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.

The eight questions cover the following topics:

• Standard form
• Turning points and roots of quadratic equations
• Probability trees
• Simultaneous equations
• Composite area involving circles
• 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 – 4Ï€ cm2. About three quarters who wrote 90 – 4Ï€ 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 â€˜turning pointâ€™ and â€˜rootsâ€™ 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 â€“ P(not blue).

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 worldwide to continue to engage and inspire their students with my lessons.

## If you liked this you may like ….

### Grade 8 and 9 Maths Problems

A selection of challenging Grade 8 and 9 problems