Grade 5 Maths Problems

In my experience students aiming for between grades 4 and 5 often struggle with the grade 5 maths problems in the latter half of the non-calculator paper.  Grade 5 non-calculator questions often require more method marks and greater knowledge of specific vocabulary.  For this reason, I created this lesson to remind students of key terms while developing their written methods.

Grade 5 Maths Problems

The eight questions cover the following topics:

  • Standard form
  • Turning points and roots of quadratic equations
  • Probability trees
  • Simultaneous equations
  • Composite area involving circles
  • Expanding quadratic expressions
  • Angles in polygons
  • Column vectors

Here is a sample of four questions from eight and with a brief description of how students got on with each problem.

Composite area involving circles

In this question, most students were able to work out the area of the composite shape in the form 90 – 4π cm2. About three quarters who wrote 90 – 4π cm2 as their area were able to correctly factorise it. Some students used the formula for the circumference of a circle but this was easily corrected.

Turning points and roots of quadratic equations

Most students either got full marks or left the answer blank.  This tells me that understanding the terms ‘turning point’ and ‘roots’ are often not understood.  Some students tried to solve the equation algebraically using the balance method but gave up after a few lines of working.

Probability Trees

Most students completed the tree diagram correctly.  However, when working out the probability of picking at least one blue counter a common mistake was to add the fractions rather than multiply them.  Of those who added the fractions about half did so incorrectly, without using a common denominator. 

Most students who realised to multiply the fractions worked out the correct probability using P(at least one blue) = 1 – P(not blue).


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About Mr Mathematics

My name is Jonathan Robinson and I am passionate about teaching mathematics. I am currently Head of Maths in the South East of England and have been teaching for over 15 years. I am proud to have helped teachers all over the world to continue to engage and inspire their students with my lessons.


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