Partitioning methode | Academic Owl Tuition

Numbers are made of digits, a digit is:

Numbers can have two, three, and four digits or even more:

thousands hundreds tens units digits



two digits




three digits





four digits

Ordering numbers

The more digits a number has, the higher it is.

To order the numbers faster is easier to use number line:

44 comes before 47 on the number line because is smaller

If you need to put in order two numbers with the same amount of digits then you need to see which one has the highest first digit

428 is bigger then 328

428 is smallest then 482

321 is smaller then 322

Partitioning Numbers

 Partitioning is breaking up numbers into hundreds, tens and units:

Example:28= 20+8

273= 200+ 70+3

427= 400+ 20+7

More examples:

427= 300+120+7

258= 200+40+18

845= 600+245

You can even calculate easier this way:

23+66 = > 23=   20 + 3

                       66=  60 + 6

                          =>80 + 9 = 89

275 + 314 = > 275= 200 +70 +5

                              314=300 +10 +4

                                       500+ 80+ 9 = 589

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Decimal Numbers | Academic Owl Tuition

Learning Objectives:

  • Using a number line
  • Partitioning decimals
  • Compare decimals
  • Rounding decimals

Key words: Number line, decider, decimal point, less then, greater then,

It is easy to understand decimals using a number line

Number Sequences with decimals

Number sequences are about counting on or counting back

Start counting the decimals between 4 and 5 adding 0.2

Now let’s count from 4 to 6 using the same method adding 0.4 :

4.0;  4.4;  4.8;  5.2;  5.6;  6

Other examples:

0; 0.5; 1.0; 1.5; 2.0; 2.5; 3.0;

0; 0.3; 0.6; 0.9; 1.2; 1.5; 1.8;

0; 0.4; 0.8; 1.2; 1.6; 2.0; 2.4;

 Partitioning decimals

Any decimal number has a whole number part and a decimal part

3.24=          3      +        0.24
whole        decimal

There are other ways of partitioning a decimal number:

4.25 = 1+3+ 0.20+ 0.05

71.2 = 70+ 1+ 0.2

1.47 = 1+ 0.47

Decimals can be compared

To compare numbers you need to use Inequality symbols:   

>  means “is less then ”

2.1 because the whole number is bigger

2.3 2.4        or       4.2=>2.4

5.3>4.2         or       5.3=>4.2

7.4 round up

4 d.p-  4.0164-  the decider is 2 round down

3 d.p-  4.016- the decider is 4 round down

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Negative numbers explaint and practice | Academic Owl Tuition

Learning Objectives:

  • What is a negative number
  • How to place a negative number on a number line
  • Opposite numbers
  • Comparing negative numbers

 Key words: negative number, less then, greater then, opposite umbers, number line,

Imagine that you need £5 to buy a book but you only have £3 but your friend burrows you the other £2, so you owe him £2

You can write this as:  £3-£5= -£2

Negative numbers are all less then zero

Number line is really useful for understanding the negative numbers

The further right you go the greater the numbers get.

-6 is less then -2 because is further to the left on the number line

-3 is more then -5 because is further to the right on the number line

On this number line the smallest number is -8 because it is the last number on the left side

Opposite numbers

Numbers that are the same but have different sign are opposite numbers

Example:       4 and -4        2 and -2        8 and -8

If you add two opposite numbers it will always equal 0

4+ (-4) =0

2+ (-2) =0

8+ (-8) =0

Comparing numbers

To compare numbers you need to use Inequality symbols:   

[note color=”#f4c25f”] > means “is less then”

-2              or        -242           or       42-8            or        -85                or         5-20          or        -20-2             or        -242         or       42-8          or        -8

Factors and multiples KS3 | Academic Owl Tuition

Learning Objectives

• What are factors

• How to find factors

• Divisibility rules

• What are multiples

• How to find multiples

Key words: factors, multiples, division rules,

The factors of a number are all the numbers that divide into it
Imagine factors as all ingredients used to build the number:

Take the example above:
In order to build 75 we need do multiply 3, 2 and 5

[note color=”#f4c06d”]To find out the factors of as number we need to divide the number applying the divisibility rules:[/note]
Dividing by 2: All even numbers are divisible by 2.
Example: all numbers ending in 0,2,4,6
Dividing by 3: Add up all the digits in the number and find out what the sum is. If the sum is divisible by 3, so is the number.
Example: 12123 (1+2+1+2+3=9) 9 is divisible by 3, therefore 12123 is too!
Dividing by 4: See if the last two digits in your number are divisible by 4.
Example: 358912 ends in 12 which is divisible by 4, thus so is 358912.
Dividing by 5: Numbers ending in a 5 or a 0 are always divisible by 5.
Example: 25, 65, 200,
Dividing by 6: If the Number is divisible by 2 and 3 it is divisible by 6 also.
Example: 66; 30, 42
Dividing by 8: if the last 3 digits are divisible by 8, so is the entire number.
Example: 6008 – The last 3 digits are divisible by 8, therefore, so is 6008.
Dividing by 9: Almost the same rule and dividing by 3. Add up all the digits in the number, if the sum is divisible by 9, so is the number.
Example: 43785 (4+3+7+8+5=27) 27 is divisible by 9, therefore 43785 is too!
Dividing by 10: If the number ends in a 0, it is divisible by 10.
Example: 10, 100, 1000,

Finding the factors of a number
Just apply the divisibility rules using any of the next schemes above: 

Multiples of a number

The concept of Multiple is the opposite to that of a
factor. If some number A is a factor of a number B, that
means that B is a multiple of A.
Any number has a set of multiples. These multiples are
that number multiplied by various integers. A number can
have infinity of multiples.


The multiples of 3 are it’s time tables





Some multiples of 12 : 24, 36, 48, 60

Odd and even numbers | Academic Owl Tuition

Learning  Objectives

  • Learn what is an even number
  • Learn how to recognize an even number
  • Learn what is an odd number
  • Learn how to recognize an odd number

Key words: odd, even, consecutive,

Even numbers

The even numbers are 2, 4, 6, 8,
An Even number is a number that can be divided exactly by 2:
2÷2= 1

All Even numbers end in 0, 2, 4, 6, 8,

22 is even because it ends in 2
46 is even because it ends in 6
328 is even because it ends in 8
7520 is even because it ends in 0
148 is even because it ends in _______
122 is even because it ends in _______
428 is even because it ends in _______
632 is even because it ends in _______
844 is even because it ends in _______
548 is even because it ends in _______

Odd numbers

Odd numbers are the ones ending in 1, 3, 5, 7, 9. They can never be divided exactly by 2

21 is odd because it ends in 1
67 is odd because it ends in 7
233 is odd because it ends in 3
2739 is odd because it ends in 9
943 is odd because it ends in _______
841 is odd because it ends in _______
459 is odd because it ends in _______
231 is odd because it ends in _______
43 is odd because it ends in _______

 Secret rules

No matter how long is the number, the last digit will always tell if the number is odd or even
Even + even

Any two even numbers added together will give an even number

2 + 2 = 4 (even)
2(even)+4(even) = 6 (even)
8(even) + 20 (even) = ____(even)
6(even) + 14 (even) = ____(even)
___(even) + ___(even) = ____( _____)
___(even) + ___(even) = ____( _____)

Odd + even

Any two consecutive numbers added will give an odd number

1 + 4 = 5 (odd)
5(odd) + 6(even) = 11 (odd)
7(odd) + 4 (even) = ____ (odd)
3(odd) + 4(even) = ____ (odd)
7(odd) + 6 (even) = ____ (odd)
___(even) + ___(odd) = ____( _____)
___(even) + ___(odd) = ____( _____)

Odd + odd

Any two odd numbers added together will give an even number
ex: 3 + 3 = 6 (even)
5(odd) + 7(odd)= ___ (even)
5(odd) + 7(odd)= ___ (even)
___(odd) + 3(odd)= ___ (even)
___(odd) + ___(odd) = ____( _____)
___(odd) + ___(odd) = ____( _____)

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Equations | Academic Owl Tuition – London Tutors

This category refers to different types of equations: simple equations, quadratic and cubic equations, and how each one of then has to be solved.

Elimination method: 2X + 5Y =2 (-3) 3X + 8Y = 4 (2) In order to reduce the x term we need to make it have the same coefficient as the other equation, so we multiply the first one by -3 and the next one by 2 -3 x 2X -3 x 5Y= -3 x […]

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Equation with brackets – Example 1  5x+3(x-6)=7x+13        After expanding the brackets the equation becomes 5x + 3x -18 = 7x +13  the numbers containing x need to be moved on one side of the “=” sign and the resto of the numbers moved on the other side. 8x-7x= 13+18 x=31 Equation with […]

Solving equations with fractions is not as complicated as it seems . Here are some examples to prove this to you:  Before adding or subtracting any fraction the denominator (bottom number) needs to be the same. To get the common denominator, multiply the first fraction by 2 and the next two fractions by 9. After […]

Post Tagged with algebra, algebraic equations, equations, fractions, maths Read More

The new CRB check

Starting with January 2013, the new CRB check is called DBS check (Disclosure and Barring Service). The good news about this change is that there is no need for tutors and teacher to apply several times a year for different employers or institutions .

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Post Tagged with CRB turns into DBS, DBS is the old CRB, New CRB 2013

PGCE tutor | Academic Owl Tuition – London Tutors

Passing this numeracy test is vital if you need to start a Postgraduate teacher’s training this September, and we strongly suggest to do it as soon as possible, because changes are scheduled for this exam and it will not make the test easier.

How to obtain the PGCE degree with our tutor’s help

Before being accepted to study for the PGCE , first you must pass the QTS literacy and numeracy tests. Our PGCE tutors are able to assist you from the moment you decided to get qualified, until you obtain the Postgraduate Certificate.

How PGCE numeracy tuition works

First, you can fill in the form on the right sidebar and we will contact you for a free consultation about your upcoming qts skills test.

If you decide to go forward with the PGCE tuition we will revise together you :

  • Fractions, decimals and percentages for QTS
  • Long multiplication and division
  • Questions about time and conversion,
  • Shortcuts and audio practice
  • Scatter graphs, pie charts, whiskers and boxes

Tuition after getting into PGCE training

Our PGCE tutors are also able to support you with getting into the PGCE (initial tests and interview) lesson planning and teaching according to National Curriculum.

Find out more about taking  the QTS numeracy test .

Or read about the QTS literacy test

QTS maths tuition

  QTS numeracy practice 

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IGCSE maths tuition | Academic Owl Tuition – London Tutors

This exam is important because it is a solid foundation for further study, like AS/A level exams but also because it prepares you for the university exams.

IGCSE maths exam in Schools

Edexcel Vs Cambridge IGCSE exams 

This is just our opinion but Cambridge always had higher standards and more complex syllabus. It all depends on your level and your ambitions, after all any international exam has a higher importance then a usual GCSE and that includes the Edexcel IGCSE. 

Our IGCSE maths tuition strategy

To practice for your IGCSE exams you should start with some past papers

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Primary tuition | Academic Owl Tuition – London Tutors

The competition in London is fierce for Grammar School and Independent School, even for the primary level. Because of this, we recommend you to book at least one hour week

On the first primary tuition session

The tutor will give the student a file, where he will put all the materials provided by the tutor every week. All lessons are designed according to the National Curriculum. Our tutors use a vast range of learning methods, that are suitable for all types of cognitive profile, so your child will visualize, hear and write the information in order to assimilate it. When teaching the lessons, we use all of these methods, to help him learn according to his needs.

We are doing our best to make lessons more enjoyable. Most of the time, we use a reward system of stickers or other things to motivate the student, depending on the child’s preference and age. We like to please and encourage him when he does a good job.

Verbal reasoning tuition for primary 

Verbal reasoning is quite a popular subject required for entry exams. The students are asked to write texts, give synonyms and other exercises. All this tasks are meant to test their level of comprehension and ability to write correctly and to use their imagination. The mission can easily be accomplish if the child is used to the specific type of tests, compositions and if he has a broad vocabulary. The tests are the ones that he is going to practice with his tutor but he should read a book from time to time, in order to improve his vocabulary and stimulate his imagination.

Transferable skills from primary level 

If you child is getting maths tuition he will also improve his reading and spelling, by writing the exercises himself, and reading the requirements for the quizzes.

At the end of every primary level tuition session we use games and fun exercises to make the lessons even more enjoyable. We also prepare children for SAT’s and 11+exams using past papers.

To avoid confusing the student, first we do a complete revision of all the lessons in the National Curriculum for his level, and then we start practicing on mix exercises and tests. If you consider that our approach to tutoring is suitable for your child do not hesitate to book your primary level tutor.

Advantages of primary tuition with us

Our tutors are very capable to improving your child’s level of knawledge in a short periode of time, but we all know that this is not the best way of doing things. Your child could get confused and stressed if he is pushed too hard, that is why it is better to start taking primary tuition lessons earlier and have one hour per week.

What a primary tutor can not do

The primary tutor who is preparing your child needs your full support and you need to continue his work when he is gone. He will to be able to helo your child to pass the verbal reasoning exam if the student doesn’t read books and write texts, compositions essays or letter to practice his handwriting.

The primary maths tutor will not be able to help your child pass the maths exam if you do not check your child’s homework and do something about it if he hasn’t done it.

Secondary Level

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Related articles:

Odd and even Numbers

Counting, ordering, partitioning

Decimal numbers

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