Welcome to our Parents Maths Workshop Primary School 23rd October 2017

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

Programme Introduction to changes in Mathematics How parents can support Maths at home MyMaths – online homework Opportunity to listen to Key Stage specific information: Miss Hargreaves – Early Years Mrs McGuinnes – Years 1,2,3 Mr Hall – Years 4,5,6

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

Shall I use a pencil and paper method? Calculations Shall I use a pencil and paper method? Do I need jottings ? Can I do it in my head? The aim is that children will always be able to recognise when calculations can be done ‘ in their heads’ and choose effective and efficient strategies to work out the answers.

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.

Key Messages To develop written calculation strategies, children need: Secure mental strategies from YR. A solid understanding of the number system. Practical, hands on experience including counters and base 10 apparatus. Visual images including number lines and arrays. Experience of expanded methods to develop understanding and avoid rote learning. Secure understanding of each stage before moving onto the next. The questions at the forefront of their minds: ‘Can I do it in my head? If not which method will help me?’

How to help your child with mathematics!

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

Visual maths Number lines Noticing numbers 1 6 2 5 3 4 23

Rhymes/songs 5 little speckled frogs; 10 huge dinosaurs (bottles); 1, 2, 3, 4, 5 once I caught a fish alive;

Sorting Socks Cars Shoes

Measures Keep a record of your child's growth; Scales and balances eg see-saws Capacity – different containers to play with in the sink or bath;

Shape and space square oblong triangle circle Recognising shapes around them eg doors, windows, cans, boxes etc Construction sets, Lego, Shapes of cakes, biscuits, sandwiches. oblong triangle circle

MyMaths Homework set from Year 2/3 Online maths activities Results and attempts logged and accessible by teachers for analysis.

Key Stage 2 Written calculations and methods from Year 3 - 6

Laying the foundations…… Number lines. Practical equipment Multilink cubes Real life contexts. Number bonds Patterns

Jottings

Partitioning…….. Arrow cards Place value Partitioning Recombining

Stage 1: Mental method using partitioning:   47 + 76 = (40 + 70) + (7 + 6) = 110 + 13 = 123 Stage 2/3: Use an expanded layout 47 + 76 13 110 123

Beginning to use column addition, step 1….. Continue to use partitioning 364+ 34 =300+60+4+30+4 =300+90+8 Then we recombine it all, to be left with the answer, 398.

Using column addition, step 2…… Continue to use partitioning. 364+54= 364 + 54 8 110 + 300 418

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

Common calculation errors! 99 158 +101 + 184 1901 612 4 1 9 add 10 =19 The 4 has been carried rather than the TEN

Vocabulary. Add Plus Altogether Addition Total Count on

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

78 – 12? How do you work out…. 74 – 57?

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

Stage 1: Mental method using partitioning.   76 – 32 = (70 – 30) + (6– 2) = 44 Stage 2: Expanded vertical layout Stage 3: Compact decomposition Ongoing methods: mental methods and subtraction using a number line

Stage 2: Expanded vertical layout 89 = 80 + 9 - 57 50 + 7 30 + 2 = 32 Stage 2: Expanded vertical layout

Stage 3: Compact decomposition 5 13 1 6467 - 2684 3783

Subtraction Vocabulary Take (away) How many are left? How many have gone? 1 less Difference between How many fewer is ... than ... Leave 10 less How many are left over?

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

Using multiplication facts ·It is vital that children know their times tables as all the work higher up the school relies on them knowing their tables. ·Tables should be learned at least 2-3 times a week. What is expected Year 2 2 times table 5 times table 10 times table Year 3 2 times table 3 times table 4 times table 6 times table Year 4 Derive and recall all multiplication facts up to 10 x 10 (5 second recall) Years 5 & 6 Derive and recall quickly all multiplication facts up to 10 x 10 (3 second recall) Use table knowledge in all aspects of Mathematics – ratio, fractions, decimals, percentages etc.

Children will develop their understanding of multiplication and use jottings to support calculation: Repeated addition 3 times 5 is 5 + 5 + 5 = 15 or 3 lots of 5 or 5 x 3 Repeated addition can be shown easily on a number line: 5 x 3 = 5 + 5 + 5 5 5 5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 and on a bead bar: 5 x 3 = 5 + 5 + 5 5 5 5

Using a number line

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

Grid method of multiplication 10 3 60 18 60 + 18 = 78 6 so 6 x 13 = 78

TU x TU (Short multiplication - multiplication by more than a single digit) 72 x 38 X 70 2 30 2100 60 8 560 16 2100 + 560 + 60 + 1 6 2736 HTU x TU (Short multiplication - multiplication by more than a single digit) 6000 372 x 24 X 300 70 2 20 6000 1400 40 4 1200 280 8 + 1400 + 1200 + 280 + 40 + 8 8928

HTU x TU (Standard Method for long multiplication) 372 x 24 372 24 372 x 24 8 1488 280 7440 1200 8928 8928 40 1400 6000 8928

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

Using a number line Ensure that the emphasis in Y3 is on grouping rather than sharing. Children will continue to use: repeated subtraction using a number line an empty number line to support their calculation. e.g. 24 ÷ 4 = 6 Children should also move onto calculations involving remainders. e.g. 13 ÷ 4 = 3 r 1

Sharing equally 6 sweets are shared between 2 people Sharing equally 6 sweets are shared between 2 people. How many do they each receive?

6 sweets shared between two people equals 3 Three! 6 sweets shared between two people equals 3

This child has used a strategy of grouping tallies to find the answer. This child has used a strategy of counting equal groups to find the answer.

Then, move on to…… Chunking

Stage 1: Short division. i.e. TU ÷ U, HTU ÷ U Known as the ‘chunking’ method.   6 72 - 60 x 10 12 - 6 x 1 6 Answer = 12 9 97 - 90 x 10 7 Answer = 10 r 7

Stage 3 Long division (HTU ÷ TU)   15 432 15 432 - 150 x 10 - 300 x 20 282 132 - 150 x 10 - 120 x 8 132 12 - 60 x 4 72 Answer = 28 r 12 12 Answer = 28 r 12

This moves on to the standard method, once a child is confident with the process of division. 12 712 This can be expanded for long division involving HTU ÷ TU