Calculation 12th October 2017 Maths KS2 Calculation 12th October 2017

Welcome to the KS2 Maths Workshop on Calculation Have a go at the Key Stage 2 Maths Quiz and fill in the first part of the evaluation

Aims of the Session Enjoy maths and play around with numbers. Learn a little about how we teach maths across KS2. Learn how we teach: Addition Subtraction Multiplication Division

Maths in KS2 at Applecroft School Fun and something to be played with Relevant to everyday life and especially the children’s everyday life. Involves practical and oral/mental work as well as ‘traditional’ book work. Taught once a day for between60 minute sessions Contained within a 3 part lesson : Oral/mental starter Main activity Plenary Is supported by numerous additional sessions for booster and enhancement. Challenging.

Mentally or pen and paper? Mental calculations – the children are encouraged to ask the question ‘Can I do this in my head?’ If not they are encouraged to do informal jottings and then formal written calculations when necessary. If a baby was born in 1998 how old were they in 2001? or 2001 1998

Mental Calculation The ability to calculate mentally forms the basis of all methods of calculation. This involves instant recall of number facts (+ - x ÷) having a secure understanding of place value and the number system having a range of strategies to apply to a calculation understand the language and rules of maths

Resources Number line Counters Unifix cubes Number square Place value cards Dienne rods

Written Calculation Throughout their primary years, children should progress from informal jottings to efficient written methods for each of the four operations. Standard written methods should only be introduced when a child has a secure knowledge and understanding of the process involved and can clearly explain the strategies they have used. Children become secure with these methods when they have regular practice and persevere!

It is ok to make mistakes – this is part of learning!

Addition

Addition Written calculations: Models & images: Mental calculations:

Now, have a go at this question on your whiteboards using one of the methods here, then try a different method: 128 + 76 =

Informal jottings 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:

Addition continued Expanded written form Partition and recombine 122 + 236 = 100+200 =300 20 + 30 = 50 2 + 6 = 8 300 + 50 + 8 = 358

Column method- standard written form t o h t o o.1/10 6 7 1 5 6 3.6 + 2 5 + 7 5 + 1.6 9 2 2 3 1 5.2 1 1 1 1

Have a go The empty number line Partitioning and recombining The Column Method On-line resources to support the learning in school - espresso

Subtraction

Subtraction Written calculations: Models & images: Mental calculations:

Now, have a go at this question on your whiteboards using one of the methods here, then try a different method: 68 - 27 =

Practical Subtraction Taking away using different objects and materials Counting back on number tracks Use resources to understand relationship between addition and subtraction

Subtraction

Subtraction

And finally

Have a go Number Line Decomposition

Multiplication

Understanding number Number bonds are the window to success in KS2 and it is vital that your child knows these securely as they enter this phase. By the end of Year 4, your child is expected to know all their times tables up to 12 x 12. To ensure this, we practise the tables daily and explore connections between the tables, e.g. to find 6 x 8, we know 5 x 8 is 40, so 6 x 8 is one more 8, so is 48.

Multiplication Times tables are key. Related facts 5 x 6 = 30 50 x 6 = 300 Arrays (knowing 3 x 4= 4 x 3) 15 x 5= (partitioning) Repeated addition.

Multiplication Written calculations: Models & images: Mental calculations:

The Grid method This can then be developed into traditional long multiplication when the children are confident in how and why it works.

Written methods for Multiplication 38 X 7 56 8 x 7 210 30 x 7 266 38 X 7 266 5 When they are ready The next step is to represent the method in a column format, but showing the working. Attention should be drawn to the links with the grid method above. Children should describe what they do by referring to the actual values of the digits in the columns. For example, the first step in 38 × 7 is ‘thirty multiplied by seven’, not ‘three times seven’, although the relationship 3 × 7 should be stressed.

Have a go The Grid Method Column Napiers!

Division

Last but not least…… ……the one most children dread! Many children can partition and multiply with confidence. But this is not the case for division. One reason for this may be that mental methods of division, stressing the correspondence to mental methods of multiplication, have not in the past been given enough attention. The aim is that children use mental methods when appropriate, but for calculations that they cannot do in their heads they use an efficient written method accurately and with confidence. The stages building up to long division span Years 4 to 6 - first introducing TO ÷ O, then extending to HTO ÷ O, and finally HTO ÷ TO.

Language of Division Sharing Grouping How many lots of (how many times) Chunking Remainder (left over) Divisor

Division Written calculations: Models & images: Mental calculations:

Division Chunking

Division Bus stop Short division

Long division- It’s back! Long division for HTU ÷ TU The next step is to tackle HTU ÷ TU, which for most children will be in Year 6. The layout on the right, which links to chunking, is in essence the 'long division' method. Conventionally the 20, or 2 tens, and the 3 ones forming the answer are recorded above the line, as in the second recording.

Now, have a go at this question on your whiteboards using one of the methods here, then try a different method: 853 ÷ 5 =

Maths Dos and Don’ts Do Play maths- make it fun Make maths a casual part of things you are doing. Lots of hands on maths. Recognise there is more than one way to solve a calculation. Don’t Be afraid to show them different ways. Expect them to get it after you have explained it once! Tell them you are hopeless at maths!