Progression in Addition

FS to Key Stage 2

Welcome Maths is FUN!

Aims• To have an overview of the addition skills

children need to calculate.

• To understand how to support your child with addition.

• To be more aware of the models, images and resources used to support the teaching and learning of addition.

• Think about the progression from mental addition towards written methods.

Strategies for AdditionSecure addition requires the ability to:

recall key number facts instantly (number pairs/bonds to 10, 20 & 100, doubles etc) and to apply these to similar calculations

recognise that addition can be done in any order and use this to add mentally different combinations of numbers

partition multi-digit numbers in different ways, including adding the hundreds tens and units separately before recombining

understand the language of addition including more than, sum, plus, greater than, total, altogether etc

Addition• Counting on using objects• Counting on using number

line/tracks• Counting on using a numeral roll• Counting on using a hundred square• Blank number line (bridging)• Partitioning• Column addition

The Importance Of Finger Patterns

Fingers are one of the first strategies children use to count

They begin as being ‘grown’ and with confidence and practice become ‘thrown’

It is crucial that a child develops strategies to move ‘beyond 10’ as they enter KS1

Beginning to addPractical, counting objects and relating addition to combining two groups of objects

Beginning to use a number track

Use of the number track- hopping and recording.(a) 2 and 3 makes 5 0 1 2 3 4 5 6 7 8 9 10

resources to support understanding

for larger numbers, or too many numbers to deal with mentally

Written Methods

We will attempt to touch on as many written methods as we can in the time we have. Please stay at the end and ask if you are unsure or have any further questions.

When ready, the children will move on to more formal written methods. Moving to written procedures too fast can mean:

•Children add/subtract the digits in a column by rote, without understanding what their value is, or what a sensible answer is likely to be•Children who rely on written procedures can be more likely to look for a calculator when stuck, not a mental strategy•Children can hide their understanding of mathematical concepts behind having a good memory for procedure.

Stage 1 – The Empty Number Line

The empty number line helps to record the steps on the way to calculating the total. The steps often bridge through a multiple of 10.

8 + 7 = 15

48 + 36 = 84 or:

Over to you!Use an empty number line to find answers to these sums.

53 + 24

86 + 17

149 + 38

Stage 2 - PartitioningThe next stage is to record mental methods using partitioning. Partitioning both numbers into tens and ones mirrors the column method where ones are placed under ones and tens under tens. This also links to mental methods.

Eg: 47 + 76 = 47 + 70 + 6 = 117 + 6 = 123 or 47 + 76 = 40 + 70 + 7 + 6 = 110 + 13 = 123

Partitioned numbers are then written under one another:

Over to you!

Use partitioning to find answers to these sums.

65 + 38

71 + 26

94 + 45

Stage 3 – Expanded Method In Columns

Children can now move on to a layout showing the addition of the tens to the tens and the ones to the ones separately. Children should start by adding the ones digits first.

NB The addition of the tens in the

calculation 47 + 76 is described as

40 + 70 = 110 as opposed to

4 + 7 = 11.

Over to you!Use the expanded column method to find answers to these sums.

65 + 38

123 + 59

315 + 172

Written methods for Addition

Stage 3: Expanded method in columns

The expanded method leads children to the more compact method so that they understand its structure and efficiency. The amount of time that should be spent teaching and practising the expanded method will depend on how secure the children are in their recall of number facts and in their understanding of place value.

Stage 4 – The Column Method

In this method, recording is reduced further. Carry digits are recorded below the line, using the words 'carry 10' or 'carry 100', not 'carry 1'.

Later, extend to adding three two-digit numbers, two three-digit numbers, numbers with different numbers of digits and decimals.

Helping at homeSome Dos… …And Some Don’ts!

• Play (maths) with your child - There are opportunities for impromptu learning in games with real people that you can't get from a DS or Xbox

• Let your child win or be better than you - Otherwise all they learn is that you are better at maths than them

• Recognise that there is more than one way of doing calculations - You may have learned one method, but children are actively encouraged to seek out alternative methods in school and choose one which works for them, no matter how long winded

• Be an actor - Get excited about maths and your child will get excited too

• Don't expect them to understand after you've explained it once - It is normal for a child to 'get it' one day, and then in a different context not know how to find an answer

• Don't tell them you are hopeless at maths - You may remember maths as being hard, but you were probably not hopeless, and even if you were, that implies to your child, “I was hopeless at maths, and I'm an adult, therefore maths is not important”

• Don't get into an argument over homework - It will be something that your child has covered in class, and if they really can't do it without a lot of tears and frustration, leave it and LET US KNOW!

 

Helping at home FS/KS1• Play board games

• Look at numbers in the environment e.g. telephone keys, number plates, door numbers, book pages, sleeps until Christmas!

• Money

• Birthdays, Months of the year, Days of the week

Props around the house •A traditional wall calendar-Calendars help with counting days and spotting number patterns

•Board games that involve dice or spinners-helps with counting and the idea of chance

•A pack of playing cards- Card games can be adapted in many ways to learn about number bonds, chance, adding and subtracting

•A calculator- A basic calculator will help with maths homework when required, there are also many calculator games you can play, too.

•Dried peas, pasta or Smarties- for counting and estimating

•A tape measure and a ruler- Let your child help when measuring up for furniture, curtains etc

•Fridge magnets with numbers on- can be used for practice of written methods

•Indoor/outdoor Thermometer- especially useful in winter for teaching negative numbers when the temperature drops below freezing

•A dartboard with velcro darts- Helps with doubling, trebling, adding and subtracting.

Addition Apps