Blog



Maths revision challenge for 11+ and Pre-Test students
By Sarah Collins
04 Jul

Kick-start your 11+ maths revision

Keeping focused for any of us can be tough, though when we do we can achieve great things. When was the last time you saw Johanna Konta update her Facebook between games or Harry Kane look at his messages before taking a penalty? Sport requires total concentration for a relatively short period of time, as does effective revision. We look at how your child can achieve this, along with the success it brings, in this series of summer blogs.

Each of the four blogs will look at a different subject: maths, English, verbal reasoning and non-verbal reasoning. Along with tips to aid your child’s concentration, we focus on securing their basic knowledge and skills. Beginning their revision in this way will then enable your child to focus on the problem-solving element of challenging questions, necessary for tackling their Pre-Test or 11+ with confidence.

1  Focus workout

Learning how to focus is like any other skill – it needs working on! You and your child will know the time of day when they naturally work at their best, so pick that time for their 11+ revision.
Taking exercise about 20 minutes before studying or taking a test is known to help boost concentration, so plan a short burst of activity before they begin. Even a brisk walk to the shop or a game of French cricket in the garden will help your child to concentrate for the one or two hours work ahead. These short bursts of work a few days a week are far more effective time than a whole afternoon when they are tired.

Of course, there is always the additional distraction of social media; a trap nearly all of us fall into these days. If your child has access to their phone in their study periods, they might find it helpful to look at one of the blocking apps such as Stay Focused or SelfControl for Mac. These apps allow you to manually restrict connection to sites of your choice for a defined period of time and can be helpful for maintaining concentration.

The Galore Park 11+ Revision Guides work in small sections of two–four page sections, designed for small bursts of revision. Each section takes around 30 minutes each to complete and every chapter ends with a short test.  The Galore Park 11+ Study Skills book also suggests many strategies to help both pupil and parent at the revision stage

2  First steps

The maths Pre-Tests and 11+ do not allow children to use calculators. Consequently, it is essential that your child is very confident in performing basic calculations. These skills not only cover addition, subtraction, multiplication and division but also working with ratios, proportion, fractions and percentages.

The Galore Park Learning ladders (shown at the front of each Revision Guide) help to guide your child through the key steps in their revision from basic skills at the bottom to the most demanding skills at the top. In this blog we are looking at extracts from the first two steps on this ladder. [graphic from page 6 of the Maths Revision Guide]



revision ladder



3  Building the basics

Number and place value

Although very familiar skills – reviewing tips to help with mental calculations will enable your child to work to the speeds required in the tests.
Here are some basic rules of divisibility to help your child work out division calculations and factors.

 

A number is divisible by...

Example

2 if…

the last digit is even (0, 2, 4, 6, 8, 10)

16: 6 is an even number  16 ÷ 2 = 8

3 if…

the sum of the numbers (digit sum) is a multiple of 3

39: the digit sum is  3 + 9 = 12 and 12 ÷ 3 = 4

4 if…

the last two digits can be divided by 4

5324: 24 can be divided by 4  24 ÷ 4 = 6

5 if…

the last digit is 0 or 5

2485: the last digit is 0  2485 ÷ 5 = 497

9 if…

the digit sum is a multiple of 9

684: is  6 + 8 + 4 = 18 and  18 ÷ 9 = 2

10 if…

the last digit is 0

760: the last digit is 0  760 ÷ 10 = 76

 


Once your child has retained these basic number facts the following question should be straightforward. 


Maths Challenge Question One..
 
Dilip’s mother is taking him and seven of his friends to a cricket match. They all want to sit together in one row. There are empty rows in five separate blocks. One block will allow them to take up a whole row without being split up or anyone else sitting next to them. Which block should they choose if the numbers below give the total number of seats in each block?

 
Block 2: 529        Block 3: 1018      Block 5: 496        Block 7: 756        Block 9: 728
     A                          B                       C                        D                        E      



The answer to this complex cricket question will be available at the end of the Summer Challenge. If you think you have the correct answer, why not let us know on Twitter @galore_park, Instagram @galore_park or Facebook @galore1park.

Page 18 in the Galore Park 11+ Maths Revision Guide reviews index numbers, roots, factors and multiples, includes more examples and provides further practice exercises.

 

Calculations

Negative numbers are an area where children can make mistakes when working at speed and so revising these basic rules can be helpful. Drawing a number line can help visualise what is happening with these numbers. Pencil and paper is allowed in the tests to enable children to work out their solutions, even when taking electronic tests and so they can draw a number line to help with these workings.


      -10    -9   -8   -7   -6   -5      -4   -3      -2   -1      0    1    2       3    4       5    6       7    8    9    10 


 

Use the number line above to help work out the following calculations.
Adding a negative integer (or number) is the same as subtracting the ‘opposite’ positive number. For example…


4 + (-7) = -3     -6 + (-2) = -8
Subtracting a negative integer is the same as adding the ‘opposite’ positive number. For example…
6 – (-3) = 9      -9 – (-4) = -5


Once your child has revised these basic rules, the following question should be straightforward. 


Maths Challenge Question Two...

 
A new freezer has been bought for the tennis club. They decide to put a thermometer inside to find out when it reaches the correct temperature.At 2pm, after it has been switched on for an hour, the temperature is -6°C. The temperature drops 3°C each hour from that point. 


1. How many hours does it take the freezer to get to its ideal temperature of -18 °C?

2. The matches finish at 6pm. If the stock of ice creams arrives 1 hour before then will the freezer be cold enough (assuming it must reach -15 °C to keep them frozen)?



The answer to this tricky tennis question will be available at the end of the Summer Challenge. If you think you have the answer, why not let us know on Twitter @galore_park, Instagram @galore_park or Facebook @galore1park.

Page 26 in the Galore Park 11+ Maths Revision Guide reviews negative numbers, includes more examples and provides further practice exercises.


 

Ratio and proportion

Ratios and proportions are two ways of looking at parts of a whole. Often it is the language in these questions that confuses children so revising these terms is useful groundwork for some challenging questions.

Ratios are another way to compare parts of a whole and are always expressed with a colon, e.g. 2 : 1 or the words ‘to’ i.e. 2 to 1. Ratio questions often look at the scale on a plan or quantities, such as cooking measurements. Here are two examples:

1) A rugby coach decided to draw up a plan of the pitch so that the team can discuss tactics. He decided to mark out the pitch to scale on the floor of the gym to a scale of 2 : 25. If the length of the plan is 2 metres long, how long is the actual pitch?


The actual pitch must be 100 metres long.

scale : actual =  2 : 25        write the scale
         =  2m : 25m                write the units
         =  (2m x 2m)  : __m    write the dimensions you know
         =  4m : 100 m             calculate the missing dimension (4 x 25).


2) A cycle race is going to pass through a village and the school has decided to make money by selling themed cupcakes, the baker estimates they will need 200. The amount of sugar to flour to be used is in the ratio 2 : 3. For a standard batch of 20 cupcakes the baker uses 150g of flour. What are the quantities of flour and sugar needed to make all 200 cakes?


The quantities needed for 200 cupcakes are 1000g of sugar and 1500g of flour.  
ratio                                                       =  2 : 3 (so five parts of ingredients all together)
Information known                                  = 150g flour for 20 cupcakes
Work out the final quantity for total cakes = 150g x 10 (to make 200 as 20 x 10 = 200)
                                                             = 1500g flour
Work out one ‘part’ of the ratio 2 : 3         = 1500g ÷ 3 = 500g
Work out the final quantities                    =  500g x 2 = 1000g sugar       


Proportions are often expressed as fractions or percentages. Here are two examples of proportions, one explained as a fraction and one as a percentage:


1) A school lacrosse team is made up of 18 girls of whom 12 are on the field at any one time. What proportion of the team are substitutes?


 The proportion of girls that are substitutes is one-third.
The total players is 18, so the number of substitutes is 18 – 12 = 6
So 1/3 of the team are substitutes.


 
2) 20 children from a Year 6 class compete in a cross-country run. Six children finishing under 12 minutes, ten children finish between 12 and 15 minutes, two between 15 and 20 minutes and the remaining two children finishing under 25 minutes. What proportion of children finish under 12 minutes, expressed as a percentage?


The proportion of children finishing under 12 minutes is 30%. 
6/20 = 3/10  children finished the race. So as a percentage 3/10 x 100 = 30%


Once your child has revised these methods, the following questions should be straightforward.


Maths Challenge Question Three...



It is the school sports day and there are 30 sporting activities going on. Races are always popular so the ratio of races to other events has been planned as one to five in favour of these track events.


1. How many of the events on the sports day are not races?
2. In order to raise money for the school charity, it was decided to sell tickets. The proportion of the 428 tickets sold was 75%. How many tickets were sold? 



The answer to this strenuous sports day question will be available at the end of the Summer Challenge. If you think you have the answer, why not let us know on Twitter @galore_park, Instagram @galore_park or Facebook @galore1park.

Page 48 in the Galore Park 11+ Maths Revision Guide reviews proportions and ratios, includes more examples and provides further practice exercises.

 

Fractions

Fraction questions often involve converting them to decimals and vice versa so it is worth your child practicing these techniques. As with all the questions in this blog, a very confident knowledge of basic calculations is essential to working through these questions quickly and accurately.

Changing fractions to decimals can often be done simply in many questions if the fraction can be turned into an equivalent fraction with the bottom number (denominator) of 10, 100 or 1000.
The top number (numerator) can then be written as a decimal, being careful to put the decimal point in the correct place! For example…


 

 fractions




Changing decimals to fractions is quite a straightforward process. It is important to be careful about place value (where the decimal point falls) when writing the fraction. The fraction can then be reduced to its simplest form by looking for factors.



fraction



Once your child has revised these basic rules, the following question should be straightforward.


Maths Challenge Question Four...


Emily is watching the World Cup semi-final. At full time, the England team has had three fifths of the possession (the match is made up of two 45 minute periods).


1. Express the time the England team have possession as a decimal.   
2. How many minutes are the England team in possession of the ball?
3. The match goes into six minutes of injury time. The team had a number of shots at the goal and Emily works out that at the time the final whistle blows this was a shot, on average, every 12 minutes.
     i)   Express this statistic as a fraction.
     ii) How many shots on target did the team take?


The answer to this fiddly football question will be available at the end of the Summer Challenge. If you think you have the answer, why not let us know on Twitter @galore_park, Instagram @galore_park or Facebook @galore1park.

Page 52 in the Galore Park 11+ Maths Revision Guide reviews fractions and decimals, includes more examples and provides further practice exercises.


 

4  Conclusions

Although some of these questions can seem daunting, the methods are straightforward and practice builds confidence and speed. Many children fall down because they spend too long working out solutions when some simple tricks can make their calculations quicker and more accurate. This is particularly important in CEM and Pre-Tests where a very rapid response is needed to reach the final questions.

So, why not kick-start your child’s revision with building confidence in these basic skills and help them to shoot for success!



In the meantime, if you need a little maths help, take a look at our Mathematics Revision Guide for 11+ and pre-tests. Covering all the key content for pre-tests and 11+ independent school entrance exams, this vital revision guide will ensure confidence in every topic with end-of-chapter tests and a comprehensive progress record.
Buy now for only £12.99

We also sell an 11+ Mathematics Revision Pack which will take your child step-by-step through their maths revision - consolidating knowledge, teaching children how to apply this knowledge in questions, and finally building confidence and exam technique.

maths pack

Tags: 11+, 11+ Revision, 11, 11 plus, 11plus

Share this post: