ESF Number

Phase 1 Phase 2 Phase 3 Phase 4

K1 K2 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6
Learners will understand that numbers are Learners will develop their understanding of Learners will develop the understanding that Learners will understand that the base
used for many different purposes in the real the base 10 place value system and will fractions and decimals are ways of representing 10 place value system extends
world. They will develop an understanding of model, read, write, estimate, compare and whole-part relationships and will demonstrate infinitely in two directions and will be
one-to-one correspondence and conservation order numbers to hundreds or beyond. this understanding by modelling equivalent able to model, compare, read, write
of number, and be able to count and use They will have automatic recall of addition fractions and decimal fractions to hundredths and order numbers to millions or
number words and numerals to represent and subtraction facts and be able to model or beyond. They will be able to model, read, beyond, as well as model integers.
quantities. addition and subtraction of whole numbers write, compare and order fractions, and use They will develop an understanding of
Overall Expectations

using the appropriate mathematical them in real-life situations. Learners will have ratios. They will understand that
language to describe their mental and automatic recall of addition, subtraction, fractions, decimals and percentages
written strategies. Learners will have an multiplication and division facts. They will are ways of representing whole-part
IBO

understanding of fractions as select, use and describe a range of strategies to relationships and will work towards
representations of whole-part relationships solve problems involving addition, subtraction, modelling, comparing, reading,
and will be able to model fractions and use multiplication and division, using estimation writing, ordering and converting
fraction names in real-life situations. strategies to check the reasonableness of their fractions, decimals and percentages.
answers. They will use mental and written
strategies to solve problems involving
whole numbers, fractions and decimals
in real-life situations, using a range of
strategies to evaluate reasonableness
of answers.

Numbers are a naming system. The base 10 place value system is used to The base 10 place value system can be The base 10 place value system
represent numbers and number extended to represent magnitude. extends infinitely in two directions.
Numbers can be used in many ways for relationships.
different purposes in the real world. Fractions and decimals are ways of Fractions, decimal fractions and
Conceptual Understanding

Fractions are ways of representing whole- representing whole-part relationships. percentages are ways of representing
Numbers are connected to each other part relationships. whole-part relationships.
through a variety of relationships. The operations of addition, subtraction,
The operations of addition, subtraction, multiplication and division are related to each For fractional and decimal
IBO

Making connections between our experiences multiplication and division are related to other and are used to process information to computation, the ideas developed for
with number can help us to develop number each other and are used to process solve problems. whole-number computation can apply.
sense. information to solve problems.
Even complex operations can be modelled in a Ratios are a comparison of two
Number operations can be modelled in a variety of ways, for example, an algorithm is a numbers or quantities.
variety of ways. way to represent an operation.
 Phase 1 Phase 2 Phase 3 Phase 4

K1 K2 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6

Count by Count by naming Count by naming Count by naming

naming numbers in numbers in numbers in
numbers in sequence to and sequences, to 100, sequences, to and
sequence, from 20 moving from any back from 1000,
initially to and starting point moving from any
from 10 starting point

Apply one to Apply one to one- Apply place value Apply place value Apply place value Apply place value to Apply place value to Apply place value
one- correspondence to partition and to partition and to partition and partition and rename partition and rename to partition and
corresponden when counting up rename two-digit rename three-digit rename four-digit five-digit numbers numbers to tenths rename numbers
ce when to 20 objects numbers numbers numbers and hundredths. to thousandths
counting up to
10 objects. Skip count in tens Skip count by twos, Skip count by twos,
starting from zero fives and tens fives, tens and
starting from zero hundreds starting
Place Value Outcomes

from a number
other than zero

Recognise, Recognise, model, Recognise, model, Recognise, model, Recognise, model, Recognise, represent Recognise and order Recognise, and
model, read, read, and order read, write and read, write and represent and order and order five-digit numbers to order integers
and order numbers to at order numbers to order three-digit four-digit numbers numbers millions or beyond (including
numbers to at least 20 write 100 numbers negative integers)
least 10 numbers to 10

Use the Use mathematical Use mathematical Recognise, model Recognise, model
language of language for language for and order decimal and order
Mathematics example more, example more, less fractions to decimal fractions
to compare less (cardinal) (cardinal) first, hundredths or to thousandths or
quantities, for first, second second (ordinal) beyond. beyond.
example, (ordinal)
more, less.
Round numbers to Round numbers to Round numbers to Round decimal Round decimal
the nearest 10 the nearest 10 or the nearest 10, 100, fractions to the fractions to the
100 1000 nearest whole nearest tenth or
number whole number
 Phase 1 Phase 2 Phase 3 Phase 4

K1 K2 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6

Subitise Subitise small Estimate and Estimate up to 20

ordered collections of subitise groups of objects
patterns in objects in real life up to ten objects
real life situations
situations e.g.
dots on a dice

Recall addition facts Recall addition facts Recall addition facts

for single-digit for numbers at least of multiples of ten
numbers and to 20 and related to at least 100 and
related subtraction subtraction facts related subtraction
facts facts

Model addition and Model addition and Model addition and Model addition and
subtraction of subtraction of subtraction of whole subtraction of
whole numbers whole numbers numbers decimal fractions up
to hundredths

Represent and solve

Four Operations

addition problems
(including real life
and word) involving
2 digit numbers,
Understand Solve simple Solve simple using appropriate Solve addition Solve addition Solve addition Use efficient
simple addition and addition and strategies problems (including problems (including problems including mental and
addition and subtraction subtraction real life and word) real life and word) decimals in the form written strategies
subtraction problems up to problems using Represent and solve using appropriate using a range of of money and to add integers
using ten using concrete material subtraction written and mental efficient mental and measurement. and decimals
concrete concrete material problems (including strategies written strategies
materials in Solve simple real life and word)
situations Solve problems, addition and involving 2 digit Solve subtraction Solve subtraction Solve subtraction Use efficient
including subtraction numbers, using problems (including problems (including problems including mental and
doubling, halving problems using appropriate real life and word) real life and word) decimals in the form written strategies
and sharing part/whole strategies using appropriate using appropriate of money and subtract integers
strategies written and mental efficient mental and measurement. and decimals
strategies written strategies
 Phase 1 Phase 2 Phase 3 Phase 4

K1 K2 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6

Model Model Model multiplication Model

multiplication and multiplication and and division using multiplication and
division using division using groups and/or arrays division of
groups and/or groups and/or Uses known times decimals by a
arrays arrays tables facts to single digit integer
mentally multiply
Skip count by twos, Recall Recall multiplication any 2 digit number
fives and tens multiplication and facts up to 10 × 10 by a 1 digit number
starting from zero division facts to at and related division
least two, five, facts
three and ten times
tables.

Recognise and Solve multiplication Solve multiplication Solve problems Use efficient
represent division problems problems (including (including real life mental and
as grouping into (including real life real life and word) and word) involving written strategies
equal sets and solve and word) using using efficient multiplication of to multiply
simple problems appropriate written mental and written large numbers by decimal fractions
using these and mental strategies one- or two-digit by a one-digit
representations strategies numbers using integer
efficient mental and
written strategies

Use estimation to Solve division Solve division Use efficient mental Use efficient
check problems problems (including and written mental and
reasonableness of (including real life real life and word) strategies for written strategies
answers to and word) using involving division by division for division
calculations written and mental a one digit number, representing
strategies for including those with remainders as
division without remainders fractions
remainders decimal fractions

Use estimation and Use estimation and Use estimation and

rounding to check rounding to check rounding to check
the reasonableness the reasonableness the reasonableness
of answers to of answers to of answers to
calculations calculations calculations
 Phase 1 Phase 2 Phase 3 Phase 4

K1 K2 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6

Share collections Find equal parts of Model, represent, Read, write, Read, write,
into equal parts shapes and compare and order compare and order compare and order
collections fractions in a fractions common fractions
Divide objects into practical context and decimal
equal parts fractions to
hundredths or
Use the language Use the language Use the language of beyond Understand the
of fractions, for of fractions, for fractions, for relationship and
example, half, example, example, numerator, Understand the convert between
whole, equal numerator, denominator relationship and common
denominator convert between fractions, decimal
common fractions fractions and
and decimal percentages
fractions
Find fractions of Find fractions of Find percentages
shapes and shapes, numbers and of numbers or
Fractions and Ratio

quantities quantities quantities with

and without a
calculator

Model equivalent Investigate Simplify fractions to Simplify fractions

fractions equivalent fractions the lowest common in mental and
used in context denominator written form

Add and subtract Model addition and Model, read, write Solve problems
fractions with the subtraction of and compare involving addition
same denominator fractions with improper fractions and subtraction
using concrete related and mixed numbers of common
materials and denominators fractions with the
pictorial same or related
representations Model and compare Model, read, write denominators
improper fractions and compare
and mixed numbers percentages Convert improper
understanding them fractions to mixed
as the number of numbers and vice
parts in every 100 versa
 Phase 1 Phase 2 Phase 3 Phase 4

K1 K2 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6

Count in quarters Model and solve Read, write and

halves and thirds, simple problems solve problems
including mixed involving ratio and involving ratio
numbers proportion

Model and solve

simple problems
involving fractions