Britney/bowland/pw
MA1: Using and Applying Mathematics
Problem Solving
Level 5
Level 4
Level 3
Level 2
 select the mathematics they use in some classroom
activities, e.g. with support
– find a starting point, identifying key facts/relevant
information
– use apparatus, diagrams, role play, etc. to represent and clarify a
problem
– move between different representations of a problem e.g. a
situation described in words, a diagram etc.
– adopt a suggested model or systematic approach
– make connections and apply their knowledge to similar situations
Communicating
Reasoning
 discuss their work using
 explain why an answer is correct,
mathematical language, e.g. with
e.g. with support
support
– test a statement such as ‘The
– describe the strategies and methods
number 12 ends with a 2 so
they use in their work
12 sweets can’t be shared equally
– listen to others’ explanations, try to
by 3 children’
make sense of them, compare.…
 predict what comes next in a
evaluate…
simple number, shape or
 begin to represent their work using
spatial pattern or sequence and
symbols and simple diagrams, e.g.
give reasons for their
with support
opinions
– use pictures, diagrams and symbols
to communicate their thinking, or
demonstrate a solution or process
– begin to appreciate the
Pupils select the mathematics they use in some classroom activities. They discuss their work using mathematical language and are beginning to
represent it using symbols and simple diagrams. They explain why an answer is correct.
 select the mathematics they use in a wider range of
 begin to organise their work and
 understand a general
classroom activities, e.g. teacher obs during project
check results, e.g. audio rec
statement by finding
particular examples that
– use classroom discussions to break into a problem, recognising
– begin to develop own ways of
match it, e.g. discussion with
similarities to previous work
recording
– put the problem into their own words
– develop an organised approach as
teacher
– use mathematical content from levels 2 and 3
they get into recording their work on a
– make a generalisation with the
– choose their own equipment appropriate to the task, including
problem
assistance of probing questions
calculators
and prompts
 discuss their mathematical work
and begin to explain their thinking,
 try different approaches and find ways of overcoming
 review their work and
difficulties that arise when they are solving problems,
reasoning, e.g. discussion with
e.g. paired discussions, audio of the
eg.observation by teacher across project- very persistent
cube discussion
teacher
– check their work and make appropriate corrections,
– use appropriate mathematical
– respond to ‘What if?’ questions
e.g. decide that two numbers less than 100 cannot give a total more vocabulary
– when they have solved a
than 200 and correct the addition
– talk about their findings by referring to
problem, pose a similar problem
– begin to look for patterns in results as they work and use them to
their written work
for a partner
use and interpret mathematical
find other possible outcomes
symbols and diagrams
Pupils try different approaches and find ways of overcoming difficulties that arise when they are solving problems. They are beginning to organise
their work and check results. Pupils discuss their mathematical work and are beginning to explain their thinking. They use and interpret mathematical
symbols and diagrams. Pupils show that they understand a general statement by finding particular examples that match it.
 develop own strategies for solving problems, e.g.
 present information and results in a  search for a solution by trying
clear and organised way, e.g.
out ideas of their own, e.g.
– make their own suggestions of ways to tackle a range of problems
– make connections to previous work
– organise written work, e.g. record
– check their methods and justify
– pose and answer questions related to a problem
results in order
answers
– check answers and ensure solutions make sense in the context of
– begin to work in an organised way
– identify patterns as they work
the problem identifying out of line data
from the start
project sheets
and form their own
– review their work and approaches reflections
generalisations/rules in words
– consider appropriate units
teacher observation during project
 use their own strategies within mathematics and in applying
– use related vocabulary accurately
and conclusion/recommendations
mathematics to practical context
on project sheets
– use mathematical content from levels 3 and 4 to solve problems
and investigate
Pupils are developing their own strategies for solving problems and are using these strategies both in working within mathematics and in applying
mathematics to practical contexts. They present information and results in a clear and organised way. They search for a solution by trying out ideas of
their own.
 identify and obtain necessary information to carry through a
 show understanding of situations
 draw simple conclusions of
task and solve mathematical problems, e.g.
by describing them mathematically
their own and give an
using symbols, words and
explanation of their reasoning,
– recognise information that is important to solving the
diagrams, e.g.
problem, determine what is missing and develop lines
e.g.
of enquiry out of line data – with ca
– organise their work from the outset,
– explain and justify their methods
– break a several-step problem or investigation into
looking for ways to record
and solution
simpler steps
systematically
– identify more complex patterns,
– consider efficient methods, relating problems to
– decide how best to represent
making generalisations in words
previous experiences
conclusions, using appropriate
and begin to express
generalisations using symbolic
 check results, considering whether these are reasonable, e.g. recording
– begin to understand and use formulae notation
– check as they work, spotting and correcting errors and reviewing
and symbols to
– use examples and countermethods out of line data
represent problems
examples to justify conclusions
 solve word problems and investigations from a range of
Able to interpret resultsand draw
contexts, e.g.
clear conclusions and
– use mathematical content
recommendations
In order to carry through tasks and solve mathematical problems, pupils identify and obtain necessary information. They check their results,
considering whether these are sensible. Pupils show understanding of situations by describing them mathematically using symbols, words and
diagrams. They draw simple conclusions of their own and give an explanation of their reasoning.
Level 2
Level 3
Level 4
Low
Secure
High
Low Secure
High
Low
Secure
High
Low
Level 5
Secure
High