Exploring mathematics: Tier 7 NC levels 8 and EP
Autumn
35 lessons
N7.1 Powers and roots
Zero and negative powers
Fractional indices and the index laws
Rational and irrationals numbers
Surds
3 lessons
Spring
32 lessons
S7.2 Probability 1
Mutually exclusive independent
events
Outcomes of compound events and
calculations of probabilities
5/6 lessons
N7.2 Decimals and accuracy
Significant figures and estimating
results of calculations
Standard form calculations
Bounds of intervals and accuracy of
measurements
Dimensions
5 lessons
N7.3 Proportional reasoning
Repeated proportional change
Direct and inverse proportion,
including algebraic methods
Proportion and square roots
4/5 lessons
R7.1 Revision/support
Number, algebra, geometry
and measures, statistics
5 lessons
Summer
33 lessons
S7.3 Enquiry 2
Sampling
Histograms (unequal class intervals)
Moving average
Cumulative frequency, box plots
Estimating mean, median and
interquartile range
7/8 lessons
S7.4 Probability 2
Probability investigation
4/5 lessons
A7.2 Expressions and formulae
Simplifying more complex expressions.
Factorising quadratic expressions
Changing the subject of more complex
formulae
6 lessons
A7.3 Equations
Solving equations with algebraic fractions
Solving quadratic equations graphically and
algebraically by factorisation, completing the
square or by formula
Solving simultaneous equations (one linear,
one quadratic) graphically and algebraically
7/8 lessons
A7.4 Functions and graphs
Graphs of simple loci, including a circle
Graphs of linear, quadratic, cubic,
reciprocal, trigonometric and exponential
functions
Transforming graphs of functions
8/9 lessons
100 lessons
1 | Exploring mathematics | Tier 6 (brown)
G7.2 Trigonometry 1
Pythagoras' theorem in 2D and 3D
Using sine, cosine and tangent to solve
problems in 2D
3 lessons
G7.3 Geometrical reasoning
Circle theorems
Similarity and congruence
7 lessons
R7.2 Revision/support
Number, algebra, geometry
and measures, statistics
5 lessons
N7.4 Using and applying maths
Investigating problems
Algebraic proof
History of mathematics
Careers in mathematics
3/4 lessons
G7.1 Measures and mensuration
Sectors and arcs
Volume and surface area of cones,
pyramids and spheres
Problem solving and more complex
shapes
5/6 lessons
G7.4 Transformations and vectors
Transformation patterns
Vector notation; sum of two vectors;
commutative and associative properties
Scalar multiple of a vector; resultant of
two vectors; problem solving
5/6 lessons
G7.5 Trigonometry 2
Sine and cosine rules
Formula for area of scalene triangle
Solving problems in 2D and 3D using
trigonometry and Pythagoras
6/7 lessons
Mathematical processes and applications are integrated into each unit
S7.1 Enquiry 1
Sampling and reliability
Non-responses and missing data
Histograms with equal class intervals
Moving average
6 lessons
A7.1 Linear graphs and inequalities
Parallel or perpendicular straight line graphs
Inequalities in two variables
6 lessons
Units
SUPPORT
Number 1:
Powers and roots
(3 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• recognise that a recurring decimal is an exact
• model contexts or problems through precise use of symbols and
fraction
• use the index laws to multiply and divide positive
Integers, powers and roots
CORE
and negative integer powers
representations
• select and apply a range of mathematics and mathematical techniques to
find solutions
(56–59)
• use the power and root keys of a calculator
• show insight into mathematical connections in the context or problem
Calculations
• estimate square roots and cube roots.
• use accurate notation
(108–109)
• calculate accurately, using mental methods or calculating devices as
appropriate
• extend generalisations
• examine critically strategies adopted and arguments presented
• communicate solutions to problems in familiar and unfamiliar contexts
and to:
• understand and use rational and irrational numbers
• use the index laws for fractional values
• use inverse operations, understanding that the inverse of raising a
positive number to power
power
1
n
n
is raising the result of this operation to
• use surds and  in exact calculations, without a calculator, and rationalise
a denominator such as
1
3

3
3
.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
2 | Exploring mathematics | Tier 6 (brown)
Number 2:
Decimals and accuracy
(5 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• round numbers to a given number of decimal
• choose and combine representations from a range of perspectives
places
• multiply and divide by powers of 10
Place value
(36–47)
Calculations
(88–107, 110–111)
• understand the effects of multiplying or dividing by
numbers between 0 and 1
• express numbers in standard form, including by
using a calculator
• show insight into mathematical connections in the context or problem
• select and apply a range of mathematics and mathematical techniques to
find solutions
• manipulate numbers and apply routine algorithms
• calculate accurately, using mental methods or calculating devices as
appropriate
Calculator methods
• convert between units of measurement
• use accurate notation
(108–109)
• recognise that measurements may be inaccurate
• follow through a sustained chain of reasoning
Solving problems
(28–31)
Measures and mensuration
(230–233)
by up to one half of the unit in either direction
• use a calculator efficiently.
• use appropriate checking procedures, evaluating their effectiveness at
each stage
• recognise limitations in the accuracy of results and conclusions
• examine critically strategies adopted and arguments presented
and to:
• use significant figures to approximate answers when multiplying or
dividing large numbers
• use standard index form to make sensible estimates for calculations
involving multiplication and/or division
• calculate with standard index form, using a calculator as appropriate
• understand how errors can be compounded in calculations
• understand upper and lower bounds and use calculators, or written
methods, to calculate the upper and lower bounds of calculations in a
range of contexts, particularly when working with measurements
• consider the dimensions of a formula and recognise the difference
between formulae for perimeter, area and volume.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
3 | Exploring mathematics | Tier 6 (brown)
Number 3:
Proportional reasoning
(5 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• divide a quantity in a given ratio
• choose and combine representations from a range of perspectives
• multiply and divide fractions
• show insight into mathematical connections in the context or problem
Fractions, decimals, percentages,
• calculate interest
• select and apply a range of mathematics and mathematical techniques to
ratio and proportion
(64–65, 78–81)
• calculate reverse percentage changes using a
decimal multiplier
Calculations
(82–103, 108–111)
• use the unitary method for direct proportion
• use compound measures such as rate, speed and
density
• enlarge 2D shapes, and recognise the effect of
enlargement on perimeter.
find solutions
• explore mathematical tasks, developing alternative approaches
• calculate accurately, using mental methods or calculating devices as
appropriate
• follow through a sustained chain of reasoning
• use appropriate checking procedures, evaluating their effectiveness at
each stage
• recognise limitations in the accuracy of results and conclusions
• examine critically strategies adopted and arguments presented
and to:
• use fractions or percentages to solve problems involving repeated
proportional changes, or the calculation of the original quantity given the
proportional change, e.g. compound interest
• use calculators to explore exponential growth and decay, using a
multiplier and the power key
• calculate an unknown quantity from quantities that vary in direct
proportion using algebraic methods where appropriate
• solve problems involving inverse proportion (including inverse squares)
using algebraic methods
• understand and use the effects of enlargement on areas and volumes of
shapes and solids.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
4 | Exploring mathematics | Tier 6 (brown)
Number 4:
Using and applying
mathematics
(4 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• choose and combine representations from a
• solve routine and non-routine problems in a range of familiar and
range of perspectives
• sub-divide problems to make solving them more
manageable
Solving problems
(2–35)
• select and apply a range of mathematics and
techniques to find solutions
• present and explain methods and solutions,
interpreting results, including calculator results, in
the context of the problem.
unfamiliar contexts
• show insight into mathematical connections in the context or problem
• model contexts or problems through precise use of symbols and
representations
• select and apply a range of mathematics and mathematical techniques to
find solutions
• follow through a sustained chain of reasoning, including proof
• consider the efficiency of alternative lines of enquiry or procedures
• draw conclusions, providing mathematical justifications
• use mathematical language and symbols effectively to communicate
convincing arguments and solutions
• identify other contexts or problems with similar structures and explain how
and why the same or different strategies were used
and to:
• be aware of some current applications of mathematics
• gain a sense of the history of mathematics and cultural influences on its
development.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
5 | Exploring mathematics | Tier 6 (brown)
Algebra 1:
Linear graphs and inequalities
(6 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• simplify algebraic expressions by taking out
• model contexts or problems through precise use of symbols and
single-term common factors, including cancelling
an algebraic fraction
Equations, formulae and identities
(118–121, 126–131)
• use algebraic and graphical methods to solve a
pair of simultaneous linear equations.
representations
• select and apply a range of mathematics and mathematical techniques to
find solutions
• show insight into mathematical connections in the context or problem
Solving problems
• use accurate notation
(6–13)
• manipulate algebraic expressions and equations
• draw accurate graphs on paper and on screen
• consider the assumptions in the model and recognise limitations in the
accuracy of results and conclusions
and to:
• identify the equations of straight-line graphs that are parallel and find the
gradient and equation of a straight-line graph that is perpendicular to a
given line
• solve linear inequalities in one and two variables find and represent the
solution set
• explore ‘optimum’ methods of solving simultaneous equations in different
forms.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
6 | Exploring mathematics | Tier 6 (brown)
Algebra 2:
Expressions and formulae
(6 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• simplify expressions by taking out common
• model contexts or problems through precise use of symbols and
factors
• substitute integers into expressions and formulae
representations
• select and apply a range of mathematics and mathematical techniques to
find solutions
Equations, formulae and identities
• simplify algebraic fractions
(118–121, 138–143)
• solve linear equations with fraction coefficients
• use accurate notation
• square a linear expression, expand the product of
• manipulate algebraic expressions and equations
two linear expressions of the form ax  b
• follow through a sustained chain of reasoning
• establish identities such as a2 – b2 = (a + b)(a – b)
and to:
• change the subject of a formula.
• factorise quadratic expressions, including the difference of two squares,
e.g. x 2 9 ( x 3)( x 3)
• cancel common factors in rational expressions,
2( x 1)2
e.g.
( x 1)
• simplify simple algebraic fractions to produce linear expressions and use
factorisation to simplify compound algebraic fractions
• derive and use more complex formulae, and change the subject of a
formula, including cases where the subject occurs twice
• derive relationships between different formulae that produce equal or
related results.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
7 | Exploring mathematics | Tier 6 (brown)
Algebra 3:
Solving equations
(8 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• factorise quadratic expressions
• model contexts or problems through precise use of symbols and
• find approximate solutions of equations such as
x3 + x = 20
Sequences, functions and graphs
(148–163, 172–177)
Solving problems
(26–27)
• plot the graphs of linear functions and their
inverses
• identify and use the gradients of parallel lines and
lines perpendicular to these lines
• solve linear inequalities in one variable, and
represent the solution set on a number line
• use graphical and algebraic methods to solve
simultaneous linear equations in two variables.
representations
• select and apply a range of mathematics and mathematical techniques to
find solutions
• draw accurate graphs on paper and on screen
• manipulate algebraic expressions and equations
• explore mathematical tasks, developing alternative approaches
• follow through a sustained chain of reasoning
• recognise limitations in the accuracy of results and conclusions
and to:
• solve equations involving algebraic fractions with compound expressions
as the numerators and/or denominators
• find approximate solutions of a quadratic equation from the graph of the
corresponding quadratic function
• solve quadratic equations by factorisation, completing the square and
using the quadratic formula, including those in which the coefficient of the
quadratic term is greater than 1
• know and understand that the intersection points of the graphs of a linear
and quadratic function are the approximate solutions to the corresponding
simultaneous equations
• solve exactly, by elimination of an unknown, two simultaneous equations
in two unknowns, where one is linear in each unknown and the other is
linear in one unknown and quadratic in the other or of the form
x2  y2 r2 .
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
8 | Exploring mathematics | Tier 6 (brown)
Algebra 4:
Functions and graphs
(9 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• know simple properties of quadratic functions
• model contexts or problems through precise use of symbols and it
• find the next term and the nth term of quadratic
sequences and functions
Sequences, functions and graphs
• plot graphs of simple quadratic and cubic
representations
• identify the situation or problem and the mathematical methods needed to
tackle it
(148–153, 170–177)
functions, e.g. y = x ,
• show insight into mathematical connections in the context or problem
Solving problems
y = 3x2 + 4, y = x,, on paper and using ICT
• draw accurate graphs on paper and on screen
(6–13)
2
• sketch and interpret the graphs of quadratic,
functions, and graphs that model real situations
• find the approximate solutions of equations from
their graphs
•• transform 2D shapes, identifying properties that
are preserved under particular transformations.
• manipulate algebraic expressions and equations
• follow through a sustained chain of reasoning
• interpret and communicate solutions to problems in familiar and unfamiliar
contexts
• recognise limitations in the accuracy of results and conclusions
and to:
• plot graphs of more complex quadratic and cubic functions estimate
values at specific points, including maxima and minima
• identify and sketch graphs of linear and simple quadratic and cubic
functions understand the effect on the graph of addition of (or
multiplication by) a constant
• construct the graphs of simple loci, including the circle x 2  y2 r 2 find
graphically the intersection points of a given straight line with this circle
and know this represents the solution to the corresponding two
simultaneous equations
• plot and recognise the characteristic shapes of graphs of simple cubic
1
functions (e.g. y  x3 ), reciprocal functions (e.g. y  , x0 ),
x
exponential functions ( y  kx for integer values of
values of
x
and simple positive
k ) and trigonometric functions, on paper and using ICT
• apply to the graph y f( x) the transformations y f( x ) a , y f(ax ) ,
y f( x  a) and y  af( x ) for linear, quadratic, sine and cosine functions
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
9 | Exploring mathematics | Tier 6 (brown)
Geometry and measures 1:
Measures and mensuration
(6 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• convert between units of area and between units
• choose and combine representations from a range of perspectives
Geometrical reasoning: lines, angles
• know and use formulae for the circumference and
and shapes
(184–189, 198–201)
Mensuration
(238–241)
Solving problems
(30–31)
of volume
area of a circle
• calculate the surface area and volume of cubes,
cuboids, right prisms and cylinders
• know and use the formulae for length of arcs and
area of sectors of circles
• recognise that measurements may be inaccurate
by up to one half of the unit in either direction
• appreciate the continuous nature of scales used
to make measurements.
• identify the situation or problem and the mathematical methods needed to
tackle it
• show insight into mathematical connections in the context or problem
• make accurate mathematical diagrams and constructions
• use accurate notation
• calculate accurately, using mental methods or calculating devices as
appropriate
• use appropriate checking procedures, evaluating their effectiveness at
each stage
• follow through a sustained chain of reasoning
• consider the assumptions in the model and recognise limitations in the
accuracy of results and conclusions
• examine critically strategies adopted and arguments presented
and to:
• recognise and use 2D representations of 3D objects
• understand and use the formulae for the length of a circular arc and area
and perimeter of a sector
• calculate and solve problems involving the surface area of cylinders and
volumes of cones, pyramids and spheres
• solve problems involving more complex shapes and solids, including
segments of circles and frustums of cones.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
10 | Exploring mathematics | Tier 6 (brown)
Geometry and measures 2:
Trigonometry 1
(3 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• recognise that if two 2D shapes are similar,
• choose and combine representations from a range of perspectives
corresponding angles are equal and
corresponding sides are in the same ratio
Measures and mensuration
(242–247)
• use sine, cosine and tangent in right-angled
triangles to solve simple problems in two
dimensions
• use the trigonometric function keys of a calculator
• use Pythagoras’ theorem to calculate lengths in
right-angled triangles.
• show insight into mathematical connections in the context or problem
• make accurate mathematical diagrams and constructions
• use accurate notation
• calculate accurately, using mental methods or calculating devices as
appropriate
• use appropriate checking procedures, evaluating their effectiveness at
each stage
• follow through a sustained chain of reasoning
• consider the assumptions in the model and recognise limitations in the
accuracy of results and conclusions
• examine critically strategies adopted and arguments presented
and to:
• understand and use Pythagoras’ theorem to solve 2D and 3D problems
• use trigonometric relationships in right-angled triangles to solve 2D
problems.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
11 | Exploring mathematics | Tier 6 (brown)
SUPPORT
Geometry and measures 1:
Geometrical reasoning
(7 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• solve problems using properties of angles, of
• choose and combine representations from a range of perspectives
parallel and intersecting lines, and of triangles and
other polygons
Geometrical reasoning: lines, angles
and shapes
(178–197)
Construction and loci
(220–227)
Solving problems
(14–17)
CORE
• apply conditions SSS, SAS, ASA or RHS to
establish the congruence of triangles
• understand that the tangent at any point on a
circle is perpendicular to the radius at that point
• prove and use the facts that:
– the perpendicular from the centre to the chord
bisects the chord
– tangents to a circle from an external point are
equal in length
• recognise that if two 2D shapes are similar,
corresponding angles are equal and
corresponding sides are in the same ratio
• understand and apply Pythagoras’ theorem.
• show insight into mathematical connections in the context or problem
• make accurate mathematical diagrams and constructions on paper and
on screen
• follow through a sustained chain of reasoning, including proof
• use mathematical language and symbols effectively in presenting
convincing arguments or conclusions
• review and refine arguments, conclusions and approaches
• interpret and communicate solutions to problems in familiar and unfamiliar
contexts
and to:
• prove and use the facts that:
– the angle subtended by a chord at the centre of a circle is twice the
angle subtended at the circumference
– the angle subtended at the circumference by a diameter is a right angle
– angles in the same segment are equal
– opposite angles of a cyclic quadrilateral sum to 180°
• prove and use the alternate segment theorem.
• prove the congruence of triangles, and verify standard ruler and compass
constructions using formal arguments.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
12 | Exploring mathematics | Tier 6 (brown)
Geometry and measures 4:
Vectors
(6 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• use ratio in a range of contexts
• choose and combine representations from a range of perspectives
• apply Pythagoras’ Theorem
• select and apply a range of mathematics and mathematical techniques to
• identify similar triangles
Transformations
(202–217)
Coordinates
(218–219)
Ratio and proportion
(78–81)
• find points that divide a line in a given ratio, using
properties of similar triangles
• given coordinates of points A and B, calculate the
length of AB
• transform 2D shapes, identifying properties that
are preserved under particular transformations.
find solutions
• show insight into mathematical connections in the context or problem
• make accurate mathematical diagrams and constructions
• use accurate notation
• follow through a sustained chain of reasoning
• examine critically strategies adopted and arguments presented
• extend generalisations
and to:
• recognise combinations of transformations in patterns
• understand and use vector notation to describe transformation of 2D
shapes by combinations of translations
• calculate and represent graphically the sum of two vectors, the difference
of two vectors and a scalar multiple of a vector
• calculate the resultant of two vectors
• understand and use the commutative and associative properties of vector
addition
• solve simple geometrical problems in 2D using vectors.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
13 | Exploring mathematics | Tier 6 (brown)
Geometry and measures 5:
Trigonometry 2
(7 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• use sine, cosine and tangent in right-angled
• choose and combine representations from a range of perspectives
triangles to solve problems in two dimensions
• understand and apply Pythagoras' theorem to
Measures and mensuration
(242–7)
solve problems in two dimensions
• solve problems using properties of angles, of
parallel and intersecting lines, and of triangles and
other polygons.
• show insight into mathematical connections in the context or problem
• make accurate mathematical diagrams and constructions
• use accurate notation
• calculate accurately, using mental methods or calculating devices as
appropriate
• use appropriate checking procedures, evaluating their effectiveness at
each stage
• follow through a sustained chain of reasoning
• consider the assumptions in the model and recognise limitations in the
accuracy of results and conclusions
• examine critically strategies adopted and arguments presented
and to:
• use trigonometric relationships in right-angled triangles to solve 2D and
3D problems, including finding the angles between a line and a plane
• calculate the area of a triangle using the formula
1
2
ab sin C
• draw, sketch and describe the graphs of trigonometric functions for
angles of any size, including simple transformations of the functions
• use the sine and cosine rules to solve 2D and 3D problems.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
14 | Exploring mathematics | Tier 6 (brown)
SUPPORT
Statistics 1:
Enquiry 1
(6 hours)
CORE
Before they start, pupils should be able to:
In this unit, pupils learn to:
• identify possible sources of bias and plan how to
• explore practical problems in familiar and unfamiliar contexts
minimise the effect
• construct and interpret:
Statistics
– frequency polygons
(248–275)
– scatter diagrams and lines of best fit
• determine the modal class and estimate the
mean, median and range of sets of grouped data
• use measures of average and range to compare
distributions and make inferences.
• identify the problem and the mathematical methods needed to tackle it
• select and apply a range of mathematics and mathematical techniques to
find solutions
• choose and combine representations from a range of perspectives
• follow through a sustained chain of reasoning
• draw conclusions and provide mathematical justifications
• recognise the limitations of any assumptions and the effects that varying
the assumptions could have on the conclusions drawn
• consider the efficiency of alternative lines of enquiry or procedures
• interpret and communicate solutions
and to:
• consider possible difficulties with planned approaches, practical problems
such as non-response or missing data
• select and justify a sampling scheme and a method to investigate a
population, including random and stratified sampling
• use a range of statistical methods to explore and summarise data,
including calculating an appropriate moving average for a time series
• select, construct and modify, on paper and using ICT, suitable graphical
representations, including histograms for grouped continuous data with
equal class intervals
• compare two or more distributions and make inferences, using the shape
of the distributions and measures of average and spread, including
median and quartiles
• recognise the limitations of any assumptions and the effects that varying
the assumptions could have on the conclusions drawn
• identify what extra information may be required to pursue a further line of
enquiry.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
15 | Exploring mathematics | Tier 6 (brown)
Statistics 2:
Probability 1
(6 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• recognise that the sum of probabilities of all
• explore practical problems in familiar and unfamiliar contexts
mutually exclusive outcomes is 1 and use this
when solving problems
Probability
• compare experimental and theoretical
(276–283)
probabilities in a range of contexts
Fractions
(66–69)
• use relative frequency as an estimate of
probability to compare outcomes of experiments
• select and apply a range of mathematics and mathematical techniques to
find solutions
• choose and combine representations from a range of perspectives
• follow through a sustained chain of reasoning
• examine and extend generalisations
• consider the assumptions in the model and recognise limitations in the
accuracy of results and conclusions
• interpret and communicate solutions
• examine critically strategies adopted and arguments presented
and to:
• use tree diagrams to represent outcomes of compound events,
recognising when events are independent and distinguishing between
contexts involving selection, both with and without replacement
• 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)), and use this knowledge in solving problems
• understand that if an experiment is repeated, the outcome may – and
usually will – be different, and that increasing the sample size generally
leads to better estimates of probability and population parameters.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
16 | Exploring mathematics | Tier 6 (brown)
Statistics 3:
Enquiry 2
(8 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• identify sources of bias and plan how to minimise
• explore practical problems in familiar and unfamiliar contexts
the effect
• construct and interpret:
Statistics
– frequency polygons
(250–251, 254–275)
– scatter diagrams and lines of best fit
Solving problems
(28–29)
• determine the modal class and estimate the
mean, median and range of sets of grouped data.
• identify the problem and the mathematical methods needed to tackle it
• select and apply a range of mathematics and mathematical techniques to
find solutions
• choose and combine representations from a range of perspectives
• follow through a sustained chain of reasoning
• draw conclusions and provide mathematical justifications
• recognise the limitations of any assumptions and the effects that varying
the assumptions could have on the conclusions drawn
• consider the efficiency of alternative lines of enquiry or procedures
• interpret and communicate solutions
and to:
• understand how methods of sampling and sample sizes affect the
reliability of conclusions
• use a moving average to identify seasonality and trends in time series
data, using them to make predictions
• construct, use, interpret and compare histograms, including those with
unequal class intervals, , and cumulative frequency tables, diagrams and
box plots
• compare two or more distributions and make inferences, using the shape
of the distributions and summary statistics, including median and
quartiles.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
17 | Exploring mathematics | Tier 6 (brown)
Statistics 4:
Probability 2
(5 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• identify all the outcomes of a combination of two
• explore practical problems in familiar and unfamiliar contexts
experiments
• select and apply a range of mathematics and mathematical techniques to
• use relative frequency as an estimate of
Probability
(276–283)
probability to compare outcomes of experiments
• use tree diagrams to represent outcomes of
compound events, recognising when events are
independent
• calculate the probability of a compound event
• recognise when and how to work with probabilities
associated with independent mutually exclusive
find solutions
• choose and combine representations from a range of perspectives
• follow through a sustained chain of reasoning
• examine and extend generalisations
• consider the assumptions in the model and recognise limitations in the
accuracy of results and conclusions
• interpret and communicate solutions
• examine critically strategies adopted and arguments presented
events.
and to:
• use tree diagrams to represent outcomes of compound events,
recognising when events are independent and distinguishing between
contexts involving selection, both with and without replacement
• know when to add or multiply two probabilities and use this knowledge in
solving problems.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
Revision 1 and 2 - process objectives
Previous learning
Objectives based on NC levels 6 and 7 (mainly level 7)
Pupils should already be able to apply and use
In this unit, pupils consolidate their ability to:
many of the skills shown on the right. This unit
• solve routine and non-routine problems in a range of familiar and unfamiliar contexts
offers is an opportunity to consolidate and refine
these skills.
• choose and combine representations from a range of perspectives
• show insight into mathematical connections in the context or problem
• select and apply a range of mathematics and the mathematical techniques to find solutions
• consider the efficiency of alternative lines of enquiry or procedures
• follow through a sustained chain of reasoning
• use appropriate checking procedures, evaluating their effectiveness at each stage
• draw conclusions, providing mathematical justifications
• recognise limitations in the accuracy of results and conclusions
• interpret and communicate solutions
and to:
Number
as in unit
18 | Exploring mathematics | Tier 6 (brown)
Algebra
as in unit
Geometry and measures
as in unit
Statistics
as in unit
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
19 | Exploring mathematics | Tier 6 (brown)