Geometry tuition – 2D maths shapes | Academic Owl Tuition – London Tutors

First you need to learn the name of maths shapes and then you have to calculate the perimeter  area or volume, depending on the level you are on. We are only going to remember the 2D shapes.

First of all, a 2D shapes is a shape that can be represented on a bi-dimensional graphic which has two axis: X and Y.

The most common geometric shapes are:


Aria= s*s

Perimeter= 4*s


Aria = l * L

Perimeter= 2L+2I

All angles have 900


Aria = l * L

Perimeter= 2L+2I

L is parallel with L and the other two sides are parallel to each other


Perimeter = 3*a


Perimeter= 4*l

Aria= d2*d1/2


Aria= (l+L)*h/2

The trapezium has four sides, two of them are parallel, one is smaller than the other.


Any pentagon has five sides


All hexagons have six sides


This shape is called like this because it has eight sides


Perimeter= 2∏r

Aria= ∏ r2

Geometry lessons are very interesting and catchy if you have a geometry tutor who knows how to teach you. 

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KS1 lesson: ODD and EVEN numbers

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) = ____( _____)

Need to practice ? Click here to download a worksheet

counting, partitionig

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Primary Level Tuition

For  primary level tuition, we recommend you to book  at least one hour weekly.

On the first 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 apply a vast range of learning methods, that are suitable for all types of cognitive profile, so you 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. We like to please and encourage him when he does a good job.

Transferable skills

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 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 you child, 

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Related articles:  

Odd and even Numbers

Counting, ordering, partitioning

Decimal numbers

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Elven Plus exam preparation

How to pass the QTS numeracy skills test

I know, it sounds hard to have just two shots at this test BUT if you think better there are just three chapters that you need to remember in order to pass you QTS numeracy skills test:

  • Working with fractions, decimals and percentages. On this chapter you only need to know how to turn decimals => fractions => percentages and vice versa.
  • Mode, Median, Mean, Range. You have to apply these notions if you have series of data that need to be analyzed. The mode is the most common found value in the series of data. The median is the value in the middle of the series of data, if you have 5 values the median would be the 3th number. The mean can be calculated if you add all the numbers together and divide the sum by how many there are. The range is the difference between the smallest and the biggest number.
  • Interpreting graphs like histograms and whiskers and boxes. For histograms you just need to follow the two axis and understand what they represent.



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1.Make contact. The first step is to have a chat. E-mail or call via the contact details provided. We need to determine the type of student, his current stage and goals. This allows us to find the type of help the student may need.

2.Find a Suitable Tutor. We can establish together whether we have someone who may be suitable for you child.

3.Join Us. Once you’ve decided to have an initial lesson, we will send you a full profile of the tutor and arrange the lessons.

4.Review and Progress. We will regularly be in touch to inform you about you child’s progress, and to ensure you are happy with the service you are receiving.


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KS2 lesson: Negative numbers

Learning Objectives:

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

[/box] 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:   

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

How I prepare students for 11+ Exam Entrance

  My approach regarding maths tuition can be structured in three important steps: Assessing the child’s knowledge, fill in the gaps and  practice.

 1.Assess the child’s needs

This process requires a 30 minutes test to find out what the student knows and what he doesn’t  The test conceived according to National Curriculum or sometimes I even use past paper from the school he wants to get into.

 2. Fill in the gaps

After assessing the student’s needs, we need to start building a solid base. This can be done by teaching the lessons that he doesn’t remember or didn’t understand in class and practicing on each one in particular. He needs to practice more at home if he is below the expected level of year group.


After covering all the lessons and getting to the expected level of year group, then we can start doing mix tests and solve some more difficult questions for each lesson. The purpose is to get above the expected level of year group.

For an average child this process lasts between 6 months and a year, depending on his ability of learning and the amount of time spent practicing.

Negative Numbers

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KS1 lesson: Counting, Ordering, Partitioning

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

Click to practice partitioning.

Decimal numbers

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KS2 lesson: Factors and Multiples

This particular lesson is an important starting point for fractions. Knowing the factors and multiples of a number is very useful when you need to cancel down a fraction or bring fractions to a common denominator.

Learning Objectives

• What are factors

• How to find factors

• Divisibility rules

• What are multiples

• How to find multiples

Key words: factors, multiples, division rules,

What are the factors?

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

To find out the factors of as number we need to divide the number applying the divisibility rules:

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

Need more practice? Download a free printable worksheet

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