With preparation in full force now Easter is over, the pressure is on for our year 5s. There is just over 4 months to go before examinations begin - all our students are expected to be practicing test papers at this stage. Now that key topics have been taught the focus is now on really gaining speed.
In both the CEM and GL papers there are elements of 'short maths', i.e. Quick fire questions that require mental agility and the ability to work through questions fast without compromising on accuracy.
Here are some tips on how to tackle common topics that come up. Nail these to ensure your child doesn't lose any precious marks....
11 Numeracy tips:
1. Percentage questions
E.g; Work out 37% of 40.
Any percentage can be worked out easily by breaking the percentage down into combination parts of 10%, 5% and 1%.
To calculate this example, first work out 10% by dividing the value by 10 (4) then divide by 10 again to calculate 1% (0.4). Then 37% is easy:
o 30% : simply multiply the 10% value by 3 to get 30% (12)
o 5% : divide the 10% value by 2 to get 5% (2)
o 2%: multiply the calculated 1% value by 2 to get 2% (0.8)
o 37%: add the three numbers together to get 37% of 40 (12+2+0.8=14.8)
Any percentage can be calculated in a similar way (i.e constructs of easier to work out percentages).
2. BIDMAS!
E.g; 15 - 4 + 2
Always remember the order of operations. Students frequently forget to do all the additions BEFORE subtraction. The answer to this example is 13 NOT 9 (15+2=17, 17-4= 13). The error usually occurs when students do 15-6=9 which is incorrect.
E.g; 15 - 4 + 2(3 +1)
In this example the steps would be:
o Brackets: 3 + 1= 4
o Multiplication: 2 x 4 = 8
o Addition: 15 + 8 = 23
o Subtraction: 23 - 4 = 19
3. Adding/ subtracting fractions
E.g; (3/4) + (1/8)
Always make sure the denominator is the same before adding or subtracting.
In this example the lowest common multiple of the denominators 4 and 8 is 8. Therefore steps would be:
o Multiply top and bottom of (3/4) by 2 to get the equivalent fraction with 8 as the denominator: (6/8)
o Now simply add the equivalent fraction to (1/8) as the denominators are now the same: (6/8) + (1/8) = (7/8)
4. Dividing Fractions
E.g;(3/4) ÷ (2/5)
Convert to multiplication by flipping the denominator and numerator of the dividing fraction then simply multiply the numerators and multiply the denominators:
o Flip the dividing fraction : (5/2)
o And now multiply instead of dividing: (3/4) x (5/2) = (15/8) = 1(7/8)
5. Ratio questions
E.g; A solution is made using 2 part dye to 3 parts water. How much solution can be made with 50ml of dye?
The trick here is to always lay out the answer in the following way, filling in the knowns and work out the multiple involved (in this question the multiple is 25) - any variant of the question can then be answered:
Letters : D : W = S
Ratio : 2 : 3 = 5
Multiple : x25 x25
Total (per part): 50 125ml
If the same question was 'the total amount of solution was 200ml, how much water would be required?' then this can also be easily answered when laid out in the same way:
Letters : D : W = S
Ratio : 2 : 3 = 5
Multiple : x40 x40
Total (per part): 120ml 200ml
6. Time questions
E.g; What is the amount of time between 7.56am and 3.52pm?
The key to 'time' type questions is to break down the times to smaller chunks to then add together at the end.
o Calculate the time to the next hour of the from time:
7.56am->8am= 4min
o Calculate the time between this hour (8am) to the hour of the to time:
8am->3pm= 7 hours
o Calculate the time between the to hour to the to time:
3pm->3.52pm=52min
o Add the times together:
4min+7hours+52min= 7hrs 56min
An alternative way is:
o Calculate the time between the from time to the to hour with the same number of minutes:
7.56am->3.56pm= 8hours
o Calculate the time between this new time to the to time in the question:
3.56pm->3.52pm= -4min
o Add the times together:
8hours-4min= 7hrs 56min
7. Indices
E.g; 3^3
Be comfortable with indices and remember 3^3 is 27 not 9!! A common mistake is to multiply by the indices instead of multiplying by itself per the indices in the question! Ensure your child gets in the habit of thinking twice whenever they see indices feature in the question.
8. Area
Remember the formulas for calculating the area of:
o Rectangles & squares (Length x width),
o Triangles (base x perpendicular height x (1/2) ),
o Circles (πr^2 where π=3.14),
o Trapeziums ((base a + parallel length ) x(1/2) x perpendicular height,
o Parallelograms (base x perpendicular height)
o Rhombus' (diagonal length a + diagonal length b) x (1/2)
o Compound shapes - split the shape into rectangles and squares and add or subtract accordingly
9. Percentage increase/decrease
E.g; What is the percentage increase of £55 if the original amount was £50?
Simply calculate the change and divide by the original amount:
o Change: 55-50=5
o Divide the change by the original value: (5/50) = 0.1= 10% increase
It's the same calculation for percentage decreases.
10. Adding different measures
E.g; 452m + 3.4km
A common mistake is to add the values as seen. Always convert values so that they are all the same measure!!
So in this example:
o Convert either all to m (3400m) or to km (0.452km)
o Add the like measures together:
(0.452km + 3.4km = 3.852km) OR (452m + 3400m = 3852m)
11. Speed
Practice being super quick in arithmetic calculations. A way to improve this is by having instant recall in the times tables (this will save time in 70% of maths questions). Print off copies of our 144 question 5 minute mental maths test to help here. Practice every day to gain an edge in speed.
We have also devised a number of numeracy tests- print these off as many times as you like to improve in all areas (both the mental maths pdf and numeracy tests can be downloaded for free from here: https://www.tutors11plus.co.uk/file-share/8587a268-da5e-478c-8e84-db3e6ea48df5). If your child doesn't get to the end of the paper in the time given, come back to it in a week and try again. We are continuing to add new tests so keep checking for new practice tests.
You will know when your child has nailed the techniques when they know which pitfalls to avoid and instantly recognise how to tackle each question type.
The above is clearly not an exhaustive list and we will add more blogs providing further advice in coming weeks, but hopefully the above will provide a good foundation to build on. We wish you and your children well in your revision efforts!