Shall I use a pencil and paper method? Goytre Fawr Primary School Parents Meeting on: Progression through Calculations 6th March 2013 Shall I use a pencil and paper method? Do I need jottings ? Can I do it in my head? Do I need to use a calculator?

DfEE 1999 (14 years ago!) ‘Parents who are confident about maths tend to have children who are also confident, and these children are ready to tackle and assimilate new ideas in a way that is impossible for children who feel uncertain about, or even fear, maths.’

Aims To look at the ways in which the teaching of mathematics has developed; To look at how children calculate; Try activities to develop calculation strategies; To look at ways in which parents can help their children

Sound familiar… When I was at school I remember the few occasions that the teacher stood at the front of the class and did some maths teaching, it involved teaching rules of how we do things. For example: long multiplication. We didn't question and often we didn't understand why we were "carrying ten" or "borrowing one". The rest of the time I was taught Maths through a text book and would line up at the teacher’s desk to get my work marked once I had finished. Activities like this were probably okay for the children who ‘got’ maths, but not for those who struggled or were uninspired by the work on offer.

How has mathematics changed? Daily mathematics lesson; Emphasis on mental calculations; Interactive whole class and group teaching; Enjoyable practical approaches; Mathematics with understanding

Overview Up to Year 3 the emphasis is on: working mentally, calculations recorded in horizontal number sentences some jottings for more challenging numbers Models and Images In Year 3-6 children will be gradually taught more formal written methods of calculation but they will still use mental methods and jottings where appropriate.

So - how can we give children the best foundations for success with written calculations? We need to encourage children to use mental calculation strategies for smaller/ simpler numbers. We need to encourage children to ask the question “Can I do it in my head?” or “Can I do it in my head with jottings/ a number line?”

4 Calculation areas Addition Subtraction Multiplication Division A S M

Bead bars to Empty Number Lines

Addition- Progression Mental calculation supported by: Modelling of method by teacher Jottings Number lines Expanded method using partitioning Compact ‘carrying’ method Demonstrate modelling use of number line Refer to expanded method in framework

Jottings Children are encouraged to develop a mental picture of the number system in their heads to use for calculation. They develop ways of recording calculations using pictures, etc.

The first stage in written addition Count all – a child doing 3 + 5 counts out three counters and then five counters and then finds the total by counting all the counters.

Counting on from the first number – a child finding 3 + 5 counts on from the first number: ‘four, five, six, seven, eight’.

Counting on from the larger number : 3 + 5 A child chooses the larger number, even when it is not the first number, and counts on from there: 'six, seven, eight' As well as children using their fingers or bead strings to add on small amounts, a number line will be introduced. It is more efficient to count on from the larger number because you have less to work out. It also shows children that addition can be done in any order ; it doesn’t matter which number you add first, you get the same answer.

_________________________________ Number lines Frequently used in each year group and provide children with a very visual method of calculation 15 + 8 = 29 + 23 = _________________________________ Can you get from a starting number to 100 in 3 hops? 27 + ? = 100 48 + ? = 100 2 + ? = 100 _________________________________100 Talk through the diagram. AIM- self sustaining systems for school improvement which would link to other systems used by the school.

Mental Method (using partitioning)   47 + 76 = (40 + 70) + (7 + 6) = 110 + 13 = 123 Use an expanded layout: 47 +76 13 (7+6) 110 (40+70) 123

Standard Method Column Addition The final step, when the children have a sound grasp of place value & of the whole process… 364 + 54 418 1

Subtraction - Progression Mental calculations supported by: Modelling of method by teacher Jottings Number line Expanded method Compact written method Refer to expanded method in framework, demo this using Base 10 apparatus/ arrow cards

Subtraction in the Foundation Phase Children develop ways of recording calculations using pictures etc. 19

Counting on – finding a difference 10 and 4 less With subtraction calculations we are careful not to over use the vocabulary of ‘taking away’ because some subtraction calculations involve ‘finding the difference’. We use the word ‘subtract’. Counting on – finding a difference Max has 5 cubes. Milly has 2 cubes. How many more cubes does Max have? How many less/fewer cubes does Milly have? What is the difference between?

Subtraction Using a Number line for Subtraction Step 1: Counting Back 78 – 12 -10 -2 66 68 78 Step 2:Counting on to find the Difference 74 – 57 +10 +3 +4 57 67 70 74

Expanded method to compact … Partitioning and decomposition 89 = 80 + 9 - 57 50 + 7 30 + 2 = 32 Initially, the children will be taught using examples that do not need the children to exchange (what you might know as borrowing). From this the children will begin to exchange. The calculation should be read as e.g. take 6 from 1.   71 = this leads to… - 46 Step 1 70 + 1 71 - 40 + 6 - 46   25 Step 2 60 70 + 11 - 40 + 6 20 + 5 = 25 Children should know that units line up under units, tens under tens, and so on. 1 6

Multiplication - Progression Mental calculation supported by: Jottings Number lines Modelling of method by teacher Understanding of multiplication as: an array repeated addition scaling Grid method Demo use of number lines with equal jumps to support in mental and oral and develop understanding Arrays on egg boxes, bun tins etc. ITP Demo grid method, have a go, discuss when introduced for policy. Discuss do ch move onto traditional compact method, stress benefits of grid method for long multiplication and the fact that ch can continue with this into Y7

Multiplication Children will experience equal groups of objects and will begin to count in 2s, 10s and 5s. They will work on practical problem solving activities involving equal sets or groups.

Show on bead bar or on a number line: 3 x 5 = 5 + 5 + 5   3 x 5 = 5 + 5 + 5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Children need to learn through practise that multiplication can be done in any order. For example: 3 x 5 = 15 and 5x3 = 15

Using Arrays   Children should be able to model a multiplication calculation using an array. 3 x 5 = 15 5 x 3 = 15

Grid method of multiplication X 70 2 30 2100 60 8 560 16 38 x 72 2160 + 576 2736

Division - Progression Mental calculations supported by: Jottings Number lines Modelling of method by teacher Understanding division as sharing and grouping. Chunking Demo ITPs,

Early Division Children will understand equal groups and share items out in play and problem solving. They will count in 2s and 10s and later in 5s.

12 ÷ 3 = 4 3 3 3 3 Grouping or repeated subtraction There are 6 sweets, how many people can have 2 sweets each? Repeated subtraction using a number line or bead bar 12 ÷ 3 = 4 3 3 3 3 0 1 2 3 4 5 6 7 8 9 10 11 12

Number line division 72 ÷ 6 = 12 0 60 72 (10 x 6) (2 x 6)

Chunking Division is repeated subtraction. Chunking uses knowledge of times tables to take away ‘chunks’ from a number. 427 ÷ 7 = 61 427 - 210 (30) 217 7 - 7 (1)

Step 3: Standard Method 22 1 1 6 1 3 2 Children would be encouraged to check division calculations by using the inverse operation eg 22 x 6 = 132 (20 x 6 = 120 2 x 6 = 12 120 + 12 = 132

How to help your child with mathematics

Parents can help by … Counting with your child Playing number games Involve your child in shopping activities Involve your child when taking measurements or weighing items Take note of numbers in real life e.g. telephone numbers, bus numbers, lottery numbers etc Give your child opportunities to use money to shop, check change etc Talking about the mathematics in football e.g.. How many points does your favourite team need to catch the next team in the division? When helping your child calculate, use the method that they have been taught at school.

Thanks for attending tonight’s Mathematics Evening