Exploring mathematics: Tier 2 NC levels 3 and 4 (3a, 4c, 4b)
Autumn
36 lessons
S2.1 Graphs, charts and tables
Tally charts, frequency tables,
pictograms, bar charts
Mode, range
3 lessons
A2.1 Patterns and sequences
Simple integer sequences and
sequences from practical contexts
Factors and primes
Number patterns; general statements
6 lessons
Spring
31 lessons
S2.3 Enquiry 1
Collecting, representing and
interpreting data in bar charts
Interpreting pie charts
Venn and Carroll diagrams
4/5 lessons
A2.2 Sequences, functions, graphs
Sequences
Simple functions and mappings
Coordinates in first quadrant
Simple graphs
5/6 lessons
R2.1 Revision/support
Number, algebra, geometry
and measures, statistics
5 lessons
Summer
33 lessons
S2.4 Probability 2
Probability scale; comparing
probability in simple cases
3 lessons
S2.5 Enquiry 2
Collecting, representing and
interpreting data in bar charts and
line graphs
Interpreting pie charts
Simple statistics; writing report
5/6 lessons
R2.2 Revision/support
Number, algebra, geometry
and measures, statistics
5 lessons
A2.3 Expressions and equations
Order of operations
Using letters; simple expressions,
collecting like terms, substituting
integers
Using inverse operations
Solving simple equations
6/7 lessons
N2.2 Whole numbers
Place value
Mental and written calculations
Using calculators
Word problems
8 lessons
N2.3 Fractions, decimals and percentages
Equivalent fractions
Simple fractions of shapes and quantities
Decimal place value; tenths and hundredths
Simple percentages of quantities
6 lessons
N2.4 Decimals
Ordering and rounding decimals
Decimals and money
Adding and subtracting decimals
Using a calculator
5/6 lessons
N2.5 Decimals and measures
Equivalent fractions and decimals
Decimals and measures; time
Reading numbers from scales
Word problems
5/6 lessons
N2.6 Fractions, percentages and direct
proportion
Equivalent fractions, decimals, percentages
Comparing fractions
Percentages of quantities
Simple ideas of ratio and proportion
5/6 lessons
N2.7 Solving number problems
Solving problems involving whole numbers,
fractions and decimals
3/4 lessons
100 lessons
1 | Exploring mathematics | Tier 2 (purple)
G2.1 Length, perimeter and area
Drawing and measuring lines; estimating lengths
Perimeter of regular polygons
Perimeter and area of squares, rectangles and
shapes drawn on grids
4 lessons
G2.2 Angles
Drawing, measuring and estimating acute and
obtuse angles in degrees
Angles in a straight line and at a point
3 lessons
G2.3 Symmetry and reflection
Line symmetry; reflection
Exploring symmetry and reflection with ICT
3 lessons
G2.4 Measures
Length, mass, capacity; using measuring
equipment; reading numbers from scales
Converting between units using decimals
Time, 24-hour clock, timetables; word problems
4/5 lessons
G2.5 Properties of shapes
Perpendicular and parallel lines
Properties of squares and rectangles
Constructions
Nets of cubes and cuboids
6/7 lessons
Using and applying mathematics is integrated into each unit
S2.2 Probability 1
Language of probability
Placing events on scale from
impossible to certain
2 lessons
N2.1 Properties of numbers
Squares, simple square roots
Multiples, divisibility
Positive and negative numbers
4 lessons
Units - levels 3a, 4c, 4b
SUPPORT
Number 1:
Properties of numbers
(3 hours)
Integers, powers and roots
(48–59)
CORE
Before they start, pupils should be able to:
In this unit, pupils learn to:
• recall addition and subtraction facts for each
• represent problems using words or diagrams
number to 20
• look for and visualise patterns
• recognise odd and even numbers
• manipulate numbers
• recognise multiples of 2, 5 and 10.
• record, explain and compare methods
• engage in mathematical discussion of results
• begin to generalise
and to:
• identify squares of numbers to 12  12
• recognise multiples and use simple tests of divisibility
• order, add and subtract positive and negative numbers in context.
2 | Exploring mathematics | Tier 2 (purple)
Number 2:
Whole numbers
(8 hours)
Place value
Before they start, pupils should be able to:
In this unit, pupils learn to:
• read, write, order and round 3-digit and 4-digit
• represent situations or problems using words, diagrams or calculations
numbers
• simplify calculations with more than one step
• use mental methods to add or subtract:
• manipulate numbers and apply routine algorithms
(36–47)
– a 1-digit number to a 2-digit number
Calculations
– a multiple of 10 or a ‘near multiple’ of 10 to a 2-
(88–91, 102–105)
• use facts to derive or deduce others
• recall addition and subtraction facts to 20
digit number
Calculator methods
• add and subtract 3-digit numbers
(108–109)
• understand multiplication as repeated addition
• calculate accurately, using mental methods or a calculator as appropriate
• choose appropriate methods and resources
• check that results are about the right size
• record, explain and compare methods
Solving problems
and division as grouping (repeated subtraction) or
• engage in mathematical discussion of results
(2–11)
sharing
• learn from mistakes
• know multiplication facts for the 2, 3, 4, 5 and 10
times tables and derive corresponding division
facts
• find remainders after simple division
• use informal methods to multiply or divide 2-digit
by 1-digit numbers.
and to:
• partition, round and order whole numbers
• consolidate recall of addition and subtraction facts to 20
• recall multiplication facts to 10  10, and quickly derive corresponding
division facts
• multiply and divide whole numbers by 10 or 100
• use mental methods to:
– add and subtract pairs of 2-digit numbers
– find remainders after division
• use efficient written methods to add and subtract whole numbers, and to
multiply and divide 2-digit or 3-digit numbers by a single-digit number.
3 | Exploring mathematics | Tier 2 (purple)
Number 3:
Fractions, decimals and
percentages
(6 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• use fraction notation and the vocabulary
• represent situations or problems using words, diagrams or calculations
numerator and denominator
• use unit fractions such as 1⁄2, 1⁄3, 1⁄4, 1⁄5, 1⁄10, … to
describe parts of shapes
Fractions, decimals, percentages
(60–77)
Calculations
(92–101, 110–111)
Solving problems
(28–31)
• recognise simple fractions that are several parts
of a whole, such as 2⁄3 or 3⁄4
• use decimal notation for tenths and hundredths
• use facts to derive or deduce others
• calculate accurately, using mental methods or a calculator as appropriate
• choose appropriate methods and resources, including ICT
• record, explain and compare methods
• engage in mathematical discussion of results
and partition decimals in contexts of money or
• make connections with ideas they have met before
measurement.
• learn from mistakes
and to:
• recognise proportions of a whole and use simple fractions and
percentages to describe these
• identify simple equivalent fractions, including relating tenths to hundredths
• understand place value in decimals with up to two places
• understand percentage as ‘the number of parts in every 100’, and find
simple equivalent fractions, decimals and percentages
• calculate simple fractions and percentages of numbers and quantities.
4 | Exploring mathematics | Tier 2 (purple)
Number 4:
Decimals
(6 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• use decimal notation for tenths and hundredths
• represent situations or problems using words, diagrams or calculations
and partition decimals
• order whole numbers and round them to the
Calculations
(82–87, 92–103, 104–107, 110–111)
Calculator methods
(108–109)
Solving problems
(28–31)
nearest 10 or 100
• recall addition and subtraction facts for each
number up to 20.
• understand and use the relationship between
addition and subtraction
• use written methods to add and subtract whole
numbers
• use a calculator for whole number and decimal
calculations.
• make connections with ideas they have met before
• manipulate numbers and apply routine algorithms
• calculate accurately, using mental methods or a calculator as appropriate
• choose appropriate methods and resources, including ICT
• check that results are reasonable by considering the context or the size of
the numbers
• record, explain and compare methods
• engage in mathematical discussion of results
• learn from mistakes
and to:
• partition, round and order decimals with up to two places
• convert between metres and centimetres. and pounds and pence
• use efficient written methods to add and subtract decimals
• interpret a calculator display in contexts such as money or measures.
5 | Exploring mathematics | Tier 2 (purple)
Number 5:
Decimals and measures
(6 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• use decimal notation for tenths and hundredths
• represent situations or problems using words, diagrams or calculations
• change metres to centimetres and pounds to
• choose appropriate resources
pence, and vice versa
Calculations
(88–107, 110–111)
• read the time to the minute on analogue and
digital clocks, and use 12-hour clock notation
Calculator methods
• recall multiplication facts to 10  10
(108–109)
•• use written methods to:
Fractions and percentages
– add and subtract whole numbers and money
(66–77)
– multiply and divide 2-digit by 1-digit numbers
Solving problems
(28–29)
understand remainders.
• make connections with ideas they have met before
• calculate accurately, using mental methods or a calculator as appropriate
• check that results are about the right size
• record, explain and compare methods and results
and to:
• use decimal notation to record measurements (e.g. 1.25 m or 0.6 kg)
• multiply whole numbers and decimals by 10, 100 or 1000
• begin to convert metric units of measurement to related units
• interpret with appropriate accuracy numbers on a range of measuring
instruments
• use am, pm and 24-hour clock notation to calculate time intervals
• express a quotient as a decimal or fraction
• interpret a calculator display in different contexts.
6 | Exploring mathematics | Tier 2 (purple)
Number 6:
Fractions, percentages and
direct proportion
(6 hours)
Fractions, decimals, percentages,
ratio and proportion
Before they start, pupils should be able to:
In this unit, pupils learn to:
• recognise simple equivalent fractions
• represent situations or problems using words, diagrams or calculations
• express one half, one quarter, three quarters, and
• make connections with ideas they have met before
tenths and hundredths, as fractions and decimals
• describe or represent situations or problems using words or diagrams
find simple fractions of small whole-number
• simplify calculations with more than one step
quantities.
(70–81)
• use facts to derive or deduce others
Calculations
• calculate accurately, using mental methods or a calculator as appropriate
(110–111)
• record, explain and compare methods
• engage in mathematical discussion of results and learn from mistakes
and to:
• recognise proportions of a whole and use simple fractions and
percentages to describe these
• find equivalent fractions, decimals and percentages
• add and subtract simple fractions with the same denominator
• multiply a fraction by an integer
• calculate simple fractions and percentages of numbers and quantities
• solve simple problems involving ideas of direct proportion by scaling
numbers up or down.
Number 7:
Solving number problems
(4 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• solve simple word problems involving numbers ,
• represent situations or problems using words, diagrams or calculations
money or measures
• choose and use appropriate operations and
Solving problems
(2–35)
appropriate ways of calculating
• recognise simple patterns and relationships
• use decimal notation for tenths and hundredths
• find simple equivalent fractions.
• choose appropriate methods and resources, including ICT
• make connections with ideas they have net before
• look for and visualise patterns
• use facts to derive or deduce others
• simplify calculations with more than one step
• check that results are about the right size
• engage in mathematical discussion of methods and results
• draw conclusions and begin to generalise
and to:
• recognise and extend simple number sequences
• calculate with simple fractions
• add, subtract and multiply decimals.
7 | Exploring mathematics | Tier 2 (purple)
Algebra 1:
Patterns and sequences
(6 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• recall addition and subtraction facts for numbers
• represent situations using numbers, words or diagrams
to 20
• look for and visualise patterns
• count on and back in steps of constant size
• use facts to derive or deduce others
Sequences and functions
• recognise square numbers to 10 × 10
• conjecture and begin to generalise
(144–163)
• recognise multiples of 2, 5 and 10
• calculate accurately, using mental methods or a calculator as appropriate
Formulae and identities
• recognise odd and even numbers
• record, explain and compare methods
• understand negative numbers as positions on a
• engage in mathematical discussion of results
(112–113)
Solving problems
number line.
(32–35)
and to:
• recognise, describe and extend simple number sequences
• recognise multiples and factors, and identify factors of 2-digit numbers.
Algebra 2:
Sequences, functions and
graphs
(6 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• count on and back in steps of constant size
• represent situations or problems using words, graphs or symbols
• describe and find the position of a point on a grid
• look for and visualise patterns
of squares where the lines are numbered.
• use facts to derive or deduce others
• conjecture and begin to generalise
Calculator methods
(108–109)
Coordinates
• draw accurate graphs on paper and on screen
• manipulate algebraic expressions and equations
(218–219)
• engage in mathematical discussion of results
Sequences, functions and graphs
and to:
(148–167)
• recognise, describe and extend simple number sequences
Solving problems
• use simple formulae expressed in words
(2–13, 26–27)
• use coordinates in the first quadrant
• plot a simple graph (e.g. for a multiplication table).
8 | Exploring mathematics | Tier 2 (purple)
Algebra 3:
Expressions and equations
(7 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• recognise the relationship between addition and
• represent situations or problems using words, diagrams or symbols
subtraction, and between multiplication and
division
Equations, formulae and identities
• check a calculation using the inverse operation.
(112–119, 138–143)
• look for and visualise patterns
• use facts to derive or deduce others
• manipulate algebraic expressions and equations
• engage in mathematical discussion of results
Solving problems
and to:
(26–27)
• begin to use the order of operations
• understand and use inverse operations
• use simple formulae expressed in words, then symbols
• simplify simple linear expressions by collecting like terms
• substitute positive integers into simple linear expressions and formulae
• solve simple linear equations using an appropriate method, e.g. 4a = 12.
•
Geometry and measures 1:
Length, perimeter and area
(4 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• measure and draw lines to the nearest centimetre
• represent situations or problems using words or diagrams
• use counting methods and standard units (cm,
• identify and visualise shapes
cm2) to find the perimeter and area of rectangles
Mensuration
(198–201, 228–231, 234–241)
Solving problems
(18–21)
and other simple shapes.
• draw accurate mathematical diagrams on paper and on screen
• choose appropriate resources
• calculate accurately, using mental methods or a calculator as appropriate
• record, explain and compare methods and results
• check that results are about the right size
• draw conclusions and begin to generalise
and to:
• estimate and measure length
• interpret with appropriate accuracy numbers on a range of measuring
instruments
• measure and draw lines to the nearest millimetre
• measure and calculate the perimeter of simple shapes
• estimate areas by counting squares
• derive and use the formula for the area of a rectangle.
9 | Exploring mathematics | Tier 2 (purple)
Geometry and measures 2:
Angles
(3 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• understand angle as a measure of turn
• represent situations or problems using words or diagrams
• recognise right angles
• choose appropriate resources
• know that one whole turn is four right angles.
• identify and visualise shapes and patterns
Geometrical reasoning: lines, angles
• draw accurate mathematical diagrams
and shapes
• use facts to derive or deduce others
(178–189)
• draw conclusions and begin to generalise
Mensuration
• engage in mathematical discussion of methods and results
(232–233)
and to:
• make and describe turns, e.g. from SW to N
• estimate, measure and draw acute and obtuse angles
• calculate angles on a straight line or at a point.
Geometry and measures 3:
Symmetry and reflection
(3 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• reflect a simple shape in a mirror line along one
• represent situations or problems using words or diagrams
edge
• identify and draw lines of symmetry in simple
Transformations
(202–212)
Solving problems
(14–17, 32–35)
shapes
• recognise shapes with no lines of symmetry.
• identify and visualise shapes and patterns
• draw accurate mathematical diagrams on paper and on screen
• choose appropriate resources, including ICT
• conjecture and begin to generalise
• use facts to derive or deduce others
• draw conclusions and begin to generalise
• engage in mathematical discussion of methods and results
and to:
• identify lines of symmetry in 2D shapes
• visualise and draw where a shape will be after reflection in a mirror line
• explore symmetry and simple transformations using ICT.
10 | Exploring mathematics | Tier 2 (purple)
Geometry and measures 4:
Measures
(5 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• use, read and write standard metric units of length
• represent situations or problems using words or diagrams
and capacity
• record estimates and measurements to the
Calculations
nearest whole or half unit (e.g. ‘about 3.5 m’), or in
(82–87, 92–103, 104–107,
mixed units (e.g. ‘3 m and 20 cm’)
110–111)
Calculator methods
(108–109)
Measures
(228–231)
Solving problems
(28–31)
• know the relationships between familiar units of
length (e.g. 100 cm in 1 metre)
• read scales to the nearest division (numbered or
unnumbered)
• read the time from an analogue clock to the
nearest minute, and from a 12-hour digital clock
• use a calendar.
• choose appropriate resources
• make connections with ideas they have met before
• calculate accurately, using mental methods or a calculator as appropriate
• record, explain and compare methods and results
• check that results are about the right size
and to:
• estimate and measure length, mass and capacity by choosing and using
appropriate standard metric units of measure and tools
• interpret with appropriate accuracy numbers on a range of measuring
instruments
• convert between units using decimals to two places
• use am, pm and 24-hour clock notation to calculate time intervals, and
use timetables.
Geometry and measures 5:
Properties of shapes
(7 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• recognise equilateral and isosceles triangles
• represent situations or problems using words or diagrams
• recognise simple properties of squares and
• identify and visualise shapes and patterns
rectangles
Geometrical reasoning: lines, angles
and shapes
(184–189, 198–201)
• recognise right angles and lines of symmetry in
2D shapes.
• choose appropriate resources, including ICT
• draw accurate mathematical diagrams on paper and on screen
• engage in mathematical discussion of methods and results
• begin to generalise
and to:
• identify, visualise and describe properties of rectangles, triangles, regular
polygons and 3D solids, including parallel and perpendicular faces or
edges
• visualise and make 3D mathematical models by linking faces or edges
• identify and draw nets of simple 3D shapes
• use coordinates in the first quadrant to draw, locate and complete shapes
with given properties
• begin to calculate angles in a triangle.
11 | Exploring mathematics | Tier 2 (purple)
SUPPORT
Statistics 1:
Graphs, charts and tables
(3 hours)
CORE
Before they start, pupils should be able to:
In this unit, pupils learn to:
• represent and interpret data in:
• conjecture and begin to generalise
– tally charts
– pictograms (symbol representing 1 or 2 units)
Statistics
– simple bar charts
(256–261, 268–271)
– simple Venn and Carroll diagrams.
• choose appropriate resources, including ICT
• draw accurate diagrams and graphs on paper and on screen
• look for patterns
• draw conclusions, and check that they are reasonable in the context
• engage in mathematical discussion of results
• communicate findings
and to:
• represent and interpret data in Venn and Carroll diagrams, pictograms,
bar charts and simple line graphs
• use the mode and range to describe sets of data.
Statistics 2:
Probability 1
(2 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• discuss events using words such as ‘likely’,
• conjecture and begin to generalise
‘unlikely’, ‘certain’, ‘impossible’.
• look for patterns
• draw conclusions, and check that they are reasonable in the context
Probability
(276–283)
• engage in mathematical discussion of results
• communicate findings
and to:
• use the language of chance or likelihood
• find probabilities based on equally likely outcomes in simple contexts.
12 | Exploring mathematics | Tier 2 (purple)
Statistics 3:
Enquiry 1
(5 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• represent and interpret data in:
• conjecture and begin to generalise
– tally charts
– pictograms (symbol representing 1 or 2 units)
Statistics
– simple bar charts
(248–255, 262–265, 268–271)
– simple Venn and Carroll diagrams.
Solving problems
• choose appropriate resources, including ICT
• draw accurate diagrams and graphs on paper and on screen
• look for patterns
• draw conclusions, and check that they are reasonable in the context
• engage in mathematical discussion of results
(24–25)
• communicate findings
and to:
• collect discrete data and record them using a frequency table, where
appropriate using equal class intervals
• represent and interpret data in tables, bar charts and Venn and Carroll
diagrams
• interpret simple pie charts
• use the mode and range to describe sets of data.
Statistics 4:
Probability 2
(3 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• discuss events using words such as ‘likely’,
• conjecture and begin to generalise
‘unlikely’, ‘certain’, ‘impossible’.
• place the probability of events on a scale from
Probability
(278–285)
impossible to certain.
• look for patterns and relationships
• draw conclusions, and check that they are reasonable in the context
• engage in mathematical discussion of results
• communicate findings
and to:
• use the language of chance or likelihood
• find probabilities based on equally likely outcomes in simple contexts.
13 | Exploring mathematics | Tier 2 (purple)
Statistics 5:
Enquiry 2
(6 hours)
Before they start, pupils should be able to:
In this unit, pupils learn to:
• represent and interpret data in:
• conjecture and begin to generalise
– tally charts
• choose appropriate resources, including ICT
– pictograms (symbol representing 1 or 2 units)
Statistics
– simple bar charts
(248–255, 262–265, 268–271)
– simple Venn and Carroll diagrams.
Solving problems
• draw accurate diagrams and graphs on paper and on screen
• look for patterns and relationships
• draw conclusions, and check that they are reasonable in the context
• engage in mathematical discussion of results
(24–25)
• communicate findings
and to:
• collect discrete data and record them using a frequency table, where
appropriate using equal class intervals
• represent and interpret data in bar charts and simple line graphs
• interpret simple pie charts
• use the mode and range to describe sets of data.
Revision units 1 and 2 <paste in LH column and process objectives from RH columns>
Previous learning
Objectives based on National Curriculum levels 3 and 4 (mainly level 4)
Pupils should already be able to apply and use
In this unit, pupils consolidate their ability to:
many of the skills shown on the right. This unit
• apply own ideas and strategies, choosing appropriate resources
offers an opportunity to consolidate and refine
these skills.
• make connections with ideas they have met before
• learn from mistakes
• simplify calculations with more than one step
• manipulate numbers, algebraic expressions and equations, and apply routine algorithms
• calculate accurately, using mental methods or a calculator as appropriate
• draw accurate mathematical diagrams and graphs
• engage in mathematical discussion of results
• check that results are about the right size
• record methods, solutions and conclusions
<content objectives are as in the unit>
and to:
Number and measures
as in unit
Algebra
as in unit
14 | Exploring mathematics | Tier 2 (purple)
Geometry and measures
as in unit
Statistics
as in unit
15 | Exploring mathematics | Tier 2 (purple)