Track back mathematics
Block E Securing number facts, relationships and calculating
Year 3
Solve one-step and
two-step problems
involving numbers,
money or measures,
including time,
choosing and carrying
out appropriate
calculations
Follow a line of enquiry
by deciding what
information is
important; make and
use lists, tables and
graphs to organise and
interpret the
information
Year 2
Solve problems
involving addition,
subtraction,
multiplication or division
in contexts of numbers,
measures or pounds
and pence
Identify and record the
information or
calculation needed to
solve a puzzle or
problem; carry out the
steps or calculations
and check the solution
in the context of the
problem
Year 1
Solve problems
involving counting,
adding, subtracting,
doubling or halving in
the context of numbers,
measure or money, e.g.
to ‘pay’ and ‘give
change’
Describe a puzzle or
problem using
numbers, practical
materials and
diagrams; use these to
solve the problem and
set the solution back in
the original context:
Linked objective for Y2
(from Block B)
Identify patterns and
relationships involving
numbers or shapes,
and use these to solve
problems
Describe patterns and
relationships involving
numbers or shapes;
make predictions and
test these with
examples
Describe simple
patterns and
relationships involving
numbers or shapes;
decide whether
examples satisfy given
conditions
P level 7–8 + Extension
Extension
 Use developing mathematical ideas and methods to solve
practical problems involving number and money in a real or
role-play context
 Begin to understand and use the vocabulary related to
money
 Describe solutions to practical problems, drawing on
experience, talking about their own ideas, methods and
choices
 Make simple estimates and predictions
P8
 Begin to use developing mathematical understanding,
ideas, methods and counting to solve practical problems
 In role-play and practical situations estimate a small number
of everyday objects and check by counting
 Begin to use developing mathematical understanding and
counting to solve simple problems involving coins that they
may encounter in play, games or other work
 Understand different coins have different values
P7
 Begin to use developing mathematical understanding and
counting to solve simple problems that they may encounter
in play, games or other work
 Respond appropriately to key vocabulary and questions
 Begin to understand coins have different values
 Use 1p coins for items up to 10p
Extension
 Sort objects making choices and talk about decisions
 Talk about recognise and recreate simple patterns
 Use a variety of objects to make models, pictures and
patterns, and describe them.
 Sort familiar objects count how many objects share a
common property, presenting results using pictures,
drawings or numerals
P8
 Describe the relationships of objects in simple models,
pictures and patterns
P7
 Sort items as instructed, following a model
 Identify when an object is different and does not belong to
a given category
1
P level 4-6
P6
 Copy simple patterns or sequences
 Use understanding of counting small amounts to solve
simple problems practically
 Use the understanding of ‘more’
 Match objects and materials according to a given criteria
relating to number
 Order things by a criteria according to a model or picture
 Begin to understand that different coins are used in ‘real
life’ giving and receiving activities
P5
 Use emerging understanding of counting small amounts
to solve simple problems practically
 Demonstrate an awareness of contrasting quantities by
making groups of objects with help
 Begin to sort sets of objects according to a single attribute
 Experience exchanging coins in exchange for items in a
practical context
P4
 Take part in activities that are concerned with adding to or
taking away from a group of objects
 Be aware of cause and effect in familiar mathematical
activities
Develop and use
written methods to
record, support or
explain addition and
subtraction of two-digit
and three-digit numbers
Derive and recall all
addition and
subtraction facts for
each number to 20,
sums and differences
of multiples of 10 and
number pairs that total
100
Derive and recall
multiplication facts for
the 2, 3, 4, 5, 6 and 10
times-tables and the
corresponding division
facts; recognise
multiples of 2, 5 or 10
up to 1000
Use the symbols +, -, x,
÷ and = to record and
interpret number
sentences involving all
four operations;
calculate the value of
an unknown in a
number sentence, e.g.
Use the vocabulary
related to addition and
subtraction and
subtraction and
symbols to describe
and record addition and
subtraction number
sentences
30 - □ = 14
Derive and recall
multiplication facts for
the 2, 5, and 10 timestables and the related
facts; recognise
multiples of 2, 5 and 10
Count on or back in
ones, twos, fives and
tens and use this
knowledge to derive the
multiples of 2, 5 and 10
to the tenth multiple
Multiply one-digit and
two-digit numbers by
10 or 100, and describe
the effect
Use practical and
informal written
methods to multiply and
divide two-digit
numbers (e.g. 13 3,
50 4); round
remainders up or down,
depending on the
context
Represent repeated
addition and arrays as
multiplication and
sharing and repeated
subtraction (grouping)
as division; use
practical and informal
written methods and
related vocabulary to
support multiplication
and division, including
calculations with
remainders
Solve practical
problems that involve
combining groups of
2,5, or 10, or sharing
into equal groups
Extension
 Count reliably up to 10 everyday objects giving just one
number name to each object
 Know that numbers identify how many objects are in a set
 Use language such as more or less, to compare two
numbers
 Find one more or one less than a number from 1 to 10
 Begin to relate addition to combining two groups of objects,
counting objects; extend to three groups of objects
 Begin to relate addition to counting on
 In practical activities and discussion begin to use the
vocabulary involved in adding
 Begin to relate subtraction to taking away
 In practical activities and discussion begin to use the
vocabulary involved in subtraction
P8
 Count reliably to at least 5; begin to count up to 10 objects
 Know the numbers 0–9 relate to different but constant sizes
of sets of objects
 Compare two given numbers of objects saying which is
more and which is less
 Continue the rote count onwards from any given small
number
P7
 Recognise numerals 0–5 and to understand that each
represents a constant number or amount
 Count reliably at least 5 objects
 Show a count up to 5 by a simple tally
 Begin to recognise difference in quantities
Understand that
division is the inverse
of multiplication and
vice versa; use this to
derive and record
related multiplication
and division number
sentence
2
P6
 Demonstrate an understanding of 1:1 correspondence in a
range of contexts
 Count reliably to 3 and make sets of up to 3 objects
 Demonstrate an understanding of the concept of more/
fewer
P5
 Use concrete resources (e.g. tokens) to record and
remember quantities or make pictorial representations
showing quantities of groups
 Indicate 1 or 2
P4
 Show an interest in number activities
 Respond to the words ‘more’ and ‘gone’
Linked objective for Y3
(from block B) :
Use knowledge of
number operations and
corresponding
inverses, including
doubling and halving, to
estimate and check
calculations
Understand that halving
is the inverse of
doubling and derive
and recall doubles of all
numbers to 20 and the
corresponding halves
Recall the doubles of
all numbers to al least
10
Find one half, one
quarter and three
quarters of shapes and
sets of objects
Use the vocabulary of
halves and quarters in
context
Find unit fractions of
numbers and quantities
(e.g. ½, 1/3, ¼, 1/6 of
12 litres
Read and write proper
fractions (e.g. ,
),
interpreting the
denominator as the
parts of a whole and
the numerator as the
number of parts;
identify and estimate
fractions of shapes; use
diagrams to compare
fractions and establish
equivalents
Extension
 Try to share things equally
P8
 Understand the notion of sharing equally between a
number of people
P7
 Understand the notion of sharing between a number of
people
3
P6
 In role-play and practical situations share a single object
P5
 In role-play and practical situations be part of sharing a
single object
P4
 When an object is being shared anticipate getting a part