and
900;
 Know the exact value of tanθ for θ =
00, 300, 450 and 600
 Use exact values for sin, cos or tanθ
Pythagoras &
Trigonometry

49

Pupils do not sketch out the problem
to visualise it.
 Trying to make an accurate drawing
and ‘measure’ lengths instead of
calculating it.
 Mixing up the ratios and not
following SOHCAHTOA.
 Using the right-angle as a starting
point instead of another given angle.
 Multiplying instead of dividing where
necessary.
 Using the wrong ratio.


Forgetting whether to multiply or
divide, dependent upon whether
calculating a side or an angle.
Trying to apply Pythagoras when
there are not enough side lengths
given.
 Using the wrong trigonometric ratio.
 Not being able to visualise the
problem.
 Pupils do not sketch the problem
they are working on to help see what
length or angle they are finding.
 Confusing the values of the different
ratios.
 Not being able to apply the
knowledge to the problem in front of
them.
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
1
when solving Trigonometry problems.
 Recognise, sketch and interpret
graphs of trigonometric functions
(y=sinx, y=cosx, y=tanx) for angles in
any size.
 Recognise and sketch graphs of
quadratic functions.
 Recognise lines of symmetry in
quadratic graphs.
 Sketch translations and reflections of
a given function (eg quadratic
functions).
2

4
Week 15
Algebra 11
Quadratic and Other
Graphs
3
Interpret and use graphs of quadratic
functions in real-life context.
 Identify and interpret intercepts,
turning points and roots of quadratic
functions graphically.
 Deduce roots algebraically and
turning points by completing the
square.
 Draw graphs of cubic and reciprocal
functions.
 Sketch and recognise graphs of cubic
and reciprocal functions (e.g. y = 1/x
with x ≠ 0)

Confusing what each graph should
look like with another.

Moving the parabola across the xaxis instead of up or down the yaxis.
 Not realising parabolas should be
symmetrical.
 Not considering how wide the curve
should be depending on the
coefficient, and sketching graphs
that look too similar.
 Not applying context when using
quadratic graphs (e.g. not
recognising that the turning point is
where a ball stops climbing in height
and stops moving).



4
Week 16
Statistics 4
1

Interpret graphs of quadratic, cubic
and reciprocal functions.
 Draw and interpret cubic and
reciprocal graphs in real-life contexts.
 Identify types of correlation
graphically.
 Describe the correlation between two
data sets (not from a graph)
 Make predictions about bivariate
50



Confusing what quadratic, cubic or
reciprocal graphs should look like.
Not plotting a few points to remind
themselves of what each type of
graph might look like before
sketching.
Forgetting that 1/x means 1 ÷ x.
 Misinterpreting the problem.
Not thinking about how the change
in x- affects the change in y-, and
vice versa.
Not understanding that correlation
does not imply causation between
two data sets.
Not considering real-life context
when considering whether it is a
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Scatter Graphs &
Tree Diagrams
2
3
data.
 Interpret points on a scatter graph.
 Identify points that may be classed as
outliers.
 Plot bivariate data as a scatter
diagram.
 Draw estimated lines of best fit.
 Estimate using a line of best fit.
 Understand and describe
interpolation and extrapolation as a
method of estimation.
Re-cap:
Represent the outcomes of two
independent events using a tree
diagram.
 Calculate the probability of two
independent events from a tree
diagram.
 Work out the probability of an event
that can happen in more than one
way using a tree diagram (the AND
OR rules).
 Represent the outcomes of
dependent events using a tree
diagram (conditional probability)
 Calculate probabilities of dependent
events from a tree diagram.

4
Week 17
Statistics 5
Probability:
10 ticks L7 P1 p712
1

Understand that the greater the
number of experimental trials the
more reliable the results.
 Estimate probability from a set of
experimental data.
 Compare estimated probability with
theoretical probability (using
51
positive or negative correlation.

Plotting as (y, x) instead of (x, y)
coordinates.
 Missing off points as not working
systematically.
 Assuming the line of best fit has to
go through (0,0).
 Not attempting to split the points
evenly either side of the line.
 Not using a suitable scale for each
axis.
 Incorrectly setting up the two events.
 Adding instead of multiplying across
branches.
 Not simplifying fractions where
required.

Not recognising when a question
involves independent events and so
adding rather than multiplying the
fractions.
 Adding across branches, multiplying
at the end.
 Incorrectly stating that the more
trials means there is less bias.
 Not understanding that as it is based
on an experiment; the probability
can change with each experiment
and is therefore only ever an
estimate.
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Experiments and
Charts.
10 ticks L7 P1
p11-13
2
Whiteboard
maths: Bar charts,
pictograms, pie
charts, two-way
tables.
3
4
Week 18
TT L9-10 P2 p7.
1
TT L9-10 P2 p8.
2
appropriate language and the
probability scale).
 Understand that empirical unbiased
samples tend towards theoretical
probability distributions, with
increasing sample size.
 Calculate relative frequency of an
outcome from an experiment.
 Predict the likely number of
successful events of an outcome.
 Calculate probability of single events
from charts (e.g. bar chart,
pictograms, pie charts, two way
tables).
 Calculate the probability of two or
more events from charts.
 Calculate probabilities from a set of
grouped data (e.g. grouped
frequency tables.
 Know and apply the sine rule to find
lengths and angles.
Geometry 18
Sine and Cosine
Rule (non-rightangled triangles)

Know and apply the cosine rule to
find lengths and angles.
Mixed Sine &
Cosine
activities:
Sumbooks Higher
worksheet (103)
page 111.
TT L9-10 P2 p
52

Comparing theoretical probability
with relative frequency without
taking into account the number of
trials carried out.
Incorrectly reading the vertical axis
of bar charts



Not understanding a grouped
frequency table.
Labelling up their triangle incorrectly
(not naming corresponding angles
and sides with the same letter).
 Not switching the formula around
depending on whether you want to
find a length or an angle.
 Using the wrong ratio (e.g. cos
instead of sin)
 Not realising that the cosine rule can
also be applied to right-angled
triangles.
 Not sketching out the problem given.
 Rearranging incorrectly to find
alternative lengths or angles.
 Rounding off calculations before
getting to final answers, making it
inaccurate.
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Sumbooks Higher
worksheet (104)
page 112.
Sumbooks Higher
worksheet (105)
page 113.
3

Know and apply ½ ab sin C to find
the area or sides of any triangle.

4
Solve geometrical problems.
NOTE: Includes Pythagoras, trigonometry,
Sine and Cosine rules, area of triangles.
Exam style
questions:
TT L9-10 P2 p1316.
Week 19
Geometry 19
Cylinders, Cones and
Spheres.
10 ticks L6 P5
p33-38
10 ticks L9-10 P4
p10-25 (mix of
surface area and
volume of 3D
shapes)
Sumbooks
(Intermediate
book) p62
Abacus
10 ticks L9-10 P4
p10-25 (mix of
surface area and
volume of 3D
shapes)
Abacus
1

Calculate the circumference and area
of a circle (re-cap).
 Calculate the volume of a cylinder.
 Calculate the surface area of a
cylinder.
 Solve problems involving the volume
and surface area of cylinders
2


Substituting in values in the wrong
places.
 Rearranging the formula incorrectly.
 Not being able to identify which
method to use to solve a problem
(i.e. Pythagoras, Trigonometry, sine
or cosine rules).
 Not sketching out the problem to
help visualise it.
 Forgetting to use inverse sin, cos or
tan where necessary.
 Not showing all stages of working
out.
 Making rounding errors.
 Forgetting to divide by 2 when the
diameter is given and the radius is
needed.
 Multiplying by  before squaring.
 Using the wrong measurement for
the radius or diameter.
 Not being able to identify the
measurements they need to use.

 Calculate the volume of a cone.
Calculate the surface area of a cone.

3


Calculate the volume of a frustum.
Solve problems involving cones or
frustums.
NOTE: Ratio or similarity may also be
included in these problems.
53

Forgetting to divide by 3 (or x 1/3)
when finding volume.
Using the vertical or slanted height
the wrong way around.
Calculating only part of the problem,
forgetting to finish it off or show final
answers.
 Using incorrect measurements.
 Not being able to work backwards or
rearrange formulae to find missing
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Week 20
10 ticks L9-10 P4
p15
4
 Calculate the volume of a sphere.
 Calculate the surface area of a
sphere.
 Solve problems involving spheres.
TT Level 7 to 8,
Pack 6, Start
Page 37.
1

AQA Methods &
Applications PDF
file, page 212.
2
AQA Methods &
Applications PDF
file, page 206209.
3
AQA Methods &
Applications PDF
file, page 218.
4
Sumbooks
(Intermediate
book) p32-34
10 ticks L7-8
1
Algebra 13
More Real Life
Graphs
Week 21
Algebra 14
Read and interpret graphs for time
series data and know their
appropriate use.
 Calculate averages using time series
data.
 Calculate gradients of linear graphs.
 Use and interpret gradients of linear
graphs.

Calculate gradients of non-linear
graphs.
 Estimate gradients of non-linear
graphs.
 Calculate or estimate areas beneath
non-linear graphs.
 Interpret gradients and areas
underneath graphs showing real life
contexts.
 Interpret results in cases such as
distance-time graphs, velocity-time
graphs and graphs in financial
contexts
 Manipulate linear equations to make
variables match.
 Eliminate one variable in any pair of
simultaneous equations.
NOTE: Students may have to manipulate
54
measurements.
Students often forget to apply the
4/3 of…
 Multiplying by 3 and dividing by 4.
 Incorrectly substituting
measurements into the formulae.
 Using a grouped label on the
horizontal axis rather than a
continuous scale.


Misinterpreting positive and negative
gradients.
 Dividing the change in x- by the
change in y- axis.
 Giving answers in the wrong units
(m/s)
 Misreading the scale on the axes.
 Not splitting up the area under the
graph accurately
 Not splitting up the area of the curve
appropriately.
 Misreading the scales on the axes
and therefore making errors.


Not interpreting areas as being
under or over estimates.

Incorrectly adding or subtracting the
equations.
 Making mistakes when using
negative numbers.
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
P4 p3-12
10 ticks L7-8
P4 p3-12
2
10 ticks L7-8
P4 p3-12
3
10 ticks L7-8
P4 p3-12
Sumbooks
(Higher book)
p92
4
Week 22
10 ticks L9-10
P4 p14
1
Geometry 20
Worksheet in
resources folder
Volume and Surface
Area of Pyramids
10 ticks L9-10
P4 p14
Worksheet in
resources folder
one or both equations.
Solve simultaneous linear equations.

Simultaneous
Equations

Solve linear / quadratic simultaneous
equations graphically.
 Solve linear / quadratic equations
algebraically.
 Form pairs of simultaneous equations
for a real-life problem.
 Set up and solve simultaneous linear
or quadratic equations to solve
problems.

Plot graphs of linear or quadratic
functions (re-cap)
 Find approximate solutions to
simultaneous equations graphically.
 Calculate the volume of a pyramid.
 Solve problems involving the volume
of pyramids.

2

Calculate the surface area of
pyramids.
Solve problems involving the surface
area of pyramids.
55

Not multiplying or dividing the entire
equation by the same thing.
 Forgetting to find both solutions.
 Errors made when substituting,
especially with negatives.
 Accuracy errors when attempting to
match variables in equations.
 Plotting points incorrectly.
 Misreading scales on axes.
 Not being able to manipulate
equations to solve algebraically.
 Misinterpreting problems and setting
up inappropriate equations.
 Not considering real-life context
when finding solutions, e.g. which
would be the best solution for the
length of this garden, -7 or +5m?
 Making mistakes when completing a
table of values or substituting.
 Not joining up points with a ruler and
therefore intersection is inaccurate.
 Not plotting more than 2 points to
check a straight line is formed.

Using the sloping height instead of
vertical height.
 Not dividing by 3 at the end, of
multiplying by 1/3
 Not checking the shape of the base,
i.e. is it square or triangular?
 Using the wrong units.
 Mixing up the formulae for volume
and surface area.
 Not including all sides of the shape.
 Working in a mixture of units.
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Sumbooks Higher
worksheet (94-95)
page 102-103.
3

Calculate volume and surface area of
composite solids
10 ticks L9-10
P3 p6-14
4

Use similarity when working with area
and volume of 2D or 3D shapes.
1
Week 23
Statistics 6

Sort numerical data into a simple
Venn diagram.
 Solve numerical problems using
Venn diagrams or algebraically.
Probability: Venn
Diagrams
2
3
Not sure where
to put this either
Understand the term ‘union’ and
‘intersection’ in a Venn diagram.
 Use set notation to describe areas of
a Venn diagram.
 Shade in areas on a Venn diagram to
satisfy given criteria.
 Calculate probabilities from a Venn
diagram.
 Calculate conditional probabilities
using Venn diagrams.


Calculate and interpret conditional
probabilities through representation
using expected frequencies with twoway tables, tree diagrams and Venn
diagrams.
56

Not being able to visualise how to
split the overall shape into it’s
separate components to find
volume.
 Not checking measurements or
volumes to help visualise what
happens to area / volume when
standard lengths change.
 Forgetting to count items on the
outside of the circles.
 Not counting items that have already
been placed.
 Not understanding that some people
in numerical problems are counted
twice when they are in the middle of
the diagram.
 Confusing union and intersection.
 Forgetting which symbol to use, i.e.
‘U’ for union.
 Shading in the area that isn’t
needed, instead of showing the one
that is.
 Forgetting that probabilities should
sum to 1.
 Miscalculating when subtracting
probabilities from 1.
 Writing answers in the wrong form,
e.g. a fraction when a decimal is
required.
 Not simplifying answers where
necessary.

NEW for Examination 2015
AQA GCSE Linear
Higher Tier
4
Week 24
Algebra 15
Sumbooks Higher
worksheet (56
and 57) page 6465.
1
2
Inequalities: Linear
and Quadratic
3
AQA Methods &
Applications PDF
file, chapter 5.1
page 92.
4

Recognise prime numbers (including
two-digit)
 Write a number as a product of prime
factors using index notation
 Use prime factors to find HCFs and
LCMs (using a Venn or otherwise)
 Solve linear inequalities in one or two
variables.
 Represent solutions on a number
line.
 Solve quadratic inequalities in one
variable and represent on a number
line.
 Represent solutions to inequalities
(linear or quadratic) using set
notation.
 Represent solutions to linear or
quadratic inequalities graphically.
Week 25
Revision
Week 26
Revision
Week 27
Revision
57



Thinking that 1 is a prime number.
Failing to recognise that a number is
not prime, when finding prime
factors
Shading in a circle instead of leaving
it empty.
 Misinterpreting inequality symbols.



Placing values in the wrong areas of
the diagram.
Confusing unions with intersections.
Shading in the wrong section of the
graph, i.e. shading in the bit needed,
instead of the part not needed.
 Only representing part of the
solution on the graph, forgetting to
show all inequalities to get a final
region.
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Week 28
Revision
Week 29
Revision
Week 30
Revision
Week 31
Revision
Week 32
Revision
Week 33
Revision
Week 34
58
NEW for Examination 2015
AQA GCSE Linear
Higher Tier
Exam Week?
Week 35
Exam Week?
Week 36
Week 37
Week 38
Week 39
59