2011-2013 SOW Maths and Statistics
Statistics
Content/
Prior
knowledge/
Time allowed
Learning objectives
Differentiation
and extension
Resource
Exemplar resources
NOTES
Module 1: 1b
 Recognise that data can be obtained from primary
and secondary sources.
 Recognise the difference between quantitative and
qualitative variables.
 Recognise the difference between discrete and
continuous data.
 Recognise and use scales of measurementcategorical, rank.
 Categorise data through the use of well-defined,
precise definitions or class boundaries.
 Appreciate the implication of grouping for loss of
accuracy in presentations.
 Understand, use and define situations for grouped
and ungrouped data.
 Understand the meaning of bi-variate data which
may be discrete, continuous, grouped or ungrouped.
 Use other scales for
data, eg ordinal scale,
ratio scale.
 Make a list of possible
pairs of bi-variate
data, eg height v
weight.
 Categories are range of
variables from a
variety of everyday
contexts.
Statistics Book
Chapter 1
 Written testing to assess knowledge of content.

Understand the meaning of the term population.
Discuss the size of the
sample needed for
particular sampling
procedures.
Discuss the feasibility of
taking a census in large
populations.
Statistics
Book Chapter
1
Written testing to assess knowledge of content.
PRIOR KNOWLEDGE
GCSE Mathematics
Higher Module 1Collecting data
TIME ALLOWED: 1 HR
Module 2: 1c
Population sampling
PRIOR KNOWLEDGE
GCSE Statistics
Higher Module 1Types of data
Time allowed: 1-2
hrs
Understand the word census with regard to small
scale and large scale populations.
Understand the reasons for sampling and that sample
data is used to estimate values in a population.
Understand the terms random, randomness and
random sample.
Understand the use of random numbers.
Understand, design and use a sampling frame.
Be able to select a random sample or stratified
sample by one (and more than one) category as a
method of investigating a population.
Appreciate how bias in a sampling procedure might
occur and how it might be minimised.
Understand and use systematic, quota and cluster
sampling.
Understand the strengths and weaknesses of various
sampling methods, including bias, influences and
convenience.
 Plan and collect data for coursework.
 Primary sources should include raw data, surveys,
questionnaires (which may have more than two
categories), investigations and experiments.
 Secondary sources include databases, published
statistics, newspapers, internet pages, etc.
 The use of terms such as class width and class
interval is expected.
 Plotting and interpreting points in a 2D frame
work is expected.
 Aspects of this module will be enhanced by
practical applications of the theory.
Plan and collect data for coursework.
Random numbers may be collected from random
number tables, calculators and spreadsheets.
An appreciation of an appropriate sample size is
expected.
Designing a sample frame is expected.
Understanding of the National Census is expected.
Understand the types of question used for a census
and how the collected data is used.
SMSC - Consider the
National Census
2011-2013 SOW Maths and Statistics
Content/
Prior
knowledge/
Time allowed
Learning objectives
Differentiation
and extension
Resource
Exemplar resources
NOTES
Module 3 1d
Collecting
data/primary data
Collect or obtain data using a variety of methods (see
notes).
Obtain primary data by questionnaires and
experiments or simulations.
Understand the effects of accuracy on measurements.
Understand the advantages and disadvantages of
using interviews versus questionnaires.
Design and use effective data capture sheets and
methods of recording data.
Understand the role, and use of pilot studies and pretesting.
Understand and account for the problems of design,
ambiguity of wording, leading questions, definitions
and obtaining truthful responses with simplest form
of random response in sensitive cases.
Understand the advantages and disadvantages of open
and closed questions.
Be aware of the problems related to identifying the
appropriate population, the distribution and
collection of surveys, errors in recorded answers,
non-response and missing data.
Design simple statistical experiments to obtain data.
Understand the need for identification of the
variables to be investigated and the meaning of
explanatory and response variables.
Investigate the collection
of primary data in the
real world, eg tax
return, passport
application, National
Census.
Investigate how the
manner of an interview
could affect the outcome
(eg, students role-play
interviews).
Investigate a leading
question – to what
extent does it affect the
response?
Investigate psychometric
testing.
Statistics
Book Chapter
1
Written testing to assess knowledge of content.
SMSC – Examine data
from the government
website
(www.statistics.gov.uk)
 Identify appropriate sources of secondary data.
 Investigate the
reliability of data
collected from
different sources, eg
the internet, news
papers, etc.
 Compare the data
collected from
different sources, eg
sporting statistics,
historic dates, etc.
 Investigate the misuse
of quoted statistics in
the media.
Statistics Book
Chapter 1
 Written testing to assess knowledge of content.
PRIOR KNOWLEDGE:
GCSE Statistics
Higher Module 2Population and
sampling
Time allowed: 2-3
hrs
Module 4: 1d
Collecting
data/secondary data
PRIOR KNOWLEDGE:
GCSE Mathematics
Higher Module 1Collecting data
GCSE Statistics Higher
Module 3- Collecting
primary data
TIME ALLOWED:1-2
HRS
 Extract data from secondary sources, including those
based on ICT.
 Understand the aspects of accuracy, reliability,
relevance and bias as related to secondary data.
 Understand surveys and the appropriateness of the
conditions.
Plan and collect data for coursework.
Data collection to include: surveys, experiments
(including controlled experiments), counting, data
logging, convenience sampling, questionnaires and
measurement.
Measurement of data to include an appreciation
that the measurement of continuous variables such
as time and length is subject to some error.
The minimisation of ambiguity and bias is
expected.
Students should be able to comment on the design
of simple experiments, eg the use of controls.
 Plan and collect data for coursework.
 Questioning the reliability of secondary data will
be expected.
 Appropriate sources of secondary data to include:
newspapers; Office of National Statistics;
internet, etc.
 SMSC – Examine data
from the government
website
(www.statistics.gov.uk
)
2011-2013 SOW Maths and Statistics
Content/
Prior
knowledge/
Time allowed
Learning objectives
Differentiation
and extension
Resource
Exemplar resources
NOTES
Module 5: 2a
Tabulation
 Construct frequency tables by tallying raw data were
appropriate, including open- ended class intervals
and classes of varying width.
 Tabulate using class intervals for discrete and
continuous data.
 Tabulate using various forms of grouping the data,
including qualitative or quantitative categories.
 Combine categories to simplify tables with an
understanding of the problems of over simplification,
the effects on readability, the identification or
masking of trends and the loss of detail.
 Problems associated with under and over
simplification through inappropriate number of
significant figures or an unsuitable group size.
 Read and interpret data presented in tabular or
graphical form.
 Design suitable tables, including summary tables and
two-way tables.
 Further examples of
tables to collect
and/or summarise
information in the real
world.
 Compare different
methods of tabulating
data for ease of use.
 Tabulate data with
two or more
characteristics, eg
choropleth tables.
Statistics Book
Chapter 2
 Written testing to assess knowledge of content.
 Use data presented in
papers, magazines etc
to show the difficulties
of drawing conclusions
from published data
 Construct, draw, use and understand
 Further examples of
these graphs
(particularly graphs
used for comparison),
eg back-to-back stem
and leaf diagrams.
 Investigate the
misrepresentation of
statistics in the media.
 Compare information
presented in different
forms, eg stem and
leaf v bar chart.
Statistics Book
Chapter 2
 Written testing to assess knowledge of content.
PRIOR KNOWLEDGE:
GCSE Mathematics
Higher Module 1Collecting data
GCSE Statistics Higher
Module 1- Types of
data
TIME ALLOWED 1-2
HRS
Module 6: 2b
Diagrams and
representations/
dicrete data
PRIOR KNOWLEDGE:
GCSE Mathematics
Higher Module 2 Charts and graphs
GCSE Statistics Higher
Module 1 - Types of
data
TIME ALLOWED: 3-4
HRS





Pictograms
Bar charts
Multiple or composite bar charts for qualitative,
quantitative and discrete data and comparative pie
charts with area proportional to frequency
Vertical line (stick) graphs for discrete data and
cumulative frequency step polygons
Stem and leaf diagrams
Choropleth maps.
Identify simple properties of the shape of
distributions of data including symmetry, positive
and negative skew.
Understand the distinction between well-presented
and poorly presented data.
Understand the potential for visual misuse, by
omission or misrepresentation.
Transform from one presentation to another.
Understand how to discover errors in data and
recognise data that does not fit a general trend or
pattern, including outliers.
 Present and interpret data collected for
coursework.
 Students should be able to list outcomes from
single or two successive events.
 Present and interpret data collected for
coursework.
 Students should be able to list outcomes from
single or two successive events.
 Reasons for choosing a particular form of
representation are expected.
 Comparative line graphs are expected.
 Analytical definitions of an outlier will be
expected.
 For box plots see Module 9.
 Use data presented in
papers, magazines etc
to show the difficulties
of drawing conclusions
from published data
2011-2013 SOW Maths and Statistics
Content/
Prior
knowledge/
Time allowed
Learning objectives
Differentiation
and extension
Resource
Exemplar resources
NOTES
Module 7: 2b
Diagrams and
Representations
continuous data
 Construct, draw, use and understand
 Further examples of
these graphs
(particular graphs used
for comparison), eg
cumulative frequency
diagrams used for
comparison, Normal
distributions, etc.
 Investigate the
misrepresentation of
graphs used to
represent continuous
data in the media or
on the Internet.
Statistics Book
Chapter 3
 Written testing to assess knowledge of content.
 Use data presented in
papers, magazines etc
to show the difficulties
of drawing conclusions
from published data
PRIOR KNOWLEDGE:
GCSE Mathematics
Higher Module 2Charts and graphs
GCSE Mathematics
Higher Module 8Histograms
GCSE Statistics Higher
Module 6- Diagrams
and representations
(discrete data)
TIME ALLOWED: 3-4
HRS




Pie charts
Histograms with equal and unequal class intervals
and the concept of frequency density
Frequency diagrams
Cumulative frequency diagrams
Population pyramids
Stem and leaf diagrams.
Identify simple properties of the shape of
distributions of data including symmetry, positive
and negative skew.
Transform from one presentation to another.
Understand that many populations can be modelled
by the Normal distribution.
Understand how to discover errors in data and
recognise data that does not fit a general trend or
pattern, including outliers.
 Present and interpret data collected for
coursework.
 Students should be able to list outcomes from
single or two successive events.
 Reasons for choosing a particular form of
representation are expected.
 Comparative line graphs are expected.
 Analytical definitions of an outlier will be
expected.
 For box plots see Module 9.
2011-2013 SOW Maths and Statistics
Content/
Prior
knowledge/
Time allowed
Learning objectives
Differentiation
and extension
Resource
Exemplar resources
NOTES
Module 8: 2c
Measures of Central
Tendency 2i
Estimation
Convert raw data to summary statistics, design,
construct and present summary tables.
 Work out the mean, median and mode of
- raw data presented as a list
- discrete data presented as a frequency distribution.
 Identify the modal class interval for grouped
frequency distributions for discrete and continuous
data.
 Work out and use estimates for the mean and
median of grouped frequency distributions for
discrete and continuous data.
 Understand the effects of transformations of the
data on the mean, mode and median.
 Understand the effect on the mean, mode and
median of changes in the data including the addition
or withdrawal of a population or sample member.
 Understand the appropriateness, advantages and
disadvantages of each of the three measures of
central tendency.
 Be able to make a reasoned choice of a measure of
central tendency appropriate to a particular line of
enquiry, nature of data and purpose of the analysis.
 Calculate and use a weighted mean.
 Understand that increasing sample size generally
leads to better estimates of population parameters.
 Estimate population means from samples.
 Estimate population proportions from samples with
applications in opinion polls and elsewhere.
 Estimate population size based on the Peterson
capture/recapture method.
 Understand the effect of sample size on estimates
and the variability of estimates, with a simple
quantitative appreciation of appropriate sample
size.
 Use box plots to
compare heights of
students in each year
group of the school.
 Investigate the use of
percentile range in
real-world statistics.
 Investigate the optimal
sample size required in
Peterson’s capture/
recapture method
 Calculate a weighted
mean in a practical
context.
Statistics Book
Chapter 4
 Written testing to assess knowledge of content.
 SMSC – Use percentile
charts for babies
height and weight to
illustrate use of normal
data
PRIOR KNOWLEDGE:
GCSE Mathematics
Higher Module 5- The
mean (large data
sets)
GCSE Mathematics
Higher Module 7Median and
interquartile range
(large data sets)
GCSE Statistics Higher
Module 1- Types of
data
TIME ALLOWED: 3-4
HRS
 No more than 30 numbers in a list will be
examined.
 Graphical and other methods for the median are
expected.
Transformation of data will be of the form
x  ax + b
 and
x
notation is expected.
2011-2013 SOW Maths and Statistics
Content/
Prior
knowledge/
Time allowed
Learning objectives
Differentiation
and extension
Resource
Exemplar resources
NOTES
Module 9: 2d
Measures of
dispersion
 Convert raw data to summary statistics, design,
construct and present summary tables.
 Work out and use the range for data presented in a
list or frequency distribution.
 Work out the quartiles, percentiles and interquartile
range for discrete and continuous data presented
either as a list, frequency table or grouped
frequency table.
 Construct, interpret and use box plots.
 Formally identify outliers.
 Calculate and use variance and standard deviation.
 Understand the advantages and disadvantages of
each of the measures of dispersion, range, quartiles,
interquartile range, percentiles, deciles,
interpercentile range, variance and standard
deviation.
 Use an appropriate measure of central tendency
together with range, quartiles, interquartile range,
percentiles, deciles, interpercentile range, variance
and standard deviation to compare distributions of
data.
 Calculate, interpret and use standardised scores to
compare values from different distributions.
 Understand how to discover errors in data and
recognise data that does not fit a general trend or
pattern, including outliers.
Use a spread sheet to
calculate standard
deviation
 Investigate standard
scores in a real world
context, eg decathlon.
 Relate mean and
standard deviation to
the Normal
distribution.
 Central limit theorem.
Statistics Book
Chapter 5
 Written testing to assess knowledge of content.

PRIOR KNOWLEDGE:
GCSE Mathematics
Higher Module 7Median and
interquartile range
(Large data sets)
GCSE Statistics Higher
Module 1- Types of
data
GCSE Statistics Higher
Module 8- Measures
of central tendency
TIME ALLOWED: 2- 3
HRS
 Present and interpret data collected for
coursework.
 The possible effect of an outlier on range is
expected.
 Numerical interpolation is expected.
 The use of box plots includes comparisons.
 Awareness that a full comparison of distributions
needs at least both a measure of central tendency
and a measure of dispersion is expected.
 and
x
notation is expected.
2011-2013 SOW Maths and Statistics
Content/
Prior
knowledge/
Time allowed
Learning objectives
Differentiation
and extension
Resource
Exemplar resources
NOTES
Module 10: 2f
Scatter diagrams 2g
Time series
 Plot points as points on a scatter diagram.
 Investigate the
relationship between
variables, eg hand
span v foot length,
volume v surface area
of cubes.
 Analyse real-world
time series graphs for
trends, eg FT100 index
over three years.
 Use a spread sheet to
fit a line (and curve) to
given bi-variate data.
 For Spearman’s
coefficient if rank
correlation tied ranks
will not be tested in
the examination.
 Students may be
required to work out
the average seasonal
variation from their
time series graph.
Statistics Book
Chapter 6, 7
 Written testing to assess knowledge of content.
 SMSC – distinguish
between correlation
and causal relationship
in real-life data
 Using moving averages
to illustrate climate
change
PRIOR KNOWLEDGE:
GCSE Mathematics
Higher Module 3Time series
GCSE Mathematics
Higher Module 4Scatter graphs and
correlation
GCSE Statistics Higher
Module 1- Types of
data
TIME ALLOWED: 3-4
HRS
 Recognise positive, negative and zero correlation by
inspection.
 Understand the distinction between correlation,
causality and a non-linear relationship.
 Draw a line of best fit through
 x, y  to the points
on a scatter diagram.
 Find the equation of the line of best fit in the form y
= ax + b and a practical interpretation of a and b in
the context.
 Fit non-linear models of the form y = axn + b and y =
kax
 Understand the pitfalls of interpolation and
extrapolation.
 Interpret data presented in the form of a scatter
diagram.
 Calculate, in appropriate cases, Spearman’s rank
correlation coefficient and use it as a measure of
agreement or for comparisons of the degree of
correlation.
 Plot points as a time series; draw a trend line by eye
and use it to make a prediction.
 Calculate and use appropriate moving averages.
 Identify and discuss the significance of seasonal
variation by inspection of time series graphs.
 Draw a trend line based on moving average.
 Recognise seasonal effect at a given data point and
average seasonal effect.
 Present and interpret data collected for
coursework.
 Explain that: correlation does not guarantee a
causal relationship between the variables;
unrelated variables may exhibit linear correlation.
 Analytical definitions of an outlier will be
expected.
 The value of n in a non-linear relationship (see
above) could be 2, -1 or ½ only.
 Questions will state when
 x, y 
is required.
2011-2013 SOW Maths and Statistics
Content/
Prior
knowledge/
Time allowed
Learning objectives
Differentiation
and extension
Resource
Exemplar resources
NOTES
Module 11: 4
Probability
 Understand the meaning of the words event and
outcome
 Understand the meaning of the words impossible,
certain, highly likely, likely, unlikely, possible,
evens, and present them on a likelihood scale.
 Put outcomes in order in terms of probability.
 Put probabilities in order on a probability scale.
 Understand the terms random and equally likely.
 Understand and use measures of probability from a
theoretical perspective and from a limiting
frequency or experimental approach, and that
increasing sample size generally leads to better
estimates of probability.
 Understand that in some cases the measure of
probability based on limiting frequency is the only
viable measure.
 Compare expected frequencies and actual
frequencies.
 Use simple cases of the binomial and discrete
uniform distribution.
 Use simulation to estimate more complex
probabilities.
 Use probability to assess risk.
 Produce, understand and use a sample space.
 Understand and use Venn diagrams and Cartesian
grids.
 Understand the terms mutually exclusive and
exhaustive and to understand the addition law P(A or
B) = P(A) + P(B) for two mutually exclusive events.
 Know, for mutually exclusive outcomes, that the sum
of probabilities is 1; and in particular the probability
of something not happening is 1 minus the
probability of it happening.
 Draw and use probability tree diagrams for
independent events and conditional cases.
 Understand, use and apply the addition for mutually
exclusive events, general addition, and
multiplication laws for independent events and
conditional events and outcomes.
 Do calculations
without the use of a
calculator, eg
probabilities with
harder fractions.
 Generate sample
spaces which require
careful specification,
eg. drawing cards from
a pack of cards.
 Investigate probability
in real life situations,
eg National Lottery.
Statistics Book
Chapter 8
 Written testing to assess knowledge of content.
 Discuss the odds in
gambling and the
National Lottery
PRIOR KNOWLEDGE:
GCSE Mathematics
Higher Module 6Probability
TIME ALLOWED: 3-4
HRS
 Probabilities may be expressed as fractions,
decimals or percentages, ie not as ratios (odds).
 Formal definition and notation of a limit is not
required.
 The expansion of (p + q)2 is expected.
 In tree diagrams, up to tree sets of branches is
required.
2011-2013 SOW Maths and Statistics
Content/
Prior
knowledge/
Time allowed
Learning objectives
Differentiation
and extension
Resource
Exemplar resources
NOTES
Module 12: 2e
Further Summary
Statistics/
Index numbers
 Understand and use simple index numbers.
 Investigate index
numbers in real-life
contexts, eg index of
house prices.
 Draw graphs to show
index numbers over
time.
Statistics Book
Chapter 9
 Written testing to assess knowledge of content.
 Consider Retail Price
Index and FTSE, Dow
Jones and other
financial indices
 Understand and use chain base index numbers.
 Understand and use weighted index numbers.
 Understand and use the Retail Price Index (RPI).
PRIOR KNOWLEDGE:
None
 Index numbers should be given to an appropriate
degree of accuracy.
 The base year will be given.
TIME ALLOWED: 1-2
HRS
GCSE Unit 1
Book
Year 10
Chapter
Ch 1:
Lesson
No. of
hours
Number: Number skills and
properties (recap)
1
Recap: Number skills and properties
1
Learning objective
Grade
Term 4
1
1
Round to a given number of significant figures.
Approximate the result before multiplying two
numbers together. Approximate the result before
dividing two numbers. Round a calculation, at the
end of a problem, to give what is considered to be
a sensible answer.
Multiply and divide positive and negative numbers.
1
Ch 2:
Number: Fractions, percentages
and ratios (recap)
3
Consolidate number work on ratio and proportion.
Convert between metric units of measure. Break
down a complex task into smaller manageable
D–C
NOTES
2011-2013 SOW Maths and Statistics
Book
Chapter
Lesson
No. of
hours
Learning objective
Grade
NOTES
tasks.
1
2.1, 2.2,
2.3
Recap: One quantity as a fraction of
another, Increasing and decreasing
quantities by a percentage,
Expressing one quantity as a
percentage of another
1
Find one quantity as a fraction of another.
D–C,
D–B,
I Express one quantity as a percentage of another.
Work out percentage change increase and
decrease quantities by a percentage.
D–C
1
2.4, 2.5
Recap: Compound interest and
repeated percentage change,
Reverse percentage (working out the
original quantity)
1
Calculate compound interest. Solve problems
involving repeated percentage change.
C–B,
C–A
1
2.6, 2.7,
2.8
Recap: Ratio, Best buys, Speed,
time and distance
1
Simplify a ratio. Express a ratio as a fraction.
D–C,
D, D–C
Divide amounts into given ratios. Complete
calculations from a given ratio and partial
information.
Find the cost per unit weight. Find the weight per
unit cost. Use the above to find which product is
the cheaper.
Recognise the relationship between speed,
distance and time. Calculate average speed from
distance and time. Calculate distance travelled
from the speed and the time. Calculate the time
taken on a journey from the speed and the
distance.
1
Ch 3:
1
3.2
Number: Number and limits of
accuracy (recap)
1
Recap: Problems involving limits of
1
Find the limits of accuracy of number that have
B–A*
Financial
Mathematics –
Income tax, VAT,
credit card interest
rates, mortgages
2011-2013 SOW Maths and Statistics
Book
Chapter
Lesson
No. of
hours
accuracy
1
Learning objective
Grade
been rounded to different degrees of accuracy.
Angles at a Point
Scales and Units
1
Algebra:
Notation
Graphs
Graphs of Function
The Data Handling Topics for Unit 1 are listed here for your information but they are all covered in the GCSE Statistics module
1
Ch 4:
1
4.1
1
4.2
Statistics: Data handling
8
Averages
½
Frequency tables
½
Use averages.
D–C
Solve more complex problems using averages.
D–C
Identify the advantages and disadvantages of
each type of average and learn which one to use
in different situations.
D–C
Calculate the mode and median from a frequency
table.
D–B
Calculate the mean from a frequency table.
D–B
1
1
4.3
4.4
Grouped data
Frequency diagrams
1
1
Identify the modal group.
C
Calculate and estimate the mean from a grouped
table.
C
Draw frequency polygons for discrete and
continuous data.
D–C
Draw histograms for continuous data with equal
intervals.
NOTES
2011-2013 SOW Maths and Statistics
Book
Chapter
Lesson
No. of
hours
Learning objective
Draw pie charts.
Grade
D–C
D
1
4.5
Histograms with bars of unequal
width
1
Draw and read histograms where the bars are of
unequal width.
A–A*
Find the median, quartiles and interquartile range
from a histogram.
A–A*
1
4.6
Surveys
½
Conduct surveys.
D–C
1
4.7
Questionnaires
½
Ask good questions in order to collect reliable and
valid data.
D–C
1
4.8
The data-handling cycle
½
Use the data-handling cycle.
C
1
4.9
Other uses of statistics
½
Apply statistics in everyday situations.
D–C
1
4.10
Sampling
1
Understand different methods of sampling.
D–C
Collect unbiased reliable data.
D–C
KS4 Test 1 and review
2
Statistics: Statistical representation
6
1
Ch 5:
1
5.1
Line graphs
1
Draw a line graph to show trends in data.
D
1
5.2
Stem-and-leaf diagrams
1
Draw and read information from an ordered stemand-leaf diagram.
D
1
5.3
Scatter diagrams
1
Draw, interpret and use scatter diagrams.
D–C
1
5.4
Cumulative frequency diagrams
1
Find a measure of dispersion (the interquartile
range) and a measure of location (the median)
using a graph.
B
NOTES
2011-2013 SOW Maths and Statistics
Book
Chapter
1
5.5
1
Ch 6:
1
Lesson
No. of
hours
Box plots
1
Probability: Probability of events
6
6.1
Experimental probability
1
6.2
1
Learning objective
Grade
Draw and read box plots.
B–A
½
Calculate experimental probabilities and relative
frequencies. Estimate probabilities from
experiments. Use different methods to estimate
probabilities.
C
Mutually exclusive and exhaustive
events
½
Recognise mutually exclusive, complementary and
exhaustive events.
C–B
6.3
Expectation
½
Predict the likely number of successful events,
given the number of trials and the probability of
any one event.
C–B
1
6.4
Two-way tables
½
Read two-way tables and use them to work out
probabilities and interpret data.
D–C
1
6.5
Addition rule for events
½
Work out the probability of two events such as
P(A) or P(B).
D–B
1
6.6
Combined events
½
Work out the probability of two events occurring at
the same time.
D–C
1
6.7
Tree diagrams
½
Use sample space diagrams and tree diagrams to
work out the probability of combined events.
B
1
6.8
Independent events 1
½
Use the connectors ‘and’ and ‘or’ to find the
probability of combined events.
B–A
1
6.9
Independent events 2
1
Use the connectors ‘and’ and ‘or’ in more
advanced examples, to find the probability of
combined events.
A
1
6.10
Conditional probability
1
Work out the probability of combined events when
A–A*
NOTES
2011-2013 SOW Maths and Statistics
Book
Chapter
Lesson
No. of
hours
Learning objective
Grade
NOTES
the probabilities change after each event.
UNITS 1 & Statistics Mock exam
1
Mock exam review
2
Revision
HALF TERM
Year 10
Term 6
UNITS 1 & Statistics EXAM
1
2
Ch 1:
Number: Using a calculator
4
2
1.1
Basic calculations and using
brackets
1
2
1.2
Adding and subtracting fractions with
a calculator
2
1.3
Multiplying and dividing fractions with
a calculator
2
FM
Functional maths lesson: Setting
up your own business
1
2
2.2
Recap: Compound interest and
repeated percentage change
2
2.3
2
2
Use some of the important keys, including the
bracket keys, to do calculations on a calculator.
D–C
½–1
Use a calculator to add and subtract fractions.
D–C
½–1
Use a calculator to multiply and divide fractions.
D–C
1
Calculate compound interest. Solve problems
involving repeated percentage change.
C–B
Recap: Reverse percentage (working
out the original quantity)
1
Calculate the original amount, given the final
amount, after a known percentage increase or
decrease.
C–A
2.4
Recap: Powers (Indices)
1
Use powers (also known as indices).
D–A*
2.5
Recap: Reciprocals and rational
1
Recognise rational numbers, reciprocals,
terminating decimals and recurring decimals.
C–A*
Only if necessary
2011-2013 SOW Maths and Statistics
Book
Chapter
Lesson
No. of
hours
numbers
Learning objective
Grade
Convert terminal decimals to fractions. Convert
fractions to recurring decimals. Find reciprocals of
numbers or fractions.
SUMMER HOILDAY
Year 11
Number: Decimals, percentages and
powers
4
Recap: Number: Decimals,
percentages and powers
1
2.6
Recap: Standard form
1
FM
Functional maths lesson: Oil
Crisis (this is the same as in book
1 so can be omitted if already
completed)
1
Number: Compound measures
4
2
Ch 2:
2
2
2
2
Term 1
Ch 3:
Change a number into standard form. Calculate
using numbers in standard form.
D–A
2
3.1
Recap: Limits of accuracy
½
Find the limits of accuracy of numbers that have
been rounded to different degrees of accuracy.
C–B
2
3.2
Recap: Speed, time and distance
½
Recognise the relationship between speed,
distance and time. Calculate average speed from
distance and time. Calculate distance travelled
from the speed and the time. Calculate the time
taken on a journey from the speed and the
distance.
D–C
2
3.3
Direct proportion problems
1
Recognise and solve problems, using direct
proportion.
D–C
NOTES
2011-2013 SOW Maths and Statistics
Book
2
Chapter
3.4
Lesson
No. of
hours
Density
1
Functional maths lesson:
Organising your birthday dinner
1
Geometry: Shape
6
Learning objective
Grade
Solve problems involving density.
B
2
FM
2
Ch 4:
2
4.1
Circumference and area of a circle
1
Calculate the circumference and area of a circle.
D–C
2
4.2
Cylinders
1
Calculate the volume and surface area of a
cylinder.
B–A*
2
4.3
Volume of a pyramid
1
Calculate the volume of a pyramid.
B–A*
2
4.4
Cones
1
Calculate the volume and surface area of a cone.
A–A*
2
4.5
Spheres
1
Calculate the volume and surface area of a
sphere.
A–A*
Functional maths lesson:
Organising a harvest
1
KS4 Test 5 and review
2
Geometry: Pythagoras’ theorem and
trigonometry
7
2
FM
2
Ch 5:
2
5.1
Pythagoras’ theorem
1
Calculate the length of the hypotenuse in a rightangled triangle.
C
2
5.2
Finding a shorter side
1
Calculate the length of a shorter side in a rightangled triangle.
C
2
5.3
Applying Pythagoras’ theorem to real
life situations
1
Solve problems using Pythagoras’ theorem.
C–B
2
5.4
Pythagoras’ theorem in three
2
Use Pythagoras’ theorem in problems involving
A–A*
NOTES
2011-2013 SOW Maths and Statistics
Book
Chapter
Lesson
No. of
hours
dimensions
Learning objective
Grade
three dimensions.
2
5.5
Trigonometric ratios
½–1
Use the three trigonometric ratios.
B
2
5.6
Calculating angles
½–1
Use the trigonometric ratios to calculate an angle.
B
2
5.7
Using the sine and cosine functions
1
Find lengths of sides and angles in right-angled
triangles using the sine and cosine functions.
B
2
5.8
Using the tangent function
1
Find lengths of sides and angles in right-angled
triangles using the tangent function.
B
2
5.9
Which ratio to use
1
Decide which trigonometric ratio to use in a rightangled triangle.
B–A
2
5.10
Solving problems using trigonometry
1
1
Solve practical problems using trigonometry.
B–A
Solving problems using trigonometry
2
1
2
5.11
Solve problems using an angle of elevation or an
angle of depression.
Solve bearing problems using trigonometry.
B–A
Use trigonometry to solve problems involving
isosceles triangles.
HALF TERM
2
FM
Functional maths lesson: Map
work using Pythagoras
1
2
Ch 6:
Geometry: Transformation geometry
5
2
6.1
Congruent triangles
½
Show that two triangles are congruent.
B–A
2
6.2
Translations
½
Translate a 2D shape.
C
2
6.3
Reflections
½
Reflect a 2D shape in a mirror line.
D–C
NOTES
2011-2013 SOW Maths and Statistics
Lesson
No. of
hours
Book
Chapter
Learning objective
Grade
2
6.4
Rotations
½
Rotate a 2D shape about a point.
D–C
2
6.5
Enlargements
1
Enlarge a 2D shape by a scale factor.
D–B
2
6.6
Combined transformations
1
Combine transformations.
D–B
2
FM
Functional maths lesson:
Developing Photographs
1
2
Ch 7:
Algebra: Equations
9
2
7.1
Changing the subject of a formula
1
Change the subject of a formula where the subject
occurs more than once.
A–A*
2
7.2
Solving linear equations
1
Solve equations in which the variable (the letter)
appears as part of the numerator of a fraction.
Solve equations where you have to expand
brackets first. Solve equations where the variable
appears on both sides of the equals sign. Set up
equations from given information and then solve
them.
D–C
2
7.3
Setting up equations
1
Set up equations from given information, and then
solve them.
D–C
2
7.4
Trial and improvement
1
Estimate the answers to some questions that do
not have exact solutions, using the method of trial
and improvement.
C
2
7.5
Simultaneous linear equations
1
Solve simultaneous linear equations in two
variables.
B–A
2
7.6
Solving problems using simultaneous
equations
1
Solve problems, using simultaneous linear
equations in two variables.
B–A
2
7.7
Linear and non-linear simultaneous
2
Solve linear and non-linear simultaneous
A–A*
NOTES
2011-2013 SOW Maths and Statistics
Book
Chapter
Lesson
No. of
hours
equations
2
FM
Learning objective
Grade
equations.
Functional maths lesson:
Choosing a mobile phone plan
1
KS4 Test 6 and review
2
CHRISTMAS
Year 11
Term 3
2
Ch 8:
Geometry: Constructions
4
2
8.1
Constructing triangles
½
Construct triangles, using compasses, a protractor
and a straight edge.
D
2
8.2
Bisectors
½
Construct the bisectors of lines and angles.
C
Construct angles of 60° and 90°.
2
8.3
Defining a locus
1
Draw a locus for a given rule.
C
2
8.4
Loci problems
1
Solve practical problems using loci.
C
2
FM
Functional maths lesson:
Planning a football pitch
1
2
Ch 9:
Geometry: Similarity
3
2
9.1
Similar triangles
½–1
Show two triangles are similar. Work out the scale
factor between similar triangles.
C–B
2
9.2
Area and volume of similar shapes
1–1½
Solve problems involving the area and volume of
similar shapes.
A–A*
2
FM
Functional maths lesson: Making
a scale model
1
NOTES
2011-2013 SOW Maths and Statistics
Book
Chapter
2
Ch 10:
2
Lesson
No. of
hours
Learning objective
Grade
Geometry: Trigonometry
7
10.1
Some 2D problems
1
Use trigonometric ratios and Pythagoras’ theorem
to solve more complex two-dimensional problems.
A*
2
10.2
Some 3D problems
1
Use trigonometric ratios and Pythagoras’ theorem
to solve more complex three dimensional
problems.
A*
2
10.3
Trigonometric ratios of angles
between 90o and 360o
1
Find the sine, cosine and tangent of any angle
from 90° to 360°.
A*
2
10.4
Solving any triangle
1
Use the sine rule and the cosine rule to find sides
and angles in any triangle.
A–A*
2
10.5
Trigonometric ratios in surd form
1
Work out trigonometric ratios in surd form.
A*
2
10.6
Using sine to find the area of a
triangle
1
Work out the area of a triangle if you know two
sides and the included angle.
A–A*
2
FM
Functional maths lesson: Building
Tree Houses
1
KS4 Test 7 and review
2
Ch 11:
Algebra: Quadratics
7
2
11.1
Expanding brackets
1
Expand two linear brackets to obtain a quadratic
expression.
C–B
2
11.2
Quadratic factorisation
1
Factorise a quadratic expression into two linear
brackets.
B–A
2
11.3
Solving quadratic equations by
factorisation
1
Solve a quadratic equation by factorisation.
C–A
NOTES
2011-2013 SOW Maths and Statistics
Lesson
No. of
hours
Book
Chapter
Learning objective
Grade
2
11.4
Solving a quadratic equation by the
quadratic formula
1
Solve a quadratic equation by using the quadratic
formula.
A
2
11.5
Solving a quadratic equation by
completing the square
1
Solve a quadratic equation by completing the
square.
A–A*
2
11.6
Problems involving quadratic
equations
1
Recognise why some quadratic equations cannot
be factorised. Solve practical problems, using
quadratic equations.
A*
2
FM
Functional maths lesson:
Stopping Distances
1
HALF TERM
Ch 12: Algebra: Graphs and their
equations
7
2
12.1
Drawing graphs by the gradientintercept method
½ –1
Draw graphs using the gradient-intercept method.
C–B
2
12.2
Finding the equation of a line from its
graph
½–1
Find the equation of a line, using its gradient and
intercept.
B
2
12.3
Quadratic graphs
Draw and read values from quadratic graphs.
C–B
2
12.4
The significant points of a quadratic
graph
½ –1
Recognise and calculate the significant points of a
quadratic graph.
B–A*
2
12.5
The circular function graphs
½–1
Use the symmetry of the graphs y = sin x, and
A*
1
y = cos x in answering questions. Understand that
for every value of sine and cosine between 1 and
–1 there are two angles between 0° and 360°.
NOTES
2011-2013 SOW Maths and Statistics
Chapter
2
12.6
Solving one linear and one nonlinear equation by the method of
intersection
1
Solve a pair of simultaneous equations where one
is linear and one is non-linear, using graphs.
A–A*
2
12.7
Solving equations by the method of
intersection
1
Solve equations by the method of intersecting
graphs.
A*
2
PS
Problem Solving lesson:
Quadratics in Bridges
1
Algebra: Fractions and proof
3
Ch 13:
Lesson
No. of
hours
Book
Learning objective
Grade
2
13.1
Algebraic fractions
2
Simplify algebraic fractions. Solve equations
containing algebraic fractions.
B–A*
2
13.2
Algebraic proof
1
Recognise and continue some special number
sequences.
A*
2
PS
Problem Solving lesson: Picture
Proofs
1
Geometry: Properties of circles
4
Ch 14:
2
14.1
Circle theorems
1
Work out the sizes of angles in circles.
B–A*
2
14.2
Cyclic quadrilaterals
1
Find the sizes of angles in cyclic quadrilaterals.
B–A*
2
14.3
Tangents and chords
1
Use tangents and chords to find the sizes of
angles in circles.
B–A*
2
14.4
Alternate segment theorem
1
Use the alternate segment theorem to find the
sizes of angles in circles.
A–A*
Revision
1
UNIT 3 Mock exam
1
NOTES
2011-2013 SOW Maths and Statistics
Book
Chapter
Lesson
Mock exam review
2
PS
Ch 15:
No. of
hours
Learning objective
Grade
1
Problem Solving lesson: Proving
properties of circles
Algebra: Inequalities and regions
2
2
15.1
Solving inequalities
1
Solve a simple linear inequality.
C–B
2
15.2
Graphical inequalities
1
Show a graphical inequality. Find regions that
satisfy more than one graphical inequality.
C–B
2
FM
Problem Solving lesson: Linear
programming
1
Number: Variation
3
Ch 16:
2
16.1
Direct variation
1
Solve problems where two variables have a
directly proportional relationship (direct variation).
Work out the constant of proportionality.
A
2
16.2
Inverse variation
2
Solve problems where two variables have an
inversely proportional relationship (inverse
variation). Work out the constant of proportionality.
A
2
FM
Functional maths lesson: Voting
in the European Union
1
Ch 18:
Algebra: Transformation of graphs
and other graphs
4
Year 11
Term 5
2
18.1
Transformation of the graph y = f (x)
2
Transform a graph.
A*
2
18.2
Cubic, exponential and reciprocal
2
Recognise and plot cubic, exponential and
reciprocal graphs
A*
graphs
NOTES
2011-2013 SOW Maths and Statistics
Book
Chapter
2
FM
Ch 17:
Lesson
No. of
hours
Functional maths lesson: Diving
at the Olympics
1
Geometry: Vectors
3
Learning objective
Grade
2
17.1
Properties of vectors
½–1
Add and subtract vectors.
A–A*
2
17.2
Vectors in geometry
1½–2
Use vectors to solve geometrical problems.
A*
2
17.3
Geometric proof
1
Understand the difference between a proof and a
demonstration.
A*
2
FM
Functional maths lesson:
Navigational techniques of ants
1
Revision and exam preparation
8
HALF TERM
UNIT 3 EXAM
NOTES