The Using and Applying Mathematics (UAM) strand
has three progression maps to support you. They are developed for Problem
Solving; Communicating and Reasoning. Alongside the progression maps
is an advice to parents, carers and mentors page that gives an overview
of UAM and suggestion for how to help your child.
The structure of UAM is the same as with the other maps  offering
objectives; examples of what pupils should know and be able to do; probing
questions and what to do if pupils find this a barrier. To help give
a pitch to the work and also to give you support in scaffolding the
learning for those pupils who are having difficulty we have used the
same set of investigations throughout to exemplify the text. These are
very limited but do help to set the pitch of the work and possible
approaches to scaffold the learner working investigatively:
For Problem Solving we have used 'Final Score' as the
vehicle to give a feel for the pitch of the work. 
Final Score
The final score in a football game was 21
 List possible halftime scores.
 How many are there?
 Investigate other final scores.

For Communicating we have used 'Shading Squares' as
the vehicle to give a feel for the pitch of the work.

Shading Squares
There are six different ways to shade two squares in this shape.
Can you find them all?
What about this shape?
How many ways are there?
Try using different rectangles made up of more squares.
Try shading three squares.

For Reasoning we have used 'Hollow Squares' as the
vehicle to give a feel for the pitch of the work. 
Hollow Squares
Here is a hollow square.
 How many pegs form the square on the outside?
 How many pegs are there in the hollow?
 Draw some more hollow squares.
 Investigate.

To support you with pupils who are finding things a barrier we have used
'Line Crossings' throughout. This is an investigation that will give pupils easy access at an appropriate level to the mathematics.

Line Crossings
 Draw three straight lines (line segments) so that some cross
over each other.
 How many crossings are there?
 Try different arrangements of the lines. What is the maximum
number of possible crossings?
 Try using more lines.
 Is there a rule for the maximum for any number of lines?
If so, write it down.

These investigations have been chosen to support you and your pupils
with understanding particular objectives but UAM is much more than mathematical
investigations. The National Curriculum states that: 'mathematics equips
pupils with a uniquely powerful set of tools to understand and change
the world. These tools include logical reasoning, problemsolving skills
and the ability to think in abstract ways.'
Pupils need to be able to select the mathematics required to solve a
problem and to recognise that an idea that they meet in one strand of
mathematics can be applied in another. A good 'diet' will
include:
 problems and applications that extend content beyond what has
just been taught;
 familiar and unfamiliar problems in a range of numerical, algebraic
and graphical contexts, some with a unique solution and some with several
possible solutions;
 activities that develop short chains of deductive reasoning
and concepts of proof in algebra and geometry;
 occasional opportunities to sustain thinking by tackling more
complex problems.