Exploring mathematics: Tier 6 NC levels 6 and 7
Autumn
37 lessons
N6.1 Powers and roots
Approximate square and cube
roots using ICT
Index notation; laws of indices;
standard form
3 lessons
N6.2 Proportional reasoning
Fractions, including reciprocals
Percentages, ratio and proportion
Rate and speed
6 lessons
A6.2 Linear functions and graphs
Graphs of linear functions and their inverses
Parallel and perpendicular lines
Linear inequalities
Solution of simultaneous equations
graphically and algebraically
6 lessons
Spring
30 lessons
S6.2 Probability 1
Mutually exclusive events
Relative frequency
Comparing experimental with
theoretical probability
4/5 lessons
A6.3 Quadratic functions and graphs
Quadratic sequences
Triangular numbers, square numbers
Simple properties of quadratic functions and
their graphs
Solution of simple quadratic equations by
factorisation
7/8 lessons
N6.3 Decimals and accuracy
Recurring decimals
Numbers between 0 and 1
Significant figures
Accuracy of measurements
Using a calculator efficiently
4/5 lessons
S6.3 Enquiry 2
Collecting, representing and
interpreting data using ICT
Scatter graphs and line of best fit
Frequency polygons
Communicating findings using ICT
7/8 lessons
S6.4 Probability 2
Probability investigation
3/4 lessons
R6.2 Revision/support
Number, algebra, geometry
and measures, statistics
5 lessons
N6.4 Using and applying maths
Investigating problems
Proof
History of mathematics
Careers in mathematics
4/5 lessons
A6.4 Using algebra
Quadratic sequences and functions
Graphs of simple quadratic and cubic
functions
Real-life graphs
7/8 lessons
100 lessons
1 | Exploring mathematics | Tier 6 (brown)
G6.2 Trigonometry 1
Pythagoras' theorem and simple
problems
Sine, cosine, tangent for acute angles
4 lessons
G6.3 Transformations and loci
Length of line segment and point
dividing it in a given ratio
Enlargement (negative and fraction
scale factors); finding angle of rotation
Combinations of transformations
Loci
6/7 lessons
G6.4 Measures and mensuration
Plans and elevations
Sectors and arcs;
Volume and surface area of cylinders
4/5 lessons
R6.1 Revision/support
Number, algebra, geometry
and measures, statistics
5 lessons
Summer
33 lessons
G6.1 Geometrical reasoning
Triangle problems
Radii, chords and tangents
Similar and congruent triangles
6 lessons
G6.5 Trigonometry 2
Pythagoras' theorem
Trigonometry
Geometrical reasoning
7/8 lessons
Mathematical processes and applications are integrated into each unit
S6.1 Enquiry 1
Identifying problems to solve;
minimising bias
Summary statistics
Scatter graphs and line of best fit
Frequency polygons
6 lessons
A6.1 Expressions and formulae
Algebraic fractions
Solving linear equations involving fractions
Expansion and factorisation of expressions
Derive and use formulae; change the
subject of a formula
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:
• use index notation and the index laws for positive
• compare representations of problems or situations, justifying the choice of
integer powers
• understand and use the order of operations, including
Place value
CORE
brackets
representation in relation to the context
• look for equivalence in different problems with similar structures
• select and apply a range of mathematics to find solutions
(36–39)
• use the power and root keys of a calculator
• use accurate notation
Integers, powers and roots
• multiply and divide integers and decimals by any
• calculate accurately, using mental methods or calculating devices when
(56–59)
Calculations
(108–109)
Algebra
(114–115)
positive integer power of 10.
appropriate
• explore the effects of varying values
• draw conclusions and make generalisations, providing mathematical
justifications
• record and communicate solutions to problems in familiar and unfamiliar
contexts
and to:
• use index notation with negative powers, recognising that the index laws
can be applied to these
• know that
1
n2
=
n
1
and
n3
=
3
n
for any positive number
n
and
estimate square roots and cube roots
• use standard index form, expressed in conventional notation and on a
calculator display, and know how to enter numbers in standard index form
• convert between ordinary and standard index form representations.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
2 | Exploring mathematics | Tier 6 (brown)
Number 2:
Proportional reasoning
(6 hours)
Fractions, decimals, percentages,
ratio and proportion
(64–65, 78–81)
Calculations
(82–103, 108–111)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• find equivalent fractions
• compare representations of problems or situations, justifying the choice of
• use fractions or percentages to compare
proportions
representation in relation to the context
• look for equivalence in different problems with similar structures
• solve problems involving percentage changes
• select and apply a range of mathematics to find solutions
• calculate and compare ratios.
• calculate accurately, using mental methods or calculating devices when
appropriate
• estimate, approximate and use appropriate checking procedures
• draw conclusions and make generalisations, providing mathematical
justifications
• record and communicate solutions to problems in familiar and unfamiliar
contexts
and to:
• add and subtract fractions, and multiply and divide fractions, interpreting
division as a multiplicative inverse
• use reciprocals, knowing that any number multiplied by its reciprocal is 1,
and that zero has no reciprocal because division by zero is not defined
• calculate an original amount when given the transformed amount after a
percentage change, and use a calculator for reverse percentage
calculations by doing an appropriate division
• understand and use proportionality and calculate the result of any
proportional change using multiplicative methods
• understand and use measures of speed and other compound measures
and solve problems involving constant or average rates of change.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
3 | Exploring mathematics | Tier 6 (brown)
Number 3:
Decimals and accuracy
(5 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• recognise recurring decimals
• compare and evaluate representations of problems or situations
• round numbers to a given number of decimal
• look for equivalence in different problems with similar structures
places and use rounding to estimate results of
Place value
(36–47)
Calculations
(88–107, 110–111)
Calculator methods
(108–109)
calculations
• convert between related units of measurement.
• select and apply a range of mathematics to find solutions
• manipulate numbers and apply routine algorithms
• calculate accurately, using mental methods or calculating devices when
appropriate
• estimate, approximate and use appropriate checking procedures
• record and communicate solutions to problems in familiar and unfamiliar
contexts
Solving problems
(28–31)
• judge the value of own findings and those presented by others, and the
strength of empirical evidence
Measures and mensuration
(230–233)
and to:
• distinguish between fractions with denominators that have only prime
factors 2 or 5 (terminating decimals), and other fractions (recurring
decimals)
• consolidate understanding of the effects of multiplying or dividing by
numbers between 0 and 1
• round to a given number of significant figures
• make and justify estimates and approximations of calculations by
rounding numbers to one significant figure and multiplying or dividing
mentally
• recognise that measurements given to the nearest whole unit may be
inaccurate by up to one half of the unit in either direction
• use an extended range of calculator keys.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
4 | Exploring mathematics | Tier 6 (brown)
Number 4:
Using and applying
mathematics
(5 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• identify the information needed to solve a problem
• understand routine and non-routine problems in a wide range of familiar
• sub-divide problems to make solving them more
and unfamiliar contexts and situations
• identify the situation or problem and the mathematical methods needed to
manageable
• present and explain methods and solutions,
Solving problems
interpreting results, including calculator results, in
(2–35)
the context of the problem.
tackle it
• select how best to model or represent a problem or situation, giving
reasons for choices
• calculate accurately, using mental methods or calculating devices as
appropriate
• produce simple proofs
• draw conclusions and make generalisations, providing mathematical
justifications
• record and communicate solutions to problems in familiar and unfamiliar
contexts
and to:
• recognise that mathematics is used as a tool in many contexts and that it
has rich historical and cultural roots.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
SUPPORT
5 | Exploring mathematics | Tier 6 (brown)
CORE
Algebra 1:
Expressions, equations and
formulae
(6 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• simplify expressions by taking out single-term
• select how best to model or represent a problem or situation, giving
common factors
reasons for choices
• add simple algebraic fractions
• use accurate notation
• substitute numbers into expressions and formulae
• manipulate algebraic expressions and equations
Equations, formulae and identities
and, in simple cases, change the subject of a
(118–121, 138–143)
formula
• construct and solve linear equations with integer
coefficients.
• produce simple proofs
• draw conclusions and make generalisations, providing mathematical
justifications
and to:
• simplify algebraic fractions
• solve linear equations in one unknown with integer and fraction
coefficients
• solve linear equations that require prior simplification of brackets,
including those with negative signs anywhere in the equation
• square a linear expression and expand the product of two linear
expressions of the form ax  b
• establish identities such as a2 – b2 = (a + b)(a – b)
• derive more complex formulae and change the subject of a formula,
including cases where a power of the subject appears in the question or
solution, e.g. find
r
given that
A  πr2 .
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
6 | Exploring mathematics | Tier 6 (brown)
Algebra 2:
Linear functions and graphs
(6 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• generate points and plot graphs of linear functions
• look for equivalence in different problems with similar structures
(y given implicitly in terms of x, e.g. ay + bx = 0,
y + bx + c = 0)
Sequences, functions and graphs
(148–163, 172–177)
Solving problems
(26–27)
• given values for m and c, find the gradient of lines
given by equations of the form y = mx + c
• interpret graphs arising from real situations,
including distance-time graphs.
• select how best to model or represent a problem or situation, giving
reasons for choices
• use accurate notation
• manipulate algebraic expressions and equations
• draw accurate graphs on paper and on screen
• explore the effects of varying values and look for invariance and
covariance in models and representations
• compare and evaluate representations of problems or situations
• draw conclusions and make generalisations, providing mathematical
justifications
and to:
• plot the graph of the inverse of a linear function
• understand that equations in the form
straight line and that
m
y  mx  c
is the gradient and
c
represent a
is the value of the
y-
intercept
• investigate 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
• solve a pair of simultaneous linear equations by eliminating one variable,
and by linking graphs of the equations to the algebraic solution
• consider cases of simultaneous linear equations that have no solution or
an infinite number of solutions.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
7 | Exploring mathematics | Tier 6 (brown)
Algebra 3:
Quadratic functions and
graphs
(8 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• generate terms of a linear sequence using term-
• look for equivalence in different problems with similar structures
to-term and position-to-term definitions of the
sequence
• generate sequences from practical contexts and
Equations, formulae and identities
write an expression to describe the nth term of an
(118–121, 126–131)
arithmetic sequence
Solving problems
(6–13)
• construct and solve linear equations with integer
coefficients
• solve linear equations with fraction coefficients
• select how best to model or represent a problem or situation, giving
reasons for choices
• use accurate notation
• manipulate algebraic expressions and equations
• draw accurate graphs on paper and on screen
• explore the effects of varying values and look for invariance and
covariance in models and representations
and one unknown on one or both sides of the
• compare and evaluate representations of problems or situations
equation
• draw conclusions and make generalisations, providing mathematical
• square a linear expression, expand the product of
two linear expressions of the form ax  b.
justifications
and to:
• solve simultaneous linear equations in two variables
• expand the product of two linear expressions of the form ax  b, and
simplify the corresponding quadratic expression
• use identities such as a2 – b2 = (a + b)(a – b)
• find the next term and the
nth
term of quadratic sequences and explore
their properties
• deduce properties of the sequences of triangular and square numbers
from spatial patterns
• explore simple properties of quadratic functions
• solve quadratic equations of the form x2 + b x + c = 0 by factorisation.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
8 | Exploring mathematics | Tier 6 (brown)
Algebra 4:
Using algebra
(8 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• plot graphs of linear functions
• look for equivalence in different problems with similar structures
• find the inverse of a linear function
• select how best to model or represent a problem or situation, giving
• solve direct proportion problems using algebraic
reasons for choices
Sequences, functions and graphs
methods, relating solutions to graphs of the
• use accurate notation
(148–153, 170–177)
equations
• manipulate algebraic expressions and equations
Solving problems
• know simple properties of quadratic functions
• draw accurate graphs on paper and on screen
(6–13)
• sketch and interpret simple graphs that model
• explore the effects of varying values and look for invariance and
real-life situations.
covariance in models and representations
• compare and evaluate representations of problems or situations
• draw conclusions and make generalisations, providing mathematical
justifications
and to:
• find the next term and the nth term of quadratic sequences and functions
and explore their properties
• plot graphs of simple quadratic and cubic functions, e.g. y = x2,
y = 3x2 + 4, y = x,, on paper and using ICT
• sketch and interpret graphs that model real situations.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
9 | Exploring mathematics | Tier 6 (brown)
SUPPORT
Geometry and measures 1:
Geometrical reasoning
(6 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• find the sums of the interior and exterior angles of
• identify the situation or problem and the mathematical methods needed to
polygons
• solve simple problems using angle and symmetry
Geometrical reasoning: lines, angles
properties of polygons, and angle properties of
and shapes
parallel and intersecting lines
(178–197)
• understand congruence
Construction and loci
• identify the parts of a circle
(220–227)
Solving problems
(14–17)
CORE
tackle it
• select and apply a range of mathematics to find solutions
• draw accurate mathematical diagrams and constructions on paper and on
screen
• draw conclusions and make generalisations, providing mathematical
justifications
• calculate squares and square roots
• produce simple proofs
• use ratio in a range of contexts.
• appreciate the difference between experimental evidence and
mathematical explanation
• judge the value of own findings and those presented by others
• record and communicate solutions to problems in familiar and unfamiliar
contexts
and to:
• solve multi-step problems using properties of angles, of parallel lines, and
of triangles and other polygons, justifying inferences and explaining
reasoning with diagrams and text
• understand from experience of constructing them that triangles given
SSS, SAS, ASA or RHS are unique, but that triangles given SSA or AAA
are not
• know that the tangent at any point on a circle is perpendicular to the
radius at that point
• explain why the perpendicular from the centre to the chord bisects the
chord
• know that if two 2D shapes are similar, corresponding angles are equal
and corresponding sides are in the same ratio, and understand from this
that any two circles and any two squares are mathematically similar while
in general any two rectangles are not.
§ 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,
• identify the situation or problem and the mathematical methods needed to
corresponding angles are equal and
corresponding sides are in the same ratio
tackle it
• select and apply a range of mathematics to find solutions
Measures and mensuration
• use ratio in a range of contexts
• draw accurate mathematical diagrams
(242–247)
• understand and apply Pythagoras’ theorem when
• use, convert and calculate using metric and, where appropriate, imperial
solving problems.
measures
• estimate, approximate and use appropriate checking procedures
• judge the value of own findings and those presented by others, and the
strength of empirical evidence
• draw conclusions and make generalisations, providing mathematical
justifications
and to:
• understand and apply Pythagoras’ theorem when solving problems
• understand and use trigonometric relationships in right-angled triangles,
and use these to solve 2D problems
• use the trigonometric function keys of a calculator.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
11 | Exploring mathematics | Tier 6 (brown)
Geometry and measures 3:
Transformations and loci
(7 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• use ratio in a range of contexts
• identify the situation or problem and the mathematical methods needed to
• find the coordinates of the midpoint of a line
segment
Transformations
• understand and apply Pythagoras’ theorem when
(202–217)
solving problems
Coordinates
transform 2D shapes by simple combinations of
(218–219)
Ratio and proportion
(78–81)
translations, rotations and reflections
• identify similar triangles
• enlarge 2D shapes, given a centre of enlargement
and a positive integer scale factor
• identify the scale factor of an enlargement as the
tackle it
• draw accurate mathematical diagrams and constructions on paper and on
screen
• explore the effects of varying values and look for invariance and
covariance in models and representations
• draw conclusions and make generalisations, providing mathematical
justifications
• record and communicate solutions to problems in familiar and unfamiliar
contexts
and to:
ratio of the lengths of any two corresponding line
• calculate the length of AB, given coordinates of points A and B
segments
• find the point that divides a line in a given ratio, using properties of similar
• construct bisectors of angles and perpendicular
bisectors of line segments.
triangles
• use any point as the centre of rotation
• measure the angle of rotation, using fractions of a turn or degrees
• transform 2D shapes by combinations of translations, rotations and
reflections, on paper and using ICT
• use congruence to show that translations, rotations and reflections
preserve length and angle
• enlarge 2D shapes using positive, fractional and negative scale factors,
on paper and using ICT, recognising the similarity of the resulting shapes
• understand and use the effects of enlargement on perimeter
• find the locus of a point that moves according to a more complex rule,
both by reasoning and by using ICT.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
12 | Exploring mathematics | Tier 6 (brown)
Geometry and measures 4:
Measures and mensuration
(6 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• calculate the surface area and volume of cubes,
• identify the situation or problem and the mathematical methods needed to
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)
cuboids and right prisms
area of a circle.
tackle it
• select and apply a range of mathematics to find solutions
• draw accurate mathematical diagrams
• calculate accurately, using mental methods or calculating devices when
appropriate
• use, convert and calculate using metric and, where appropriate, imperial
measures
• estimate, approximate and use appropriate checking procedures
• judge the value of own findings and those presented by others, and the
strength of empirical evidence
• draw conclusions and make generalisations, providing mathematical
justifications
and to:
• consolidate analysing 3D shapes through 2D projections, including plans
and elevations
• solve problems involving lengths of circular arcs and areas of sectors
• solve problems involving surface areas and volumes of cylinders.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
13 | Exploring mathematics | Tier 6 (brown)
Geometry and measures 5:
Trigonometry 2
(8 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• identify and use the properties of similar triangles
• identify the situation or problem and the mathematical methods needed to
• use ratio in a range of contexts
• understand trigonometric relationships in right-
Measures and mensuration
(242–7)
angled triangles.
tackle it
• select and apply a range of mathematics to find solutions
• draw accurate mathematical diagrams
• use, convert and calculate using metric and, where appropriate, imperial
measures
• estimate, approximate and use appropriate checking procedures
• judge the value of own findings and those presented by others, and the
strength of empirical evidence
• draw conclusions and make generalisations, providing mathematical
justifications
and to:
• understand and apply Pythagoras' theorem when solving problems in 2D
and simple problems in 3D
• understand and use trigonometric relationships in right-angled triangles,
and use these to solve problems, including those involving bearings
• solve multi-step problems using properties of angles, of parallel lines, and
of triangles and other polygons, justifying inferences and explaining
reasoning with diagrams and text.
§ 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)
Statistics
(248–275)
CORE
Before they start, pupils should be able to:
In this unit, pupils learn to:
• design and use a data collection sheet for
• identify the situation or problem and the mathematical methods needed to
grouped continuous data
tackle it
• gather data from secondary sources
• formulate hypotheses and decide on the best methods for testing them
• construct and interpret:
• select how best to model or represent a problem or situation, giving
– pie charts
– bar charts and frequency diagrams for discrete
data
– line graphs for time series
simple scatter graphs
construct and use stem-and-leaf diagrams
• use the range, mean, median and mode to
compare distributions.
reasons for choices
• compare and evaluate representations, explaining the features selected
and justifying the choice of representation in relation to the context
• look for patterns and exceptions in data
• draw conclusions and make generalisations
• interpret and communicate solutions to practical problems in familiar and
unfamiliar contexts
and to:
• independently plan a statistical project and justify the decisions made
• identify possible sources of bias and plan how to minimise it
• gather data from primary and secondary sources, using ICT and other
methods
• estimate and find the mean and median for large data sets
• construct and interpret:
– frequency polygons
– scatter diagrams and lines of best fit by eye
• understand correlation and distinguish between positive, negative and
zero correlation, using lines of best fit
• review results of a statistical enquiry, justify the choice of representations
and relate summary data to the questions being explored.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
15 | Exploring mathematics | Tier 6 (brown)
Statistics 2:
Probability 1
(5 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• recognise that the sum of probabilities of all
• identify the situation or problem and the mathematical methods needed to
mutually exclusive outcomes is 1 and use this
when solving problems
tackle it
• select how best to model or represent a problem or situation, giving
Probability
• compare experimental and theoretical
reasons for choices
(276–283)
probabilities in a range of contexts.
• use accurate notation
Fractions
• construct accurate diagrams and graphs on paper and on screen
(66–69)
• estimate, approximate and use appropriate checking procedures
• draw conclusions and make generalisations, providing mathematical
justifications
• judge the strength of empirical evidence and distinguish between
evidence and proof
• record and communicate solutions to problems in familiar and unfamiliar
contexts
and to:
• use tree diagrams to represent outcomes of two or more events and to
calculate probabilities of combinations of independent events
• 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)
• understand relative frequency as an estimate of probability and use this to
compare outcomes of experiments.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
16 | Exploring mathematics | Tier 6 (brown)
Statistics 3:
Enquiry 2
(8 hours)
Statistics
Before they start, pupils should be able to:
In this unit, pupils learn to:
• design and use a data collection sheet for
• identify the situation or problem and the mathematical methods needed to
grouped continuous data
• formulate hypotheses and decide on the best methods for testing them
• construct and interpret:
• select how best to model or represent a problem or situation, giving
(250–251, 254–275)
– pie charts
Solving problems
– bar charts and frequency diagrams for discrete
(28–29)
tackle it
• gather data from secondary sources
data
– line graphs for time series
scatter graphs
construct and use stem-and-leaf diagrams
• use the range, mean, median and mode to
compare distributions.
reasons for choices
• compare and evaluate representations, explaining the features selected
and justifying the choice of representation in relation to the context
• look for patterns and exceptions in data
• draw conclusions and make generalisations
• interpret and communicate solutions to practical problems in familiar and
unfamiliar contexts
and to:
• independent plan a statistical project and justify the decisions made
• identify possible sources of bias and plan how to minimise it
• gather data from primary and secondary sources, using ICT and other
methods
• estimate and find the mean and median for large data sets
• construct and interpret:
– frequency polygons
– scatter diagrams and lines of best fit by eye
• appreciate that zero correlation does not necessarily imply ‘no
relationship’ but merely ‘no linear relationship’
• examine critically the results of a statistical enquiry, justify the choice of
representations and relate summary data to the questions being explored.
§ Objectives in colour lay the groundwork for Functional Skills at level 2.
17 | Exploring mathematics | Tier 6 (brown)
Statistics 4:
Probability 2
(4 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• use the vocabulary of probability in interpreting
• identify the situation or problem and the mathematical methods needed to
results involving uncertainty and prediction
• identify all the mutually exclusive outcomes of an
Probability
(276–283)
experiment
tackle it
• select how best to model or represent a problem or situation, giving
reasons for choices
• recognise that the sum of probabilities of all
mutually exclusive outcomes is 1 and use this
when solving problems
• estimate probabilities from experimental data
• compare experimental and theoretical
probabilities in a range of contexts appreciate the
difference between mathematical explanation and
experimental evidence.
• use accurate notation
• construct accurate diagrams and graphs on paper and on screen
• draw conclusions and make generalisations, providing mathematical
justifications
• judge the strength of empirical evidence and distinguish between
evidence and proof
• record and communicate solutions to problems in familiar and unfamiliar
contexts
and to:
• use tree diagrams to represent outcomes of two or more events and to
calculate probabilities of combinations of independent events
• 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)
• understand relative frequency as an estimate of probability and use this to
compare outcomes of experiments.
§ 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
• identify the situation or problem and the mathematical methods needed to tackle it
offers is an opportunity to consolidate and refine
these skills.
• look for equivalence in different problems with similar structure
• select how best to model or represent a problem
• select and apply a range of mathematics to find solutions
• calculate accurately, using mental methods or calculating devices when appropriate
• manipulate numbers, algebraic expressions and equations, and apply routine algorithms
• make accurate mathematical diagrams and graphs
• estimate, approximate and use appropriate checking procedures
• draw conclusions and make generalisations, providing mathematical justifications
18 | Exploring mathematics | Tier 6 (brown)
• record and communicate solutions to problems in familiar and unfamiliar contexts
• make sense of, and judge the value of, own findings and those presented by others
and to:
<Content objectives as in unit>
Number
as in unit
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)