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# UK School Maths Syllabus

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 2 and 10 times tables by heart.

### Shape, Space and Measures

use the mathematical names for common two-dimensional and three-dimensional 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

1. tackle a problem using different approaches
2. trying out ideas of their own
3. apply maths to practical problems
4. present their results in a clear and organised way.

### Number

1. multiply and divide decimals by 10 or 100, and whole numbers by 1000 in their heads
2. put in order a set of numbers with up to three decimal places
3. work with decimals to add and subtract on paper
4. a fraction to its simplest form (for example, four-sixteenths to one-quarter)
5. work out fractions of numbers or quantities (for example, they should be able to work out five-eighths of 32, seven-tenths of 40 and nine-one hundredths of 400 centimetres)
6. understand that a percentage is the number of parts in every hundred, and work out simple percentages of whole numbers
7. solve problems involving ratio and proportion
8. know all the times tables and use them to divide as well as multiply
9. use +, -, ÷, and \ to solve problems given in words, which could be about numbers or measures (kilograms, kilometres and so on)
10. 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

1. use a protractor to measure angles to the nearest degree
2. calculate the perimeter and area of shapes that can be split into rectangles
4. interpret numbers accurately on a range of measuring instruments
5. tell the time and solve problems involving time on a 12-hour or 24-hour clock.

### Handling Data

1. solve a problem by collecting and using information in tables, graphs and charts.

It is expected that most children of around 14 years will be able to:

### use and Application of Maths

1. plan how to tackle a problem, including working out what information they need
2. solve complex problems by breaking them into smaller, more manageable tasks
3. describe mathematical situations using symbols, words and diagrams
4. link their solutions to the initial problem and present them to a sensible degree of accuracy
5. explain their reasoning and begin to give mathematical justifications for their solutions.

### Number and Algebra

1. in their heads, do some calculations involving decimals, fractions, percentages, factors, powers and roots
2. multiply and divide any whole number by 10, 100 and other powers of 10
3. estimate and approximate answers to calculations
4. use standard written methods for addition, subtraction, multiplication and
5. division involving whole numbers, decimals and fractions
6. give one number as a fraction or percentage of another
7. use efficient methods to add, subtract, multiply and divide fractions
8. use the relationships between fractions, decimals, percentages, ratio and proportion to solve problems
9. find and use prime factors of numbers
10. 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
11. use index notation and simple instances of index laws (know, for example, that 22 x 23 = 25 and 26 ÷ 22 = 24)
12. set up and use equations and their graphs to solve word problems
13. simplify and transform algebraic expressions, knowing how to substitute positive and negative numbers for symbols
14. generate terms of a sequence and use algebra to describe the nth term of a simple sequence
15. begin to use trial and improvement methodically, to find rough solutions to equations such as x3 - x = 100.

### Shape, Space and Measures

1. use a ruler, protractor and compasses to construct lines, angles and two-dimensional or three-dimensional shapes
2. use the properties of straight-sided shapes, and intersecting and parallel lines, to solve problems
3. recognise when two triangles are congruent
4. know and use formulae to calculate: -the circumferences and areas of circles -areas of straight-sided shapes -volumes of cuboids
5. use two-dimensional diagrams to analyse three-dimensional shapes
6. rotate, reflect, translate and enlarge two-dimensional shapes and understand how these transformations affect their sides, angles and position
7. write instructions for a computer to generate and transform shapes and paths.

### Handling Data

1. design a survey or experiment
2. gather the data they need from different sources (for example, from tables, lists and computer sources)
3. choose the right kind of graph to show the data they have gathered
4. summarise raw data using range and measures of average
5. interpret graphs and diagrams and draw conclusions
6. calculate probabilities and solve problems in situations where there are limited numbers of equally likely outcomes (for example, when rolling a dice)
7. 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.

1. Count from one to ten
2. Write down these numbers: 5,8,9 6,9,10 21,65,72 15,50,100
1. Write down these numbers and then put them into order. 21,9,55 44,22,33 100,9,78

### Double or half

1. What's half of ten?
2. What's double 6?
3. If you double fifteen, how many will you have?
4. 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:

x
 23 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) 102=100 Ten squared equals/is one hundred. 103=1000 Ten cubed equals/is one thousand. 106=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 English-speaking 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 2-dimensional. 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 3-dimensional. 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 .com

### MONEY

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:
Once two is two
Two twos are four
Three twos are six
Four twos are eight
Five twos are ten
Six twos are twelve
Seven twos are fourteen
Eight twos are sixteen
Nine twos are eighteen
Ten twos are twenty.

 x 0 1 2 3 4 5 6 7 8 9 10 11 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 2 3 4 5 6 7 8 9 10 11 12 2 0 2 4 6 8 10 12 14 16 18 20 22 24 3 0 3 6 9 12 15 18 21 24 27 30 33 36 4 0 4 8 12 16 20 24 28 32 36 40 44 48 5 0 5 10 15 20 25 30 35 40 45 50 55 60 6 0 6 12 18 24 30 36 42 48 54 60 66 72 7 0 7 14 21 28 35 42 49 56 63 70 77 84 8 0 8 16 24 32 40 48 56 64 72 80 88 96 9 0 9 18 27 36 45 54 63 72 81 90 99 108 10 0 10 20 30 40 50 60 70 80 90 100 110 120 11 0 11 22 33 44 55 66 77 88 99 110 121 132 12 0 12 24 36 48 60 72 84 96 108 120 132 144

### Odd and even numbers

1. 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

### Student

"Count from 1 to ten"
Check for pronunciation etc.,

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:
1. place value
2. Odd and even
3. Less than greater than , equal to
4. place value
5. Next and previous

# Questions and statements of Arithmetic

1. What is the total?
2. What does that add up to?
3. What is the sum of 3 and 6?
4. How many are there altogether?
5. How many are there in all?
6. If we put this together with that, how many will there be? (Very young beginners)
7. How much is there altogether?
8. What does that make?

2. 2 plus 2 equals 4
3. 3 and then 5 more is
4. 9 and 3
5. 1 in addition to 2
6. have 7, also have 6
8. Increase this number by 4
9. the sum of 9 and 7 is

### Question phrases for Subtraction

1. How many are left?
2. How many are left over?
3. How many more than...?
4. How many less than...?
5. How many more are needed?
6. How many fewer?
7. How much less?

### phrases of Subtraction

1. 4 minus 3 equals...
2. 7 less 2 equals...
3. 8 take away 6 equals...
4. 9 decreased by 1
5. Reduce 4 by...
6. Subtract 7 from 9
7. Deduct 2 from 3
8. 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.

1. A factor is one of the numbers to be multiplied in a multiplication problem.
2. The product is the result of multiplying two numbers together.
3. multiple A number that is a product of a number and another number.
4. 6 X 2 = 12 (12 is a multiple of 2)
5. 12 is a multiple of 6
6. 4 X 2 = 8 (8 is a multiple of 2)
7. 8 is a multiple of 4

### Question phrases to use When Forming Multiplication problems:

1. How many altogether?
2. How many in all?
3. If we multiply this number times that number, how many will there be?
4. What is the total?
5. How much altogether?

### phrases Representing Ways of Saying Multiplication problems:

1. 2 times 3 equals
2. the product of 8 and 1 is
3. repeat this set of 5, three times
4. duplicate these 4 items, three times
5. this set of 9, reproduced 6 times
6. 6 occurrences of those 2 events, yields...

# Division

### Vocabulary to use When Describing Division problems

1. division The operation used to determine how many times a given number,
2. or quantity, is contained in another number. Division is used to divide or partition a whole into parts. Division is the opposite of multiplication.
3. divisible A number is divisible by another number if it goes into the number evenly with no remainder.
4. The number or quantity being divided.
5. divisor The number by which the dividend is divided in a division problem.
6. quotient The number that results when numbers are divided.
7. 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

1. When used to put a number into a number of sets, the question is:
2. When used to put into sets of the same size, the question is:
3. How many sets?
4. How to distribute this group evenly?
5. What part of the whole goes to each?
6. How many pieces of the set go to each?
7. How many times does this number go into this number?
8. //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

1. 9 divided by 3
2. divide 8 by 4 (imperative)
3. 4 goes into 8 (statement)
4. separate into parts (imperative)
5. distribute this set of items
6. give out an equal number to each
7. break this apart into sections
8. what part of the group
9. partition this area into even sizes
10. deal out these items

### Math help - Number place Value

The numerical system that we use today is the Hindu-Arabic 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 = 1 unit
2. 10 = one ten
3. 100 = one hundred

We can express any number using only the digits 0-9. 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 "place-holder". 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 (base-ten) 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.