Download Maths Makes Sense 1 end-of-block

Maths Makes Sense
and Mathematics and
Numeracy (Northern Ireland)
For Maths Makes Sense 5 and 6
(Key Stage 2)
www.oxfordprimary.co.uk/mms/
© Oxford University Press 2012
1
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© Oxford University Press 2012
2
Maths Makes Sense and Mathematics and Numeracy
(Northern Ireland)
This document is intended to help you use the Maths Makes Sense resources
for children aged 9 to 11 alongside Mathematics and Numeracy (the statutory
requirements of the Northern Ireland Mathematics Curriculum).
This chart shows you how the Maths Makes Sense 5 and 6 end-of-block
objectives correlate to the statutory requirements of Key Stage 2 Mathematics
and Numeracy. The simple lay-out, provided in an editable format, will assist
you with your planning so that you are able to integrate Maths Makes Sense
seamlessly into your classroom.
Maths Makes Sense identifies that all learners need both informal learning
and formal learning and identifies opportunities for both. The Northern Ireland
Curriculum for Mathematics and Numeracy highlights the importance of
presenting mathematical activities in contexts that have a real meaning for
children, helping them to see the relevance of mathematics to their everyday
lives. Throughout the Maths Makes Sense Learning System opportunities
exist to help achieve this important aspiration of the Northern Ireland
Curriculum for Mathematics and Numeracy.
The significance placed on the development of mathematical language in
Maths Makes Sense mirrors its fundamental importance in the Mathematics
and Numeracy Curriculum. Pupils must understand mathematical language
and use the correct vocabulary to talk about their work.
The methodology of Maths Makes Sense will support the methodologies of
the Mathematics and Numeracy Curriculum. The direct instruction, modelled
on guided practice and partner teaching will allow teachers to help pupils to
learn the key concepts identified in this curriculum. The importance of partner
work as a key feature of Maths Makes Sense will support the requirement for
co-operative learning.
The Northern Ireland Matching Charts identify the statements from the
Northern Ireland Curriculum for Mathematics and Numeracy which sit parallel
to the end-of-block objectives. These Maths Makes Sense objectives have
been matched mainly to the requirements for Key Stage 2. However, as
Maths Makes Sense seeks to contribute to the raising of standards, the endof-block objectives on occasion match to elements in provision for Key Stage
3. In these instances, the relevant end-of-block objectives are matched to the
Northern Ireland Levels of Progression in Using Mathematics across the
curriculum for Key Stage 3 which become a statutory part of assessment in
2012/2013.
It should be noted that in Maths Makes Sense the Northern Ireland Key Stage
2 Mathematics Curriculum Processes in Mathematics are a part of virtually
every mathematics lesson. Therefore it would not be helpful to include
repeatedly statements such as ‘present information and results clearly’ and
© Oxford University Press 2012
3
‘understand mathematical language and use it to discuss their work and
explain their thinking’. Processes statements are included only when they are
very much the main feature of the Maths Makes Sense objectives. It should
be assumed that other statements of Processes in Mathematics may also be
relevant.
To find out more about Maths Makes Sense, please visit our website:
www.oxfordprimary.co.uk/mms/
© Oxford University Press 2012
4
Maths Makes Sense 5
Block 1
Maths Makes Sense 5
end-of-block objectives
Northern Ireland Curriculum Key Stage 2
Block 1, Arithmetic 1
Processes in Mathematics
 Write two or three 4-digit whole
numbers vertically and calculate
(with more than one tricky column)
using addition and subtraction
 Use the three operations + / − /÷,
with vulgar fractions or mixed
numbers with the same
denominator
 Multiply and divide vulgar fractions
and mixed numbers by a whole
number.
Communicating Mathematically
Block 1, Geometry
Processes in Mathematics
 Name the images of objects that
are points, line segments or
polygons in a symmetrical shape
 Know the line of symmetry is the
perpendicular bisector in a
symmetrical shape
 Name two congruent shapes in a
shape with an axis of symmetry.
Communicating Mathematically
 present information and results clearly.
Number
Understanding Number and Number Notation
 develop an understanding of place value [to include up to two decimal
places, use this to multiply and divide numbers by 10 and 100;]
 understand and use vulgar fractions, [decimal fractions and
percentages and explore the relationships between them;]
Operations and their Applications
 engage in a range of activities to develop understanding of the four
operations of number, [appreciate the use of brackets, add and
subtract with up to two decimal places, multiply and divide decimals by
whole numbers, use these operations to solve problems.]
 understand mathematical language and use it to discuss their work
and explain their thinking;
Shape and Space
Exploration of Shape
 construct a range of regular and irregular 2-D shapes, [classify these
through examination of angles and sides,] recognise line [and
rotational] symmetry, reflect shapes in a line, [explore tessellations,
name and describe common 2-D shapes,] begin to understand
congruence in 2-D shapes;
Position, Movement and Direction
 develop language associated with line and angle, [recognise
properties of acute, obtuse and reflex angles, investigate angles in
triangles and quadrilaterals, measure and draw angles up to 360°;]
Block 1, Data and Measure
Number
 Solve word problems (involving
capacity, volume or length) by
using a division Maths Story,
identifying the basic Real-Life Story
as a Type 1 or Type 2 division
 Solve word problems (involving
capacity, volume or length) by
finding a percentage of a value or
the result of a percentage increase
or decrease
 Choose the correct operations to
solve one-step and multi-step word
problems involving capacity,
volume or length
 Make a simple 3D shape by
drawing, cutting out and folding a
net
 Recognise that a cube cut through
one diagonal forms two congruent
Understanding Number and Number Notation
© Oxford University Press 2012
 understand and use vulgar fractions, decimal fractions and
percentages and explore the relationships between them;
Measures
 [understand the relationship between units and convert one metric unit
to another,] use the four operations to solve problems;
 calculate [perimeter and the areas and] volumes of simple shapes;
Shape and Space
Exploration of Shape
 construct 3-D shapes, [investigate the number of faces, edges and
vertices on these shapes], name and describe common 3-D shapes,
explore the relationship between 2-D and 3-D shapes.
5
triangular prisms.
Block 1, Arithmetic 2
Processes in Mathematics
 Complete missing number grids
and missing number sentences
 Complete sequences involving
square numbers
 Use information displayed in grids
to solve word problems
 Solve one- and two-step word
problems involving any of the four
operations.
Making and Monitoring Decisions
 identify and obtain the information required for a task, [suggesting
appropriate sources to find the information;]
Number
Patterns, Relationships and Sequences in Number
 explore and predict patterns and sequences of whole numbers, [follow
and devise rules for generating sequences;]
 understand and use [multiples and factors and] the terms [prime,]
square [and cube, appreciate inverse operations;]
 understand that a letter can stand for an unknown number.
Operations and their Applications
 engage in a range of activities to develop understanding of the four
operations of number, [appreciate the use of brackets, add and
subtract with up to two decimal places, multiply and divide decimals by
whole numbers,] use these operations to solve problems.
Handling Data
Collecting, Representing and Interpreting Data
 interpret a wide range of tables, [lists, graphs and diagrams, create
and interpret frequency tables, including those for grouped data;]
Block 1, Reasoning
Processes in Mathematics
 Write a.m./p.m. times using 24hour clock notation
 Write 24-hour times as a.m./p.m.
times
 Calculate the mean number of days
in four consecutive years
 Calculate the duration between two
times written using 24-hour
notation.
Mathematical Reasoning
 recognise general patterns and relationships and make predictions
about them;
Number
Patterns, relationships and sequences with number
 explore and predict patterns and sequences of whole numbers; follow
and devise rules for generating sequences;
Operations and their Applications
 engage in a range of activities to develop understanding of the four
operations of number; [appreciate the use of brackets; add and
subtract with up to two decimal places; multiply and divide decimals by
whole numbers;] use these operations to solve problems.
Measures
 recognise times on the analogue and digital clocks and understand
the relationship between the 12 and 24-hour clocks, [use timetables.]
Handling Data
Collecting, Representing and Interpreting Data
 understand, calculate [and use] the mean [and range] of a set of
discrete data.
© Oxford University Press 2012
6
Block 2
Maths Makes Sense 5
end-of-block objectives
Northern Ireland Curriculum Key Stage 2
Block 2, Arithmetic 1
Processes in Mathematics
 Write two or three 4-digit decimal
numbers vertically, with up to three
decimal places, and calculate with
more than one tricky column, using
addition and subtraction
 Multiply two vulgar fractions where
the denominator of one and the
numerator of the other are equal.
Communicating Mathematically
 present information and results clearly.
Number
Understanding Number and Number Notation
 develop an understanding of place value to include up to two decimal
places, [use this to multiply and divide numbers by 10 and 100;]
 understand and use vulgar fractions, [decimal fractions and
percentages and explore the relationships between them;]
Operations and their Applications
 engage in a range of activities to develop understanding of the four
operations of number, [appreciate the use of brackets,] add and
subtract with up to two decimal places, [multiply and divide decimals
by whole numbers, use these operations to solve problems.]
Block 2, Geometry
Processes in Mathematics
 Name and draw acute angles,
obtuse angles, reflex angles and
right angles
 Name and calculate vertically
opposite angles and supplementary
angles
 Use a protractor to draw acute
angles, obtuse angles, and right
angles.
Communicating Mathematically
Block 2, Data and Measure
Measures
 Appreciate the need for standard
units
 Know the metric units of mass: g,
kg: length: mm, cm, m, km: and
volume/capacity: ml, ℓ, cm3, m3
 Know imperial units of measure,
e.g. pound, ounce, inch, foot, yard,
mile, pint, gallon
 Interpret a reading that lies
between two unnumbered divisions
on a scale
 Convert between metric units, e.g.
kg and g to kg
 Convert between imperial units,
e.g. lb and oz to oz.
 appreciate important ideas about measurement including [the
continuous nature of measurement and] the need for appropriate
accuracy;
 understand the relationship between units and convert one metric unit
to another, [use the four operations to solve problems;]
© Oxford University Press 2012
 understand mathematical language and use it to discuss their work
and explain their thinking;
 interpret situations mathematically using appropriate symbols [or
diagrams;]
Shape and Space
Position, Movement and Direction
 understand the notion of angle in the context of turning, recognise
right angles, [understand clockwise and anti-clockwise, know the eight
points of the compass, use Logo to understand movement and
turning, be introduced to a programming language and use it to create
pictures and patterns and to generate shapes;]
 develop language associated with line and angle, recognise properties
of acute, obtuse and reflex angles, [investigate angles in triangles and
quadrilaterals,] measure and draw angles up to 360°;
 use co-ordinates to plot and draw shapes in the first quadrant.
7
Block 2, Arithmetic 2
Processes in Mathematics
 Use > / < / ≥ / ≤ with positive whole
numbers, e.g. in the form 8 < m <
10
 Use a calculator to check if a
number is a factor of another
number
 Distinguish between a factor and a
proper factor.
Communicating Mathematically
 interpret situations mathematically using appropriate symbols [or
diagrams;]
Mathematical Reasoning
 check results [and consider whether they are reasonable.]
Number
Patterns, Relationships and Sequences in Number
 understand and use [multiples and] factors [and the terms prime,
square and cube], appreciate inverse operations;
 understand that a letter can stand for an unknown number.
Block 2, Reasoning
Number
 Solve algebraic equations that
have an expression which is the
sum of two terms using algebraic
methods, one term being solely ‘x’
and the other term a 1-digit
number, e.g. x + 2 = 5
 Solve algebraic equations that
have an expression which consists
of one term using algebraic
methods, a product of ‘x’ and a 1digit number, e.g. 2x = 6.
Patterns, Relationships and Sequences in Number
© Oxford University Press 2012
 understand and use [multiples and] factors [and the terms prime,
square and cube, appreciate inverse operations;]
 understand that a letter can stand for an unknown number.
8
Block 3
Maths Makes Sense 5
end-of-block objectives
Northern Ireland Curriculum Key Stage 2
Block 3, Arithmetic 1
Processes in Mathematics
 Use a/b and a ÷ b interchangeably,
e.g. 5/8 and 5 ÷ 8
 Use the division button on a
calculator to convert vulgar
fractions to finite decimal fractions
(no vulgar fractions with infinite
decimal equivalents)
 Use the four operations (+ / − / × /
÷) with combinations of positive
and negative numbers, including
tricky examples (but not the
product of two negative numbers).
Communicating Mathematically
Block 3, Geometry
Measures
 Use a calculator to calculate the
circumference of a circle using
C=xd
 Use a calculator to calculate the
area of a circle using
A =  x r2.
 calculate [perimeter and] the areas [and volumes] of simple shapes;
Block 3, Data and Measure
Processes in Mathematics
 Interpret a calendar
 Interpret a timetable
 Use durations of minutes, hours,
days or months in calculations and
word problems
 Construct a bar chart and use it to
find the mode
 Understand that the mode is the
most common value in a set of
data.
Communicating Mathematically
 interpret situations mathematically using appropriate symbols [or
diagrams;]
Number
Understanding Number and Number Notation
 understand and use vulgar fractions , decimal fractions [and
percentages] and explore the relationships between them;
 understand and use negative numbers in context.
Operations and their Applications
 engage in a range of activities to develop understanding of the four
operations of number, [appreciate the use of brackets, add and
subtract with up to two decimal places, multiply and divide decimals by
whole numbers, use these operations to solve problems.]
Shape and Space
Exploration of Shape
 construct [a range of] regular [and irregular] 2-D shapes, [classify
these through examination of angles and side], recognise line and
rotational symmetry, reflect shapes in a line, explore tessellations,
name and describe common 2-D shapes, begin to understand
congruence in 2-D shapes;]
 present information and results clearly.
Mathematical Reasoning
 recognise general patterns and relationships and make predictions
about them;
Number
Patterns, relationships and sequences with number
 explore and predict patterns and sequences of whole numbers; follow
and devise rules for generating sequences;
Measures
 [recognise times on the analogue and digital clocks and] understand
the relationship between the 12 and 24-hour clocks, use timetables.
Handling Data
Collecting, Representing and Interpreting Data
 collect, classify, record and present data drawn from a range of
meaningful situations, using graphs [tables, diagrams and ICT
software;]
 interpret a wide range of tables, [lists,] graphs [and diagrams,] create
and interpret frequency tables, [including those for grouped data;]
© Oxford University Press 2012
9
Block 3, Arithmetic 2
Processes in Mathematics
 Use divisibility tests for 2, 3, 4, 5, 6
and 10
 Distinguish between factors and
proper factors.
Communicating Mathematically
 understand mathematical language and use it to discuss their work
and explain their thinking;
Mathematical Reasoning
 recognise general patterns and relationships and make predictions
about them;
 understand and make general statements;
Number
Patterns, Relationships and Sequences in Number
 understand and use [multiples and] factors [and the terms prime,
square and cube, appreciate inverse operations;]
Operations and their Applications
 know the multiplication facts up to 10 x 10;
 engage in a range of activities to develop understanding of the four
operations of number, [appreciate the use of brackets, add and
subtract with up to two decimal places, multiply and divide decimals by
whole numbers, use these operations to solve problems.]
Block 3, Reasoning
Processes in Mathematics
 Solve problems involving measures
and fractions by exploring patterns
and relationships in diagrams
 Solve one-, two- and three-step
word problems involving money.
Making and Monitoring Decisions
 identify and obtain the information required for a task, [suggesting
appropriate sources to find the information;]
 develop a range of strategies for problem-solving, [looking for ways to
overcome difficulties.]
Number
Understanding Number and Number Notation
 understand and use vulgar fractions, [decimal fractions and
percentages and explore the relationships between them;]
Money
 use the four operations to solve problems involving money;
Measures
 [understand the relationship between units and convert one metric unit
to another,] use the four operations to solve problems;
© Oxford University Press 2012
10
Block 4
Maths Makes Sense 5
end-of-block objectives
Northern Ireland Curriculum Key Stage 2
Block 4, Arithmetic 1
Processes in Mathematics
 Use a grid for long multiplication
with up to 2-digit by 2-digit whole
numbers
 Use a grid for long multiplication
with up to 3-digit by 2-digit decimal
numbers (one or two decimal
places), with answers up to three
decimal places.
Communicating Mathematically
 present information and results clearly.
Mathematical Reasoning
 check results and consider whether they are reasonable.
Number
Understanding Number and Number Notation
 develop an understanding of place value to include up to two decimal
places, use this to multiply [and divide] numbers by 10 and 100;
 estimate and approximate to gain an indication of the size of a solution
to a calculation [or problem;]
 understand and use [vulgar fractions,] decimal fractions [and
percentages and explore the relationships between them;]
Operations and their Applications
 know the multiplication facts up to 10 x 10;
 engage in a range of activities to develop understanding of the four
operations of number, [appreciate the use of brackets, add and
subtract with up to two decimal places,] multiply [and divide] decimals
by whole numbers, [use these operations to solve problems.]
Block 4, Geometry
Processes in Mathematics
 Recognise corresponding angles
and know they have the same
value
 Recognise vertically opposite
angles and know they have the
same value
 Recognise opposite interior angles
in a parallelogram and know they
have the same value.
Communicating Mathematically
Block 4, Data and Measure
Processes in Mathematics
 Interpret a distance-time graph
 Draw a distance-time graph from
given information
 Round measures of distance and
time.
Making and Monitoring Decisions
 understand mathematical language and use it to discuss their work
and explain their thinking;
Shape and Space
Position, Movement and Direction
 understand the notion of angle in the context of turning, [recognise
right angles, understand clockwise and anti-clockwise, know the eight
points of the compass, use Logo to understand movement and
turning, be introduced to a programming language and use it to create
pictures and patterns and to generate shapes;]
 develop language associated with line and angle, [recognise
properties of acute, obtuse and reflex angles,] investigate angles in
triangles and] quadrilaterals, [measure and draw angles up to 360°;]
 use co-ordinates to plot and draw shapes in the first quadrant.
 take increasing responsibility for selecting and using the materials and
the mathematics required for their work;
Communicating Mathematically
 present information and results clearly.
Measures
 develop skills in estimation of [length, ‘weight’, volume/capacity,] time,
[area and temperature;]
 appreciate important ideas about measurement including [the
continuous nature of measurement and] the need for appropriate
accuracy;
© Oxford University Press 2012
11
Handling Data
Collecting, Representing and Interpreting Data
 collect, classify, record and present data drawn from a range of
meaningful situations, using graphs [tables, diagrams and ICT
software;]
 interpret a wide range of [tables, lists,] graphs [and diagrams, create
and interpret frequency tables, including those for grouped data;]
Block 4, Arithmetic 2
Processes in Mathematics
 Identify prime numbers from 0-100
using Eratosthenes’ sieve
 Write numbers as the product of
their prime factors
 For n as a positive whole number,
respond to a condition that
describes a factor, e.g. 11 is a
factor of n, and conditions that use
the symbols < or ≤, e.g. 22 < n <
55, and write a value of n, i.e. 33 or
44.
Communicating Mathematically
Block 4, Reasoning
Processes in Mathematics
 Solve puzzles by calculating
quantities, e.g. numbers of bricks,
and dimensions, e.g. lengths and
heights, using pictures of 2D and
3D shapes.
Making and Monitoring Decisions
 compare their ideas and methods of working with others;
 interpret situations mathematically using appropriate symbols [or
diagrams;]
Mathematical Reasoning
 check results [and consider whether they are reasonable.]
Number
Patterns, Relationships and Sequences in Number
 understand and use [multiples and] factors and the terms prime,
[square and cube, appreciate inverse operations;]
 understand that a letter can stand for an unknown number.
 develop a range of strategies for problem-solving, [looking for ways to
overcome difficulties.]
Mathematical Reasoning
 recognise general patterns and relationships and make predictions
about them;
Number
Patterns, Relationships and Sequences in Number
 understand and use [multiples and factors and] the terms [prime,
square and] cube, [appreciate inverse operations;]
 understand that a letter can stand for an unknown number.
Measures
 [understand the relationship between units and convert one metric unit
to another,] use the four operations to solve problems;
Shape and Space
Exploration of Shape
 [construct a range of regular and irregular 2-D shapes; classify these
through examination of angles and sides; recognise line and rotational
symmetry; reflect shapes in a line; explore tessellations;] name and
describe common 2-D shapes; [begin to understand congruence in 2D shapes;]
© Oxford University Press 2012
12
Block 5
Maths Makes Sense 5
end-of-block objectives
Northern Ireland Curriculum Key Stage 2
Block 5, Arithmetic 1
Processes in Mathematics
 Use a grid for long division
including numbers with up to 3digits divided by 1-digit whole
numbers.
Communicating Mathematically
 present information and results clearly.
Number
Understanding Number and Number Notation
 develop an understanding of place value to include up to two decimal
places, use this to [multiply and] divide numbers by 10 and 100;
Patterns, Relationships and Sequences in Number
 understand and use [multiples and] factors [and the terms prime,
square and cube,] appreciate inverse operations;
Operations and their Applications
 know the multiplication facts up to 10 x 10;
 engage in a range of activities to develop understanding of the four
operations of number, [appreciate the use of brackets, add and
subtract with up to two decimal places, multiply and divide decimals by
whole numbers, use these operations to solve problems.]
Block 5, Geometry
Shape and Space
 Draw a convex polygon
 Draw and mark the exterior angles
for a convex polygon
 Show that the sum of the exterior
angles of a polygon is 360°.
Exploration of Shape
 construct a range of regular and irregular 2-D shapes, [classify these
through examination of angles and side, recognise line and rotational
symmetry, reflect shapes in a line, explore tessellations, name and
describe common 2-D shapes, begin to understand congruence in 2-D
shapes;]
Position, Movement and Direction
 understand the notion of angle in the context of turning, [recognise
right angles, understand clockwise and anti-clockwise, know the eight
points of the compass, use Logo to understand movement and
turning, be introduced to a programming language and use it to create
pictures and patterns and to generate shapes;]
 develop language associated with [line and] angle, [recognise
properties of acute, obtuse and reflex angles,] investigate angles in
triangles and quadrilaterals, [measure and draw angles up to 360°;]
Block 5, Data and Measure
Measures
 Use ratio to convert between metric
units of measure
 Use ratio to convert between metric
and imperial units of measure
 Estimate the area of a shape in
cm2.
 develop skills in estimation of [length, weight, volume/capacity, time,]
area [and temperature;]
 understand the relationship between units and convert one metric unit
to another, use the four operations to solve problems;
Block 5, Arithmetic 2
Number
 Evaluate terms in an expression
with brackets, e.g. (2 x 3) + (1 x 2)
=6+2
 Evaluate products in an expression
with brackets, e.g. 2 x (4 + 1 x 3) =
2 x (4 + 3) = 2 x 7.
Operations and their Applications
© Oxford University Press 2012
 know the multiplication facts up to 10 x 10;
 engage in a range of activities to develop understanding of the four
operations of number, appreciate the use of brackets, [add and
subtract with up to two decimal places, multiply and divide decimals by
whole numbers, use these operations to solve problems.]
13
Block 5, Reasoning
Processes in Mathematics
 Carry out investigations involving
shapes, numbers and real-life
situations using the ‘What if Not’
approach.
Making and Monitoring Decisions
 plan and organise their work, learning to work systematically;
 develop a range of strategies for problem-solving, looking for ways to
overcome difficulties.
Mathematical Reasoning
 recognise general patterns and relationships and make predictions
about them;
 ask and respond to open-ended questions and explain their thinking;
 understand and make general statements;
Number
Patterns, Relationships and Sequences in Number
 explore and predict patterns and sequences of whole numbers, follow
and devise rules for generating sequences;
 interpret, generalise and use simple relationships expressed in
numerical, spatial and practical situations, [understand and use simple
function machines;]
Measures
 calculate perimeter and the areas [and volumes] of simple shapes;
Shape and Space
Exploration of Shape
 [construct a range of regular and irregular 2-D shapes, classify these
through examination of angles and side, recognise line and rotational
symmetry, reflect shapes in a line, explore tessellations, name and
describe common 2-D shapes,] begin to understand congruence in
2-D shapes;
© Oxford University Press 2012
14
Block 6
Maths Makes Sense 5
end-of-block objectives
Northern Ireland Curriculum Key Stage 2
Block 6, Arithmetic 1
Processes in Mathematics
 Multiply decimals numbers with up
to three decimal places by
multiples of powers of 10 (product
no more than three decimal
places), using the ‘logic of the
language’
 Divide decimal numbers by
multiples of powers of 10 (no
numbers with more than three
decimal places), using the ‘logic of
the language’
 Use derived products to calculate
multiplication and division.
Mathematical Reasoning
Block 6, Geometry
Processes in Mathematics
 Recognise, name and sketch
polygons (decagon, heptagon,
hexagon, nonagon, octagon,
pentagon, quadrilateral, triangle)
 Recognise, name and sketch an
equilateral triangle, isosceles
triangle, right-angled triangle,
scalene triangle
 Recognise, name and sketch a
parallelogram, rectangle, rhombus,
square, trapezium
 Recognise the various special
triangles and quadrilaterals, use
the special name and recognise
them as the more general
polygons.
Communicating Mathematically
Block 6, Data and Measure
Processes in Mathematics
 Calculate durations for times
specified as a.m./p.m. times and
24-hour clock times
 Draw and use a double number line
showing distance and time to solve
word problems involving speed,
distance and time
 Use calculations to solve word
problems involving speed, distance
and time.
Communicating Mathematically
© Oxford University Press 2012
 recognise general patterns and relationships [and make predictions
about them;]
Number
Understanding Number and Number Notation
 develop an understanding of place value to include up to two decimal
places, use this to multiply and divide numbers by 10 and 100;
Operations and their Applications
 know the multiplication facts up to 10 x 10;
 engage in a range of activities to develop understanding of the four
operations of number, [appreciate the use of brackets, add and
subtract with up to two decimal places,] multiply and divide decimals
by whole numbers, [use these operations to solve problems.]
 understand mathematical language and use it to discuss their work
and explain their thinking;
Shape and Space
Exploration of Shape
 construct a range of regular and irregular 2-D shapes, classify these
through examination of angles and side, [recognise line and rotational
symmetry, reflect shapes in a line, explore tessellations,] name and
describe common 2-D shapes, [begin to understand congruence in 2D shapes;]
Position, Movement and Direction
 develop language associated with line and angle; [recognise
properties of acute, obtuse and reflex angles;] investigate angles in
triangles and quadrilaterals; [measure and draw angles up to 360°;]
 compare their ideas and methods of working with others;
Measures
 understand the relationship between units [and convert one metric unit
to another], use the four operations to solve problems;
 recognise times on the analogue and digital clocks and understand
the relationship between the 12 and 24-hour clocks, [use timetables.]
15
Block 6, Arithmetic 2
Number
 Evaluate terms in an expression
that includes brackets, e.g.
recognise 5 + 4 + 2 × 5 as an
expression with three terms,
evaluate 5 + 4 + 10 and recognise
5 + (4 + 2) × 5 as an expression
with two terms and evaluate 5 + 30
 Insert brackets in an expression so
it has a specified value, e.g.
calculate and write ‘2 × 5 + 1 + 2 =
13 and 2 x (5 + 1) + 2 = 14’ and
also insert brackets for 2 × 5 + 1 +
2 to have the value 16.
Patterns, Relationships and Sequences in Number
Block 6, Reasoning
Number
 Calculate durations of shop
opening times from information in a
grid
 Use information in a grid about
duration of tracks on a CD to
calculate differences between
durations, total durations and mean
durations
 Calculate equivalences and
fractions of periods of time using
years, days, hours, minutes and
seconds.
Understanding Number and Number Notation
 understand and use [multiples and] factors and the terms prime,
[square and cube; appreciate inverse operations];
Operations and their Applications
 know the multiplication facts up to 10 x 10;
 engage in a range of activities to develop understanding of the four
operations of number, appreciate the use of brackets, [add and
subtract with up to two decimal places, multiply and divide decimals by
whole numbers, use these operations to solve problems.]
 understand and use vulgar fractions, [decimal fractions and
percentages and explore the relationships between them;]
Measures
 understand the relationship between units [and convert one metric unit
to another], use the four operations to solve problems;
 recognise times on the analogue [and digital] clocks and understand
the relationship between the 12 and 24-hour clocks, use timetables.
Handling Data
Collecting, Representing and Interpreting Data
 interpret a wide range of tables, [lists, graphs and diagrams; create
and interpret frequency tables, including those for grouped data;]
 understand, calculate [and use] the mean [and range] of a set of
discrete data.
© Oxford University Press 2012
16
For coverage of the following Key Stage 3 Levels of Progression in
Using Mathematics objectives please see Maths Makes Sense 5 as
detailed below:
Expansion of the Levels of
Maths Makes Sense 5 Main teaching
Progression in Using Mathematics
across the Curriculum: Key Stage
3 (Levels 1–7)
Level 6
Number and Algebra
 [add, subtract,] multiply and divide decimals;
Level 6
Number and Algebra
 understand and use order of precedence in
 Block 4, Arithmetic 1
 Block 6, Arithmetic 1
 Block 5, Arithmetic 2
 Block 6, Arithmetic 2
numerical calculations, including the use of
brackets;
Level 6
Number and Algebra
 understand, use and calculate ratio [and
 Block 2, Data and Measure
 Block 5, Data and Measure
 Block 6, Reasoning
proportion;]
Level 6
 Block 1, Data and Measure
Number and Algebra
 use equivalences between fractions, decimals
and percentages to solve problems;
Level 6
 Block 2, Reasoning
Number and Algebra
 use conventional notation in algebra;
Level 6
Shape, Space and Measures
 Block 2, Data and Measure
 Block 3, Data and Measure
 use, convert and calculate measures involving
metric and, where appropriate, imperial units;
Level 6
 Block 3, Geometry
Shape, Space and Measures
 calculate the circumference and area of circles;
Level 6
 Block 6, Data and Measure
Shape, Space and Measures
 understand and use compound measures;
Level 6
 Block 1, Geometry
Shape, Space and Measures
 use co-ordinates in all four quadrants;
Level 6
Handling Data :
 work out [and use] the [median and] mode;
Level 7
 Block 3, Data and Measure
 Block 5, Data and Measure
 Block 2, Arithmetic 1
Number and Algebra
 use the four operations with fractions;
© Oxford University Press 2012
17
Maths Makes Sense 6
Block 1
Maths Makes Sense 6
end-of-block objectives
Northern Ireland Curriculum Key Stage 2
Block 1, Arithmetic 1
Processes in Mathematics
 Use a grid for long multiplication of
HTU by TU, e.g. 324 × 23 = 7452
 Estimate the value of products by
rounding each factor
 Use the product of a 3-digit whole
number and a 2-digit whole number
and, using approximation, work out
a related product of decimal
numbers
Communicating Mathematically
 present information and results clearly.
Mathematical Reasoning
 check results and consider whether they are reasonable.
Number
Understanding Number and Number Notation
 develop an understanding of place value to include up to two decimal
places, use this to multiply [and divide] numbers by 10 and 100;
 estimate and approximate to gain an indication of the size of a solution
to a calculation [or problem;]
Operations and their Applications
 know the multiplication facts up to 10 x 10;
 engage in a range of activities to develop understanding of the four
operations of number, [appreciate the use of brackets, add and
subtract with up to two decimal places], multiply [and divide] decimals
by whole numbers, [use these operations to solve problems.]
Block 1, Geometry
Processes in Mathematics
 Find the sum of the exterior angles
of a polygon
 Find the sum of the interior angles
of a polygon
Communicating Mathematically
 understand mathematical language and use it to discuss their work
and explain their thinking;
Shape and Space
Exploration of Shape
 construct a range of regular and irregular 2-D shapes, [classify these
through examination of angles and side, recognise line and rotational
symmetry, reflect shapes in a line, explore tessellations, name and
describe common 2-D shapes, begin to understand congruence in 2-D
shapes;]
Position, Movement and Direction
 understand the notion of angle in the context of turning, [recognise
right angles, understand clockwise and anti-clockwise, know the eight
points of the compass, use Logo to understand movement and
turning, be introduced to a programming language and use it to create
pictures and patterns and to generate shapes];
 develop language associated with [line and] angle, [recognise
properties of acute, obtuse and reflex angles,] investigate angles in
triangles and quadrilaterals, [measure and draw angles up to 360°;]
Block 1, Data and Measure
Number
 Solve distance word problems
using kilometres
 Solve volume word problems using
millilitres and litres
 Solve mass word problems using
grams and kilograms
Understanding Number and Number Notation
© Oxford University Press 2012
 estimate and approximate to gain an indication of the size of a solution
to a calculation or problem;
Operations and their Applications
 develop strategies to add and subtract mentally;
 engage in a range of activities to develop understanding of the four
operations of number, [appreciate the use of brackets, add and
subtract with up to two decimal places, multiply and divide decimals by
whole numbers,] use these operations to solve problems.
18
Measures
 understand the relationship between units and convert one metric unit
to another, use the four operations to solve problems;
Block 1, Arithmetic 2
Processes in Mathematics
 Use a short method for
multiplication of up to 3-digit by 2digit whole numbers, e.g. 712 × 39
= 27768
 Use a short method for division of
up to 3-digit by 2-digit whole
numbers, including remainders,
e.g. 474 ÷ 13 = 36 r 6
Communicating Mathematically
 present information and results clearly.
Mathematical Reasoning
 check results and consider whether they are reasonable.
Number
Understanding Number and Number Notation
 estimate and approximate to gain an indication of the size of a solution
to a calculation or problem;
Operations and their Applications
 know the multiplication facts up to 10 x 10;
 engage in a range of activities to develop understanding of the four
operations of number, [appreciate the use of brackets, add and
subtract with up to two decimal places, multiply and divide decimals by
whole numbers, use these operations to solve problems.]
Block 1, Reasoning
Processes in Mathematics
 Calculate the mean, median, mode
and range of a sample
Communicating Mathematically
 understand mathematical language and use it to discuss their work
and explain their thinking;
Number
Patterns, Relationships and Sequences in Number
 understand that a letter can stand for an unknown number.
Understanding Number and Number Notation
 [count, read, write and] order whole numbers;
Handling Data
Collecting, Representing and Interpreting Data
 understand, calculate [and use] the mean and range of a set of
discrete data.
© Oxford University Press 2012
19
Block 2
Maths Makes Sense 6
end-of-block objectives
Northern Ireland Curriculum Key Stage 2
Block 2, Arithmetic 1
Processes in Mathematics
 Use a grid for long division of
ThHTU by U, e.g. 6342 ÷ 6 = 1057
 Estimate the value of quotients by
rounding
 Use the quotient of a 4-digit whole
number and a 1-digit whole number
and, using approximation, work out
a related quotient of decimal
numbers, e.g. 63.42 ÷ .6 = 105.7
Communicating Mathematically
 present information and results clearly.
Mathematical Reasoning
 recognise general patterns and relationships [and make predictions
about them;]
 check results and consider whether they are reasonable.
Number
Understanding Number and Number Notation
 develop an understanding of place value to include up to two decimal
places, use this to multiply and divide numbers by 10 and 100;
 estimate and approximate to gain an indication of the size of a solution
to a calculation [or problem;]
Operations and their Applications
 know the multiplication facts up to 10 x 10;
 engage in a range of activities to develop understanding of the four
operations of number, [appreciate the use of brackets, add and
subtract with up to two decimal places, multiply and] divide decimals
by whole numbers, [use these operations to solve problems.]
Block 2, Geometry
Processes in Mathematics
 Recognise reflection, translation,
enlargement and rotation as
transformations
 For an object and its image,
recognise and name the
transformation
Communicating Mathematically
 present information and results clearly.
Shape and Space
Exploration of Shape
 [construct a range of regular and irregular 2-D shapes; classify these
through examination of angles and sides; recognise line and rotational
symmetry]; reflect shapes in a line; [explore tessellations; name and
describe common 2-D shapes]; begin to understand congruence in 2D shapes;
Position, Movement and Direction
 understand the notion of angle in the context of turning; recognise
right angles; understand clockwise and anti-clockwise; [know the eight
points of the compass; use logo to understand movement and turning;
be introduced to a programming language and use it to create pictures
and patterns and to generate shapes;]
Block 2, Data and Measure
Processes in Mathematics
 Draw a pie chart from data
presented in a frequency table
Making and Monitoring Decisions
 take increasing responsibility for selecting and using [the materials
and] the mathematics required for their work;
Communicating Mathematically
 interpret situations mathematically using appropriate [symbols or]
diagrams;
 present information and results clearly.
Handling Data
Collecting, Representing and Interpreting Data
 interpret a wide range of tables, lists, graphs and diagrams, create
and interpret frequency tables, [including those for grouped data;]
© Oxford University Press 2012
20
Shape and Space
Position, Movement and Direction
 [develop language associated with line and angle, recognise
properties of acute, obtuse and reflex angles, investigate angles in
triangles and quadrilaterals, measure and] draw angles up to 360°;
Block 2, Arithmetic 2
Number
 Convert a vulgar fraction to a
percentage
 Convert a percentage to a decimal
fraction
 Convert a decimal fraction to a
percentage
Understanding Number and Number Notation
Block 2, Reasoning
Handling Data
 Measure the probability of events,
e.g. the probability of rolling a 3 on
a fair dice numbered 1-6 is 1/6
Introduction to Probability
© Oxford University Press 2012
 understand and use vulgar fractions, decimal fractions and
percentages and explore the relationships between them;
Patterns, Relationships and Sequences in Number
 understand that a letter can stand for an unknown number.
 become familiar with and use the language of probability;
 understand possible outcomes of simple random events, understand
that there is a degree of uncertainty about the outcome of some
events while others are certain or impossible;
21
Block 3
Maths Makes Sense 6
end-of-block objectives
Northern Ireland Curriculum Key Stage 2
Block 3, Arithmetic 1
Number
 Use equivalent fractions in
calculations using each of the four
operations
Understanding Number and Number Notation
Block 3, Geometry
Processes in Mathematics
 Use a protractor to measure the
size of an angle, in degrees, and a
ruler to measure the length of a
line, in millimetres
 Draw the image of a polygon in a
mirror line
 Complete the drawing of a named,
partially-drawn shape on a pair of
axes
 Calculate the size of the two equal
angles in an isosceles triangle
 Sort quadrilaterals according to
their properties
 Complete the co-ordinates of the
corners of a named shape using
knowledge of its properties
 Find the angle of rotation for an
object and image polygon
Communicating Mathematically
understand and use vulgar fractions, [decimal fractions and percentages
and explore the relationships between them;]
 understand mathematical language and use it to discuss their work
and explain their thinking;
 present information and results clearly.
Measures
 appreciate important ideas about measurement including [the
continuous nature of measurement and] the need for appropriate
accuracy;
Shape and Space
Exploration of Shape
 construct a range of regular and irregular 2-D shapes, classify these
through examination of angles and side, recognise line [and rotational]
symmetry, reflect shapes in a line, [explore tessellations,] name and
describe common 2-D shapes, [begin to understand congruence in 2D shapes;]
Position, Movement and Direction
 develop language associated with line and angle, recognise properties
of acute, obtuse [and reflex angles], investigate angles in triangles and
quadrilaterals, measure [and draw] angles up to 360°;
Block 3, Data and Measure
Processes in Mathematics
 Solve problems involving ratio and
proportion by scaling up or scaling
down
 Interpret and read a scale to
measure mass
 Compare the usefulness of
different weighing scales for
measuring mass
Making and Monitoring Decisions
Block 3, Arithmetic 2
Processes in Mathematics
 Write the ratio of one quantity to
another
 Write a quantity as a fraction or
percentage of the total quantity
 Solve word problems by calculating
a quantity following a percentage
increase or decrease
Making and Monitoring Decisions
 take increasing responsibility for selecting and using the materials and
mathematics required for their work;
Patterns, Relationships and Sequences in Number
 understand that a letter can stand for an unknown number.
Measures
 develop skills in estimation of [length,] weight, [volume/capacity, time,
area and temperature;]
 appreciate important ideas about measurement including the
continuous nature of measurement and the need for appropriate
accuracy;
 understand the relationship between units and convert one metric unit
to another, use the four operations to solve problems;
 develop a range of strategies for problem-solving, looking for ways to
overcome difficulties.
Number
Understanding Number and Number Notation
 understand and use vulgar fractions, decimal fractions and
percentages and explore the relationships between them;
Handling Data
© Oxford University Press 2012
22
Collecting, Representing and Interpreting Data
 interpret a wide range of tables,[ lists, graphs and diagrams; create
and interpret frequency tables, including those for grouped data;]
Block 3, Reasoning
Processes in Mathematics
 Interpret a distance-time graph for
distance travelled and time taken
 Interpret a distance-time graph for
faster and slower (speed)
 Interpret a temperature-time graph
for rise, fall and difference in
temperature
Communicating Mathematically
© Oxford University Press 2012
 understand mathematical language and use it to discuss their work
and explain their thinking;
Handling Data
Collecting, Representing and Interpreting Data
 explain their work orally and/or through writing and draw conclusions;
 interpret a wide range of [tables, lists,] graphs [and diagrams, create
and interpret frequency tables, including those for grouped data;]
23
Block 4
Maths Makes Sense 6
end-of-block objectives
Northern Ireland Curriculum Key Stage 2
Block 4, Arithmetic 1
Number
 Calculate with negative numbers
using the four operations (using 1 +
-1 = 0 with tricky examples)
 Calculate with vulgar fractions
using the four operations (using
equivalent fractions and improper
fractions with tricky examples)
Understanding Number and Number Notation
Block 4, Geometry
Shape and Space
 Draw the lines of symmetry of a
polygon
 Write the number of lines of
symmetry for any polygon
 Identify and write the order of
rotational symmetry for any
polygon
Exploration of Shape
Block 4, Data and Measure
Processes in Mathematics
 Collect, select, process and
present data, making use of ICT
 Interpret data to answer questions
and solve problems
 Construct and interpret frequency
tables, bar charts and pie charts,
making use of ICT
 Plan and carry out a survey,
suggesting and developing lines of
enquiry, to collect discrete or
discrete grouped data
Making and Monitoring Decisions
Block 4, Arithmetic 2
Processes in Mathematics
 Solve word problems involving
money using addition, subtraction,
multiplication or division
 Add and subtract ‘squares’ and
‘cubes’ of numbers, e.g. find the
sum of 102 and 8.73
 Calculate the product of a given
number closest to a specified
number, e.g. find the product of 28
that is closest to 298
Making and Monitoring Decisions
 understand and use vulgar fractions, [decimal fractions and
percentages and explore the relationships between them]
 understand and use negative numbers [in context.]
 [construct a range of regular and irregular 2-D shapes, classify these
through examination of angles and side,] recognise line and rotational
symmetry, reflect shapes in a line, [explore tessellations,] name and
describe common 2-D shapes, begin to understand congruence in 2-D
shapes;
 identify and obtain the information required for a task, [suggesting
appropriate sources to find the information;]
 plan and organise their work, learning to work systematically;
Mathematical Reasoning
 ask and respond to open-ended questions and explain their thinking;
Handling Data
Collecting, Representing and Interpreting Data
 collect, classify, record and present data drawn from a range of
meaningful situations, using graphs, tables, diagrams and ICT
software;
 explain their work orally and/or through writing and draw conclusions;
 interpret a wide range of tables, [lists,] graphs and diagrams, create
and interpret frequency tables, including those for grouped data;
 design and use a data collection sheet, interpret the results, [enter
information in a database or spreadsheet, and interrogate and
interpret the results;]
 take increasing responsibility for selecting and using the [materials
and] mathematics required for their work;
Number
Patterns, Relationships and Sequences in Number
 understand and use multiples and factors and the terms [prime]
square and cube, [appreciate inverse operations;]
Operations and their Applications
 engage in a range of activities to develop understanding of the four
operations of number, [appreciate the use of brackets], add and
subtract with up to two decimal places, multiply and divide decimals by
whole numbers, use these operations to solve problems.
Money
 use the four operations to solve problems involving money;
© Oxford University Press 2012
24
Block 4, Reasoning
Number
 Identify terms and products in
expressions
 Evaluate expressions with and
without brackets, e.g. 3 + 2 × 3 = 9,
(3 + 2) × 3 = 15
 Insert brackets in an expression for
it to take a specified value, e.g.
insert brackets so that the
expression 3 + 2 × 3 has the value
15
Operations and their Applications
© Oxford University Press 2012
 engage in a range of activities to develop understanding of the four
operations of number, appreciate the use of brackets, [add and
subtract with up to two decimal places, multiply and divide decimals by
whole numbers, use these operations to solve problems.]
25
Block 5
Maths Makes Sense 6
end-of-block objectives
Northern Ireland Curriculum Key Stage 2
Block 5, Arithmetic 1
Number
 Use the formulae for diameter,
circumference and area of a circle
 Use the formula for the area of a
triangle
 Use the formula for the volume of a
cuboid and a cylinder
Patterns, Relationships and Sequences in Number
 understand that a letter can stand for an unknown number.
Measures
 calculate [perimeter and] the areas and volumes of simple shapes;
Shape and Space
Exploration of Shape
 [construct a range of regular and irregular 2-D shapes; classify these
through examination of angles and sides; recognise line and rotational
symmetry; reflect shapes in a line; explore tessellations]; name and
describe common 2-D shapes; [begin to understand congruence in 2D shapes;]
 [construct 3-D shapes; investigate the number of faces, edges and
vertices on these shapes]; name and describe common 3-D shapes;
[explore the relationship between 2-D and 3-D shapes.]
Block 5, Geometry
Processes in Mathematics
 Calculate an exterior angle of a
regular polygon
 Calculate an interior angle of a
regular polygon
 Calculate the third angle in a
triangle
Communicating Mathematically
 present information and results clearly.
Number
Operations and their Applications
 engage in a range of activities to develop understanding of the four
operations of number; [appreciate the use of brackets; add and
subtract with up to two decimal places; multiply and divide decimals by
whole numbers; use these operations to solve problems.]
Shape and Space
Position, Movement and Direction
 develop language associated with [line and] angle, [recognise
properties of acute, obtuse and reflex angles], investigate angles in
triangles and quadrilaterals, [measure and draw angles up to 360°;]
Block 5, Data and Measure
Processes in Mathematics
 Convert between yards and metres
 Calculate the perimeter and the
area of compound shapes
 Calculate surface area and volume
of cuboids
 Solve problems involving
dimensions and volume of cuboids
Making and Monitoring Decisions
 take increasing responsibility for selecting and using the materials and
mathematics required for their work;
 develop a range of strategies for problem-solving, looking for ways to
overcome difficulties.
Number
Operations and their Applications
 engage in a range of activities to develop understanding of the four
operations of number; [appreciate the use of brackets; add and
subtract with up to two decimal places; multiply and divide decimals by
whole numbers; use these operations to solve problems.]
Measures
 calculate perimeter and the areas and volumes of simple shapes;
© Oxford University Press 2012
26
Block 5, Arithmetic 2
Processes in Mathematics
 Use inequalities to identify a range
of possible values for a number,
e.g. find the value of m, where 15 <
m < 20 and m is a whole number
 Use algebraic notation for the sum,
difference, product and quotient of
two numbers, e.g. m + n, m – n,
mn, m/n
 Find the greatest or smallest sums,
differences, products and quotients
of two numbers with a range of
possible values
 Calculate the product of a given
number closest to a specified
number, e.g. calculate the product
of 34 closest to 241
Communicating Mathematically
Block 5, Reasoning
Number
 Solve linear equations that involve
one operation with whole and
decimal numbers
Patterns, Relationships and Sequences in Number
© Oxford University Press 2012
 understand mathematical language and use it to discuss their work
and explain their thinking;
 interpret situations mathematically using appropriate symbols [or
diagrams;]
Number
Patterns, Relationships and Sequences in Number
 understand that a letter can stand for an unknown number.
Operations and their Applications
 engage in a range of activities to develop understanding of the four
operations of number, [appreciate the use of brackets; add and
subtract with up to two decimal places, multiply and divide decimals by
whole numbers, use these operations to solve problems.]
 [understand and use multiples and factors and the terms prime square
and cube], appreciate inverse operations;
 understand that a letter can stand for an unknown number.
27
Block 6
Maths Makes Sense 6
end-of-block objectives
Northern Ireland Curriculum Key Stage 2
Block 6, Arithmetic 1
Processes in Mathematics
 Write a vulgar fraction as a decimal
fraction to three decimal places,
using a calculator for division, e.g.
7/11 = .636
 Convert decimal fractions to vulgar
fractions using tenths, hundredths
and thousandths,
e.g. .625 = 625/1000
 Write recurring infinite decimals as
abbreviations using the
conventional of ‘dots’ above one or
two
. digits, e.g. write .83333333 as
.83
Communicating Mathematically
Block 6, Geometry
Processes in Mathematics
 Draw the perpendicular bisector of
a line segment
 Draw the bisector of an angle
 Draw the circum-circle of a triangle
 Draw the in-circle of a triangle
Communicating Mathematically
 interpret situations mathematically using appropriate symbols [or
diagrams;]
Mathematical Reasoning
 recognise general patterns [and relationships and make predictions
about them;]
Number
Understanding Number and Number Notation
 understand and use vulgar fractions, decimal fractions [and
percentages] and explore the relationships between them;
 understand mathematical language and use it to discuss their work
and explain their thinking;
Shape and Space
Exploration of Shape
 construct a range of regular and irregular 2-D shapes, [classify these
through examination of angles and side, recognise line and rotational
symmetry, reflect shapes in a line, explore tessellations, name and
describe common 2-D shapes, begin to understand congruence in 2-D
shapes;]
Position, Movement and Direction
 develop language associated with line and angle, [recognise
properties of acute, obtuse and reflex angles, investigate angles in
triangles and quadrilaterals], measure [and draw angles] up to 360°;
© Oxford University Press 2012
28
Block 6, Data and Measure
Processes in Mathematics
 Understand the ‘golden ratio’ Φ
(phi), is a constant with an
approximate value of 1.618
 Calculate ratios, and use ratios to
calculate lengths and construct
shapes
 Plan and develop lines of enquiry
to research a topic, interpret and
evaluate findings
 Collect, organise, select and
present information using
appropriate methods, including the
use of ICT
 Work effectively in a group
Making and Monitoring Decisions
 take increasing responsibility for selecting and using the materials and
mathematics required for their work;
 identify and obtain the information required for a task, suggesting
appropriate sources to find the information;
 plan and organise their work, learning to work systematically;
 develop a range of strategies for problem-solving, looking for ways to
overcome difficulties.
Communicating Mathematically
 understand mathematical language and use it to discuss their work
and explain their thinking;
 compare their ideas and methods of working with others;
 present information and results clearly.
Mathematical Reasoning
 recognise general patterns and relationships and make predictions
about them;
 ask and respond to open-ended questions and explain their thinking;
Number
Patterns, Relationships and Sequences in Number
 understand that a letter can stand for an unknown number.
Measures
 appreciate important ideas about measurement, including the
continuous nature of measurement and the need for appropriate
accuracy;
Block 6, Arithmetic 2
Processes in Mathematics
 Solve number puzzles involving
algebraic terms, use flow diagrams
to identify inverse operations
 Recognise algebraic
representations of odd and even
numbers
 Identify two factors of a number,
including numbers represented
algebraically, and divide it by each
factor, e.g. for 3k, 3k ÷ 3 = k,
3k ÷ k = 3
Communicating Mathematically
Block 6, Reasoning
Number
 Express vulgar fractions as
percentages
Understanding Number and Number Notation
© Oxford University Press 2012
 interpret situations mathematically using appropriate symbols [or
diagrams;]
Number
Patterns, Relationships and Sequences in Number
 understand and use [multiples and] factors [and the terms prime,
square and cube,] appreciate inverse operations;
 [interpret, generalise and use simple relationships expressed in
numerical, spatial and practical situations,] understand and use simple
function machines;
 understand that a letter can stand for an unknown number.
 understand and use vulgar fractions, [decimal fractions] and
percentages and explore the relationships between them;
29
For coverage of the following Key Stage 3 Range
objectives, please see Maths Makes Sense 6 as
detailed below:
Expansion of the Levels of
Progression in Using Mathematics
across the Curriculum: Key Stage 3
(Levels 1–7)
Maths Makes Sense 6 Main
Teaching and Daily Practices
Level 6
 Block 1, Arithmetic
 Block 2, Arithmetic 1
Number and Algebra
 [add, subtract,] multiply [and divide] decimals;
Level 6
Number and Algebra
 round to a given number of decimal places;
Level 6





Block 4, Arithmetic 2
Block 5, Arithmetic 2
Block 5, Reasoning
Block 6, Arithmetic 1
Block 6, Reasoning
 Block 4, Reasoning
Number and Algebra
understand and use precedence in numerical calculations,
including the use of brackets;
 understand, use [and calculate] ratio and proportion;






Level 6
 Block 3, Arithmetic 1
 Block 4, Arithmetic 1
Level 6
Number and Algebra
Number and Algebra
Block 2, Arithmetic 2
Block 2, Reasoning
Block 3, Arithmetic 1
Block 3, Data and Measure
Block 3, Arithmetic 2
Block 6, Data and Measure
 add and subtract fractions, including mixed numbers;
Level 6
Number and Algebra
 Block 3, Arithmetic 2
 Block 6, Reasoning
 use equivalences between fractions, decimals and
percentages to solve problems;
Level 6
 Block 5, Arithmetic 1
Number and Algebra
 use appropriate formulae;
Level 6
Number and Algebra
 use conventional notation in algebra;
Level 6




Block 5, Arithmetic
Block 5, Arithmetic 2
Block 5, Reasoning
Block 6, Arithmetic 2
 Block 5, Data and Measure
Shape, Space and Measure
 use, convert and calculate measures involving metric,
and where appropriate, imperial measures;
Level 6
 Block 5, Data and Measure
Shape, Space and Measure
 calculate perimeters and areas of composite shapes
involving squares, rectangles [and triangles];
© Oxford University Press 2012
30
Level 6
 Block 5, Data and Measure
Shape, Space and Measure
 calculate surface areas and [composite] volumes of
cubes and cuboids;
Level 6
 Block 5, Arithmetic 1
Shape, Space and Measure
 calculate the circumference and area of circles;
Level 6
 Block 3, Reasoning
Shape, Space and Measures
 understand and use compound measures;
Level 6
Number and Algebra
 Block 2, Geometry
 Block 3, Geometry
 use co-ordinates in all four quadrants;
Level 6
Handling Data
 Block 2, Data and Measure
 Block 3, Reasoning
 [construct and] interpret a variety of [diagrams and]
graphs for discrete and continuous data;
Level 6
 Block 1, Reasoning
Handling data
 work out [and use] the median and mode
Level 7
Number and Algebra
 Block 3, Arithmetic 1
 Block 4, Arithmetic 1
 use the four operations with fractions;
Level 7
Number and Algebra
 Block 5, Reasoning
 Block 6, Arithmetic 2
 manipulate simple algebraic [expressions,] equations
[and formulae];
Level 7
 Block 2, Geometry
Shape, Space and Measure
 enlarge a 2-D shape by a given scale factor;
Level 7
 Block 2, Reasoning
Handling Data
 apply their knowledge of the rules of probability to
calculate an outcome or combination of outcomes;
© Oxford University Press 2012
31