St David’s C of E Primary School Parents’ Mathematics Workshop Thursday 23rd April 2015

An answer given on a SATs paper!

So what do we hope to achieve this afternoon? For you to become more familiar with calculation strategies we teach the children in Mathematics To know some of the mathematical language we expect children to learn To point you towards our Maths Page on the school website

A little warm-up How would you calculate these “sums”? Feel free to discuss with the person next to you and jot down your calculations. 43 + 24 3 + 2 4627 + 2518 98 + 45 345 + 208 17 + 44 48.367 + 2.59 Please hand your answers to Mrs Brinnicombe and we will mark them – scores will be given at the end of the workshop.

There are many ways that calculations can be performed Our aim is for children to complete calculations in the most efficient manner for their stage of development. They need to be able to choose appropriate strategies and then record them in a way that is clear, they can understand them and minimises errors.

Let’s now consider the progression in Addition Early Years 4 + 3 =

At this stage they will learn you can add numbers in any order. Early Years (cont) Children will learn to bridge through ten 8 + 5 = 8 + 2 + 3 Bridging through tens, hundreds and thousands takes alot of understanding conceptually!! Moving onto 14 + 5 or 7 + 12 or 3 + 4 + 2 At this stage they will learn you can add numbers in any order.

Early Years By the end of Year 1 children will be expected to: count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number given a number, identify one more and one less Addition and subtraction read, write and interpret mathematical statements involving addition (+), subtraction (–) and equals (=) signs represent and use number bonds and related subtraction facts within 20 add and subtract one-digit and two-digit numbers to 20, including zero solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = –9

Number-lines are a key part of their learning Year 2 Children will move to calculating addition of numbers to 100 34 + 23 – start with the larger number Number-lines are a key part of their learning We now tend not to split both numbers into 30 + 20 and 4 + 3 – This comes later when moving into column methods

Year 2 Bridging through ten can help children become more efficient.

Year 2 recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100 add and subtract numbers using concrete objects, pictorial representations, and mentally, including: – a two-digit number and ones – a two-digit number and tens – two two-digit numbers – adding three one-digit numbers show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems

Year 3 86 + 38 Further use of the number line

Year 3 67 = 60 + 7 +24 20 + 4 91 = 80 + 11 243 = 200 + 40 + 3 +435 400 + 30 + 5 678 = 600 + 70 + 8 Here the children need to be familiar with 80 + 11 = 80 + 10 +1 Bridging the tens and hundreds!!

Year 3 By the end of Year 3 add and subtract numbers mentally, including: – a three-digit number and ones – a three-digit number and tens – a three-digit number and hundreds add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction estimate the answer to a calculation and use inverse operations to check answers

Expanded Column Method Year 4 Expanded Column Method 67 = 60 + 7 2000 +300 +20 +7 +24 20 + 4 +500 +40 +2 91 = 80 + 11 2000 +800 +60 +9 = 2869

Year 4 625 + 324 900 40 9 949 2327 + 542 2000 800 60 2869

Year 4 – Compact Column Method

Year 5 Number lines using efficient counting on 4526ml + 3807ml = 8333ml = 8.333 litres + 1000 + 1000 + 1000 + 500 + 300 + 4 +3 4526 5526 6526 7526 8026 8326 8330 8333 ml 4526ml + 3000ml + 800ml + 7 ml

Compensation when adding Year 5 Compensation when adding £4.95 + £9.14 = £5.00 – 5p + £9 + 14p =

Year 6 Consolidating and applying all of these strategies when solving numerical and word problems.

The vocabulary used throughout Addition Sum Total Plus How much all together + More

Another test!! How do you calculate these? 54 – 49 4003 – 2998 11 – 2 54 – 49 4003 – 2998 11 – 2 7383 – 5728 £15 - £13.98

A Look at Subtraction Subtraction is taught hand in hand with Addition so that the children see the connections E.g 4 + 5 = 9 9 – 4 = 5 9 – 5 = 4 5 + 4 = 9

Is this addition or subtraction? If I have collected 35 stickers out of 50 in total. How many more stickers do I need to collect? Is it? 50 – 35 = Or 35 + ____ = 50

Early Years There are 8 biscuits on a plate. Take 3 of them to eat. How many are left on the plate? -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 10 9 8 7 6 5 4 3 2 1 0 6 – 2 = 4

Are we super reliant on games on computers and tablets? Playing Games An essential part of children’s early years experience of number and calculating. Shut the Box + Any other dice and card games What games do you have or have you had? Are we super reliant on games on computers and tablets?

Early Years How many more green cubes than red cubes? What is the difference between 8 and 4?

Early Years 8 – 3 =

Year 2 Counting back across the tens boundary

Children need to see how counting on can be more efficient. Year 2 Children need to see how counting on can be more efficient. Compensating Children need to see that when subtracting 9 we can subtract 10 and add 1 back on.

Year 3 147 - 63

Year 3 / 4 -24 = 20 + 4 43 = 40 + 3 And then into 164 = 100 + 60 + 4 Expanded informal method using place value 67 = 60 + 7 -24 = 20 + 4 43 = 40 + 3 And then into 164 = 100 + 60 + 4 - 47 = 40 + 7 = 100 + 10 + 7 50 14

Year 4

Using Base 10 to reinforce this understanding is essential Year 4 / 5 Using Base 10 to reinforce this understanding is essential

Year 5 1209 – 388 Children must be secure with number-lines

Year 6 Decomposition – Only when confident with the expanded column subtraction 3 12 2 16 3000 1200 20 16 4 2 3 6 4000 200 30 6 -2 8 2 7 - 2000 800 20 7 1 4 0 9 1000 400 0 9

Year 6 Negative column subtraction (optional) Then it is all about applying these skills to numerical and word problems

A Little Trick – The power of nines Think of a three digit number where the first and third digits are different.

A brief look at multiplication 3 x 5 = 15 5 x 3 = 15 15 ÷ 3 = 5 15 ÷ 5 = 3 6 x 10 = 60 6 x 8 = 48 60 + 48 = 108 6 x 10 = 60 6 x 8 = 48

A Final look at arrays 16 x 12 X 10 6 10 100 60 2 20 12

Children need to know their multiplication facts Division Basically children are taught division through sharing and grouping through practical examples. They will cover remainders in practical situations They will end up with the good old bus-stop method and with all the stages in between. Children need to know their multiplication facts

And finally Our calculation Policy is on the School Website in a tab marked Maths We use Sumdog with the children and they all now have a log-in – We need to familiarise Ruby and Emerald class with theirs and demonstrate it to them. – The children love it!