1. Welcome to Addition and Subtraction at RAB
Please feel free to have a look/play with some of the resources we have put out on the tables.
Tuesday 13th June
1.45pm/6.30pm

2. At today’s workshop we hope to:
Provide you with a greater understanding of how addition and subtraction are taught in school from Reception to Year 6
Demonstrate and share the vocabulary that we use to describe addition and subtraction
Demonstrate the importance of mental maths and associated strategies
Share with you the importance of using concrete resources and the development from this to pictorial representations (drawings/jottings) to the more abstract form (written calculations) in relation to addition and subtraction
Share with you some ideas of ways to best support your child at home

3. Objectives
Each year group has a different set of objectives that we follow for all aspects of maths including addition and subtraction.
All children will have exposure to these objectives, though not all children will grasp them at the same time.
We believe it is important to give every child the opportunity to succeed and to achieve to their full potential.

4. Key Learning Documents
These are available for each year group 1-6 on the school website

5. Number in EYFS
• Selects the correct numeral to represent 1 to 5, then 1 to 10 objects. • Counts an irregular arrangement of up to ten objects. • Estimates how many objects they can see and checks by counting them. • Uses the language of ‘more’ and ‘fewer’ to compare two sets of objects. • Finds the total number of items in two groups by counting all of them. • Says the number that is one more than a given number. • Finds one more or one less from a group of up to five objects, then ten objects. • In practical activities and discussion, beginning to use the vocabulary involved in adding and subtracting. • Records, using marks that they can interpret and explain. • Begins to identify own mathematical problems based on own interests and fascinations. Early Learning Goal Children count reliably with numbers from one to 20, place them in order and say which number is one more or one less than a given number. Using quantities and objects, they add and subtract two single-digit numbers and count on or back to find the answer. They solve problems, including doubling, halving and sharing.

6. Early Learning Goal Children count reliably with numbers from one to 20, place them in order and say which number is one more or one less than a given number. Using quantities and objects, they add and subtract two single-digit numbers and count on or back to find the answer. They solve problems, including doubling, halving and sharing.
There is not an abstract stage for this age group – all learning will be based on concrete and pictorial resources.
Adding by combining two sets of objects into one group (5 cubes and 3 cubes)

7. Much of the addition/subtraction in the Autumn/Spring Term is verbal
Practical resources are essential to EYFS – they use lots of different things to aid their counting and simple addition.
Numicon is used to support number recognition and counting on
Use of the children as a resource
Using fingers
Using number lines/number tracks
Using 100 squares
The importance of 1:1 correspondence when counting is key
Use of the children – There were 3 children on the bus, 2 more children got on. How many now? Physically moving the children in order to be able to count them.

8. Addition in Year 1
The children will have access to a wide range of counting equipment, everyday objects, number tracks and number lines, and be shown numbers in different con- texts.
Read and write the addition (+) and equals (=) signs within number sentences.
They will predominately use the bar modelling method and resources – show actions for part/part/whole
They will be introduced to missing number sums and also sums where the answer is placed first .
This academic year has seen a huge increase in the use of bar-modelling. This is began in year 1 with a simple part/part:whole model.
Key vocabulary: add, more, plus, and, make, altogether, total, equal to, equals, double, most, count on, number line

9. Addition in Year 2 Add with 2-digit numbers Developing mental fluency with addition and place value involving 2-digit numbers, then establish more formal methods.
To add 2 digit numbers and tens To add 1 digit numbers to 2 digit numbers
To add 2 digit numbers to 2 digit numbers.
When adding two 2-digit numbers the children will usually be taught to add the ones and then the tens, but may well be shown to add the tens and then the ones too – both examples are appropriate.
Expanded addition
In this method, the numbers being added are partitioned and set out in place value order. The tens and units/ones can then be totalled individually before regrouping the number at the end.
The children will also be shown to write this without a formal sum. =
= 50
4 + 3 = 7
= 57
Key vocabulary: add, more, plus, and, make, altogether, total, equal to, equals, double, most, count on, number line, sum, tens, units, ones, partition, addition, column, tens boundary
Leading into a more formal partitioned column method.
Vocabulary: sum, tens, units, ones, partition, addition, column, tens boundary

10. Addition in Year 3 To use an expanded column method of addition
After mastering the partitioned method, children will be introduced to an expanded column method. Children will need to recognise the place value of each digit without partitioning the whole number. Each row represents a single step of the calculation. Children can then add down the columns as they did in the partitioned method.
Children will be taught to add the units/ones first e.g = 9, recording the 9 in the ones column
Then they will be taught to say = 100 NOT = 10 They will record this underneath
They may be shown to put a zero in the gap under the 200 so that they are clear that there are no other 100s to add.
Compact column method
Add ones first
Add tens – still using the vocab of add tens and recording as 10 tens so need to exchange the tens for a 1 hundred (demo using dienes apparatus)
Then adding the 100s
Children who are confident with the expanded method will move on to the compact column addition method, with exchanging

11. Addition in Year 4 Use of ‘ones’ not ‘units’.
Demo writing place value and how place value counters can support exchanging. Refer to different locations of exchanging used by other schools/countries.
Use of ‘ones’ not ‘units’.
Use of the term ‘exchange’ not ‘carry over’. Place value headings can be added above the calculation to support children. Place value counters and Diennes will support.

12. Addition in Year 5
Show place value counters – have some on each desk and explain. Refer to place holder terminology.
Children should understand the place value of tenths and hundredths and use this to align numbers with different numbers of decimal places.
Use of place value counters to support this.

13. Addition in Year 6
Children need to apply these methods to adding numbers of increasing complexity within multi-step problems. Reasoning and problem solving is very important.
Concrete apparatus is still used to support children although children now independently decide to use the resources.

14. Subtraction EYFS
There is not an abstract stage for this age group – all learning will be based on concrete and pictorial resources.

15. Again the use of practical resources in paramount in EYFS
The children will practise physical taking away resources and counting how many they have left
The children will look at how many more by matching
The written notation of subtraction is not introduced until the children are ready – for many this will not be until the summer term

16. Subtraction Year 1 Subtract from numbers up to 20
Subtract by taking away
Count back in ones on a numbered number line to take away, with numbers up to 20:
Model subtraction using hundred squares and numbered number lines/tracks and practically.
Key vocabulary: equal to, take, take away, less, minus, subtract, leaves, distance between, how many more, how many fewer / less than, most, least, count back , how many left, how much less is_?
Key skills for subtraction at Y1:
· Given a number, say one more or one less.
· Count to and over 100, forward and back, from any number.
· Represent and use subtraction facts to 20 and within 20.
· Subtract with one-digit and two-digit numbers to 20, including zero.
· Solve one-step problems that involve addition and subtraction, using concrete objects (ie bead string, objects, cubes) and pictures, and missing number problems.
· Read and write numbers from 0 to 20 in numerals and words.
Find the difference between
This will be introduced
practically with the language – find the distance between‘ and ‘how many more?’ in a
range of familiar contexts. 7 4 ?

17. Subtraction Year 2 Subtract with 2-digit numbers
Subtract on a number line by counting back, aiming to develop mental subtraction skills.
Move towards more efficient jumps back, as below:
= 24
Partition the second number
and subtract it in tens and units, subtract
the tens first and then the ones as below:
Mental strategies – subtract numbers close together by counting on
Move towards more efficient jumps back, as below:
This strategy will be used for:
*2-digit numbers subtract units e.g. 36 – 7
*2-digit numbers subtract tens e.g. 48 – 30
*Subtracting pairs of 2-digit numbers
Many mental strategies are taught. Children are taught to recognise that when numbers are close together, it is more efficient to count on the difference. They need to be clear about the relationship between addition and subtraction.
Key vocabulary: equal to, take, take away, less, minus, subtract, leaves, distance between, how many more, how many fewer / less than, most, least, count back , how many left, how much less is_? difference, count on, strategy, partition, tens, units
Some Year 2 children will also be taught to use the expanded method (see yr 3)

18. Subtraction Year 3 Subtracting with 2 and 3-digit numbers.
Introduce the expanded partitioned column subtraction method.
89 – 35 = 54
80 + 9
50 + 4
STEP 2: introduce ‘exchanging’ through practical subtraction.
Make the larger number with Base 10, then subtract 47 from it.
STEP 3: Once pupils are secure
with the understanding of
‟exchanging‟, they can use the
partitioned column method to
subtract any 2 and 3-digit numbers.
You can use the terms ‘and’ or ‘add’
between the tens and units eg 100 and 30 and 8.
STEP 1: introduce this method with examples where no exchanging is required.
Demo step 2 using dienes apparatus – show parents how need to first create 72 using tens and ones and then demo how we teach the exchanging as cannot physically take away 7 ones unless exchange 1 ten stick for 10 ones and then have 12 ones take away 7.
Even with step 3 need to demo it first using dienes
Key vocabulary: equal to, take, take away, less, minus, subtract, leaves, distance between, how many more, how many fewer / less than, most, least, count back , how many left, how much less is_? difference, count on, strategy, partition, tens, units exchange, decrease, hundreds, value, digit

19. Subtraction Year 4
Use place value headings if needed and keep referring to 15 tens etc. Use counters to support understanding of exchanging.
Partitioned column subtraction with exchanging. Continuing from Year 3 but using more complex numbers.
Move on to introducing the compact column subtraction method only when the children are completely secure with place value and can explain it.

20. Subtraction Year 5
Ideally move as many as possible to compact method but it is vital they have the understanding of place value and how to exchange between them. Again use place value counters and Diennes to visualise the problem. Also use Bar Modelling to ensure children choose the correct operation (addition/subtraction)
Moving to the compact column method of subtraction video
Solve multi-step addition and subtraction problems using up to 4 digits and 2 decimal places.

21. Subtraction Year 6
Stlll use concrete apparatus as and when needed and also bar modelling.
Increasingly large and more complex numbers including decimals as part of multi-step problems and being able to reason and explain the process clearly.
Solve problems involving multi-operations including those with missing numbers.

22. Now it’s your turn…
On your tables you will find some example questions from Year 1 to Year 6. Please have a look at the questions and think about how you would support your child were they to bring this type of question home.
Please make use of any of the resources we have put out on the tables.
Please do ask if we can help or explain any method further.

23. At home
You can access several important documents at home from the RAB Website including the Key Learning documents for each year group, the RAB Calculation Policy, a copy of today’s PPT, the addition and subtraction hand-outs you have.
Refer to your child’s homework, there should always be a worked example included in the introduction, if not please do ask the class teacher for clarification if your child is unsure of the strategy they have been using in class.
Please speak to any of the maths team – we will always be happy to help – Jo Cooper, Andy Leeman, Ben Parke, Brenda Kimber

24. Props around the home
A prominent clock- digital and analogue is even better. Place it somewhere where you can talk about the time each day.
A traditional wall calendar-Calendars help with counting days, 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

25. A calculator- a basic calculator will help with maths homework when required, there are also many calculator games you can play too.
Measuring Jug-Your child will use them in school, but seeing them used in real life is invaluable. Also useful for discussing converting from metric to imperial
Dried beans, Macaroni or Smarties- for counting and estimating
A tape measure and a ruler- Let your child help when measuring up for furniture, curtains etc

26. A large bar of chocolate (one divided into chunks)- a great motivator for fractions work
Fridge magnets with numbers on- can be used for a little 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.

27. Practise Practise! Number bonds Number bonds
Children in KS1 will spend significant time learning their number bonds, first of 10 and then of all numbers to 10; and then of all numbers to 20.
e.g = 10, = 10, = 10 etc
10 – 8 = 2, 10 – 7 = 3, 10 – 4 = 6 etc
It is important they know the addition facts and the corresponding subtraction facts.
Speedy recall will really help them as they move through the school and encounter larger numbers.
Practise
Practise!

28. Any questions?