Mathematics menu

  1. Using and Applying
    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 2-1
    • List possible half-time 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.
    		 a diagram with a two by two grid and a two by three gridShading 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.

    diagram showing the hollow square created by circling dots on squared paper.
    • How many pegs form the square on the outside?
    • How many pegs are there in the hollow?
    • Draw some more hollow squares.
    • Investigate.
    diagram showing how the formula 2x+2(x-2) equals number of pegs around the outside of a square and to work out the hollow would be (x-1)squared equals the size of the hollow, where x is equal to the number of pegs along the top side.

    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.
    diagram depicting 4 lines crossing at 4 points    		 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, problem-solving 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.

    Problem SolvingCommunicatingReasoning
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