Download Foundation – Unit 1

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Foundation – Unit 2
OVERVIEW for Foundation Tier
Notes:
1 hour 15 minutes non-calculator exam
66 marks – 33.3%
Topic
Y10 Spring & SUMMER TERM
7. Number skills
8. Factors,
multiples and
powers
9. Basic rules of
algebra
10. Fractions
30 -40% Functional Elements
44 marks Number, 22 marks Algebra
Teaching
hours
4
4
AQA Modular specification reference
4
The Language of Algebra: N4.1
Expressions and Equations: N5.1
Working with numbers and the number system: N1.2, N1.3,
N1.5
Fractions, Decimals and Percentages: N2.1, N2.2, N2.7
Working with numbers and the number system: N1.1, N1.2
Fractions, Decimals and Percentages: N2.3, N2.4
Expressions and Equations: N5.4, N5.7
6
11. Decimals
3
12. Equations and
inequalities
13. Indices and
formulae
6
14. Percentages
15. Sequences
and proof
16. Linear graphs
4
6
17. Ratio and
proportion
4
4
7
Working with numbers and the number system: N1.2, N1.4
Working with numbers and the number system: N1.6, N1.7,
N1.8, N1.9
Working with numbers and the number system: N1.9
The Language of Algebra: N4.2
Expressions and Equations: N5.6
Fractions, Decimals and Percentages: N2.5, N2.7
Expressions and Equations: N5.9
Sequences, Functions and Graphs: N6.1, N6.2
Expressions and Equations:
Sequences, Functions and Graphs: N6.3, N6.4, N6.11, N6.12
Ratio and Proportion: N3.1, N3.2, N3.3
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 7 Number skills
Time: 4 hours
N1.2 Add, subtract, multiply and divide any number.
N1.4 Approximate to a given power of 10, up to three decimal places and one significant figure.
AQA
Spec
ref
N1.2,
N1.4
Learning objectives
Grade
Common mistakes and
misconceptions
Multiply whole numbers using written methods
Use repeated subtraction for division of whole numbers
Round up or down in context – interpret a remainder in a given context
E, D
N1.4
Check and estimate answers to problems
Estimate answers to problems involving decimals
Make estimates and approximations of calculations
E, D, C
N1.4
perform money calculations, writing answers using the correct notation
round numbers to the nearest whole number, 10, 100 or 1000
round to one, two or three decimal places
round to one significant figure
Multiply and divide negative numbers
G, F, E
Forgetting to add the numbers to find the
final answer when using the grid method.
Forgetting the zero when multiplying by
tens when using the standard method.
Writing 3.6 to represent 3 remainder 6.
Not giving an answer in the context of the
problem.
Finding an approximate value
independent of the context in which it is
set.
Working out the actual answer instead of
an approximation.
Rounding down always.
Not rounding to 1sf to estimate
N1.2
E
Applying the ‘general rules’ (the signs are
different, so the answer is negative; the
signs are the same, so the answer is
positive) without constraint.
Applying the rules for multiplying/dividing
negative numbers to adding/subtracting
negative numbers.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 9.1 – 9.3
AQA Modular GCSE Mathematics Foundation Tier
 Place value P186
 Number lines P190
 Everyday arithmetic P193
 Negative numbers P198
 Rounding P205
 Multiplication and division of negative numbers P222
 Multiplying and dividing P239
 One significant figure and bounds P302
 Estimation P305
Foundation Practice Book sections 9.1-9.4, 9.6, 11.1, 15.2, 15.3
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 2/Number/Teaching Resources
Lesson plans/problem sheets/homework sheets
Functional skills activities 1.1 – 1.4, 12.1 -12.2, 12.4
Notes:
Multiplication and division of integers will be limited to 3 digit by 2 digit. Decimals will be limited to multiplying or dividing by a single digit
integer or a decimal number to 1 significant figure.
Candidates may use any algorithm for addition, subtraction, multiplication and division.
Closely related - N1.1 Understand integers and place value to deal with arbitrarily large positive numbers.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 8 Factors, Multiples and Powers
Time: 4 hours
N1.6 The concepts and vocabulary of factor (divisor), multiple, common factor, highest common factor, least common multiple, prime number and prime factor
decomposition.
N1.7 The terms square, positive and negative square root, cube and cube root.
N1.8 Index notation for squares, cubes and powers of 10.
N1.9 Index laws for multiplication and division of integer powers.
AQA
Mod
spec
ref
N1.6
N1.6
N1.7,
N1.8
N1.9
Learning objectives
Grade
Common mistakes and misconceptions
Solve problems involving multiples
Find lowest common multiples
identify multiples, factors and prime numbers from lists of numbers
write out lists of multiples and factors to identify common multiples or common
factors of two or more integers
Solve problems involving factors
Recognise two-digit prime numbers
Find highest common factors
write a number as the product of its prime factors and use formal and informal
methods for identifying highest common factors (HCF) and lowest common multiples
(LCM); (abbreviations will not be used in examinations)
Calculate squares and cubes
Calculate square roots and cube roots
Understand the difference between positive and negative square roots
Evaluate expressions involving squares, cubes and roots
Quote squares of numbers up to 15 x 15 and the cubes of 1, 2, 3, 4, 5 and 10, also
knowing the corresponding roots
recognise the notation √25 and know that when a square root is asked for only the
positive value will be required; candidates are expected to know that a square root
can be negative
solve equations such as x² = 25, giving both the positive and negative roots
Apply index laws for multiplication and division of integer powers
G, F, E,
C
Confusing factors and multiples.
Multiplying numbers with a common factor
when attempting to find the LCM.
G, F, E,
C
Confusing factors and multiples.
Missing out 1 as a factor.
Forgetting whether it is the highest or lowest
common factor that needs to be found.
Thinking that 1 is a prime number.
E, D, C
Multiplying by 2 instead of squaring.
Writing 36 = –6 or 36 = ±6 when finding
the negative square root.
Maximum power of 10 will be 6. Candidates
should know that 1 million = 10^6
C
Multiplying or dividing powers instead of
adding and subtracting
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 10.1 – 10.3
AQA Modular GCSE Mathematics Foundation Tier
 Square roots P213, 215
 Powers P218
 Order of operations P232
 Factors P243
 Multiples P245
 Prime numbers P248
 More about squares, square roots, cubes and cube roots P298
 Products of prime factors P353
 Highest common factor P357
 Least common multiple P360
Foundation Practice Book 10.1 -10.3, 12.1 -12.4, 15.1, 19.1 – 19.3
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 2/Number /Teaching Resources
Lesson plans/worksheets/homework sheets
2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 2/Indices/Teaching Resources
Lesson plans/homeworksheet/powerpoints/spreadsheet/worksheet
Functional skills activities 12.3
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 9 Basic rules of Algebra
Time: 4 hours
N4.1 Distinguish the different roles played by letter symbols in algebra, using the correct notation.
N5.1 Manipulate algebraic expressions by collecting like terms, by multiplying a single term over a bracket, and by taking out common factors.
.
AQA
Mod
spec ref
N4.1,
N5.1
Learning objectives
Grade
Common mistakes and
misconceptions
Simplify algebraic expressions by collecting like terms
use notations and symbols correctly
understand that letter symbols represent definite unknown numbers in equations,
defined quantities or variables in formulae, and in functions they define new
expressions or quantities by referring to known quantities
Multiply together two simple algebraic expressions
understand that the transformation of algebraic expressions obeys and generalises
the rules of generalised arithmetic
write expressions using squares and cubes
Multiply terms in a bracket by a number outside the bracket
Multiply terms in a bracket by a term that includes a letter
E, F, G
Failing to comprehend that x = 1x.
Combining unlike terms.
x2 is not acceptable for 2x
E
Treating terms in m2 and in m as like
terms (e.g. simplifying 3m2 + m wrongly
to 4m2).
D
Forgetting to multiply the second term in
the bracket by the term outside (e.g.
expanding 2(x + 3) as 2x + 3), or
ignoring minus signs (e.g. writing 3(m –
2) as 3m + 6).
N5.1
Simplify expressions involving brackets
D, C
N5.1
Recognise factors of algebraic terms
Simplify algebraic expressions by taking out common factors
factorise algebraic expressions by taking out common factors
D
Forgetting to multiply the second term in
the bracket by the term outside.
Getting the wrong signs when
multiplying negative values.
Not realising that x is a factor of x and
x2.
Not taking out the highest common
factor.
N5.1
N5.1
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 11.1 – 11.5
AQA Modular GCSE Mathematics Foundation Tier
 Using letter symbols P390
 Simplifying expressions P401
 Expanding brackets and simplifying expressions P604
 Factorising simple expressions P610
Foundation Practice Book 22.1 -22.4, 33.2 -33.3
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 2/Basic Algebra/Teaching Resources
lesson plans/worksheets/homework sheet/problem sheet/powerpoint/flowchart
Functional skills activities
Closely related – N4.2 Distinguish in meaning between the words ‘equation’, ‘formula’, and ‘expression’.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 10 Fractions – non-calculator methods
Time: 6 hours
N1.2 Add, subtract, multiply and divide any number.
N1.3 Understand and use number operations and the relationships between them, including inverse operations and hierarchy of operations.
N1.5 Order rational numbers.
N2.1 Understand equivalent fractions, simplifying a fraction by cancelling all common factors.
N2.2 Add and subtract fractions.
N2.7 Calculate with fractions, decimals and percentages.
AQA
Mod
spec ref
N1.5,
N2.1
Learning objectives
Grade
Common mistakes and misconceptions
Compare fractions with different denominators
identify equivalent fractions
write a fraction in its simplest form
convert between mixed numbers and improper fractions
compare fractions
G, F, E, D
Multiplying the denominator but not the
numerator when finding equivalent
fractions.
N2.2
Add and subtract fractions when one denominator is a multiple of the other
Add and subtract fractions when both denominators have to be changed
E, D
N2.2
Add and subtract mixed numbers
C
N1.2
Multiply a fraction by a fraction
E
N2.7
D, C
N1.3
Multiply a whole number by a mixed number
Multiply a fraction by a mixed number
Multiply a mixed number by a mixed number
calculate a fraction of a quantity
work out one quantity as a fraction another quantity
use fractions to calculate proportions
Find the reciprocal of a whole number, a decimal or a fraction
Adding/subtracting the denominators as well as
the numerators.
Not converting to equivalent fractions to
make the denominators the same.
Incorrectly converting a mixed number to an
improper fraction.
Not converting the final answer back to a
mixed number.
Multiplying diagonally as though ‘cross2 5 12
multiplying’ is being done (e.g. 3 × 6 = 15).
Multiplying both the numerator and the
denominator by the whole number (e.g. 3 ×
5 15
6 = 18).
N1.2
Divide a whole number or a fraction by a fraction
D, C
C
Leaving denominators as decimal numbers.
Not simplifying answers when asked to do
so.
Finding the reciprocal of the wrong fraction,
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Divide mixed numbers or fractions by whole numbers
Divide mixed numbers by mixed numbers
Resources:
or finding the reciprocal of both fractions.
AQA GCSE Maths Middle sets Book Sections 12.1 – 12.7
AQA Modular GCSE Mathematics Foundation Tier
 Fraction of a quantity P258
 Expressing one quantity as a fraction of another P268
 Addition and subtraction of fractions P273
 Multiplication and division of a fraction P279
 Reciprocals P308
 Equivalent fractions P365
Foundation Practice Book 13.2, 14.1 -14.2, 15.4, 20.1
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 2/ /Teaching Resources
lesson plans & starters/worksheets/homework sheets/problem sheets/powerpoints/interactive activities
Functional skills activities 3.1, 3.3, 14.2, 14.4
Notes:
This is part of the core number work across all units.
Closely related N2.3 Use decimal notation and recognise that each terminating decimal is a fraction.
N2.4 Recognise that recurring decimals are exact fractions and that some exact fractions are recurring decimals.
N2.5 Understand that ‘percentage’ means ‘number of parts per 100’ and use this to compare proportions.
N2.6 Interpret fractions, decimals and percentages as operators.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 11 Decimals – non-calculator methods
Time: 3 hours
N1.1 Understand integers and place value to deal with arbitrarily large positive numbers.
N1.2 Add, subtract, multiply and divide any number.
N2.3 Use decimal notation and recognise that each terminating decimal is a fraction.
N2.4 Recognise that recurring decimals are exact fractions, and that some exact fractions are recurring decimals.
AQA
Mod
spec ref
N1.1,
N1.2
Learning objectives
Grade
Common mistakes and
misconceptions
Add and subtract decimal numbers
G, F, E
N2.3
N2.4
N1.2
Convert decimals to fractions using place value
Identify common recurring decimals
Multiply and divide decimal numbers, limited to multiplying or dividing by a single
digit integer or a decimal number to 1 significant figure
E, D
Not lining up the decimal points.
Not recording the ‘carry over’ and
forgetting to add it on.
Not reducing a number during an
exchange.
Working with the incorrect power of 10.
Not giving answers in the simplest form.
Working out the equivalent wholenumber multiplication but forgetting to
return to the decimal calculation at the
end.
D, C
Confusing multiplication with the rules
for addition, writing a long multiplication
with decimal points underneath each
other.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 13.1 – 13.3
AQA Modular GCSE Mathematics Foundation Tier
 Conversions of fractions, decimals and percentages P253
 Addition and subtraction of decimals P285
 Multiplication and division of decimals P288
Foundation Practice Book 14.3 – 14.4
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 2/Decimals/Teaching Resources
lesson plans/worksheets/homework sheets/powerpoints
Functional skills activities 3.4, 14.1, 14.2
Notes: This includes questions where the answer to one calculation can be used to work out the answer to a related calculation.
Closely related
N1.4
N1.5
N2.5
N2.6
N2.7
Approximate to a given power of 10, up to three decimal places and one significant figure.
Order rational numbers
Understand that ‘percentage’ means ‘number of parts per 100’ and use this to compare proportions.
Interpret fractions, decimals and percentages as operators.
Calculate with fractions, decimals and percentages as operators.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 12 Equations and Inequalities
Time: 6 hours
N5.4 Set up and solve simple linear equations.
N5.7 Solve linear inequalities in one variable and represent the solution set on a number line.
AQA Mod
spec ref
N5.4
Learning objectives
Grade
Common mistakes and misconceptions
Solve two-step equations like 2x – 1 = 11
By using inverse operations or by transforming both sides in the same way
E, D
N5.4
Write and solve equations
E, D
N5.4
Solve equations involving brackets
D, C
N5.4
Solve equations with an unknown on both sides (can also involve brackets)
D, C
N5.7
Solve linear inequalities in one variable and represent the solution set on a number
line
F, E. D
Not appreciating that an equation can be
written in different but equivalent formats
(e.g. 2a + 7 = 9 → 7 + 2a = 9 → 9 = 2a + 7).
Not following a question carefully when
writing an equation to represent a problem.
Forgetting to multiply the second term in the
bracket by the term outside.
Getting the wrong signs when 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.
Mix up the symbols > < > <
Mix up the open circle with the closed circle
Use an = sign instead of an inequality sign
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 14.1 – 14.4
AQA Modular GCSE Mathematics Foundation Tier
 Number machines P225
 Inverse number machines P228
 Solving by inspection and working backwards P426
 The balance method P430
 Linear equations P683
 Inequalities P690
Foundation Practice Book 11.2 -11.3, 24.1 -24.2, 37.1 -37.3
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 2/Equations and Inequalities /Teaching Resources
lesson plans & starters/worksheets/problem sheets/homework sheets/powerpoint
Functional skills activities 9.1 -9.2, 20.1 -20.3
Closely related - N4.2 Distinguish in meaning between the words ‘equation’, ‘formula’, and ‘expression’.
N5.9 Use algebra to support and construct arguments.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 13 Indices and Formulae
Time: 6 hours
N1.9 Index laws for multiplication and division of integer powers.
N4.2 Distinguish in meaning between the words ‘equation’, ‘formula’, and ‘expression’.
N5.6 Derive a formula, substitute numbers into a formula and change the subject of a formula.
AQA Mod
spec ref
N1.9
Learning objectives
Grade
Common mistakes and misconceptions
Use index notation in algebra
Use index notation when multiplying or dividing algebraic terms
G, F,
E, D, C
N1.9
Use index laws to multiply and divide powers in algebra
Raise a number or variable to the power of 1 or 0
Use index laws for raising a power to another power
Use algebra to write formulae in different situations. Distinguish in meaning the
words equation, formula, expression
Substitute numbers to work out the value of simple algebraic expressions
Substitute numbers into expressions involving brackets and powers
Change the subject of a formula
C
Not realising that x means x1, or that a
number divided by 1 equals the number
(e.g. 6 ÷ 1 = 6).
Confusing unit and zero powers (e.g. stating
that x means x 0, or that x 0 = 0).
Substitute numbers into a variety of formulae
use formulae from mathematics and other subjects expressed initially in words and
then using letters and symbols
E, D
N4.2
N4.2, N5.6
N4.2, N5.6
F, E, D
Not seeing the ‘general’ case.
E, D, C
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
1
Not realising that 10 means n ÷ 10, or that 2
1
× 6 means 2 of 6 = 3.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 15.1 – 15.5
AQA Modular GCSE Mathematics Foundation Tier
 Writing expressions and formulae P395
 Substitution P406
 Using formulae written in words P457
 Using a formulae written with letter symbols P463
 Indices P599
 Substituting into expressions and formulae P642
 Writing expressions, formulae and equations P647
 Changing the subject of the formula P652
Foundation Practice Book 26.1 -26.2, 33.1, 35.1 -35.3
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 2/Equations and inequalities/Teaching Resources
lesson plans & starters/worksheets/problem sheets/homework sheets
2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 2/Algebraic argument/Teaching Resources
lesson plans & plenaries/worksheets/problem sheets/homework sheets
Functional skills activities 9.1 -9.2, 201.-20.3
Notes: The core algebra work across all units is N4.2
At tier F, formulae to be rearranged will need at most two operations. Formulae where a power appears will not be tested at tier F.
Candidates should understand the words equation, formula, expression and term but their meaning will not be tested.
Questions in Unit 2 will include formulae for generating sequences; for example, write down the first three terms of a sequence where the nth term is given by
2n + 4 (see spec. reference N6.1). Questions in Unit 2 will include formulae in words using a functional context; for example, a formula for cooking a turkey.
Questions may include formulae out of context; for example, substitute positive and negative numbers into expressions such as, 3(2 – 3y), 3x2 and 2x3
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 14 Percentages – non-calculator methods
Time: 4 hours
N2.5 Understand that ‘percentage’ means ‘number of parts per 100’ and use this to compare proportions.
N2.7 Calculate with fractions, decimals and percentages.
AQA Mod
spec ref
N2.7
Learning objectives
Grade
Common mistakes and misconceptions
Calculate a percentage increase or decrease
Candidates should be able to calculate 1% or 10% of quantities as a starting point
E, D
N2.5, N2.7
Perform calculations involving VAT
Perform calculations involving credit
Perform simple interest calculations
Understand that percentage means number of parts per hundred and use this to
compare proportions
Calculate a percentage profit or loss
G,F,E,
D
Giving the actual increase/decrease as the
answer when the amount after the
increase/decrease is what is required.
Using the multiplier as 1.5 rather than 1.05
for an increase of 5%.
Writing ‘=’ between quantities that are not
equal, because the ‘=’ sign is used as a
shorthand for ‘then I do this’.
Not seeing that 17.5% = 10% + 5% + 2.5%.
Forgetting to add on the initial deposit in
credit calculations.
C
Confusing cost price and selling price.
calculate a percentage of a quantity
solve percentage increase and decrease problems
use, for example, 1.12 x Q to calculate a 12% increase in the value of Q and 0.88 x
Q to calculate a 12% decrease in the value of Q
work out one quantity as a percentage of another quantity
use percentages to calculate proportions
C
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%.
N2.7
N2.7
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 16.1 – 16.4
AQA Modular GCSE Mathematics Foundation Tier
 Percentage of a quantity P261
 Expressing one quantity as a percentage of another P314
 Increasing and decreasing by a percentage P318
 Finding a percentage change P321
 Percentages in real life P324
Foundation Practice Book 13.1, 13.3, 13.4, 16.1 -16.4
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 2/Percentages /Teaching Resources
lesson plans/matching cards/worksheets/homework sheets/powerpoint
Functional skills activities 3.2, 14.2 – 14.3
Notes:
Percentages 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. Candidates will not be required to calculate repeated percentage change or compound interest in this unit. These are
assessed in Unit 1 only. Candidates should be able to interpret percentage problems using a multiplier.
Closely related - N2.6 Interpret fractions, decimals and percentages as operators.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 15 Sequences and Proof
Time: 6 hours
N5.9 Use algebra to support and construct arguments.
N6.1 Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence.
N6.2 Use linear expressions to describe the nth term of an arithmetic sequence.
AQA Mod
spec ref
N6.1
Learning objectives
Grade
Common mistakes and misconceptions
Find the next term in a sequence
Describe the rule for continuing a sequence
Generate common integer sequences, including sequences of odd or even integers,
squared integers, powers of 2, powers of 10 and triangular numbers
Find any term of a sequence given a formula for the nth term
Find the nth term of a linear sequence using the common difference
Use the nth term to find terms in a sequence
G, F,
E, D
Expecting all sequences to have common
differences.
Looking at the first two numbers and
assuming that the rest follow this pattern.
Mistaking x2 for 2x.
N6.2
Find the next few terms in a sequence of patterns
Find the nth term for a sequence of diagrams
Generate simple sequences derived from diagrams and complete a table of results
describing the pattern shown by the diagrams
G, F,
E, D, C
N6.1
Find the first few terms of a quadratic sequence by using the nth term
Find the next few terms of a quadratic sequence by looking at differences
Find the nth term of a simple quadratic sequence e.g n² + 4
C
Show step-by-step deduction when proving results
Use algebraic expressions to support an argument or verify a statement
Show something is false by using a counter-example
C
N6.2
N6.2
N6.1
N5.9
N5.9
E, C
C
C
E, D
Not comprehending that when finding the
50th term it is not necessary to find all the
terms up to that term.
Not writing down the sequence and trying to
do it all mentally.
Not making the connection between the
structure of the physical pattern and the
form the nth term takes.
Mistaking x2 for 2x.
Thinking that (3x)2 = 3x2.
Not checking whether the derived quadratic
rule works.
Not appreciating that a proof shows
something works for all values.
Assuming that ‘number’ means positive
whole number.
Not identifying an appropriate counterexample.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 17.1 – 17.8
AQA Modular GCSE Mathematics Foundation Tier
 Continuing and completing sequences P483
 Sequences from patterns of shapes P490
 Generating sequences using nth term rules P724
 Finding the nth term of a sequence P731
Foundation Practice Book 28.1 -28.2, 39.1 - 39.2
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 2/Sequences/Teaching Resources
lesson plans /problem sheets/homework sheets/worksheets/powerpoints
2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 2/Formulae and Algebraic Argument/Teaching Resources
lesson plans and plenaries/problem sheets/homework sheets/worksheets
Functional skills activities
Notes: Candidates should be able to describe how a sequence continues and will need to be familiar with the idea of a non-linear sequence, such as the
triangular numbers or a sequence where the nth term is given by n2 + 4. Candidates should know that the nth term of the square number sequence is given by
n2.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 16 Linear Graphs
Time: 7 hours
N6.3 Use the conventions for coordinates in the plane and plot points in all four quadrants, including using geometric information.
N6.4 Recognise and plot equations that correspond to straight-line graphs in the coordinate plane, including finding their gradients.
N6.11 Construct linear functions from real-life problems and plot their corresponding graphs.
N6.12 Discuss, plot and interpret graphs (which may be non-linear) modelling real situations.
AQA Mod
spec ref
N6.3
N6.3
N6.4
N6.11
N6.11,
N6.12
Learning objectives
Grade
Common mistakes and misconceptions
Use the conventions for coordinates in the plane and plot points in all four quadrants,
using geometric information
Find the mid-point of a line segment
G,F
Transpose coordinates
D, C
Recognise straight-line graphs parallel to the x- or y-axis
Work out coordinates of points of intersection when two graphs cross
Plot graphs of linear functions
recognise that equations of the form y = mx + c correspond to straight line graphs in
the coordinate plane
plot graphs of functions in which y is given explicitly in terms of x or implicitly
complete partially completed tables of values for straight line graphs
calculate the gradient of a given straight line using the y-step/x-step method
Plot a graph representing a real-life problem from information given in words or in a
table or as a formula
identify the correct equation of a real-life graph from a drawing of the graph
read from graphs representing real-life situations; for example, the cost of a bill for so
many units of gas or working out the number of units for a given cost, and also
understand that the intercept of such a graph represents the fixed charge
Draw, read and interpret distance–time graphs
Construct linear functions from real-life problems and plot their corresponding graphs
Discuss, plot and interpret real-life graphs modelling real situations
draw linear graphs with or without a table of values
interpret linear graphs representing real-life situations; for example, graphs
representing financial situations (e.g. gas, electricity, water, mobile phone bills,
council tax) with or without fixed charges, and also understand that the intercept
represents the fixed charge or deposit
F, E, D,
C
Subtracting the coordinates (instead of
calculating an average) when finding the
mid-point.
Incorrectly calibrating the coordinate axes.
Not using a third point as a check when
drawing a straight line.
E
Inaccurately reading from one value on a
graph to find another value.
E, D, C
Drawing and labelling axes before working
out the axes range appropriate to the
problem.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 18.1 – 18.5
AQA Modular GCSE Mathematics Foundation Tier
 Patterns of coordinates P502
 Drawing straight line graphs P511
 Conversion graphs and other real-life graphs P553
 Distance-time graphs P562
 More real-life graphs P572
 Linear graphs P741
Foundation Practice Book 29.1, 29.2, 31.1 -31.3, 40.1
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 2/Coordinates and graphs/Teaching Resources
lesson plans/worksheets/problem sheets/homework sheets/powerpoints
Functional skills activities
Notes: Tier F students will not be expected to plot graphs using the gradient-intercept method.
In unit 2 candidates will be required to identify points with given coordinates and identify coordinates of given points.
In unit 2 candidates will be expected to use graphs that model real situations where a calculator is not required.
In unit 2 candidates will not be expected to answer questions related to shapes and other geometrical applications. This will be assessed in unit 3.
Foundation tier candidates will not be expected to know that m represents gradient and c represents the y-intercept.
Candidates should note that distance-time graphs will be assessed in Unit 2 only.
Conversion graphs and non-linear graphs will be assessed in Unit 3.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 17 Ratio and proportion – non-calculator methods
Time: 4 hours
N3.1 Use ratio notation, including reduction to its simplest form and its various links to fraction notation.
N3.2 Divide a quantity in a given ratio
N3.3 Solve problems involving ratio and proportion, including the unitary method of solution.
AQA Mod
spec ref
N3.2
N3.1
N3.1, N3.3
N3.3
N3.3
N3.3
N3.3
Learning objectives
Grade
Common mistakes and misconceptions
Divide a quantity in a given ratio
Revise from Unit 1
Understand the meaning of ratio notation
Simplify a ratio to its lowest terms a:b where a and b integers
Use a ratio in practical situations
Revise from Unit 1
Write a ratio as a fraction
Use a ratio to find one quantity when the other is known
Use a ratio and proportion to solve statistical and number problems
D,C
G, F,
E, D
Assuming shares will be fair
Swapping over the numbers in the ratio
(e.g. 2 : 5 becomes 5 : 2).
Simplifying ratios without ensuring the
quantities are in the same units.
Turning a ratio into a fraction (e.g. the ratio
4
4 : 5 becomes 5).
Failing to find the value of the unit fraction in
more complex problems.
Revise from Unit 1
Write a ratio in the form 1 : n or n : 1
Revise from Unit 1
Solve word problems involving ratio
C
Revise from Unit 1
Understand direct proportion
Solve proportion problems, including using the unitary method
Revise from Unit 1
Work out which product is the better buy
D
E, D, C
C
D
Ignoring different units in a ratio (e.g.
simplifying 2 days : 15 hours to 1 : 7½) .
Not multiplying both sides of the ratio by the
same number.
Giving an answer without considering the
context.
Not always seeing the relationships
between numbers (e.g. if the cost of 4 items
is given, and the price of 8 is asked for).
Not making the units the same for each
item.
Comparing unlike unit rates (e.g. price per
gram for one item but amount for 1p for the
other).
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 7.1 to 7.8 (7.8 higher)
AQA Modular GCSE Mathematics Foundation Tier
 Ratio P331
 Proportion and best value P336
Foundation Practice Book 17.1, 17.2
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 1/Ratio/Teaching Resources
lesson plans & starters/sorting activity/problem sheets/homework sheets
Functional skills activities 4.1, 4.2, 15.1 – 15.3
Notes: This is part of the core number work required across all units. Division in a given ratio is only tested in Unit 2.
Candidates should be able to use informal strategies, use the unitary method of solution, multiply by a fraction or other valid method.