…… Primary School Parents Meeting on: Progression through Calculations Can I do it in my head? Do I need jottings ? Do I need to use a calculator? Shall.

…… …… Primary SchoolPrimary School Parents Meeting on:Parents Meeting on:Progression through Progression through

CalculationsCalculations

Can I do it in my head?

Do I need

jottings ?

Do I need to use a

calculator?

Shall I use a pencil and

paper method?

Starter Starter (use a calculator!)(use a calculator!)

• Think of a number between 1 and 9• Multiply by 2 (x 2) • Add 5 (+5)• Multiply by 50 (x50)• If you have had your birthday this

year add 1 760. If not add 1759.• Subtract the year of your birth.

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

How has mathematics How has mathematics changed?changed?

• Daily mathematics lesson;• Emphasis on mental calculations;• Interactive whole class and group

teaching;• Enjoyable practical approaches;• Mathematics with understanding

CalculationsWays to help children to remember…• Practice with just one fact a day, or try a ‘fact of

the week’• Practice ‘fact families’, e.g. 6+8=14, 8+6+14,

14-6=8, 14-8=6• Work from answers back to facts – how many

facts do you know with an answer of 12?• Make an addition or multiplication table and cross

out all those facts you already know. Now focus on those you need to learn.

• Encourage children to work out their own ways to remember facts

• Draw pictures to accompany particular facts.• Repeat it and repeat it!

Skills of mental calculation

• Remembering number facts and recalling them without hesitation.

• Using facts that are known by heart to figure out new facts.

• Applying understanding of place value and ability to partition numbers into parts

• Understanding and using the laws of arithmetic and relationships between the four operations to find answers and check results

• Having a repertoire of mental strategies to do calculations with some thinking time

• Solving word problems

Mental gymnastics

• Think of a number and keep doubling it. How far can you go?

• Face the person next to you and alternate!• In two’s – one person recites all the

numbers from 1 to 100• The other person raises their hand at any

number that can be divided by 3 or …• Divided by 4 or …• Divided by 3 and 4 or …• Divided by 5You can use your number square to help you!

Mental calculations

Children are encouraged to count in different ways and to calculate mentally.

Number lines – Bead bar / number stick / individual number lines / Number ladders

Calculations

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:o working mentally, o calculations recorded in horizontal number

sentenceso some jottings for more challenging numberso Models and Images

In Year 3-6 children will be gradually taught moreformal written methods of calculation butthey will still use mental methods and jottingswhere appropriate.

Developing children’s mental Developing children’s mental picture of number systempicture of number system

o DEMONSTRATE on a number line children’s DEMONSTRATE on a number line children’s response to a calculation.response to a calculation.

o DISPLAY number lines and washing lines DISPLAY number lines and washing lines around the room for the children to access.around the room for the children to access.

o MODEL the use of number lines and tracks MODEL the use of number lines and tracks to aid calculation from YR and empty to aid calculation from YR and empty number lines from Y2number lines from Y2

o CONTINUE to demonstrate, display and CONTINUE to demonstrate, display and model use of a number line all the way to model use of a number line all the way to Y6!Y6!

Early RecordingEarly Recording

So - how can we give children So - how can we give children the best foundations for the best foundations for

success with written success with written calculations?calculations?

o We need to encourage children to useWe need to encourage children to use mental calculation strategies formental calculation strategies for smaller/ simpler numbers.smaller/ simpler numbers.

o We need to encourage children toWe need to encourage children to ask the question “Can I do it in my ask the question “Can I do it in my head?” or “Can I do it in my head with head?” or “Can I do it in my head with jottings/ a number line?”jottings/ a number line?”

Laying the foundations for Laying the foundations for addition and subtractionaddition and subtraction

o PartitioningPartitioning

o RoundingRounding

o CompensatingCompensating

o Counting onCounting on

o Bridging through 10s, 100s, 1000s boundariesBridging through 10s, 100s, 1000s boundaries

o Addition and subtraction factsAddition and subtraction facts

Laying the foundations for Laying the foundations for multiplication and divisionmultiplication and division

o Doubling/ HalvingDoubling/ Halving

o Grouping/ equal groups/ equal jumpsGrouping/ equal groups/ equal jumps

o Repeated addition/ subtractionRepeated addition/ subtraction

o ArraysArrays

o Multiplication and division factsMultiplication and division facts

Multiply• Slap, clap, click (not as violent as it sounds!)

• ‘Show me’ –

1.The product of a multiplication

2.A multiple of 2, 3, 5, 10, 4, etc

3.A number that is exactly divisible by 3, 5, 2, 10, 4, etc

4.A common multiple of 2 and 3, 3 and 5, 3 and 10

1.In groups have a go at ‘Hot Seat’

You can use your number square or calculator to help

Common calculation errors!Common calculation errors!

99 158+101 + 1841901 612 4 1

945 1 1 1

- 237 2000 712 - 108 902

Dartboard Activity

Rules: You have 3 darts. You can hit the same section of the board more than once, but all three must score. Show how you could score each of these totals.

Demonstrate the first oneWork with a partnerDo you always make the totals in the

same way?How might you differentiate this game?

Addition- ProgressionAddition- Progression

o Mental calculation supported by:Mental calculation supported by: Modelling of method by teacher Modelling of method by teacher JottingsJottings Number linesNumber lines

o Expanded method using partitioningExpanded method using partitioning

o Compact ‘carrying’ methodCompact ‘carrying’ method

JottingsJottings

When do children still use When do children still use jottings/ number lines??jottings/ number lines??

• When they can calculate mentally When they can calculate mentally and need a little support.and need a little support.

• When they are not completely secure When they are not completely secure with ‘carrying’.with ‘carrying’.

• When they are dealing with addition When they are dealing with addition of decimals, negative numbers, time, of decimals, negative numbers, time, measurement scales, etc.measurement scales, etc.

• Stage 1: Mental method using partitioning:

  47 + 76 = (40 + 70) + (7 + 6) = 110 + 13 = 123

• Stage 2/3: Use an expanded layout

47 47

+ 76 + 76 110 13

13 110 123 123

Subtraction - ProgressionSubtraction - Progression

• Mental calculations supported by:Mental calculations supported by:

Modelling of method by teacherModelling of method by teacher

JottingsJottings

Number lineNumber line

• Expanded decomposition using Expanded decomposition using partitioningpartitioning

• Compact decompositionCompact decomposition

78 – 12?

74 – 57?

How do you work

out….

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

When do children still use When do children still use jottings/ number lines??jottings/ number lines??

o When they can calculate mentally and need a When they can calculate mentally and need a little support.little support.

o When they are calculating the difference between When they are calculating the difference between two numbers relatively close together.two numbers relatively close together.

o When not completely secure with decompositionWhen not completely secure with decomposition

o When calculating with decimals.When calculating with decimals.

o When decomposition is made difficult by ‘trapped When decomposition is made difficult by ‘trapped zeroes’.zeroes’.

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 andsubtraction using a number line

Multiplication - ProgressionMultiplication - Progression

o Mental calculation supported by:Mental calculation supported by: JottingsJottings Number linesNumber lines Modelling of method by teacherModelling of method by teacher

o Understanding of multiplication as:Understanding of multiplication as: an arrayan array repeated additionrepeated addition scalingscaling

o Grid methodGrid methodMultiplication facts ITP

Multiplication Facts ITP

Using a number lineUsing a number line

0 1 2 3 4 5 6 7 8 9 10

0 6 12 18 24 30 36 42 48 54 60

1010 33

66 18186060 60 + 18 = 60 + 18 = 7878

so 6 x 13 = so 6 x 13 = 7878

Grid ITP

Grid method of Grid method of multiplicationmultiplication

Division - ProgressionDivision - Progression

o Mental calculations supported by:Mental calculations supported by: JottingsJottings Number linesNumber lines Modelling of method by teacherModelling of method by teacher

o Understanding division as sharing and grouping.Understanding division as sharing and grouping.

o Visualising division using:Visualising division using: arraysarrays repeated subtractionrepeated subtraction

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.

Table Trios and Multiplication Clocks!

Division - ProgressionDivision - Progression

ChunkingChunking

Step 1:Step 1:Demonstrate practically by repeatedly subtracting Demonstrate practically by repeatedly subtracting

groups of objects and keeping countgroups of objects and keeping count

Step 2:Step 2:Model on a number lineModel on a number line

Step 3:Step 3:Model vertical method Model vertical method

•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 - 6 x 1 0 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 - 60 x 4 12 Answer = 28 r 12

How to help your child with How to help your child with mathematics!mathematics!

Visual mathsVisual maths

• Number lines

• Noticing numbers

12 3 4 5

6

23

Rhymes/songsRhymes/songs

• 5 little speckled frogs;

• 10 huge dinosaurs (bottles);

• 1, 2, 3, 4, 5 once I caught a fish alive;

SortingSorting

• Socks

• Cars

• Shoes

MeasuresMeasures

• Keep a record of your child's growth;• Scales and balances e.g. see-saws• Capacity – different containers to

play with in the sink or bath;

Rectangle

Spot the Shape 1 and 2

Shape and spaceShape and space

• Recognising shapes around them e.g. doors, windows, cans, boxes etc

• Construction sets, Lego,• Shapes of cakes, biscuits,

sandwiches.

How can parents help?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 e.g. telephone numbers, bus numbers, lottery numbers etc• Give children 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 their children calculate use the method that they have been taught.

Key MessagesKey MessagesTo develop written calculation strategies, children need:To develop written calculation strategies, children need:

o Secure mental strategies from YR.Secure mental strategies from YR.

o A solid understanding of the number system.A solid understanding of the number system.

o Practical, hands on experience including counters and base 10 Practical, hands on experience including counters and base 10 apparatus.apparatus.

o Visual images including number lines and arrays.Visual images including number lines and arrays.

o Experience of expanded methods to develop understanding and Experience of expanded methods to develop understanding and avoid rote learning.avoid rote learning.

o Secure understanding of each stage before moving onto the next.Secure understanding of each stage before moving onto the next.

o The questions at the forefront of their minds:The questions at the forefront of their minds:

‘ ‘Can I do it in my head? If not which method will help me?’Can I do it in my head? If not which method will help me?’