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AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Higher Tier – Unit 1
OVERVIEW for Higher Tier
1 hour calculator exam
54 marks – 26.7%
20 -30% Functional Elements
14 marks Number, 40 marks Statistics
ALL FOUNDATION TOPICS ARE SUBSUMED INTO HIGHER
Topic
Y10 AUTUMN TERM
Y9
SUMMER
TERM
1. Data collection
Teaching
hours
4
2. Interpreting and
representing data
10
3. Range and
averages
4. Probability
4
5. Fractions,
decimals and
percentages
6. Ratio and
proportion
7. Indices and
Standard Form
12
AQA Modular specification reference
The Data Handling Cycle: S1
Data Collection: S2.1, S2.2, S2.3, S2.4, S2.5
Data presentation and analysis: S3.1
Data presentation and analysis: S3.2, S3.2h, S3.3h
Data Interpretation: S4.2, S4.3, S4.4
6
Data presentation and analysis: S3.3, S3.3h
Data Interpretation: S4.1
Data presentation and analysis: S3.1
Probability: S5.1, S5.2, S5.3, S5.4, S5.5h, S5.6h S5.7, S5.8,
S5.9
Working with numbers and the number system: N1.13h, N1.14
Fractions, Decimals and Percentages: N1.4h, N2.1, N2.5,N2.6,
N2.7, N2.7h
Ratio and Proportion: N3.1, N3.3, N3.3h
6
Working with numbers and the number system: N1.10h
7
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 1 Data collection
Time: 4 hours
SEE FOUNDATION SCHEME OF WORK
S1 Understand and use the statistical problem solving process which involves

specifying the problem and planning

collecting data

processing and presenting the data

interpreting and discussing the results.
S2.1 Types of data: qualitative, discrete, continuous. Use of grouped and ungrouped data.
S2.2 Identify possible sources of bias.
S2.3 Design an experiment or survey.
S2.4 Design data collection sheets distinguishing between different types of data.
S2.5 Extract data from printed tables and lists.
S3.1 Design and use two-way tables for grouped and ungrouped data.
ADDITIONAL HIGHER CONTENT
None
Resources:
AQA GCSE Maths Middle sets Book Sections 1.1 to 1.8, 5.3
AQA GCSE Mathematics Higher Tier
 Primary and secondary data P388
 Collection of data P389
 Databases P390
 Questionnaires P392
 Hypothesis P392
 Two way tables P393
 Sampling methods P395
Higher Practice Book sections 3.1 – 3.3, 9.1 – 9.2
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 1/Collecting Data/Teaching Resources
Lesson plans/starters/handouts/worksheets/homework sheets
2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 1/Representing Data/Teaching Resources
Two way tables /worksheet/homework sheet
Functional skills activities 2.1, 13.1
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Notes:
Questions may be set that require candidates to go through the stages of the Data Handling cycle without individual prompts
Questions may explicitly test knowledge of the words discrete, continuous, qualitative, grouped etc but it is recognition of the type of data that will be more
important – e.g. ‘Draw a suitable diagram for the data’. An understanding of the terms ‘primary data’ and ‘secondary data’ is expected.
Causes of bias will be clear for candidates to identify.
Real data may be used in examination questions. Including knowing and using the term ‘hypothesis’ for a general prediction which is to be tested.
Higher tier candidates will be expected to choose suitable sampling methods, discuss bias, provide sophisticated and rigorous interpretations of their data
and provide an analysis of how significant their findings are.
Closely related -
N6.12 Discuss, plot and interpret graphs (which may be non-linear) modelling real situations
S5.9 Understand that increasing sample size generally leads to better estimates of probability and population
characteristics
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 2 Interpreting and representing data
SEE FOUNDATION SCHEME OF WORK
Time: 10 hours
S3.2 Produce charts and diagrams for various data types. Scatter graphs, stem-and-leaf, tally charts, pictograms, bar charts, dual bar charts, pie charts, line
graphs, frequency polygons, histograms with equal class intervals.
S4.2 Look at data to find patterns and exceptions.
S4.3 Recognise correlation and draw and/or use lines of best fit by eye, understanding what they represent.
ADDITIONAL HIGHER CONTENT
Produce charts and diagrams for various data types. Histograms with equal or unequal intervals. Cumulative frequency graphs will only be for
continuous data and may be curves or polygons.
S3.3h Calculate quartiles and interquartile range
S4.4
Compare distributions and make inferences
S3.2h
AQA
Mod
spec
ref
S3.2h,
S3.3h
S3.2h
Learning objectives
Grade
Common mistakes and misconceptions
Compile a cumulative frequency table and draw cumulative frequency diagrams
Use cumulative frequency diagrams to analyse data
Draw a box plot from a cumulative frequency diagram
Understand and produce relative frequency diagrams (probability)
B
Mis-reading the graph axes scales.
Inaccurately summing the frequencies.
Mis-reading the medians and quartiles.
Drawing the lower end of the box plot at zero,
rather than at the bottom of the lowest class.
S3.2h
S3.2h,
S4.4
Produce a histogram with unequal intervals. Calculate frequency density.
Use cumulative frequency diagrams and box plots to compare data and draw
conclusions
A
B
S3.3h
calculate quartiles and inter-quartile range from a small data set using the positions
of the lower quartile and upper quartile respectively and calculate inter-quartile range
read off lower quartile, median and upper quartile from a cumulative frequency
diagram or a box plot
find an estimate of the median or other information from a histogram
choose an appropriate measure according to the nature of the data to be the
‘average’
Understand which of the diagrams are appropriate for different types of data
S3.2h
B
Inaccurately plotting cumulative frequency
diagrams and box plots.
Not appreciating the need for a coherent
written analysis of diagrams.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
S4.4
S4.2
N6.12
4.1
compare two diagrams in order to make decisions about an hypothesis
compare two distributions in order to make decisions about an hypothesis by
comparing the range, or the inter-quartile range if available, and a suitable measure
of average such as the mean or median.
find patterns in data that may lead to a conclusion being drawn
look for unusual data values such as a value that does not fit an otherwise good
correlation
Interpret or obtain information from any of the statistical graphs described in S3.2 &
S3.2h and draw conclusions
Resources:
AQA GCSE Maths Middle sets Book Sections 3.1 to 3.6, 6.1 to 6.3
AQA GCSE Mathematics Higher Tier
 Bar charts, Pie charts P408
 Stem and leaf diagrams P409
 Scattergraphs, correlation, line of best fit P411
 Frequency diagrams, histograms (equal class widths) P420
 Frequency polygons P421
 Histograms (unequal class widths) P423
 Cumulative frequency tables, graphs P430
 Comparing distributions P435
 Box plots P437
Higher Practice Book 1.1 -1.3, 5.1 – 5.2, 8.1 -8.2
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 1/Representing Data/Teaching Resources
Histogram lesson plans/worksheets/homework sheets/powerpoints
2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 1/Scattergraphs/Teaching Resources
Scattergraphs lesson plans/homeworksheet/powerpoint
Functional skills activities 2.2, 2.3, 2.4, 5.1, 13.1, 13.2, 13.3, 16.1, 16.2, 16.3
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Notes:
Candidates may be asked to draw a suitable diagram for data. An understanding of the type and nature of the data is expected from the candidate in order to
make a choice. Axes and scales may or may not be given.
In large data sets on a cumulative frequency diagram, the position of the lower quartile will be accepted as n/4 or,(n + 1)/4 the position of the median will be
accepted as n/2 or (n + 1)/2 and the position of the upper quartile will be accepted as 3n/4 or 3(n+1)/4
Though the words interpolation and extrapolation will not be used in the examination, the idea that finding estimates outside of the data range is less reliable
than finding estimates from within the data range is expected to be understood by candidates.
A formal treatment of outliers, for example in box plots, will not be tested.
Though the words interpolation and extrapolation will not be used in the examination, the idea that finding estimates outside of the data range is less reliable
than finding estimates from within the data range is expected to be understood by candidates.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 3 Range and averages
SEE FOUNDATION SCHEME OF WORK
Time: 4 hours
S3.3 Calculate median, mean, range, mode and modal class.
S4.1 Interpret a wide range of graphs and diagrams and draw conclusions
ADDITIONAL HIGHER CONTENT
S.3.3h Calculate quartiles and interquartile range.
AQA
Mod
spec ref
S3.3h
Learning objectives
Grade
calculate quartiles and inter-quartile range from a small data set using the positions
of the lower quartile and upper quartile respectively and calculate inter-quartile range
read off lower quartile, median and upper quartile from a cumulative frequency
diagram or a box plot
find an estimate of the median or other information from a histogram
choose an appropriate measure according to the nature of the data to be the
‘average’
B/A
Common mistakes and
misconceptions
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 4.1 to 4.5
AQA GCSE Mathematics Higher Tier
 Range, types of average P399
 Frequency distributions, calculating averages from diagrams P400
 Grouped frequency distributions P402
 Comparing distributions P403
 Which is the best average to use? P405
Higher Practice Book 4.1 – 4.4, 6.1
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 1/Statistical measures/Teaching Resources
lesson plans/worksheets/homework sheet/problem sheet
Functional skills activities 6.1, 6.2, 17.1 – 17.3
Notes:
Candidates may be asked to draw a suitable diagram for data. An understanding of the type and nature of the data is expected from the candidate in order to
make a choice. Axes and scales may or may not be given.
Closely related –
N6.12 Discuss, plot and interpret graphs (which may be non-linear) modelling real situations
S4.4 Compare distributions and make inferences - average and interquartile range at Tier H
S3.2 Produce charts and diagrams for various data types
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 4 Probability
SEE FOUNDATION SCHEME OF WORK
Time: 7 hours
S5.1 Understand and use the vocabulary of probability and the probability scale.
S5.2 Understand and use estimates or measures of probability from theoretical models (including equally likely outcomes), or from relative frequency.
S5.3 List all outcomes for single events, and for two successive events, in a systematic way and derive related probabilities.
S5.4 Identify different mutually exclusive outcomes and know that the sum of the probabilities of all these outcomes is 1.
S5.7 Compare experimental data and theoretical probabilities.
S5.8 Understand that if an experiment is repeated, this may – and usually will – result in different outcomes.
S5.9 Understand that increasing sample size generally leads to better estimates of probability and population characteristics.
ADDITIONAL HIGHER CONTENT
S5.5h Know when to add or multiply two probabilities: if A and B are mutually exclusive, then the probability of A or B occurring is P(A) + P(B), whereas if A
and B are independent events, the probability of A and B occurring is P(A) × P(B)
S5.6h Use tree diagrams to represent outcomes of compound events, recognising when events are independent.
AQA
Mod
spec ref
S5.5h
Learning objectives
Grade
determine when it is appropriate to add probabilities
determine when it is appropriate to multiply probabilities
understand the meaning of independence for events
understand conditional probability
understand the implications of with or without replacement problems for the
probabilities obtained
B/A
5.6h
complete a tree diagram to show outcomes and probabilities
use a tree diagram as a method for calculating probabilities for independent or conditional
events.
B/A
Common mistakes and misconceptions
Adding probabilities along the branch rather
than multiplying.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 5.1 to 5.7
AQA Modular GCSE Mathematics Higher Tier
 Probability scale P442
 Equally likely outcomes P443
 Estimating probabilities using relative frequency P445
 Mutually exclusive events, probability of an event not happening P448
 Combining two events P450
 Independent events, using tree diagrams P453
 Conditional probability P457
Higher Practice Book 2.1 – 2.3, 7.1 – 7.3
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 1/Probability/Teaching Resources
lesson plans & starters/worksheets/homework sheets/problem sheets/plenary
Functional skills activities 7.1, 7.2, 18.1, 18.2
Notes:
The words candidates should be familiar with will be limited to impossible, (very) unlikely, evens or even chance, (very) likely and certain.
Candidates should not use word forms or ratio for numerical probabilities such as 1 out of 2 or 1 : 2.
Situations will be familiar, such as dice or bags containing numbered counters.
Probabilities and relative frequencies should be written using fractions, decimals or percentages. Cancelling a fraction to its simplest form may be required.
If not directed, listing can be done using lists, tables or sample space diagrams.
The term sample space will not be tested.
The term mutually exclusive will not be tested though the principle will.
Templates may or not be given to candidates.
Some of the probabilities may or may not already be on a tree diagram.
Tree diagrams will be for two or three successive or independent events with two or three branches per event
Closely related
S3.1 Design and use two-way tables for grouped and ungrouped data.
S3.2h Read, interpret and produce relative frequency diagrams
Work from N2.1 may be assessed with this specification reference.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 5 Fractions, decimals and percentages
SEE FOUNDATION SCHEME OF WORK
Time: 12 hours
N1.14 Use calculators effectively and efficiently, including statistical functions.
N2.1 Understand equivalent fractions, simplify by cancelling all common factors
N2.5 Understand that percentage means parts per hundred and use this to compare proportions
N2.6 Interpret fractions, decimals and percentages as operators.
N2.7 Calculate with fractions, decimals and percentages.
ADDITIONAL HIGHER CONTENT
N1.4h Approximate to specified or appropriate degrees of accuracy, including a given number of decimal places and significant figures.
N1.13h Calculate and use upper and lower bounds.
N2.7h Calculate with fractions, decimals and percentages including reverse percentage calculations.
AQA
Mod
spec ref
N1.3
N1.4h
N1.3h
Learning objectives
Grade
add, subtract, multiply and divide using commutative, associative and distributive
laws
understand and use inverse operations
use brackets and the hierarchy of operations
round numbers to the nearest 10, 100, 1000 or million
round to the nearest whole number
round to a given number decimal places
round to a given number of significant figures
choose an appropriate degree of accuracy to round to based on the figures in the
question
write down the maximum or minimum figure for a value rounded to a given accuracy
combine upper or lower bounds appropriately to achieve an overall maximum or
minimum for a situation
work with practical problems involving bounds including in statistics, e.g. finding the
midpoint of a class interval such as 10< x < 20 in order to estimate a mean
C/B
use a calculator for calculations involving four rules
use a calculator for checking answers
B
Common mistakes and
misconceptions
B
B
Questions will be set in context and
could be linked to statistical problems
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
N2.1
N2.7h
enter complex calculations, for example, to estimate the mean of a grouped
frequency distribution
enter a range of calculations including those involving money and
statistical measures
understand and use functions including, +, - , x ,÷ , x², x³, x ⁿ, √x, ³√x, memory,
brackets
understand the calculator display, knowing how to interpret the display, when the
display has been rounded by the calculator and not to round during the intermediate
steps of calculation
interpret the display, for example for money interpret 3.6 as £3.60
identify equivalent fractions
simplify a fraction by cancelling all common factors using a calculator where
appropriate. For example, simplifying fractions that represent probabilities.
calculate with decimals
calculate with compound interest in problems
calculate reverse percentages
Resources:
B
B/A
AQA GCSE Maths Middle sets Book Sections 2.1 to 2.7, 8.1 to 8.2
AQA Modular GCSE Mathematics Higher Tier
 Order of operations P4
 Using a calculator P6
 Decimals P8
 Numerical calculations with a calculator P11
 Fractions on a calculator P17
 Approximation, rounding P20-24
 Percentages, fractions, decimals P28
 Expressing one quantity as a percentage of another P29
 Finding a percentage of a quantity, percentage change P30
 Percentage increase P31
 Reverse percentage problems P33
 Wages, income tax, spending, best buys, household bills, VAT, savings P34 – 38
 Simple and compound interest P39
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Higher Practice Book 10.3 – 10.5, 11.1 – 11.4, 14.1, 19.1 -19.3, 20.1 – 20.3
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/HigherTier/Unit 1/Fractions and Decimals/Teaching Resources
lesson plans/worksheets/homework sheets/target boards
2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 1/Percentages/Teaching Resources
Lesson plans/powerpoints/homework sheets/activity sheet/problem sheet
Functional skills activities 3.1 – 3.4, 14.1 -14.4
Notes: This is part of the core number work required across all units. The term common denominator will not be used. Candidates should be able to
interpret percentage problems using a multiplier.
For example, the maximum value of a – b is obtained from use of the maximum value for a and the minimum value for b.
Upper bounds do not necessarily require the use of recurring decimals. For example if the answer to the integer is 7, the maximum could be given as
7.5, 7.49... or 7.49•
If this value of 7 represented £7, £7.49 would be expected for the maximum.
Closely related
N1.3 Understand and use number operations and the relationships between them, including inverse operations and the hierarchy of
operations
N1.4 Approximate to a given power of 10 (nearest 10,100, 1000), up to 3 decimal places and 1 significant figure
The core number work will be assessed so that it is linked to other specification references within that unit, for example rounding a
value obtained for the mean of a frequency distribution.
N1.14 Use a calculator effectively and efficiently, including statistical functions
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 6 Ratio and proportion
Time: 6 hours
SEE FOUNDATION SCHEME OF WORK
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.
ADDITIONAL HIGHER CONTENT
N3.3h Solve problems involving ratio and proportion, including the unitary method of solution and repeated proportional change .
AQA Mod
spec ref
N3.1
N3.3h
Resources:
Learning objectives
Grade
interpret ratio as a fraction
Ratio may be linked to probability; for example, candidates should know that if, say,
red balls and blue balls are in the ratio 3 : 4 in a bag then the probability of randomly
obtaining a red ball is 3/7.
use ratio and proportion to solve statistical and number problems
solve problems involving repeated proportional change
Candidates may use the unitary method, scaling, multiplying by a fraction or any
other valid method.
B
Common mistakes and misconceptions
B/A
AQA GCSE Maths Middle sets Book Sections 7.1 to 7.8 (7.8 higher)
AQA Modular GCSE Mathematics Higher Tier
 Ratio P43
 Proportion – direct and inverse P46
 Direct proportion P114
 Inverse proportion P117
Higher Practice Book 13.1 - 13.2, 21.1 – 21.2
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 1/Ratio/Teaching Resources
lesson plans/worksheets/problem sheets/homework sheets/powerpoints
Functional skills activities 4.1, 4.2, 15.1 – 15.3
Notes: This is part of the core number work required across all units. Ratio may be linked to a probability. Division in a given ratio is only tested in Unit 2.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 7 Indices & Standard Form
Time: 6 hours
N1.10h Interpret, order and calculate numbers written in standard index form.
AQA Mod
spec ref
N1.10h
Resources:
Learning objectives
Grade
understand and use functions including, +, - , x ,÷ , x², x³, x ⁿ, √x, ³√x, memory,
brackets
convert an ordinary number into standard form
convert a standard form number into ordinary form
order and calculate with numbers in standard form
interpret standard form on a calculator
use a calculator effectively for standard form calculations
A/A*
Common mistakes and misconceptions
AQA GCSE Maths Middle sets Book Sections 8.3, 10.3 – 10.6
AQA Modular GCSE Mathematics Higher Tier
 Index notation P49
 Square and cube numbers P51
 Using a calculator P52
 Multiplying and dividing numbers with powers, rules of indices P53
 Standard Form P60 - 65
Higher Practice Book 10.2, 17.1 – 17.2,
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 1/Indices and Standard Form/Teaching Resources
lesson plans/worksheets/homework sheets/powerpoints
Functional skills activities 4.1, 4.2, 15.1 – 15.3
Notes: The term standard form will be used in the examination.