St Peter’s CofE Primary School Maths Parents’ Workshop 23rd February 2016 Aims To introduce the new Mastery approach to teaching Mathematics. To show you some of what we do at school. To provide tips and ideas for how to help your children at home.

A Mastery Level Curriculum There are three key features of the primary programme that deliver pupils with a deep understanding of mathematics. Objects and pictures: Children use concrete manipulatives (objects) and pictorial representations (pictures), before moving to abstract symbols (numbers and signs). Language development: The way that children speak and write about mathematics has been shown to have an impact on their success. Every lesson includes opportunities for children to explain or justify their mathematical reasoning. Problem solving: Mathematical problem solving is at the heart of this approach – it is both how children learn maths, and the reason why they learn maths. By accumulating knowledge of mathematics concepts, children can develop and test their problem solving in every lesson.

Mathematical Thinking Teaching for Mastery Number Facts Table Facts Making Connections Procedural Conceptual Chains of Reasoning Access Pattern Representation & Structure Mathematical Thinking Fluency Variation Coherence Small connected steps are easier to take

Use of Technology Activelearn Mathletics

Laying the foundations…… Number lines/square Practical equipment Numicon Multilink cubes Real life contexts Number bonds Patterns 1 2 3 4 5 6 7 8 9 10 11 12 13

Addition Arrow cards Place value Recombining Missing numbers Commutativity Renaming Counting on Number squares (Spider and Fly)

Beginning to use column addition step 1….. use partitioning 364+ 34 =300+60+4 +30+4 =300+90+8 Then we recombine it all, to be left with the answer, 398 step 2…… 364+54= 364 + 54 8 110 +300 418 . The final step…. when the children have a sound grasp of place value & of the whole process… 364 + 54 418 1 300 + 60 + 4 + 50 + 4 300 +110 + 8 = 418

Subtraction - KS1 use of 100 square, number line, blank number line.

Subtraction 3-2= - Taking away practically. Recognise the size and position of numbers Count back in ones and tens Know number facts for all numbers to 20 Subtract multiples of 10 from any number

Use of a number line/100 square 12-6=6 1 2 3 4 5 6 7 8 9 10 11 12 13 -

Written methods for Subtraction Stage 1: The empty number line Counting Back - a calculation like 74 - 27 can be recorded by counting back 27 from 74 to reach 47. or Counting Up - the steps can also be recorded by counting up from the smaller number to find the difference Children who have not achieved the age related expectations for Year 2 should not move onto formal written methods until they are secure with mental recall and used the dienes to see the place value of numbers. https://www.activelearnprimary.co.uk/resource/192480

Written methods for Subtraction Stage 2: Partitioning to write use facts so that calculations that are easier to carry out mentally. For 74 - 27 partitioning 27 into 20 and 7, then subtract 20 then 7. 74 – 20 – 7 74 – 20 = 54 54 – 7 = 47 It can be applied to 3 digit 741 - 367 Stage 3: Expanded column method The partitioning stage should be followed by the expanded column method, where tens and units are placed under each other. This is where the concept of ‘borrowing’ is introduced Depending on the numbers it can get quite complicated and this stage may need a lot of time and perseverance!

Written methods for Subtraction Stage 4: Column method The expanded method is eventually reduced to:

Multiplication x

Multiplication- repeated addition 3x5= (3 groups of 5) xx x xx x xx x x Start by drawing the groups, then just the numbers. 5 + 5 + 5= 15

Arrays Children should be able to model a multiplication calculation using an array. This knowledge will support with the development of the grid method. 3 x 5 5 x 3

Times tables By end of Year 2 children should know x2,x5,x10 Plus ????? Practise counting in 2s, 3s, 4s, 5s, 10s Matching pairs (question on one card, answer on another) By the end of year 4 – all times tables!

Written methods for Multiplication Stage 1: Mental multiplication using partitioning allows the tens and ones to be multiplied separately to form partial products. These are then added to find the total product. 14 x 3 = 43 x 6 =

Written methods for Multiplication Stage 2: The Grid Method This links directly to the mental method. It is an alternative way of recording the same steps. It is better to place the number with the most digits in the left-hand column of the grid so that it is easier to add the partial products. For TU x TU, the partial products in each row are added, and then the two sums at the end of each row are added to find the total product

Written methods for Multiplication Stage 3: Expanded short multiplication The next step is to represent the method in a column format, but showing the working. - link with the grid method. 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 ’30 x 7’ not ‘3 x 7’, although the relationship 3 × 7 should be stressed. Some children should be able to use this method by the end of Year 5. 30 + 8 38 x7 x 7 56 (8 x 7) 56 210 (30 x 7) 210 266 266 TU x TU. 56 x 27 42 (6 x 7) 350 (50 x 7) 120 (6 x 20) 1000 (50 x 20) 1512 1

Written methods for Multiplication Stage 4: Short multiplication The expanded method is eventually reduced to the standard method for short multiplication, with carry digits recorded below the line. If, after practice, children cannot use the compact method without error, they should return to the expanded stage 3. The step here involves adding 210 and 50 mentally with only the 5 in the 50 recorded. They need to be able to add a multiple of 10 to a two-digit or three-digit number mentally before this stage Stage 5: Long multiplication This is applied to TU x TU as follows. 56 x 27 392 1120 1512 1 The carry digits in the partial products of 56 × 20 = 120 and 56 × 7 = 392 are usually carried mentally. The aim is for some children to use this long multiplication method for TU × TU by the end of Year 6.

Written methods for Multiplication In Year 6, children apply the same steps to multiply HTU x TU 286 x 29 8294 1 This expanded method is cumbersome, so there is plenty of incentive to move on to a more efficient method. Start with the grid method, asking the children to estimate their answer first. Children who are already secure with multiplication for TU × U and TU × TU should have little difficulty in using the same method for HTU × TU.

÷ Division

Written methods for Division Initially division is introduced as ‘sharing’ using real objects or pictures. Share 10 apples equally between 2 children which eventually becomes 10 ÷ 2 = 5

Written methods for Division There is a strong link with multiplication, with questions such as How many groups of 4 can be made with 12 stars? How many 5s are in 15? Children need to understand grouping and sharing; I have 10 cubes, can you share them equally in 2 groups? I have 10 cubes, how many groups of 2 can you make?

Written methods for Division Children also need to see the link with doubling and halving; understanding that dividing by 10 is the same as halving and dividing by 4 (or finding a quarter of something) is halving twice. Arrays can be used as physical equipment and also link to the idea of repeated subtraction; 3 6 9 12 12 ÷ 3 = 4 and 12 ÷ 4 = 3

Written methods for Division Stage 1: Mental division using partitioning One way to work out TU ÷ U mentally is to partition TU into smaller multiples of the divisor, then divide each part separately. Informal recording in Year 4 for 84 ÷ 7 might be: In this example, using knowledge of multiples, the 84 is partitioned into 70 (most children will be secure with a multiple of 10) plus 14

Written methods for Division Stage 1: Mental division using partitioning and with a remainder

Stage 2 ‘Chunking’ WDIK 10 x 4 20 x 4 30 x 4 etc

Written methods for Division Stage 2: 'Expanded' method for TU ÷ U and HTU ÷ U This method, often referred to as 'chunking', is based on subtracting multiples of the divisor, or 'chunks'. It is useful for reminding children of the link between division and repeated subtraction. However, children need to recognise that chunking is inefficient if too many subtractions have to be carried out.

Written methods for Division Stage 3: Refining the 'Expanded' method for HTU ÷ U Initially children subtract several chunks, but with practice they should look for the biggest multiples that they can find to subtract, to reduce the number of steps. Once they understand and can apply the expanded method, children should try the standard method for short division.

Written methods for Division Stage 4: 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.

Any Questions? Please take a copy of our calculation policy with you. Please leave any feedback on the post-it notes provided on the tables. Please make sure you have added your name to the register by the door.

Thank you and Goodbye!