Exploring mathematics: Tier 5 NC levels 5 to 6 (level 5A/6CBA)
Autumn
33 lessons
N5.1 Powers and roots
Prime factor decomposition
Using ICT to estimate squares and roots
Simple cases of index laws
3 lessons
Spring
34 lessons
S5.2 Probability 1
Mutually exclusive events
Sum of probabilities
Estimating probabilities from
experimental data; comparing with
theoretical probability
3/4 lessons
N5.2 Proportional reasoning
Fractions four operations and brackets
Percentage change
Ratio and proportion
Mental and calculator calculations
Solving problems
6 lessons
N5.3 Calculations and calculators
Multiplying and dividing by powers of 10;
rounding and estimating calculations
Mental and written calculations with
decimals, all four operations
Use of calculator
Solving problems, including with measures
5/6 lessons
R5.1 Revision/support
Number, algebra, geometry
and measures, statistics
5 lessons
Summer
33 lessons
S5.3 Enquiry 2
Collecting, representing and
interpreting data on paper and using
ICT frequency tables and diagrams for
grouped continuous data
Comparing two distributions
Communicating findings, using ICT
6/7 lessons
S5.4 Probability 2
Identifying outcomes of an experiment
Comparing experimental with
theoretical probability
4/5 lessons
A5.2 Equations and formulae
Single-term common factors; adding simple
algebraic fractions; substitution in and
changing subject of simple formulae
Constructing and solving linear equations with
integer coefficients
Approximate solutions of equations using ICT
6 lessons
A5.3 Functions and graphs
Linear graphs, gradient and intercepts
Simple properties of quadratic functions
Deriving formulae
5/6 lessons
A5.4 Using algebra
Constructing, plotting and interpreting real-life
functions
Solving direct proportion problems
3 lessons
R5.2 Revision/support
Number, algebra, geometry
and measures, statistics
5 lessons
N5.4 Solving problems
Investigating problems using number and
algebra
Proof; finding a counter-example
History of mathematics
4/5 lessons
A5.5 Equations, formulae and graphs
Adding/subtracting algebraic fractions;
removing/cancelling common factors;
changing subject of simple formulae
Constructing and solving equations by exact
and approximate methods
Graphs of linear functions; direct proportion
and distance-time graphs
7/8 lessons
100 lessons
1 | Exploring mathematics | Tier 5 (blue)
G5.1 Measures and mensuration
Using measures to estimate, measure and
calculate; converting measures
Circumference and area of circle
Volume and surface area of simple prisms
5/6 lessons
G5.2 Angles and constructions
Angle sum and exterior angle of polygons
Finding unknown angles; geometrical
reasoning
Straight edge and compass constructions
Simple loci
9 lessons
G5.3 Transformations
Plane symmetry of 3-D shapes
Simple combinations of rotations, reflections
and translations, on paper and using ICT
Enlargement; scale drawings
Exploring transformations with ICT
5/6 lessons
G5.4 2-D and 3-D shapes
Visualising 3-D shapes; plans and elevations
Geometrical reasoning angles and shapes
Surface area and volume of prisms
7/8 lessons
Mathematical processes and applications are integrated into each unit
S5.1 Enquiry 1
Designing survey to collect data,
including data collection sheet
Representing and interpreting data, on
paper and using ICT line graphs for
time series, scatter graphs
Calculating statistics, including with a
calculator; comparing distributions
Communicating findings, using ICT
6 lessons
A5.1 Sequences and graphs
Generating sequences on paper and with ICT;
finding the nth term of an arithmetic sequence
Graphs of linear functions; gradient and
intercepts; interpreting graphs of real-life
functions, including distance-time
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 and use multiples, factors (divisors),
• identify problems and the methods needed to tackle them
common factor, highest common factor, lowest
common multiple and primes.
Integers, powers and roots
(52–59)
Calculations
CORE
• use squares, positive and negative square roots,
cubes and cube roots, and index notation for
small positive integer powers.
(86–101, 108–109)
Equations, formulae and identities
(114–115)
• select and apply mathematics to find solutions
• represent problems and synthesise information in different forms
• use accurate notation
• calculate accurately, selecting mental methods or a calculator as
appropriate
• use appropriate checking procedures
• record methods, solutions and conclusions
• make convincing arguments to justify generalisations or solutions
• interpret and communicate solutions to problems
and to:
• use index notation for integer powers
• know and use the index laws for multiplication and division of positive
integer powers
• extend mental methods of calculation with factors, powers and roots
• use the power and root keys of a calculator
• use ICT to estimate square roots and cube roots
• use the prime factor decomposition of a number.
Objectives in colour lay the groundwork for Functional Skills.
2 | Exploring mathematics | Tier 5 (blue)
Number 2:
Proportional reasoning
(6 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• order and round decimals
• identify problems and the methods needed to tackle them
• recognise fraction, decimal and percentage
• select and apply mathematics to find solutions
equivalents
Fractions, decimals, percentages,
ratio and proportion
• add and subtract simple fractions, and multiply
and divide a fraction by an integer
• break down substantial tasks to make them more manageable
• use connections with related contexts
• move from one form of representation to another to gain a different
(66–81)
• find fractions and percentages of quantities
Calculations
• express one number as a percentage of another
• use accurate notation
• simplify rations and divide a quantity in a given
• calculate accurately, selecting mental methods or a calculator as
(82–103, 110–111)
ratio
• solve problems involving direct proportion using
the unitary method.
perspective on a problem
appropriate
• use appropriate checking procedures
• review and refine own approaches on the basis of discussions with others
• record and communicate methods, solutions and conclusions
and to:
• extend mental methods of calculation with fractions, percentages and
ratios
• use efficient written methods to add and subtract fractions, and to multiply
or divide fractions, interpreting division as a multiplicative inverse, and
cancelling common factors before multiplying
• recognise when fractions or percentages are needed to compare
proportions
• solve problems involving percentage changes
• use proportional reasoning to solve problems, choosing the correct
numbers to take as 100%, or as a whole
• compare two ratios and calculate ratios in a range of contexts.
3 | Exploring mathematics | Tier 5 (blue)
Number 3:
Calculations and calculators
(6 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• read and write positive integer powers of 10
• select and apply mathematics to find solutions to problems
• multiply and divide by 0.1 and 0.01
• break down substantial tasks to make them more manageable
• use mental and efficient written methods to:
• build on previous experience of similar situations and outcomes
Place value
– add and subtract integers and decimals
(36–47)
– multiply and divide integers and decimals,
Fractions, decimals, percentages,
including by decimals such as 0.6 or 0.06,
ratio and proportion
understanding where to position the decimal
(60–65)
point by considering equivalent calculations.
Calculations
(82–85, 104–107, 110–111)
Calculator methods
(108–109)
Solving problems
(28–29)
• manipulate numbers and apply routine algorithms, selecting mental
methods or a calculator as appropriate
• recognise the impact of constraints or assumptions
• record and communicate methods, solutions and conclusions
and to:
• understand and use equivalences between 0.1, 1⁄10 and 10–1, and multiply
and divide by any integer power of 10
• understand the effects of multiplying or dividing by numbers between 0
and 1
• use positive and negative numbers of any size, the laws of arithmetic and
inverse operations
• understand the order of operations, including powers
• use known facts to derive unknown facts and extend mental methods of
calculation with decimals, including solving problems mentally
• use efficient written methods to add and subtract decimals of any size, to
multiply by decimals, and to divide by decimals by transforming to division
by an integer
• use a calculator efficiently and appropriately for complex calculations,
knowing not to round during intermediate steps
• use rounding to make estimates and to give solutions to an appropriate
degree of accuracy
• know that a recurring decimal is an exact fraction.
4 | Exploring mathematics | Tier 5 (blue)
Number 4:
Before they start, pupils should be able to:
In this unit, pupils learn to:
Solving problems
• identify the mathematical features of a context or
• solve routine and non-routine problems in familiar and unfamiliar contexts
(5 hours)
problem
• try out and compare mathematical
Solving problems
(2–35)
Percentages and proportion
(75–81)
Sequences, functions and graphs
(148–153)
representations
• use logical argument to interpret the mathematics
in a context or to establish the truth of a statement
• give accurate solutions appropriate to the context
or problem
• evaluate the efficiency of alternative strategies
and approaches.
• identify the situation or problem and the mathematical methods needed to
tackle it
• build on previous experience of similar situations and outcomes
• break down substantial tasks to make them more manageable
• select and apply mathematics to find solutions
• represent problems and synthesise information in different forms
• move from one form of representation to another to gain a different
perspective on a problem
• use connections with related contexts
• generate fuller solutions by presenting a concise, reasoned argument
• draw conclusions, identifying special cases and counter examples, and
provide mathematical justifications
• look for and reflect on other approaches and review and refine own
findings and approaches on the basis of discussions with others
• interpret and communicate solutions to problems
and to:
• appreciate the rich historical and cultural roots of mathematics.
5 | Exploring mathematics | Tier 5 (blue)
Algebra 1:
Sequences, functions and
graphs
(6 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• generate and describe integer sequences
• identify situations or problems and the methods needed to tackle them
• plot graphs of linear functions, where y is given
• select and apply mathematics to find solutions
explicitly in terms of x, on paper and using ICT
• recognise that equations of the form y = mx + c
Sequences, functions and graphs
(148–159, 172–177)
Solving problems
(26–27)
correspond to straight-line graphs
• discuss and interpret simple linear graphs arising
from real situations.
• represent and interpret problems in algebraic or graphical form
• move from one form to another to gain a different perspective on the
problem
• manipulate algebraic expressions and equations
• draw accurate graphs on paper and on screen
• draw conclusions and provide mathematical justifications
• make convincing arguments to justify generalisations or solutions,
considering special cases
and to:
• generate terms of a sequence using term-to-term and position-to-term
rules, on paper and using ICT
• generate sequences from practical contexts and write and justify an
expression for the nth term of an arithmetic sequence
• generate points and plot graphs of linear functions (y given implicitly in
terms of x, e.g. ay + bx = 0, y + bx + c = 0), on paper and using ICT
• find the gradient of lines given by equations of the form y = mx + c, given
values for m and c
• construct functions arising from real situations and plot and interpret
graphs their corresponding graphs.
6 | Exploring mathematics | Tier 5 (blue)
Algebra 2:
Equations and formulae
(6 hours)
Equations, formulae and identities
(112–113, 116–125, 132–135)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• simplify linear expressions by collecting like terms
• represent and interpret problems in algebraic form
• multiply a single term over a bracket
• build on previous experience of similar situations and outcomes
• construct and solve linear equations with integer
• manipulate algebraic expressions and equations
coefficients (unknown on either or both sides)
• substitute integers into simple expressions and
formulae
• use appropriate checking procedures
• generate fuller solutions by presenting a concise, reasoned argument
using symbols and related explanations
and to:
• factorise algebraic expressions by taking out single-term common factors
• add simple algebraic fractions
• substitute numbers into expressions and formulae and, in simple cases,
change the subject of a formula
• construct and solve linear equations with integer coefficients (with and
without brackets, negative signs anywhere in the equation, positive or
negative solution)
• use systematic trial and improvement methods and ICT tools to find
approximate solutions of equations such as x3 + x = 20.
Algebra 3:
Functions and graphs
(6 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• plot graphs of linear functions, where y is given
• break down substantial tasks to make them more manageable
explicitly in terms of x, on paper and using ICT
• represent and interpret problems in algebraic or graphical form
• recognise that equations of the form y = mx + c
Equations, formulae and identities
(136–143)
Sequences, functions and graphs
(160–177)
Solving problems
(26–27)
correspond to straight-line graphs
• express simple functions in symbols.
• draw accurate graphs on paper and on screen
• move from one form to another to gain a different perspective on the
problem
• manipulate algebraic expressions and equations
• use appropriate checking procedures
• generate fuller solutions by presenting a concise, reasoned argument
using symbols, diagrams, graphs and related explanations
• make convincing arguments to justify generalisations or solutions,
considering special cases
• review and refine own findings and approaches on the basis of
discussions with others
and to:
• find the inverse of a linear function
• generate points and plot graphs of linear functions (y given implicitly in
terms of x, e.g. ay + bx = 0, y + bx + c = 0)
• find the gradient of lines given by equations of the form y = mx + c, given
values for m and c.
7 | Exploring mathematics | Tier 5 (blue)
Algebra 4:
Using algebra
(3 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• plot graphs of linear functions, where y is given
• break down substantial tasks to make them more manageable
explicitly in terms of x, on paper and using ICT
• represent and interpret problems in algebraic or graphical form
• given values for m and c, find the gradient of lines
Equations, formulae and identities
given by equations of the form y = mx + c
(136–143)
• substitute values in expressions of the form y  kx
Sequences, functions and graphs
• express simple functions in symbols.
(160–177)
Solving problems
(26–27)
• draw accurate graphs on paper and on screen
• move from one form to another to gain a different perspective on the
problem
• manipulate algebraic expressions and equations
• use appropriate checking procedures
• generate fuller solutions by presenting a concise, reasoned argument
using symbols, diagrams, graphs and related explanations
• make convincing arguments to justify generalisations or solutions,
considering special cases
• justify the mathematical features drawn from a context and the choice of
approach
and to:
• use algebraic methods to solve problems involving direct proportion,
relating solutions to graphs of the equations, using ICT as appropriate
• use formulae from mathematics and other subjects, derive a formula and,
in simple cases, change its subject
• substitute numbers into expressions and formulae
• construct functions arising from real-life problems and plot their
corresponding graphs
• interpret graphs arising from real situations
• explore simple properties of quadratic functions.
8 | Exploring mathematics | Tier 5 (blue)
Algebra 5:
Equations, formulae and
graphs
(8 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• simplify linear expressions by collecting like terms
• break down substantial tasks to make them more manageable
• multiply a single term over a bracket
• represent and interpret problems in algebraic or graphical form
• construct and solve linear equations with integer
• draw accurate graphs on paper and on screen
coefficients (unknown on either or both sides)
Fractions
using appropriate methods (e.g. inverse
(62–63)
operations, transforming both sides in the same
Equations, formulae and identities
way)
(122–125, 132–143)
• plot the graphs of linear functions, where y is
Graphs
given explicitly in terms of x, on paper and using
(164–171)
ICT.
Solving problems
(6–13)
• move from one form to another to gain a different perspective on the
problem
• manipulate algebraic expressions and equations
• use appropriate checking procedures
• generate fuller solutions by presenting a concise, reasoned argument
using symbols, diagrams, graphs and related explanations
• make convincing arguments to justify generalisations or solutions,
considering special cases
and to:
• factorise algebraic expressions by taking out single-term common factors
• add and subtract simple algebraic fractions
• substitute numbers into expressions and formulae and, in simple cases,
change the subject of a formula
• construct and solve linear equations with integer coefficients
• use systematic trial and improvement methods and ICT tools to find
approximate solutions of equations such as x3 + x = 20
• generate points and plot graphs of linear functions (y given implicitly in
terms of x, e.g. ay + bx = 0, y + bx + c = 0)
• find the gradient of lines given by equations of the form y = mx + c, given
values for m and c.
9 | Exploring mathematics | Tier 5 (blue)
Geometry and measures 1:
Measures and mensuration
(6 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• convert a metric unit of length, mass or capacity to
• identify situations or problems and the methods needed to tackle them
a related larger or smaller unit
• make sensible estimates of a range of measures
Coordinates
(218–219)
in relation to everyday situations
• know and use the formulae for the area of a
Measures and mensuration
rectangle, the area of a triangle, trapezium and
(228–231, 234–241)
parallelogram, and the volume of a cuboid.
• select and apply mathematics to find solutions
• break down substantial tasks to make them more manageable
• justify the mathematical features drawn from a context and the choice of
approach
• use accurate notation
• manipulate numbers and apply routine algorithms, selecting mental
methods or a calculator as appropriate
• use appropriate checking procedures
• recognise the impact of constraints or assumptions
• record, interpret and communicate solutions to problems
and to:
• solve problems involving measurements in a variety of contexts
• convert between area measures and between volume measures
• know and use the formulae for the circumference and area of a circle, and
use the  key of a calculator
• calculate the surface area and volume of right prisms.
10 | Exploring mathematics | Tier 5 (blue)
SUPPORT
CORE
Geometry and measures 2:
Angles and constructions
(9 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• identify alternate angles and corresponding
• identify situations or problems and the methods needed to tackle them
Geometrical reasoning: lines, angles
• understand a proof that:
angles
and shapes
– the sum of the angles of a triangle is 180°
(178–189, 194–197)
– the exterior angle of a triangle is equal to the
Construction and loci
220–227)
Solving problems
(14–17)
sum of the two interior opposite angles
• solve problems using side and angle properties of
triangles and quadrilaterals
• use ruler and compasses to construct:
– the midpoint and perpendicular bisector of a
• select and apply mathematics to find solutions
• break down substantial tasks to make them more manageable
• represent problems in geometric form, making accurate mathematical
diagrams on paper and on screen
• generate, explain and communicate fuller solutions using diagrams and
related explanations
• make convincing arguments to justify generalisations or solutions
• review and refine own findings and approaches on the basis of
discussions with others
line segment
– the bisector of an angle
– a triangle, given three sides (SSS).
and to:
• explain how to find, calculate and use:
– the sums of the interior and exterior angles of quadrilaterals,
pentagons and hexagons
– the interior and exterior angles of regular polygons
• solve problems using properties of angles, of parallel and intersecting
lines, and of triangles and other polygons, justifying inferences and
explaining reasoning with diagrams and text
• know the definition of a circle and the names of its parts, and inscribe
regular polygons by constructing equal divisions of a circle
• use straight-edge and compasses to construct::
– the perpendicular from a point to a line
– the perpendicular to a line from a point on the line
– triangles, given right angle, hypotenuse and side (RHS)
• find the locus of a point that moves according to a simple rule, both by
reasoning and by using ICT
• use ICT to explore constructions of triangles and other 2D shapes
11 | Exploring mathematics | Tier 5 (blue)
Geometry and measures 3:
Transformations
(6 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• identify all the symmetries of 2D shapes
• identify situations or problems and the methods needed to tackle them
• understand that if two 2D shapes are congruent,
• select and apply mathematics to find solutions
corresponding sides and angles are equal
Geometrical reasoning: lines, angles
and shapes
• transform 2D shapes by rotations, reflections and
translations
• break down substantial tasks to make them more manageable
• represent problems in geometric form, making accurate mathematical
diagrams on paper and on screen
(178–179, 190–191)
• simplify a ratio
• generate, explain and communicate fuller solutions using diagrams
Transformations
• make simple scale drawings.
• make convincing arguments to justify generalisations or solutions
(202–217)
Mensuration
and to:
(242–247)
• identify reflection symmetry in 3D shapes
Ratio and proportion
• use a coordinate grid to solve problems involving translations, rotations,
(78–81)
reflections and enlargements
• recognise that translations, rotations and reflections preserve length and
angle, and map objects onto congruent images
• explore and compare combinations of translations, reflections and
rotations of 2D shapes, on paper and using ICT
• enlarge 2D shapes, given a centre of enlargement and a positive integer
scale factor, identifying the scale factor as the ratio of the lengths of any
two corresponding line segments
• recognise that enlargements preserve angle but not length
• devise instructions for a computer to generate and transform shapes
• use and interpret maps and scale drawings.
12 | Exploring mathematics | Tier 5 (blue)
Geometry and measures 4:
2D and 3D shapes
(8 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• solve problems using side and angle properties of
• identify situations or problems and the methods needed to tackle them
Geometrical reasoning: lines, angles
• classify quadrilaterals
• break down substantial tasks to make them more manageable
and shapes
• calculate volumes and surface areas of cuboids
• represent problems in geometric form, making accurate mathematical
(184–189, 198–201)
Transformations
(216–217)
triangles and quadrilaterals
and shapes made from cuboids.
• select and apply mathematics to find solutions
diagrams on paper and on screen
• generate fuller solutions by presenting a concise, reasoned argument
using accurate notation, diagrams and related explanations
Mensuration
(238–241)
Solving problems
(14–19, 30–31)
• make convincing arguments to justify generalisations or solutions
• interpret and communicate solutions to problems
• review and refine own findings and approaches on the basis of
discussions with others
• look for and reflect on other approaches
and to:
• solve problems using properties of angles, of parallel and intersecting
lines, and of triangles and other polygons
• visualise and use 2D representations of 3D objects, and analyse 3D
shapes through 2D projections, including plans and elevations
• solve problems involving measurements in a variety of contexts
• calculate the surface area and volume of right prisms.
13 | Exploring mathematics | Tier 5 (blue)
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 data
• pose questions and use statistical methods to investigate situations
• plan how to collect data
• break down substantial tasks to make them more manageable
• construct frequency tables with equal class
• collect and represent discrete and continuous data, using ICT where
Statistics
intervals for continuous data and two-way tables
(248–275)
for discrete data
• construct and interpret:
– pie charts
– bar charts and frequency diagrams for discrete
data
– simple scatter graphs
• compare two simple distributions, using the range
and one of the mode, median or mean.
appropriate
• use and interpret statistical measures, tables and diagrams, for discrete
and continuous data, using ICT where appropriate
• draw conclusions to support or cast doubt on initial conjectures and make
convincing arguments to justify generalisations
• recognise the impact of constraints or assumptions
• review and refine own findings and approaches on the basis of
discussions with others
• justify the mathematical features drawn from a context and the approach
• interpret and communicate fuller solutions to problems using selected
tables, diagrams, graphs and related explanations
and to:
• identify the sample size and degree of accuracy needed, and possible
primary or secondary sources of data, including the internet
• design, trial and if necessary refine data collection sheets
• construct frequency tables for gathering discrete or continuous data,
choosing suitable class intervals
• calculate statistics and select those which address the questions posed,
constructing stem-and-leaf diagrams where appropriate
• select, construct and modify, on paper and using ICT, suitable graphs and
diagrams to progress an enquiry, e.g. frequency diagrams, pie charts
• compare distributions and make inferences, using the shape of the
distributions and appropriate statistics.
14 | Exploring mathematics | Tier 5 (blue)
Statistics 2:
Probability 1
(4 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• recall that if the probability of an event occurring is
• pose questions and use statistical methods to investigate situations
p, then the probability of it not occurring is 1 – p
• use diagrams and tables to record in a systematic
Probability
way all possible mutually exclusive outcomes for
(276–285)
single events and two successive events
Fractions
(66–69)
• understand that:
– if an experiment is repeated there may be
different outcomes
– increasing the number of times an experiment
• break down substantial tasks to make them more manageable
• draw accurate diagrams and graphs
• look for patterns
• draw conclusions and make convincing arguments to justify
generalisations
• review and refine own findings and approaches on the basis of
discussions with others
is repeated generally leads to better estimates
• record methods, solutions and conclusions
of probability.
• interpret and communicate fuller solutions to problems using diagrams,
graphs and related explanations
and to:
• identify all the mutually exclusive outcomes of an experiment
• know that the sum of probabilities of all mutually exclusive outcomes is 1
and use this when solving problems
• use a numerical scale from 0 to 1 to express and compare experimental
and theoretical probabilities in a range of contexts.
15 | Exploring mathematics | Tier 5 (blue)
Statistics 3:
Enquiry 2
(7 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• design and use two-way tables for discrete data
• pose questions and use statistical methods to investigate situations
• construct and interpret:
• break down substantial tasks to make them more manageable
– pie charts
Statistics
(250–251, 254–275)
Solving problems
(28–29)
– bar charts and frequency diagrams for discrete
data
– simple scatter graphs
• construct and use stem-and-leaf diagrams
• compare two simple distributions, using the range
and one of the mode, median or mean.
• collect and represent discrete and continuous data, using ICT where
appropriate
• use and interpret statistical measures, tables and diagrams, for discrete
and continuous data, using ICT where appropriate
• draw conclusions to support or cast doubt on initial conjectures and make
convincing arguments to justify generalisations
• recognise the impact of constraints or assumptions
• review and refine own findings and approaches on the basis of
discussions with others
• justify the mathematical features drawn from a context and the approach
• interpret and communicate fuller solutions to problems using selected
tables, diagrams, graphs and related explanations
and to:
• design, trial and if necessary refine data collection sheets
• select, construct and modify, on paper and using ICT, suitable graphs and
charts to progress an enquiry, including:
– line graphs for time series
– scatter graphs to develop further understanding of correlation.
16 | Exploring mathematics | Tier 5 (blue)
Statistics 4:
Probability 2
(5 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• recall that if the probability of an event occurring is
• pose questions and use statistical methods to investigate situations
p, then the probability of it not occurring is 1 – p
• use diagrams and tables to record in a systematic
Probability
way all possible mutually exclusive outcomes for
(276–285)
single events and two successive events
• break down substantial tasks to make them more manageable
• draw accurate diagrams and graphs
• look for patterns
• draw conclusions and make convincing arguments to justify
• understand that:
– if an experiment is repeated there may be
different outcomes
– increasing the number of times an experiment
generalisations
• review and refine own findings and approaches on the basis of
discussions with others
is repeated generally leads to better estimates
• record methods, solutions and conclusions
of probability.
• interpret and communicate fuller solutions to problems using diagrams,
graphs and related explanations
and to:
• identify all the mutually exclusive outcomes of an experiment
• know that the sum of probabilities of all mutually exclusive outcomes is 1
and use this when solving problems
• use a numerical scale from 0 to 1 to express and compare experimental
and theoretical probabilities in a range of contexts.
• appreciate the difference between mathematical explanation and
experimental evidence.
Revision 1 and 2 - here are the process objectives
Previous learning
Objectives based on NC levels 5 and 6 (mainly level 5)
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
• build on previous experience of similar situations and outcomes
offers is an opportunity to consolidate and refine
these skills.
• identify the methods needed to tackle problems
• select and apply mathematics to find solutions
• calculate accurately, using mental methods or a calculator as appropriate
• manipulate numbers, algebraic expressions and equations, and apply routine algorithms
• make accurate mathematical diagrams and graphs
• use appropriate checking procedures, giving accurate solutions appropriate to the context
• record and communicate solutions to problems
• review and refine own findings and approaches on the basis of discussions with others
and to:
Number
content objectives are as in the unit remind me to
colour functional skills objectives
17 | Exploring mathematics | Tier 5 (blue)
18 | Exploring mathematics | Tier 5 (blue)