We encourage children’s confidence and enjoyment of mathematics whilst acquiring the skills of measuring, observing, weighing, calculating, estimating, computing and recording in different ways.Providing a structured approach to the development of mathematical skills. Problem solving and investigating is seen as a method of drawing all these skills together.

The school follows the programme of study as set out in the National Curriculum we are constantly striving to improve learning and teaching and as part of this process we are introducing Maths No Problem - Singapore Maths in January 2015.

### Progression in Calculation

#### What you need to know about calculations

Mathematics will be at the core of your child’s schooling from the moment they start to the moment they leave. They will be involved in drawing, measuring, handling data and lots of other practical activities that will help your child to understand and enjoy the subject. This information offers guidance to the methods used to help our pupils with calculations. The methods we are advocating are in line with the new National Curriculum (from September 2014). We hope this will be helpful to you and that you will be able to support your child in learning by heart the basic rules which will assist in mental recall eg. number bonds and multiplication tables.

The methods that we use in school may or may not be familiar to you. Children are often confused when they ask parents for help at home and they try to teach the methods that they themselves were taught. Knowing how the methods in this booklet work will help you to help your children. All staff in school work from this document so that we can ensure the consistency of our approach and can make sure that the children move onto the next step when they are ready.

The four operations that are covered by this booklet are addition, subtraction, multiplication and division. Whichever operation is being taught the child needs to experience all of these steps to completely conquer it.

- Using objects
- Using pictures
- Using a number line
- Using an expanded method
- Using a compact written method

#### Mental methods first

Children should always be encouraged to consider if a mental calculation would be appropriate before using written methods. These are covered in the first part of each section.

Why do children need to do written calculations?

- To represent work that has been done practically.
- To support, record and explain mental calculation
- To keep track of steps in a longer task
- To work out calculations that are too difficult to do mentally

Children should be taught when it is appropriate to do an approximate or estimate first and should check with the inverse operation at the end.

By upper Key Stage 2, children should be confident in choosing and using a strategy that they know will get them to the correct answer as efficiently as possible.

When are children ready to move on to written calculations?

#### Addition and subtraction

- Do they know addition and subtraction facts to 20?
- Do they understand place value and can they partition numbers?
- Can they add three single digit numbers mentally?
- Can they add and subtract any pair of two digit numbers mentally?
- Can they explain their mental strategies orally and record them using informal jottings?

#### Multiplication and division

- Do they know the 2, 3, 4, 5 and 10 time table
- Do they know the result of multiplying by 0 and 1?
- Do they understand 0 as a place holder?
- Can they multiply two and three digit numbers by 10 and 100?
- Can they double and halve two digit numbers mentally?
- Can they use multiplication facts they know to derive mentally other multiplication facts that they do not know?
- Can they explain their mental strategies orally and record them using informal jottings?

The above lists are not exhaustive but are a guide for the teacher to judge when a child is ready to move from informal to formal methods of calculation.

#### What can parents do to help?

- Count with their child
- Play number games
- Involve children when taking measurements or weighing items
- Take note of numbers in real life e.g. telephone numbers, bus numbers, lottery numbers etc.
- Give children opportunities to use money to shop, check change etc.
- Talking about the mathematics in football e.g. ‘How many points does your favourite team need to catch the next team in the league?’
- When helping their children calculate use the method that they have been taught

#### Please don’t…

- Teach your children that to multiply by 10 you ‘just add a zero’. – you ‘move the digits to the left and add a zero as a place holder’
- Tell them that you can move the decimal point. – You can’t. You can only move the digits to the left or to the right
- Tell them that they are doing ‘sums’ – ‘sum’ is a mathematical word that means ‘addition’, everything else is a ‘calculation’

#### Glossary

**2-digit -**a number with 2 digits like 23, 45, 12 or 60**3-digit -**a number with 3 digits like 123, 542, 903 or 561**Addition facts**- knowing that 1+1 = 2 and 1+3 = 4 and 2+5 = 7. Normally we only talk about number facts with totals of 20 and under.**Array**-An array is an arrangement of a set of numbers or objects in rows and columns -it is mostly used to show how you can group objects for repeated addition or subtraction.**Bridge to ten**-a strategy when using numberlines. Adding a number that takes you to the next ‘tens’ number.**Bus Stop Method**- traditional method for division with a single digit divisor**Concrete apparatus**- objects to help children count -these are most often cubes (multilink) but can be anything they can hold and move.**Dienes**(purple hundreds, tens and units blocks), Numicon, Cuisenaire rods are also referred to as concrete apparatus.**Column chunking**-method of division involving taking chunks or groups or the divisor away from the larger number**Decimal number**-a number with a decimal point**Divisor**-the smaller number in a division calculation. The number in each group for chunking.**Double**-multiply a number by 2**Exchanging**- moving a ‘ten’ or a ‘hundred’ from its column into the next column and splitting it up into ten ‘ones’ (or ‘units’) or ten ‘tens’ and putting it into a different column**Expanded Multiplication -**a method for multiplication where each stage is written down and then added up at the end in a column**Find the difference**- A method for subtraction involving counting up from the smaller to the larger number**Grid method**- a method for multiplying two numbers together involving partitioning**Half**- a number, shape or quantity divided into 2 equal parts**Halve**-divide a number by 2**Integer**- a number with no decimal point**Inverse**-the opposite operation. Addition is the inverse of subtraction, multiplication is the inverse of division**Long Multiplication -**column multiplication where only the significant figures are noted**Number bonds to ten**- 2 numbers that add together to make ten, like 2 and 8, or 6 and 4.**Number bonds to 100**- 2 numbers that add together to make 100 like 20 and 80, or 45 and 65 or 12 and 88**Numberline**- a line either with numbers or without (a blank numberline). Children use this tool to help them count on for addition of subtraction and also in multiplication and divison.**Numberline Chunking**- method of division involving taking chunks or groups or the divisor away from the larger number**Number sentence**-writing out a calculation with just the numbers in a line E.G. 2+4=6 or 35 ÷7 = 5 or 12 x 3 =36 or 32 – 5 = 27**Partition**- split up a larger number into the hundreds, tens and units. E.G. 342 – 300 and 40 and 2**Place Value**– knowing that in the number 342 – the ‘3’ means ‘3 hundreds’, the ‘4’ means ‘4 tens’ and the ‘2’ means ‘2’.**Quarter**- a number, shape or quantity divided into 4 equal parts**Recombine**-for addition, once you have partitioned numbers into hundreds, tens and units then you have to add then hundreds together, then add the tens to that total, then add the units to that total**Remainder -**a whole number left over after a division calculation**Repeated addition**- repeatedly adding groups of the same size for multiplication**Significant digit -**the digit in a number with the largest value. E.G in 34 - the most significant digit is the 3, as it has a value of ‘30’ and the ‘4’ only has a value of ‘4’**Single digit**-a number with only one digit. These are always less than 10.**Taking away-**a method for subtraction involving counting backwards from the larger to the smaller number**Tens number**- a number in the ten times tables - 10,20,30,40 50,etc.**Unit -**another term for single digit numbers. The right hand column in column methods is the ‘units’ column