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Foundation Maths Primary MathsLinks to Pages
2D shape 3D Shape Adding fractions same denominator Area of a circle Area of a rectangle Area of a Circle Averages Balanced Equations Bidmas bodmas Capacity Changing decimals to fractions Changing fractions to percentages Circumference of a circle Division Chunking Method Estimation and approximation Minus Opposite Plus Multiplication Napier method Place Value Surface Area Manipulating SurdsSet : variable this>Title
UK state system Maths syllabus and curriculum.Mathematics in the English language
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
Tables
Know the two times table and ten times table by heart.
Times TablesShape, Space and Measures
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.
Key Stage 2
It is expected that most children of around 11 years will be able to:
Use and Application of Maths
 tackle a problem using different approaches
 trying out ideas of their own
 apply maths to practical problems
 present their results in a clear and organised way.
Number
 multiply and divide decimals by 10 or 100, and whole numbers by 1000 in their heads
 put in order a set of numbers with up to three decimal places
 work with decimals to add and subtract on paper
 a fraction to its simplest form (for example, foursixteenths to onequarter)
 work out fractions of numbers or quantities (for example, they should be able to work out fiveeighths of 32, seventenths of 40 and nineone hundredths of 400 centimetres)
 understand that a percentage is the number of parts in every hundred, and work out simple percentages of whole numbers
 solve problems involving ratio and proportion
 know all the times tables and use them to divide as well as multiply
 use +, , ÷, and \ to solve problems given in words, which could be about numbers or measures (kilograms, kilometres and so on)
 use paper and pencil methods of multiplying and dividing for harder calculations (for example, 434.25 multiplied by 8, 195 divided by 6 and 352 multiplied by 27).
Shape, Space and Measures
 use a protractor to measure angles to the nearest degree
 calculate the perimeter and area of shapes that can be split into rectangles
 read and plot coordinates in all four quadrants
 interpret numbers accurately on a range of measuring instruments
 tell the time and solve problems involving time on a 12hour or 24hour clock.
Handling Data
 solve a problem by collecting and using information in tables, graphs and charts.
use and Application of Maths
 plan how to tackle a problem, including working out what information they need
 solve complex problems by breaking them into smaller, more manageable tasks
 describe mathematical situations using symbols, words and diagrams
 link their solutions to the initial problem and present them to a sensible degree of accuracy
 explain their reasoning and begin to give mathematical justifications for their solutions.
Number and Algebra
 in their heads, do some calculations involving decimals, fractions, percentages, factors, powers and roots
 multiply and divide any whole number by 10, 100 and other powers of 10
 estimate and approximate answers to calculations
 use standard written methods for addition, subtraction, multiplication and
 division involving whole numbers, decimals and fractions
 give one number as a fraction or percentage of another
 use efficient methods to add, subtract, multiply and divide fractions
 use the relationships between fractions, decimals, percentages, ratio and proportion to solve problems
 find and use prime factors of numbers
 use calculators efficiently and interpret the display in the context of the problem; use the constant, the sign change key, pi, function keys for powers, roots and fractions; use brackets and the calculator memory
 use index notation and simple instances of index laws (know, for example, that 22 x 23 = 25 and 26 ÷ 22 = 24)
 set up and use equations and their graphs to solve word problems
 simplify and transform algebraic expressions, knowing how to substitute positive and negative numbers for symbols
 generate terms of a sequence and use algebra to describe the nth term of a simple sequence
 begin to use trial and improvement methodically, to find rough solutions to equations such as x3  x = 100.
Shape, Space and Measures
 use a ruler, protractor and compasses to construct lines, angles and twodimensional or threedimensional shapes
 use the properties of straightsided shapes, and intersecting and parallel lines, to solve problems
 recognise when two triangles are congruent
 know and use formulae to calculate: the circumferences and areas of circles areas of straightsided shapes volumes of cuboids
 use twodimensional diagrams to analyse threedimensional shapes
 rotate, reflect, translate and enlarge twodimensional shapes and understand how these transformations affect their sides, angles and position
 write instructions for a computer to generate and transform shapes and paths.
Handling Data
 design a survey or experiment
 gather the data they need from different sources (for example, from tables, lists and computer sources)
 choose the right kind of graph to show the data they have gathered
 summarise raw data using range and measures of average
 interpret graphs and diagrams and draw conclusions
 calculate probabilities and solve problems in situations where there are limited numbers of equally likely outcomes (for example, when rolling a dice)
 estimate probabilities from data gathered in experiments.
To arrange a voice call about English lessons send an email to this address and mention English Lessons in the subject
Count to one hundred with songs
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
Verbal questions
Read these questions to your student and listen for correct verbal responses.
 Count from one to ten
 Write down these numbers: 5,8,9 6,9,10 21,65,72 15,50,100
 Write down these numbers and then put them into order. 21,9,55 44,22,33 100,9,78
Double or half
 What's half of ten?
 What's double 6?
 If you double fifteen, how many will you have?
 If you divide one hundred by two, what will the result be?
The Grid Method of Multiplication
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:
Image or diagram goes here!!!
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 
The Grid Method for Three Digit Numbers
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
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.
Reading arithmetic
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. 
Measurements
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)
DISTANCE
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
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
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 .comMONEY
Most 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
Maths in English
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: 

Odd and even numbers
 Say the odd numbers from one to 10. one, three, five, seven, nine.
Basic number drills
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.
Counting
Teacher  Student 
"Count from 1 to ten" 
one, two, three, four, five, six, seven, eight, nine, ten. 
Drill
Verbal instruction 
Student says: 
Odds and evens
Say the odd numbers from one to 10 
Student says: one, three, five, seven, nine. 
Write the number that teacher says
Verbal instruction 
Student says: 
 place value
 Odd and even
 Less than greater than , equal to
 place value
 Next and previous
Questions and statements of Arithmetic
Question phrases for Addition
 What is the total?
 What does that add up to?
 What is the sum of 3 and 6?
 How many are there altogether?
 How many are there in all?
 If we put this together with that, how many will there be? (Very young beginners)
 How much is there altogether?
 What does that make?
Language phrases of Addition
 add 1 to 8
 2 plus 2 equals 4
 3 and then 5 more is
 9 and 3
 1 in addition to 2
 have 7, also have 6
 add 3 to 0
 Increase this number by 4
 the sum of 9 and 7 is
Addition Games
Test the toadQuestion phrases for Subtraction
 How many are left?
 How many are left over?
 How many more than...?
 How many less than...?
 How many more are needed?
 How many fewer?
 How much less?
phrases of Subtraction
 4 minus 3 equals...
 7 less 2 equals...
 8 take away 6 equals...
 9 decreased by 1
 Reduce 4 by...
 Subtract 7 from 9
 Deduct 2 from 3
 Remove 2 from 5
Multiplication
Vocabulary to use When Describing Multiplication problems
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.
 A factor is one of the numbers to be multiplied in a multiplication problem.
 The product is the result of multiplying two numbers together.
 multiple A number that is a product of a number and another number.
 6 X 2 = 12 (12 is a multiple of 2)
 12 is a multiple of 6
 4 X 2 = 8 (8 is a multiple of 2)
 8 is a multiple of 4
Question phrases to use When Forming Multiplication problems:
 How many altogether?
 How many in all?
 If we multiply this number times that number, how many will there be?
 What is the total?
 How much altogether?
phrases Representing Ways of Saying Multiplication problems:
 2 times 3 equals
 the product of 8 and 1 is
 repeat this set of 5, three times
 duplicate these 4 items, three times
 this set of 9, reproduced 6 times
 6 occurrences of those 2 events, yields...
Division
Vocabulary to use When Describing Division problems
 division The operation used to determine how many times a given number, or quantity, is contained in another number. Division is used to divide or partition a whole into parts. Division is the opposite of multiplication.
 divisible A number is divisible by another number if it goes into the number evenly with no remainder.
 The number or quantity being divided.
 divisor The number by which the dividend is divided in a division problem.
 quotient The number that results when numbers are divided.
 remainder The number that is left over in a division problem if the dividend was not evenly divisible by the divisor.
Question phrases to use When Forming Division problems
 When used to put a number into a number of sets, the question is:
 When used to put into sets of the same size, the question is:
 How many sets?
 How to distribute this group evenly?
 What part of the whole goes to each?
 How many pieces of the set go to each?
 How many times does this number go into this number? //4 into 13 goes 3 times remainder 1 (with 1 left over)
Long division
This is a way of setting out a division problem on paper.phrases Representing Ways of Saying Division problems
 9 divided by 3
 divide 8 by 4 (imperative)
 4 goes into 8 (statement)
 separate into parts (imperative)
 distribute this set of items
 give out an equal number to each
 break this apart into sections
 what part of the group
 partition this area into even sizes
 deal out these items
Math help  Number place Value
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.
 1 = 1 unit
 10 = one ten
 100 = one hundred
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.
Explaining place Value
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.
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