Tier 4 Lesson Objectives Map
Unit
and
lesson
Class
book
page
A4.1
30-39
A4.1
30-39
A4.1
30-39
A4.1
30-39
A4.1
30-39
A4.1
30-39
A4.1-1
30
Strand
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
3 Algebra
Sub-section
1.1 Representing
1.1 Representing
1.2 Analysing – use mathematical reasoning
1.2 Analysing – use mathematical reasoning
1.3 Analysing – use appropriate mathematical
procedures
1.5 Communicating and reflecting
3.2 Sequences, functions and graphs
Revised Framework objectives Year 8

try out and compare mathematical
representations;

select appropriate procedures and tools, including
ICT 

conjecture and generalise;

move between the general and the particular to
test the logic of an argument;

record methods, solutions and conclusions; 

refine own findings and approaches on the basis
of discussions with others;

generate terms of a linear sequence using term-toterm and position-to-term rules, on paper and using a
spreadsheet or graphics calculator

A4.1-2
32
3 Algebra
3.2 Sequences, functions and graphs
generate terms of a linear sequence using term-toterm and position-to-term rules, on paper and using a
spreadsheet or graphics calculator

A4.1-2
32
3 Algebra
3.2 Sequences, functions and graphs
use linear expressions to describe the nth term of
a simple arithmetic sequence, justifying its form by
referring to the activity or practical context from which
it was generated 

A4.1-3
35
3 Algebra
3.2 Sequences, functions and graphs
generate terms of a linear sequence using term-toterm and position-to-term rules, on paper and using a
spreadsheet or graphics calculator
Tier 4 Lesson Objectives Map
Unit
and
lesson
Class
book
page
Strand
Sub-section
Revised Framework objectives Year 8

A4.1-4
37
3 Algebra
3.2 Sequences, functions and graphs
A4.2
76-86
1 Mathematical processes
and applications
1.1 Representing
A4.2
76-86
1 Mathematical processes
and applications
1.3 Analysing – use appropriate mathematical
procedures
A4.2
76-86
1.3 Analysing – use appropriate mathematical
procedures
A4.2
76-86
1 Mathematical processes
and applications
1 Mathematical processes
and applications
A4.2-1
76
3 Algebra
A4.2-1
76
3 Algebra
A4.2-1
76
3 Algebra
1.5 Communicating and reflecting
3.1 Equations, formulae, expressions and
identities
3.1 Equations, formulae, expressions and
identities
3.1 Equations, formulae, expressions and
identities
A4.2-2
79
3 Algebra
3.1 Equations, formulae, expressions and
identities
A4.2-2
79
3 Algebra
3.1 Equations, formulae, expressions and
identities
A4.2-2
79
3 Algebra
3.1 Equations, formulae, expressions and
identities
use linear expressions to describe the nth term of
a simple arithmetic sequence, justifying its form by
referring to the activity or practical context from which
it was generated 

try out and compare mathematical
representations;

manipulate numbers, algebraic expressions and
equations, and apply routine algorithms; 

use accurate notation, including correct syntax
when using ICT; 

refine own findings and approaches on the basis
of discussions with others;

understand that algebraic operations, including the
use of brackets, follow the rules of arithmetic;

simplify or transform linear expressions by
collecting like terms;

multiply a single term over a bracket 

recognise that letter symbols play different roles in
equations, formulae and functions;

know the meanings of the words formula and
function 

use graphs and set up equations to solve simple
problems involving direct proportion 
Tier 4 Lesson Objectives Map
Unit
and
lesson
Class
book
page
Strand
A4.2-2
79
3 Algebra
A4.2-3
82
3 Algebra
A4.2-3
82
3 Algebra
3.1 Equations, formulae, expressions and
identities
Sub-section
3.1 Equations, formulae, expressions and
identities
3.1 Equations, formulae, expressions and
identities
A4.2-3
82
3 Algebra
3.1 Equations, formulae, expressions and
identities
A4.2-4
84
3 Algebra
3.1 Equations, formulae, expressions and
identities
A4.2-4
84
3 Algebra
3.1 Equations, formulae, expressions and
identities
84
3 Algebra
3.1 Equations, formulae, expressions and
identities
146160
146160
146160
146160
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
A4.2-4
A4.3
A4.3
A4.3
A4.3
1.1 Representing
1.1 Representing
1.1 Representing
1.2 Analysing – use mathematical reasoning
Revised Framework objectives Year 8

use formulae from mathematics and other
subjects;

use index notation for small positive integer
powers 

construct and solve linear equations with integer
coefficients (unknown on either or both sides, without
and with brackets) using appropriate methods (e.g.
inverse operations, transforming both sides in same
way) 

substitute integers into simple formulae, including
examples that lead to an equation to solve; 

use formulae from mathematics and other
subjects;

substitute integers into simple formulae, including
examples that lead to an equation to solve; 

substitute positive integers into expressions
involving small powers e.g. 3x2 + 4 or 2x3;

identify the mathematical features of a context or
problem;

try out and compare mathematical
representations;

select appropriate procedures and tools, including
ICT 

visualise and manipulate dynamic images;
Tier 4 Lesson Objectives Map
Unit
and
lesson
Class
book
page
Strand
Sub-section
146160
146160
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1.2 Analysing – use mathematical reasoning
A4.3
146160
1 Mathematical processes
and applications
1.3 Analysing – use appropriate mathematical
procedures
A4.3
146160
1 Mathematical processes
and applications
1.3 Analysing – use appropriate mathematical
procedures
A4.3
A4.3
1.2 Analysing – use mathematical reasoning
Revised Framework objectives Year 8

conjecture and generalise;

identify exceptional cases or counter-examples;

make accurate mathematical diagrams, graphs
and constructions on paper and on screen;

manipulate numbers, algebraic expressions and
equations, and apply routine algorithms; 

A4.3-1
146
3 Algebra
3.2 Sequences, functions and graphs
A4.3-2
150
3 Algebra
3.2 Sequences, functions and graphs
generate points in all four quadrants and plot the
graphs of linear functions, where y is given explicitly in
terms of x, on paper and using ICT;

express simple functions algebraically and
represent them in mappings or on a spreadsheet 

A4.3-3
152
3 Algebra
3.2 Sequences, functions and graphs
A4.3-4
154
3 Algebra
3.2 Sequences, functions and graphs
generate points in all four quadrants and plot the
graphs of linear functions, where y is given explicitly in
terms of x, on paper and using ICT;

express simple functions algebraically and
represent them in mappings or on a spreadsheet 

A4.3-4
154
3 Algebra
3.2 Sequences, functions and graphs
generate points in all four quadrants and plot the
graphs of linear functions, where y is given explicitly in
terms of x, on paper and using ICT;
Tier 4 Lesson Objectives Map
Unit
and
lesson
Class
book
page
Strand
Sub-section
A4.3-4
154
3 Algebra
3.2 Sequences, functions and graphs
A4.3-5
155
3 Algebra
3.2 Sequences, functions and graphs
Revised Framework objectives Year 8

recognise that equations of the form y = mx + c
correspond to straight-line graphs 

recognise that equations of the form y = mx + c
correspond to straight-line graphs 

A4.3-5
155
3 Algebra
3.2 Sequences, functions and graphs
A4.3-6
156
3 Algebra
3.2 Sequences, functions and graphs
203218
203218
1 Mathematical processes
and applications
1 Mathematical processes
and applications
A4.4
203218
1 Mathematical processes
and applications
1.3 Analysing – use appropriate mathematical
procedures
A4.4
203218
1 Mathematical processes
and applications
1.3 Analysing – use appropriate mathematical
procedures
A4.4
203218
1 Mathematical processes
and applications
1.4 Interpreting and evaluating
A4.4
203218
1 Mathematical processes
and applications
1.4 Interpreting and evaluating
A4.4
203218
1 Mathematical processes
and applications
1.4 Interpreting and evaluating
construct linear functions arising from real-life
problems and plot their corresponding graphs;

A4.4
A4.4
1.1 Representing
1.1 Representing
discuss and interpret graphs arising from real
situations, e.g. distance–time graphs 

identify the mathematical features of a context or
problem;

try out and compare mathematical
representations;

manipulate numbers, algebraic expressions and
equations, and apply routine algorithms; 

use accurate notation, including correct syntax
when using ICT; 
 use logical argument to interpret the mathematics
in a given context or to establish the truth of a
statement;

use logical argument to interpret the mathematics
in a given context or to establish the truth of a
statement;

evaluate the efficiency of alternative strategies and
approaches 
Tier 4 Lesson Objectives Map
Unit
and
lesson
Class
book
page
Strand
Sub-section
A4.4
203218
1 Mathematical processes
and applications
1.5 Communicating and reflecting
A4.4-1
203
3 Algebra
3.2 Sequences, functions and graphs
Revised Framework objectives Year 8

refine own findings and approaches on the basis
of discussions with others;

generate points in all four quadrants and plot the
graphs of linear functions, where y is given explicitly in
terms of x, on paper and using ICT;

A4.4-1
203
3 Algebra
3.2 Sequences, functions and graphs
recognise that equations of the form y = mx + c
correspond to straight-line graphs 

A4.4-2
A4.4-2
205
205
3 Algebra
3.1 Equations, formulae, expressions and
identities
3 Algebra
3.1 Equations, formulae, expressions and
identities
construct and solve linear equations with integer
coefficients (unknown on either or both sides, without
and with brackets) using appropriate methods (e.g.
inverse operations, transforming both sides in same
way) 

substitute integers into simple formulae, including
examples that lead to an equation to solve;

A4.4-2
205
3 Algebra
3.2 Sequences, functions and graphs
generate points in all four quadrants and plot the
graphs of linear functions, where y is given explicitly in
terms of x, on paper and using ICT;

A4.4-3
208
3 Algebra
3.1 Equations, formulae, expressions and
identities
construct and solve linear equations with integer
coefficients (unknown on either or both sides, without
and with brackets) using appropriate methods (e.g.
inverse operations, transforming both sides in same
way) 
Tier 4 Lesson Objectives Map
Unit
and
lesson
Class
book
page
Strand
Sub-section
Revised Framework objectives Year 8

A4.4-4
210
3 Algebra
3.1 Equations, formulae, expressions and
identities
construct and solve linear equations with integer
coefficients (unknown on either or both sides, without
and with brackets) using appropriate methods (e.g.
inverse operations, transforming both sides in same
way) 

A4.4-5
212
3 Algebra
3.1 Equations, formulae, expressions and
identities
construct and solve linear equations with integer
coefficients (unknown on either or both sides, without
and with brackets) using appropriate methods (e.g.
inverse operations, transforming both sides in same
way) 

A4.4-6
A4.5
A4.5
A4.5
A4.5
215
3 Algebra
264284
264284
264284
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
264284
1 Mathematical processes
and applications
3.1 Equations, formulae, expressions and
identities
1.1 Representing
1.1 Representing
1.2 Analysing – use mathematical reasoning
1.3 Analysing – use appropriate mathematical
procedures
construct and solve linear equations with integer
coefficients (unknown on either or both sides, without
and with brackets) using appropriate methods (e.g.
inverse operations, transforming both sides in same
way) 

try out and compare mathematical
representations;

select appropriate procedures and tools, including
ICT 

visualise and manipulate dynamic images;

make accurate mathematical diagrams, graphs
and constructions on paper and on screen;
Tier 4 Lesson Objectives Map
Unit
and
lesson
Class
book
page
Strand
Sub-section
A4.5
264284
1 Mathematical processes
and applications
1.3 Analysing – use appropriate mathematical
procedures
A4.5
264284
1 Mathematical processes
and applications
1.4 Interpreting and evaluating
264284
264284
264284
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
A4.5-1
264
3 Algebra
A4.5-1
264
3 Algebra
A4.5-2
267
3 Algebra
A4.5-3
269
3 Algebra
A4.5
A4.5
A4.5
Revised Framework objectives Year 8

manipulate numbers, algebraic expressions and
equations, and apply routine algorithms; 

1.4 Interpreting and evaluating
1.5 Communicating and reflecting
1.5 Communicating and reflecting
3.1 Equations, formulae, expressions and
identities
3.1 Equations, formulae, expressions and
identities
3.1 Equations, formulae, expressions and
identities
3.1 Equations, formulae, expressions and
identities
use logical argument to interpret the mathematics
in a given context or to establish the truth of a
statement;

evaluate the efficiency of alternative strategies and
approaches 

refine own findings and approaches on the basis
of discussions with others;

relate the current problem and structure to
previous situations 

simplify or transform linear expressions by
collecting like terms;

multiply a single term over a bracket 

simplify or transform linear expressions by
collecting like terms;

construct and solve linear equations with integer
coefficients (unknown on either or both sides, without
and with brackets) using appropriate methods (e.g.
inverse operations, transforming both sides in same
way) 

A4.5-4
272
3 Algebra
3.2 Sequences, functions and graphs
generate points in all four quadrants and plot the
graphs of linear functions, where y is given explicitly in
terms of x, on paper and using ICT;
Tier 4 Lesson Objectives Map
Unit
and
lesson
Class
book
page
Strand
Sub-section
Revised Framework objectives Year 8

A4.5-5
276
3 Algebra
3.2 Sequences, functions and graphs
A4.5-6
277
3 Algebra
3.1 Equations, formulae, expressions and
identities
A4.5-6
277
3 Algebra
3.2 Sequences, functions and graphs
generate points in all four quadrants and plot the
graphs of linear functions, where y is given explicitly in
terms of x, on paper and using ICT;

use graphs and set up equations to solve simple
problems involving direct proportion 

A4.5-7
279
3 Algebra
3.1 Equations, formulae, expressions and
identities
A4.5-8
281
3 Algebra
3.1 Equations, formulae, expressions and
identities
A4.5-8
281
3 Algebra
3.1 Equations, formulae, expressions and
identities
G4.1
15-28
G4.1
15-28
1 Mathematical processes
and applications
1 Mathematical processes
and applications
G4.1
15-28
1 Mathematical processes
and applications
G4.1
15-28
1 Mathematical processes
and applications
1.1 Representing
1.2 Analysing – use mathematical reasoning
1.3 Analysing – use appropriate mathematical
procedures
1.3 Analysing – use appropriate mathematical
procedures
construct linear functions arising from real-life
problems and plot their corresponding graphs;

substitute integers into simple formulae, including
examples that lead to an equation to solve; 

substitute integers into simple formulae, including
examples that lead to an equation to solve; 

derive simple formulae 

select appropriate procedures and tools, including
ICT 

visualise and manipulate dynamic images;

make accurate mathematical diagrams, graphs
and constructions on paper and on screen;

use accurate notation, including correct syntax
when using ICT; 
Tier 4 Lesson Objectives Map
Unit
and
lesson
Class
book
page
Strand
Sub-section
G4.1
15-28
1 Mathematical processes
and applications
1.4 Interpreting and evaluating
G4.1
15-28
G4.1
15-28
G4.11
G4.12
G4.13
1 Mathematical processes
and applications
1 Mathematical processes
and applications
Revised Framework objectives Year 8

1.4 Interpreting and evaluating
1.5 Communicating and reflecting
15
4 Geometry and measures
4.1 Geometrical reasoning
18
4 Geometry and measures
4.1 Geometrical reasoning
21
4 Geometry and measures
4.1 Geometrical reasoning
use logical argument to interpret the mathematics
in a given context or to establish the truth of a
statement;

evaluate the efficiency of alternative strategies and
approaches 

refine own findings and approaches on the basis
of discussions with others;

identify alternate angles and corresponding
angles;

identify alternate angles and corresponding
angles;

solve geometrical problems using side and angle
properties of equilateral, isosceles and right-angled
triangles and special quadrilaterals, explaining
reasoning with diagrams and text;

G4.13
21
4 Geometry and measures
4.1 Geometrical reasoning
G4.14
23
4 Geometry and measures
4.1 Geometrical reasoning
G4.15
25
4 Geometry and measures
4.1 Geometrical reasoning
G4.2
88105
1 Mathematical processes
and applications
1.1 Representing
understand a proof that:

the angle sum of a triangle is 180° and of a
quadrilateral is 360°

the exterior angle of a triangle is equal to
the sum of the two interior opposite angles 

know that if two 2-D shapes are congruent,
corresponding sides and angles are equal 

classify quadrilaterals by their geometrical
properties

identify the mathematical features of a context or
problem;
Tier 4 Lesson Objectives Map
Unit
and
lesson
G4.2
G4.2
G4.2
G4.2
G4.2
G4.21
G4.21
G4.22
G4.23
G4.24
G4.24
G4.24
Class
book
page
Strand
88105
88105
1 Mathematical processes
and applications
1 Mathematical processes
and applications
88105
1 Mathematical processes
and applications
1.3 Analysing – use appropriate mathematical
procedures
88105
88105
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1.3 Analysing – use appropriate mathematical
procedures
88
4 Geometry and measures
4.4 Measures and mensuration
Sub-section
1.1 Representing
1.2 Analysing – use mathematical reasoning
1.5 Communicating and reflecting
Revised Framework objectives Year 8

select appropriate procedures and tools, including
ICT 

move between the general and the particular to
test the logic of an argument;

calculate accurately, selecting mental methods or
calculating devices as appropriate; 

estimate, approximate and check working 

refine own findings and approaches on the basis
of discussions with others;

choose and use units of measurement to measure,
estimate, calculate and solve problems in a range of
contexts;

88
4 Geometry and measures
4.4 Measures and mensuration
92
4 Geometry and measures
4.4 Measures and mensuration
96
4 Geometry and measures
4.4 Measures and mensuration
99
4 Geometry and measures
4.1 Geometrical reasoning
99
4 Geometry and measures
4.4 Measures and mensuration
99
4 Geometry and measures
4.4 Measures and mensuration
know rough metric equivalents of imperial
measures in common use, such as miles, pounds (lb)
and pints

derive and use formulae for the area of a triangle,
parallelogram and trapezium;

derive and use formulae for the area of a triangle,
parallelogram and trapezium;

use geometric properties of cuboids and shapes
made from cuboids;

calculate areas of compound shapes

know and use the formula for the volume of a
cuboid;
Tier 4 Lesson Objectives Map
Unit
and
lesson
Class
book
page
Strand
Sub-section
G4.24
99
4 Geometry and measures
4.4 Measures and mensuration
102
4 Geometry and measures
4.1 Geometrical reasoning
102
4 Geometry and measures
4.4 Measures and mensuration
102
4 Geometry and measures
4.4 Measures and mensuration
184201
184201
184201
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1.2 Analysing – use mathematical reasoning
184201
1 Mathematical processes
and applications
1.3 Analysing – use appropriate mathematical
procedures
184201
184201
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1.3 Analysing – use appropriate mathematical
procedures
G4.31
184
4 Geometry and measures
4.2 Transformations and coordinates
G4.32
187
4 Geometry and measures
4.2 Transformations and coordinates
G4.25
G4.25
G4.25
G4.3
G4.3
G4.3
G4.3
G4.3
G4.3
Revised Framework objectives Year 8

calculate volumes and surface areas of cuboids
and shapes made from cuboids 

use geometric properties of cuboids and shapes
made from cuboids;

calculate areas of compound shapes

1.1 Representing
1.2 Analysing – use mathematical reasoning
1.5 Communicating and reflecting
calculate volumes and surface areas of cuboids
and shapes made from cuboids 

select appropriate procedures and tools, including
ICT 

visualise and manipulate dynamic images;

conjecture and generalise;

make accurate mathematical diagrams, graphs
and constructions on paper and on screen;

use accurate notation, including correct syntax
when using ICT; 

refine own findings and approaches on the basis
of discussions with others;

transform 2-D shapes by rotation, reflection and
translation, on paper and using ICT 

transform 2-D shapes by rotation, reflection and
translation, on paper and using ICT 
Tier 4 Lesson Objectives Map
Unit
and
lesson
Class
book
page
Strand
Sub-section
G4.32
187
4 Geometry and measures
4.2 Transformations and coordinates
G4.33
189
4 Geometry and measures
4.2 Transformations and coordinates
G4.34
191
4 Geometry and measures
4.2 Transformations and coordinates
G4.34
191
4 Geometry and measures
4.2 Transformations and coordinates
G4.35
194
4 Geometry and measures
4.2 Transformations and coordinates
G4.35
194
4 Geometry and measures
4.2 Transformations and coordinates
197
4 Geometry and measures
4.2 Transformations and coordinates
197
4 Geometry and measures
4.2 Transformations and coordinates
197
4 Geometry and measures
4.2 Transformations and coordinates
G4.36
G4.36
G4.36
Revised Framework objectives Year 8

try out mathematical representations of simple
combinations of these transformations 

transform 2-D shapes by rotation, reflection and
translation, on paper and using ICT 

understand and use the language and notation
associated with enlargement;

enlarge 2-D shapes, given a centre of enlargement
and a positive integer scale factor;

understand and use the language and notation
associated with enlargement;

enlarge 2-D shapes, given a centre of enlargement
and a positive integer scale factor;

identify all the symmetries of 2-D shapes 

understand and use the language and notation
associated with enlargement;

enlarge 2-D shapes, given a centre of enlargement
and a positive integer scale factor;

G4.37
199
4 Geometry and measures
4.2 Transformations and coordinates
G4.4
238262
1 Mathematical processes
and applications
1.1 Representing
find the midpoint of the line segment AB, given the
coordinates of points A and B 

identify the mathematical features of a context or
problem;
Tier 4 Lesson Objectives Map
Unit
and
lesson
Class
book
page
Strand
238262
238262
238262
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1.2 Analysing – use mathematical reasoning
G4.4
238262
1 Mathematical processes
and applications
1.3 Analysing – use appropriate mathematical
procedures
G4.4
238262
1 Mathematical processes
and applications
1.3 Analysing – use appropriate mathematical
procedures
G4.41
238
4 Geometry and measures
4.3 Construction and loci
G4.4
G4.4
G4.4
Sub-section
1.1 Representing
1.2 Analysing – use mathematical reasoning
Revised Framework objectives Year 8

select appropriate procedures and tools, including
ICT 

visualise and manipulate dynamic images;

make connections with related contexts 

make accurate mathematical diagrams, graphs
and constructions on paper and on screen;

record methods, solutions and conclusions; 

use straight edge and compasses to construct: 

use straight edge and compasses to construct
the midpoint and perpendicular bisector of a line
segment 
G4.42
242
4 Geometry and measures
4.3 Construction and loci
G4.42
242
4 Geometry and measures
4.3 Construction and loci
G4.42
242
4 Geometry and measures
4.3 Construction and loci

use straight edge and compasses to construct
the bisector of an angle 

use straight edge and compasses to construct
the perpendicular from a point to a line 
G4.42
242
4 Geometry and measures
4.3 Construction and loci

use straight edge and compasses to construct
the perpendicular from a point on a line 
G4.43
245
4 Geometry and measures
4.3 Construction and loci

use straight edge and compasses to construct a
triangle, given three sides (SSS)
G4.44
248
4 Geometry and measures
4.3 Construction and loci

use ICT to explore these constructions 
Tier 4 Lesson Objectives Map
Unit
and
lesson
G4.46
G4.47
G4.48
G4.49
Mental
Test
N4.1
Class
book
page
Strand
Sub-section
252
4 Geometry and measures
4.2 Transformations and coordinates
255
4 Geometry and measures
4.4 Measures and mensuration
259
4 Geometry and measures
4.3 Construction and loci
Revised Framework objectives Year 8

make scale drawings 

use bearings to specify direction

find simple loci, both by reasoning and by using
ICT, to produce shapes and paths, e.g. an equilateral
triangle

260
4 Geometry and measures
4.3 Construction and loci
find simple loci, both by reasoning and by using
ICT, to produce shapes and paths, e.g. an equilateral
triangle

TB14
2 Number
2.5 Mental calculation methods
strengthen and extend mental methods of
calculation, working with decimals, fractions,
percentages, squares and square roots, cubes and
cube roots;

Mental
Test
N4.2
TB68
Mental
Tests
TB14,
68,
138,
198,
335
N4.1
1-14
N4.1
1-14
N4.1
1-14
2 Number
2.5 Mental calculation methods
strengthen and extend mental methods of
calculation, working with decimals, fractions,
percentages, squares and square roots, cubes and
cube roots;

2 Number
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
solve problems mentally
2.5 Mental calculation methods
1.1 Representing
1.1 Representing
1.2 Analysing – use mathematical reasoning

identify the mathematical features of a context or
problem;

try out and compare mathematical
representations;

conjecture and generalise;
Tier 4 Lesson Objectives Map
Unit
and
lesson
Class
book
page
Strand
Sub-section
N4.1
1-14
1 Mathematical processes
and applications
1.2 Analysing – use mathematical reasoning
N4.1
1-14
1 Mathematical processes
and applications
1.3 Analysing – use appropriate mathematical
procedures
N4.1
1-14
N4.1
1-14
1.3 Analysing – use appropriate mathematical
procedures
1.3 Analysing – use appropriate mathematical
procedures
N4.1
1-14
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
N4.1-1
1
2 Number
2.4 Number operations
N4.1-1
1
2 Number
2.7 Calculator methods
N4.1-2
3
2 Number
2.2 Integers, powers and roots
N4.1-3
6
2 Number
2.2 Integers, powers and roots
1.5 Communicating and reflecting
Revised Framework objectives Year 8

identify exceptional cases or counter-examples;

calculate accurately, selecting mental methods or
calculating devices as appropriate; 

use accurate notation, including correct syntax
when using ICT; 

record methods, solutions and conclusions; 

refine own findings and approaches on the basis
of discussions with others;

use the order of operations, including brackets,
with more complex calculations

use brackets and the memory

add, subtract, multiply and divide integers 

add, subtract, multiply and divide integers 

N4.1-4
8
2 Number
2.2 Integers, powers and roots
use squares, positive and negative square roots,
cubes and cube roots, and index notation for small
positive integer powers 

N4.1-5
11
2 Number
2.2 Integers, powers and roots
N4.1-5
11
2 Number
2.2 Integers, powers and roots
N4.2
40-56
1 Mathematical processes
and applications
1.1 Representing
use multiples, factors, common factors, highest
common factors, lowest common multiples and
primes;

find the prime factor decomposition of a number,
e.g. 8000 = 26 × 53 

identify the mathematical features of a context or
problem;
Tier 4 Lesson Objectives Map
Unit
and
lesson
Class
book
page
Strand
Sub-section
N4.2
40-56
1 Mathematical processes
and applications
1.2 Analysing – use mathematical reasoning
N4.2
40-56
1 Mathematical processes
and applications
1.3 Analysing – use appropriate mathematical
procedures
N4.2
40-56
1 Mathematical processes
and applications
1.3 Analysing – use appropriate mathematical
procedures
N4.2
40-56
N4.2
40-56
1.3 Analysing – use appropriate mathematical
procedures
1.3 Analysing – use appropriate mathematical
procedures
N4.2
40-56
N4.2
40-56
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
N4.2-1
40
2 Number
2.1 Place value, ordering and rounding
N4.2-1
40
2 Number
2.1 Place value, ordering and rounding
N4.2-2
42
2 Number
2.1 Place value, ordering and rounding
N4.2-2
42
2 Number
2.6 Written calculation methods
N4.2-3
45
2 Number
2.8 Checking results
1.4 Interpreting and evaluating
1.4 Interpreting and evaluating
Revised Framework objectives Year 8

make connections with related contexts 

calculate accurately, selecting mental methods or
calculating devices as appropriate; 

manipulate numbers, algebraic expressions and
equations, and apply routine algorithms; 

use accurate notation, including correct syntax
when using ICT; 

estimate, approximate and check working 

give accurate solutions appropriate to the context
or problem;
 evaluate the efficiency of alternative strategies and
approaches 

round positive numbers to any given power of 10;

round decimals to the nearest whole number or to
one or two decimal places 

order decimals 

use efficient written methods to add and subtract
integers and decimals of any size, including numbers
with differing numbers of decimal places 

select from a range of checking methods, including
estimating in context and using inverse operations 
Tier 4 Lesson Objectives Map
Unit
and
lesson
Class
book
page
Strand
Sub-section
Revised Framework objectives Year 8

N4.2-3
45
2 Number
2.6 Written calculation methods
N4.2-4
47
2 Number
2.7 Calculator methods
2.3 Fractions, decimals, percentages, ratio
and proportion
2.3 Fractions, decimals, percentages, ratio
and proportion
N4.2-5
50
2 Number
N4.2-5
50
2 Number
N4.2-5
50
2 Number
2.5 Mental calculation methods
N4.2-5
50
2 Number
2.7 Calculator methods
N4.2-6
53
2 Number
N4.2-6
53
2 Number
N4.2-6
53
2 Number
107124
107124
1 Mathematical processes
and applications
1 Mathematical processes
and applications
107124
1 Mathematical processes
and applications
2.3 Fractions, decimals, percentages, ratio
and proportion
2.3 Fractions, decimals, percentages, ratio
and proportion
use efficient written methods for multiplication and
division of integers and decimals, including by
decimals such as 0.6 or 0.06;

use brackets and the memory
add and subtract fractions by writing them with a
common denominator;

multiply and divide an integer by a fraction


recall equivalent fractions, decimals and
percentages;

carry out more difficult calculations effectively and
efficiently using the function keys for sign change,
powers, roots and fractions;

add and subtract fractions by writing them with a
common denominator;

calculate fractions of quantities (fraction answers);

N4.3
N4.3
N4.3
2.4 Number operations
1.1 Representing
1.2 Analysing – use mathematical reasoning
1.3 Analysing – use appropriate mathematical
procedures
understand and use the rules of arithmetic and
inverse operations in the context of integers and
fractions 

identify the mathematical features of a context or
problem;

make connections with related contexts 

calculate accurately, selecting mental methods or
calculating devices as appropriate; 
Tier 4 Lesson Objectives Map
Unit
and
lesson
Class
book
page
Strand
Sub-section
107124
107124
107124
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1.3 Analysing – use appropriate mathematical
procedures
N4.3-1
107
2 Number
N4.3-1
107
2 Number
N4.3
N4.3
N4.3
N4.3-1
107
2 Number
N4.3-2
110
2 Number
N4.3-2
110
2 Number
N4.3-2
110
2 Number
1.4 Interpreting and evaluating
1.4 Interpreting and evaluating
2.3 Fractions, decimals, percentages, ratio
and proportion
2.3 Fractions, decimals, percentages, ratio
and proportion
2.3 Fractions, decimals, percentages, ratio
and proportion
2.3 Fractions, decimals, percentages, ratio
and proportion
2.3 Fractions, decimals, percentages, ratio
and proportion
2.3 Fractions, decimals, percentages, ratio
and proportion
N4.3-2
110
2 Number
2.7 Calculator methods
N4.3-3
112
2 Number
2.1 Place value, ordering and rounding
N4.3-4
116
2 Number
2.1 Place value, ordering and rounding
N4.3-4
116
2 Number
2.5 Mental calculation methods
Revised Framework objectives Year 8

use accurate notation, including correct syntax
when using ICT; 
 give accurate solutions appropriate to the context
or problem;
 evaluate the efficiency of alternative strategies and
approaches 

recognise that a recurring decimal is a fraction;

use division to convert a fraction to a decimal;

order fractions by writing them with a common
denominator or by converting them to decimals 

add and subtract fractions by writing them with a
common denominator;

calculate fractions of quantities (fraction
answers);

multiply and divide an integer by a fraction

carry out more difficult calculations effectively
and efficiently using the function keys for sign change,
powers, roots and fractions;

multiply and divide integers and decimals by 0.1,
0.01 

multiply and divide integers and decimals by 0.1,
0.01 

make and justify estimates and approximations
of calculations 
Tier 4 Lesson Objectives Map
Unit
and
lesson
N4.3-4
Class
book
page
116
Strand
2 Number
Sub-section
Revised Framework objectives Year 8
2.6 Written calculation methods

use efficient written methods to add and subtract
integers and decimals of any size, including numbers
with differing numbers of decimal places 
N4.3-4
116
2 Number
2.6 Written calculation methods

use efficient written methods for multiplication
and division of integers and decimals, including by
decimals such as 0.6 or 0.06;
N4.3-4
116
2 Number
2.6 Written calculation methods

understand where to position the decimal point
by considering equivalent calculations 
N4.3-4
116
2 Number
2.8 Checking results
N4.3-5
119
2 Number
2.3 Fractions, decimals, percentages, ratio
and proportion
N4.3-5
119
2 Number
2.3 Fractions, decimals, percentages, ratio
and proportion
N4.3-5
N4.3-5
119
119
2 Number
2 Number

select from a range of checking methods,
including estimating in context and using inverse
operations

interpret percentage as the operator 'so many
hundredths of' and express one given number as a
percentage of another;

use the equivalence of fractions, decimals and
percentages to compare proportions 
2.5 Mental calculation methods

use known facts to derive unknown facts,
including products involving numbers such as 0.7 and
6, and 0.03 and 8
2.7 Calculator methods

carry out more difficult calculations effectively
and efficiently using the function keys for sign change,
powers, roots and fractions;
Tier 4 Lesson Objectives Map
Unit
and
lesson
Class
book
page
Strand
Sub-section
N4.3-5
119
2 Number
2.7 Calculator methods
N4.3-6
121
2 Number
2.3 Fractions, decimals, percentages, ratio
and proportion
162182
162182
1 Mathematical processes
and applications
1 Mathematical processes
and applications
162182
1 Mathematical processes
and applications
1.3 Analysing – use appropriate mathematical
procedures
162182
162182
162182
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1.3 Analysing – use appropriate mathematical
procedures
1.3 Analysing – use appropriate mathematical
procedures
N4.4-1
162
2 Number
2.3 Fractions, decimals, percentages, ratio
and proportion
N4.4-1
162
2 Number
2.3 Fractions, decimals, percentages, ratio
and proportion
N4.4-1
162
2 Number
2.3 Fractions, decimals, percentages, ratio
and proportion
N4.4-1
162
2 Number
2.3 Fractions, decimals, percentages, ratio
and proportion
N4.4
N4.4
N4.4
N4.4
N4.4
N4.4
1.1 Representing
1.2 Analysing – use mathematical reasoning
1.5 Communicating and reflecting
Revised Framework objectives Year 8

enter numbers and interpret the display in
different contexts (extend to negative numbers,
fractions, time)

calculate percentages and find the outcome of a
given percentage increase or decrease

identify the mathematical features of a context or
problem;

make connections with related contexts 

calculate accurately, selecting mental methods or
calculating devices as appropriate; 

use accurate notation, including correct syntax
when using ICT; 

estimate, approximate and check working 

refine own findings and approaches on the basis
of discussions with others;

use the equivalence of fractions, decimals and
percentages to compare proportions 

apply understanding of the relationship between
ratio and proportion;

simplify ratios, including those expressed in
different units, recognising links with fraction notation;

divide a quantity into two or more parts in a given
ratio;
Tier 4 Lesson Objectives Map
Unit
and
lesson
Class
book
page
Strand
Sub-section
N4.4-2
167
2 Number
2.3 Fractions, decimals, percentages, ratio
and proportion
N4.4-2
167
2 Number
2.3 Fractions, decimals, percentages, ratio
and proportion
N4.4-3
170
2 Number
2.3 Fractions, decimals, percentages, ratio
and proportion
N4.4-4
175
2 Number
2.3 Fractions, decimals, percentages, ratio
and proportion
N4.4-5
178
2 Number
2.3 Fractions, decimals, percentages, ratio
and proportion
N4.4-5
178
2 Number
2.3 Fractions, decimals, percentages, ratio
and proportion
N4.4-6
181
2 Number
2.3 Fractions, decimals, percentages, ratio
and proportion
N4.5
286
N4.5
286
N4.5
286
1 Mathematical processes
and applications
1.3 Analysing – use appropriate mathematical
procedures
N4.5
286
1 Mathematical processes
and applications
1.3 Analysing – use appropriate mathematical
procedures
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1.1 Representing
1.2 Analysing – use mathematical reasoning
Revised Framework objectives Year 8

apply understanding of the relationship between
ratio and proportion;

simplify ratios, including those expressed in
different units, recognising links with fraction notation;

apply understanding of the relationship between
ratio and proportion;

use the unitary method to solve simple problems
involving ratio and direct proportion

interpret percentage as the operator 'so many
hundredths of' and express one given number as a
percentage of another;

use the equivalence of fractions, decimals and
percentages to compare proportions 

calculate percentages and find the outcome of a
given percentage increase or decrease 

identify the mathematical features of a context or
problem;

conjecture and generalise;

calculate accurately, selecting mental methods or
calculating devices as appropriate; 

record methods, solutions and conclusions; 
Tier 4 Lesson Objectives Map
Unit
and
lesson
Class
book
page
Strand
Sub-section
N4.5
286
1 Mathematical processes
and applications
1.4 Interpreting and evaluating
N4.5
286
N4.5
286
N4.5
286
N4.5
286
N4.5
286
S4.1
58-74
S4.1
58-74
S4.1
58-74
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
Revised Framework objectives Year 8

1.4 Interpreting and evaluating
1.5 Communicating and reflecting
1.5 Communicating and reflecting
1.5 Communicating and reflecting
1.5 Communicating and reflecting
1.1 Representing
1.1 Representing
1.2 Analysing – use mathematical reasoning
1.3 Analysing – use appropriate mathematical
procedures
S4.1
58-74
1 Mathematical processes
and applications
S4.1
58-74
1 Mathematical processes
and applications
1.3 Analysing – use appropriate mathematical
procedures
S4.1-1
58
5 Statistics
5.4 Probability
S4.1-1
58
5 Statistics
5.4 Probability
use logical argument to interpret the mathematics
in a given context or to establish the truth of a
statement;

give accurate solutions appropriate to the context
or problem;

refine own findings and approaches on the basis
of discussions with others;

recognise efficiency in an approach;

relate the current problem and structure to
previous situations 

relate the current problem and structure to
previous situations 

identify the mathematical features of a context or
problem;

select appropriate procedures and tools, including
ICT 

conjecture and generalise;

make accurate mathematical diagrams, graphs
and constructions on paper and on screen;

record methods, solutions and conclusions; 

interpret the results of an experiment using the
language of probability;

appreciate that random processes are
unpredictable
Tier 4 Lesson Objectives Map
Unit
and
lesson
Class
book
page
Strand
Sub-section
S4.1-2
61
5 Statistics
5.4 Probability
S4.1-3
63
5 Statistics
5.4 Probability
S4.1-4
66
5 Statistics
5.4 Probability
Revised Framework objectives Year 8

know that if the probability of an event occurring is
p then the probability of it not occurring is 1 − p;

use diagrams and tables to record in a systematic
way all possible mutually exclusive outcomes for
single events and for two successive events 

compare estimated experimental probabilities with
theoretical probabilities, recognising that:

if an experiment is repeated the outcome
may, and usually will, be different 

S4.1-5
70
5 Statistics
5.4 Probability
use diagrams and tables to record in a systematic
way all possible mutually exclusive outcomes for
single events and for two successive events 

S4.1-6
S4.2
S4.2
S4.2
S4.2
72
5 Statistics
126144
126144
126144
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
126144
1 Mathematical processes
and applications
5.4 Probability
1.1 Representing
1.1 Representing
1.2 Analysing – use mathematical reasoning
1.3 Analysing – use appropriate mathematical
procedures
compare estimated experimental probabilities with
theoretical probabilities, recognising that:

if an experiment is repeated the outcome
may, and usually will, be different 

identify the mathematical features of a context or
problem;

select appropriate procedures and tools, including
ICT 

conjecture and generalise;

make accurate mathematical diagrams, graphs
and constructions on paper and on screen;
Tier 4 Lesson Objectives Map
Unit
and
lesson
Class
book
page
Strand
Sub-section
126144
126144
126144
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1.3 Analysing – use appropriate mathematical
procedures
S4.2-1
126
5 Statistics
S4.2-1
126
5 Statistics
S4.2-1
126
5 Statistics
S4.2
S4.2
S4.2
S4.2-1
126
1.4 Interpreting and evaluating
1.5 Communicating and reflecting
5.1 Specifying a problem, planning and
collecting data
5.1 Specifying a problem, planning and
collecting data
5.1 Specifying a problem, planning and
collecting data
5 Statistics
5.2 Processing and representing data
S4.2-1
126
5 Statistics
5.1 Specifying a problem, planning and
collecting data
S4.2-1
126
5 Statistics
5.1 Specifying a problem, planning and
collecting data
5 Statistics
5.1 Specifying a problem, planning and
collecting data
Revised Framework objectives Year 8


evaluate the efficiency of alternative strategies and
approaches 

refine own findings and approaches on the basis
of discussions with others;

decide which data to collect to answer a question,
and the degree of accuracy needed;

identify possible sources;

consider appropriate sample size

construct graphical representations, on paper
and using ICT, and identify which are most useful in
the context of the problem. Include: bar charts and
frequency diagrams for discrete and continuous data

discuss a problem that can be addressed by
statistical methods and identify related questions to
explore


S4.2-2
128
record methods, solutions and conclusions; 
plan how to collect the data;
construct frequency tables with equal class
intervals for gathering continuous data and two-way
tables for recording discrete data
Tier 4 Lesson Objectives Map
Unit
and
lesson
Class
book
page
Strand
Sub-section
S4.2-2
128
5 Statistics
5.2 Processing and representing data
S4.2-2
128
5 Statistics
5.2 Processing and representing data
Revised Framework objectives Year 8

calculate statistics for sets of discrete and
continuous data, including with a calculator and
spreadsheet;

S4.2-2
128
5 Statistics
5.2 Processing and representing data
recognise when it is appropriate to use the range,
mean, median and mode and, for grouped data, the
modal class

construct graphical representations, on paper
and using ICT, and identify which are most useful in
the context of the problem. Include: pie charts for
categorical data

S4.2-2
128
5 Statistics
5.3 Interpreting and discussing results
compare two distributions using the range and one
or more of the mode, median and mean

S4.2-3
S4.2-3
S4.2-3
131
131
131
5 Statistics
5 Statistics
5 Statistics
5.1 Specifying a problem, planning and
collecting data
5.2 Processing and representing data
5.2 Processing and representing data
construct frequency tables with equal class
intervals for gathering continuous data and two-way
tables for recording discrete data

construct graphical representations, on paper
and using ICT, and identify which are most useful in
the context of the problem. Include: bar charts and
frequency diagrams for discrete and continuous data

construct graphical representations, on paper
and using ICT, and identify which are most useful in
the context of the problem. Include: stem-and-leaf
diagrams 
Tier 4 Lesson Objectives Map
Unit
and
lesson
S4.2-4
S4.2-4
S4.2-4
S4.2-5
Class
book
page
135
135
135
139
Strand
5 Statistics
5 Statistics
Sub-section
5.2 Processing and representing data
5.2 Processing and representing data
5 Statistics
5.2 Processing and representing data
5 Statistics
5.1 Specifying a problem, planning and
collecting data
Revised Framework objectives Year 8

construct graphical representations, on paper
and using ICT, and identify which are most useful in
the context of the problem. Include: pie charts for
categorical data

construct graphical representations, on paper
and using ICT, and identify which are most useful in
the context of the problem. Include: bar charts and
frequency diagrams for discrete and continuous data

construct graphical representations, on paper
and using ICT, and identify which are most useful in
the context of the problem. Include: simple scatter
graphs 

collect data using a suitable method (e.g.
observation, controlled experiment, data logging using
ICT)

S4.2-5
139
5 Statistics
5.2 Processing and representing data
construct graphical representations, on paper and
using ICT, and identify which are most useful in the
context of the problem.

S4.2-6
142
5 Statistics
5.2 Processing and representing data
construct graphical representations, on paper and
using ICT, and identify which are most useful in the
context of the problem.
Tier 4 Lesson Objectives Map
Unit
and
lesson
Class
book
page
Strand
Sub-section
Revised Framework objectives Year 8

interpret tables, graphs and diagrams for discrete
and continuous data, relating summary statistics and
findings to the questions being explored 
S4.2-6
142
5 Statistics
5.3 Interpreting and discussing results
S4.2-6
142
5 Statistics
5.3 Interpreting and discussing results
write about and discuss the results of a statistical
enquiry using ICT as appropriate;
S4.2-6
142
219236
219236
219236
219236
5 Statistics
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
5.3 Interpreting and discussing results

219236
1 Mathematical processes
and applications
1.3 Analysing – use appropriate mathematical
procedures
219236
219236
219236
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1 Mathematical processes
and applications
1.3 Analysing – use appropriate mathematical
procedures
S4.3-1
219
5 Statistics
5.1 Specifying a problem, planning and
collecting data
S4.3-1
219
5 Statistics
5.1 Specifying a problem, planning and

S4.3
S4.3
S4.3
S4.3
S4.3
S4.3
S4.3
S4.3
1.1 Representing
1.1 Representing
1.1 Representing
1.2 Analysing – use mathematical reasoning
1.4 Interpreting and evaluating
1.5 Communicating and reflecting
justify the methods used
identify the mathematical features of a context or
problem;

try out and compare mathematical
representations;

select appropriate procedures and tools, including
ICT 

conjecture and generalise;


make accurate mathematical diagrams, graphs
and constructions on paper and on screen;

record methods, solutions and conclusions; 

evaluate the efficiency of alternative strategies and
approaches 

refine own findings and approaches on the basis
of discussions with others;

decide which data to collect to answer a question,
and the degree of accuracy needed;

identify possible sources;
Tier 4 Lesson Objectives Map
Unit
and
lesson
S4.3-2
Class
book
page
221
Strand
5 Statistics
Sub-section
collecting data
5.1 Specifying a problem, planning and
collecting data
Revised Framework objectives Year 8

plan how to collect the data;

S4.3-2
S4.3-3
221
224
5 Statistics
5 Statistics
5.1 Specifying a problem, planning and
collecting data
5.2 Processing and representing data
construct frequency tables with equal class
intervals for gathering continuous data and two-way
tables for recording discrete data

construct graphical representations, on paper
and using ICT, and identify which are most useful in
the context of the problem. Include: bar charts and
frequency diagrams for discrete and continuous data

S4.3-4
226
5 Statistics
5.3 Interpreting and discussing results
S4.3-5
227
5 Statistics
5.3 Interpreting and discussing results
write about and discuss the results of a statistical
enquiry using ICT as appropriate;

compare two distributions using the range and one
or more of the mode, median and mean

S4.3-6
230
5 Statistics
5.4 Probability
compare estimated experimental probabilities with
theoretical probabilities, recognising that:

if an experiment is repeated the
outcome may, and usually will, be
different

increasing the number of times an
experiment is repeated generally
leads to better estimates of
probability
Tier 4 Lesson Objectives Map
Unit
and
lesson
S4.3-7
Class
book
page
233
Strand
5 Statistics
Sub-section
5.2 Processing and representing data
Revised Framework objectives Year 8

construct graphical representations, on paper
and using ICT, and identify which are most useful in
the context of the problem. Include: simple line graphs
for time series 