know that you can undo an addition with a subtraction know by heart all adding and subtracting facts for each number up to ten (for example, know the facts that 6 + 4 = 10, 10  4 = 6 and 10  6 = 4, 4 + 2 = 6 and 6  4 = 2, 6  2 = 4, and so on) know the pairs of numbers in tens that make 100 (for example, 30 + 70 = 100, 70 + 30 = 100) know that they can do addition in any order, and that it's easier to start with the bigger numbers understand that multiplying is the same as adding more of the same number
Know the 2 and 10 times tables by heart.
use the mathematical names for common twodimensional and threedimensional shapes say how many sides and corners a shape has, and if it has any right angles. predict how a shape would appear in a mirror. Recognise turning movements such as whole turns, half turns and quarter turns or right angles. Measure or weigh things using units such as centimetres, metres, litres or kilograms; choose sensible units to use use a ruler to draw and measure lines to the nearest centimetre tell the time to the half and quarter hour.
It is expected that most children of around 11 years will be able to:
It is expected that most children of around 14 years will be able to:
To arrange a voice call about English lessons send an email to this address and mention English Lessons in the subject
One two three four five. Once I caught a fish alive.
Two four six eight. Who do we appreciate
One banana, two banana,three banana four
One man went to mow, went to mow a meadow
Read these questions to your student and listen for correct verbal responses.
The standard method for multiplying together two numbers with two or more digits
is usually called
long multiplication
However a simpler method, which is easier to understand, and which uses easier calculations,
is now taught in schools. It is sometimes referred to as the Grid Method.
The Grid Method is based on the idea of splitting both numbers being multiplied,
into their tens and units.
We will illustrate the method by calculating 23 x 42, the 23 becoming 20 + 3
and the 42 becoming 40 + 2.
Imagine a rectangular array of counters,
with dimensions 23 x 42. The total number of counters laid out will equal
the multiplication of the two numbers.
We split the array into four segments, as shown below:
We then calculate the number of counters in each segment, and add the results together, as follows:
20  x 
40  = 
800 
20  x 
2  = 
40 
3  x 
40  = 
120 
3  x 
2  = 
6 
TOTAL  = 
966 
We don't need to draw out each of the counters but can just use rectangles as shown below:
40  2  
20  20 x 40  20 x 2 
3  3 x 40  3 x 2 
It uses the same principle but splits the numbers into
hundreds, tens and units, and the rectangle
is split into more parts.
The calculation of 26 x 145 is shown below.
20  x 
100  = 
2000 
20  x 
40  = 
800 
20  x 
5  = 
100 
6  x 
100  = 
600 
6  x 
40  = 
240 
6  x 
5  = 
30 
TOTAL 
= 
3770 
The grid method is easier to understand than standard
long multiplication
, and so is taught first.
When children are confident with this method and understand fully the concept of
units, tens and hundreds etc
number place value
then they can move onto the method that you were probably taught at school,
long multiplication
We will illustrate the method using the same calculation as before, 23 x 42. The method uses the principle that 23 x 42 is the same as 23 x (40 + 2) and get the answer by multiplying 2 x 23 and then 40 x 23 and adding the two results as follows:
x23  
42  
__  
46  ( = 2 x 23)  
920  (= 40 x 23)  
_____  
TOTAL  966 
Both methods will give the same answer, and ultimately long division is probably faster, but the grid method is easier to explain and to understand. If the long multiplication method is used without a thorough understanding of the principles behind it, the likelihood is that the incorrect positioning of the digits of the second and subsequent rows of multiplication ( eg. Forgetting to put in the zero in the above example so that 40 x 23 is put down as 92 and not 920) and a nonsensical answer.
7 + 5 = 12  Seven plus/and five equals/is twelve. 
13  6 = 7  Thirteen minus six equals seven. 
3 x 4 = 12  Three times four equals/is twelve. (three fours are twelve.) 
12 / 4 = 3  Twelve divided by four equals/is three. (Twelve over four is three) 
10^{2}=100  Ten squared equals/is one hundred. 
10^{3}=1000  Ten cubed equals/is one thousand. 
10^{6}=1,000,000  Ten to the power of 6 equals/is one million. 
Here are 7 systems of measurement for things like time, distance and money. 1. TIME 1000 milliseconds = 1 second (sec) 60 seconds = 1 minute (min) 60 minutes = 1 hour (hr) 24 hours = 1 day 7 days = 1 week (wk) 28, 30 or 31 days = 1 month (mth) 12 months = 1 year (yr) 365 days = 1 year BuT every 4th year = 366 days (a leap year) Also note: 52 weeks = 1 year (approximately) people often use the following terms: 48 hours (2 days) 72 hours (3 days)
There are two systems for measuring distance in the Englishspeaking world: a) metric 10 millimetres (mm) = 1 centimetre (cm) 100 centimetres = 1 metre (m) 1000 metres = 1 kilometre (km) b) imperial/uS 12 inches (in) = 1 foot (ft) 3 feet = 1 yard (yd) (approximately 1 metre) 1760 yards = 1 mile (approximately 1.6 km)
Area is the extent of a surface. It is 2dimensional. Area is often expressed using the word "square" + the distance. For example, if a room is 10 metres long and 5 metres wide, it is 50 square metres (50 sq. m). But we can also use the distance + the figure 2. Then we would write 50m2.
Here are two examples:
My table is 3 metres long x 2 metres wide: area = 6 sq.m, or area = 6m2 My town is 3 miles x 4 miles: area = 12 sq. miles
We often measure the area of land using: hectare = 10,000 square metres acre = 4,840 square yards
Warning! There is a difference between "square metres" and "metres square". If my room is 10 feet x 10 feet, it is 100 square feet but 10 feet square. We can only say this when the length and the width are the same.
Volume is the amount of space occupied by an object or enclosed in a container. It is 3dimensional. Volume is often expressed using the word "cubic" + the distance. For example, if a room is 5 metres long, 3 metres wide and 3 metres high, it is 45 cubic metres (45 cu. m). But we can also use the distance + the figure 3. So we write 45m3.
Other measurements of volume are:  1000 cubic centimetres (cc) = 1 litre (L or l)  gallon (approx. 4.6 litres in uK, approx. 3.8 liters in uS)
We use litres to talk about fluids like drinks and petrol. We also use gallons to talk about petrol and other fluids.
5. SpEED Speed is a measurement that combines distance, quantity, volume etc AND time. Common ways of talking about the speed of a car, for example, are:  50 miles per hour (50mph)  50 kilometres per hour (50kph) We also use the symbol / when talking about speed:  50 people/hour (50 people per hour)  1000 l/hr (1000 litres per hour) 6. WEIGHT There are two systems to measure how heavy something is: a) metric 1000 grams (g) = 1 kilogram (kg) 1000 kilograms = 1 metric ton (metric tonne) b) imperial/uS 16 ounces (oz) = 1 pound (lb) 14 pounds = 1 stone (British) 100 pounds = 1 hundredweight (cwt)* 20 hundredweights = 1 ton* *There is a slight difference between British and uS hundreweights and tons. For more detail, see: English Club .comMost countries use a basic monetary unit (for example the dollar) divided into 100 fractional units (example cents). They use a combination of paper money (banknotes or notes) and metal money (coins). Here are some examples from the world's major currencies: uSA: American Dollar (uSD or $) 1 dollar = 100 cents uK: British pound (GBp or ?) 1 pound = 100 pence European union: Euro (EuR) 1 euro = 100 cents Japan: Japanese Yen (JpY) 1 yen = 100 sen (not used today) Switzerland: Swiss Franc (CHF) 1 franc = 100 centimes
use the table to learn the 2 and 10 times tables by heart. You should be able to answer your teachers questions: Eg. "What are two sixes?" without doing any sums in your head. Know them by heart, without mental calculations.
When you chant the tables you should say them like this: 

One two three four five. Once I caught a fish alive.
Two four six eight. Who do we appreciate
One banana, two banana,three banana four
One man went to mow, went to mow a meadow
practice these drills with another student. The other student should not see this page but should follow all of your instructions.
Teacher  Student 
"Count from 1 to ten" 
one, two, three, four, five, six, seven, eight, nine, ten. 
Verbal instruction 
Student says: 
Say the odd numbers from one to 10 
Student says: one, three, five, seven, nine. 
Verbal instruction 
Student says: 
multiplication The operation used to put together a number of sets of the same size. Multiplication is indicated by the times sign (X), which may also be represented by a dot (·) or an asterisk (*). The operation of multiplication is the same as repeating addition (e.g., the answer to 2 X 3 is the same as adding 2 to itself 3 times or 2+2+2). Multiplication is the opposite of division.
The numerical system that we use today is the HinduArabic system and it is based on the concept of place value. Each numeral's value is dependant on its place. For instance look at the numeral 1 below.
We can express any number using only the digits 09.
The right hand digit is the number of units,
the next left the number of tens,
the next left the number of hundreds and so on.
In our numbering system the numeral zero has particular importance as it
is used as a "placeholder".
For instance the number 104 needs the zero to "hold"
the tens place. If it was not present we would have the number 14,
which is quite different.
It is also important to understand that ten units are equal to one ten
and ten tens are equal to one hundred etc.,
and below we show a method of teaching this to a child.
One particularly effective way of teaching place value is through the use of
(baseten) blocks.
They visually demonstrate how we can exchange ten units for one ten
and ten tens for one hundred etc.
We can put ten units together and physically make a "ten".
We can then put ten of the "ten" strips together to make a hundred.
Of course we can use 1p, 10p, and £1 coins instead.
However they do rely on being able to understand that the one pound coin is
equal to ten 10p coins and to one hundred 1p coins,
and so it is not quite so clear.
Representing numbers with blocks can then be used to teach addition and subtraction.