Progression

Solving problems

Representing

Enquiring

Reasoning

Communicating

FS

Use developing

mathematical,

ideas and

methods to

solve practical

problems.

Match sets of

objects to

numerals that

represent the

number of objects.

Sort objects,

making

choices and

justifying

decisions.

Talk about,

recognise and

recreate

simple

patterns.

Describe solutions

to practical

problems, drawing

on experience,

talking about their

own ideas,

methods and

choices.

Year 1

Solve problems

involving

counting,

adding,

subtracting,

doubling or

halving in the

context of

numbers,

measures or

money, for

example 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

in the original

context.

Answer a

question by

selecting and

using suitable

equipment,

and sorting

information,

shapes or

objects;

display results

using tables

and pictures.

Describe

simple

patterns and

relationships

involving

numbers or

shapes; decide

whether

examples

satisfy given

conditions.

Describe ways of

solving puzzles

and problems,

explaining choices

and decisions

orally or using

pictures.

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.

Follow a line

of enquiry;

answer

questions by

choosing and

using suitable

equipment

and selecting,

organising

and

presenting

information in

lists, tables

and simple

diagrams.

Describe

patterns and

relationships

involving

numbers or

shapes; make

predictions

and test these

with examples.

Present solutions

to puzzles and

problems in an

organised way;

explain decisions,

methods and

results in pictorial,

spoken or written

form, using

mathematical

language and

number sentences.

Year 3

Solve one-step

and two-step

problems

involving

numbers,

money or

measures,

including time,

choosing and

carrying out

appropriate

calculations.

Represent the

information in a

puzzle or

problem using

numbers,

images or

diagrams; use

these to find a

solution and

present it in

context, where

appropriate

using £.p

notation or units

of measure.

Follow a line

of enquiry by

deciding what

information is

important;

make and use

lists, tables

and graphs to

organise and

interpret the

information.

Use patterns

and

relationships

involving

numbers or

shapes, and

use these to

solve problems.

Describe and

explain methods,

choices and

solutions to

puzzles and

problems, orally

and in writing,

using pictures and

diagrams.

Year 4

Solve one-step

and two-step

problems

involving

numbers,

money or

measures,

including time;

choose and

carry out

appropriate

calculations,

using calculator

methods where

appropriate.

Represent a

puzzle or

problem using

number

sentences,

statements or

diagrams; use

these to solve

the problem;

present and

interpret the

solution in the

context of the

problem.

Suggest a line

of enquiry and

the strategy

needed to

follow it;

collect,

organise and

interpret

selected

information to

find answers.

Identify and

use patterns,

relationships

and properties

of numbers or

shapes;

investigate a

statement

involving

numbers and

test it with

examples.

Report solutions to

puzzles and

problems, giving

explanations and

reasoning orally

and in writing,

using diagrams

and symbols.

Solving problems

Representing

Enquiring

Reasoning

Communicating

Year 5

Solve one-step

and two-step

problems

involving whole

numbers and

decimals and

all four

operations,

choosing and

using

appropriate

calculation

strategies,

including

calculator use.

Represent a

puzzle or

problem by

identifying and

recording the

information or

calculations

needed to solve

it; find possible

solutions and

confirm them in

the context of

the problem.

Plan and

pursue an

enquiry;

present

evidence by

collecting,

organising

and

interpreting

information;

suggest

extensions to

the enquiry.

Explore

patterns,

properties and

relationships,

and propose a

general

statement

involving

numbers or

shapes;

identify

examples for

which the

statement is

true or false.

Explain reasoning

using diagrams,

graphs and text;

refine ways of

recording using

images and

symbols.

Year 6

Solve multistep

problems,

and problems

involving

fractions,

decimals and

percentages;

choose and use

appropriate

calculation

strategies at

each stage,

including

calculator use.

Tabulate

systematically

the information

in a puzzle or

problem;

identify and

record the steps

or calculations

needed to solve

it, using

symbols where

appropriate;

interpret

solutions in the

original context

and check their

accuracy.

Suggest, plan

and develop

lines of

enquiry;

collect,

organise and

represent

information,

interpret

results and

review

methods;

identify and

answer

related

questions.

Represent and

interpret

sequences,

patterns and

relationships

involving

numbers and

shapes;

suggest and

test

hypotheses;

construct and

use simple

expressions

and formulae

in words then

symbols (e.g.

the cost of c

pens at 15

pence each is

15c test

pence).

Explain reasoning

and conclusions,

using words,

symbols or

diagrams as

appropriate.

Year 6 progression to Year 7

Solve problems

by breaking

down complex

calculations

into simpler

steps, choose

and use

operations and

calculation

strategies

appropriate to

the numbers

and context; try

alternative

approaches to

overcome

difficulties;

present,

interpret and

compare

solutions.

Represent

information or

unknown

numbers in a

problem, for

example in a

table, formula or

equation;

explain

solutions in the

context of the

problem.

Develop and

evaluate lines

of enquiry;

identify,

collect,

organise and

analyse

relevant

information;

decide how

best to

represent

conclusions

and what

further

questions to

ask.

Generate

sequences

and describe

the general

term; use

letters and

symbols to

represent

unknown

numbers or

variables;

represent

simple

relationships

as graphs.

Explain and justify

reasoning and

conclusions, using

notation, symbols

and diagrams; find

a counterexample

to disprove a

conjecture; use

step-by-step

deductions to solve

problems involving

shapes.