Wise Owl Learning – Maths Notes

Read through these notes a few times and ask if you want me to explain anything.  Have an early night before any test you have – keep your pencils sharp and don’t worry/panic about anything.  Try your best and really read the questions at least twice to ensure you understand the question!!  Good luck!




Number basics

If a question asks: what is the product of 5 and 3- it means times by = 15.

If a question asks: what is the sum of – then add the numbers up!

  • Prime Numbers. A prime number is only divisible by itself and 1 – so nothing else divides into it.
  • 1,2,3,5,7,11,13,17,19,23 and so on.  2 is the only even number in this list.
  • Range: is the difference between the highest number and the lowest number.
  • Median: is the middle number in a list after you have put the list in order, lowest to highest.
  • Mode: is the most frequent number in a list.
  • Mean: is the average when you have added all the numbers in the list up and then divided by the amount of items: e.g. 3,3,4,5,6,7,8,8,8

The RANGE of above number is 5, which is the difference between 3 and 8.

The MEDIAN is 6 as it is the middle number

The MODE is 8 as it is the most common number

The MEAN is 52 divided by 9



 Patterns and Sequences

Patterns and sequences are usually straightforward. Look at the question carefully and decide what the pattern is – is it add five each time, or times by 2?

e.g. 3, 6, 9,  then next two numbers would be 12 and 15.

e.g. 1, 2, 4, 8, 16 then the next two numbers would be 32 and 64 – because the pattern is to double the number.





Lines of symmetry (mirror images) and rotational symmetry – take care to be precise. Also translations – ensure you count the squares when you move any shape!

Multiplying and dividing

 Long multiplication and division: Remember to keep your columns neat and really focus on not making ‘silly’ mistakes.  Look at your answer – does it look right? Same with adding and subtraction!!




REMEMBER: all angles within any triangle = 180 degrees

  • Angles on a straight line also = 180 degrees
  • Perimeters of shapes – simply add all sides together
  • Areas of shapes – times the length by the width and don’t forget to put the small two after your answer, which means squared.
  • Area of a triangle is half the base x the height of the triangle.
  • If you know the area of a rectangle then you can work out the area of a triangle within it – half your answer for rectangle.
  • Angles in any quadrilateral always equal 360 degrees.  Names of quadrilaterals are: square, rhombus, trapezium, parallelogram, rectangle, kite.
  • Pentagon – 5 sides; Hexagon – 6 sides; Heptagon – 7 sides; Octagon – 8 sides.



Probability ranges from 0 – 1. Where 0 = impossible and 1 = certain.  So as an example, if I say what is the likelihood of someone winning the lottery it would be ‘very unlikely’ – we cannot put ‘impossible’ as it COULD happen, but the likelihood is very very low. Questions will normally ask for fractional probability which means e.g. 10 black marbles and 5 green marbles in a bag, then the probability of pulling out a black marble is 10/15. The chance of picking a green marble is 5/15.


If there are 30 children in a class. The boys and girls are in a ratio of 7:3 which means that there are more boys than girls.  We work it out by adding the two parts of the ratio together = 10. Then we divide the number of children in the class (30) by 10 = 3. Therefore there are 3 children in EACH portion of the ratio.  So for the boys there are 3 x 7 = 21 in the class and for the girls there are 3 x 3 = 9 girls in the class. Together they add up to 30 so we know the answer is correct.





I want to buy a coat in a shop which is £120. The sale sign says it is 10pc off today.  Ten per cent of £120 = £12 therefore the cost of the coat will be £108.  Remember to always find out what 10 or 5 or 1 per cent of a number is as it makes the calculation easier.


Time: Calculate carefully – 60 minutes in an hour, and every five minutes on a clock face equals 30 degrees of a circle!  360 degrees is a complete turn and there are four right angles in a circle, measuring 90 degrees each. Compass headings N S W E – again equal four right angles and a circle.


 Fractions: adding and subtracting when the bottom number (the denominator) is the same is easy – just add or subtract the top numbers (numerators) and keep the bottom number the same.  If the bottom number is different, then times them together to make a common denominator and – whatever we do to the bottom we have to do to the top!! So if you change 5 to 10 you have x by 2 so times the top by 2 too!!!  Multiplying fractions – times the top together and the bottom together and then cancel down if you can.  Division of fractions: leave the first fraction alone, change the division sign to a multiplication sign and INVERT (turn upside down) the second fraction.  Then just multiply out as you would with a multiplication fraction!

Squared and Cubed

Squared and cubed numbers are as follows:

22  = 2 x 2 = 4 and so on

33  = 3 x 3 x 3 = 27 and so on


More marks are lost in tests because pupils make silly mistakes.  Really keep your focus and try your very best.  Good luck!!