10 Ways to Use and Apply in Maths

I’ve never wrote a ‘Maths’ blog before so this is my first attempt. I’ve spent much of my career in Y6 and one aspect I’ve worked particularly hard at is developing ‘Using and Applying’ (U&A) in maths. There are lots of definitions as to what U&A actually is however; I’m not going to get bogged down in this debate. In my opinion it’s less to do with word problems and more to do with reversing the transactional norm of a maths question. To clarify what I mean here is an ‘shape’ example:


The staple diet of this area of maths is to label a shape with its properties. Nothing wrong with this except it can be a bit ‘dry’ and for the most confident learners presents little challenge. To reverse the process try this; give pupils a list of properties, ask them to choose 5, then to draw a shape to meet the criteria they have set. Immediately pupils have to be creative, they have to USE their knowledge and because the teacher has not given a specific shape, learners have a lot of choice.

10 ways to Use and Apply across the maths spectrum:

  1. Area and Perimeter: Give pupils the answer first and then ask them to draw the shape. For example, draw an ‘L’ shape with a perimeter of 50cm. The same approach can be used for area; draw an ‘L’ shape with an area of 25cm². To extend this further create statements to investigate; for example, Rectangles with a perimeter of 20cm always have the same area.
  1. Measures: Reading scales can be notoriously laborious and often too easy for the best mathematicians. Try this though. Give the pupils a ‘menu;’ create a table with three columns, the first column is the ‘start number,’ the second is the ‘end number’ and the third column is the ‘number of intervals.’ In each column place 5-10 numbers. The pupils now have a menu to create their own scale.
  1. Shape: When the class are learning about different types of shapes or categorising triangles or quadrilaterals the concept is often picked up rapidly. To move the learning on create simple statements for the pupils; the pupils then investigate whether they are true or false (or sometimes a bit of both!) and provide evidence to support their view. For example:
  • An isosceles triangle could have a right angle.
  • A square can only be split in half along a line of symmetry.
  • Two rectangles can never make a square.
  • Two squares always make a rectangle.
  • A rhombus is half of a parallelogram.
  1. Line graphs. This is a simple one to set up; discuss with the pupils how line graphs often tell a story. Give the pupils a range of ‘blank’ line graphs; only draw the X and Y axes and the line. Do not label anything or put values on the axes. Pupils can either tell the story or create a title. This is a great activity done collaboratively. Over years I’ve heard some amazing stories!

  1. Rounding numbers; in my experience this is the archetypal ‘they’ve either got-it or they haven’t’ type lesson and when they’ve ‘got-it’ it doesn’t matter how many decimals places your throw at them it doesn’t get their brains thinking. Instead give the answer and pupils predict what the question could have been; for example. 6.7 has been rounded to the nearest tenth, what could the original number have been?

  1. Multiplication. If pupils learn the ‘grid’ method in your school, you’ll know that some get through the calculations as quite-a-pace. By giving the answer first the thinking begins. For example, A TU x TU calculation gives an answer of 475. What could the numbers have been and what would the completed ‘grid’ look like?
  1. Co-ordinates. This is an effective plenary idea if the pupils have been learning to plot co-ordinates in all four quadrants. Imagine the classroom is a grid and label each corner/area with the numbers 1-4. Give the class a co-ordinate and the pupils move to which quadrant they think the co-ordinate lives!
  1. Time: Calculating differences in time can be quite tricky for most. However, for some pupils it comes quite easily. Instead of asking pupils to find the difference between the start and finish times, give the pupils the answer and either the start or the finish time. For example, the time difference is 3hrs 56mins, the finish time is 06:34 – what is the start time?
  1. Odd one out: This can be used across maths. For this example I’ll use fractions. Write 5 fractions on the board; assign a fraction to each table/group in the class. The challenge of the table is to prove why their fraction is the odd one out. Always ask for evidence to support their argument.
  1. Plan the plenary. Again this can be used for any type or maths. This is a great idea to challenge those pupils who finish in double quick time. Their challenge is to plan a simple game/activity to finish the lesson that MUST help everyone reinforce their learning. The pupils must lead the game/activity. This idea takes some time to embed, but once it does the results are incredible.

If you have any other ideas, let us know – or even better, write them in the comments box below so they can be shared!

The Thought Weavers.

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