Numeracy Coffee Morning

Years 5 and 6

Monday 18th March 2019

Kerry WalshLead Practitioner in Numeracy

Quick Starter

- If you could turn over the paper in front of you.

- You’ve got 3 minutes.

- We aren’t really going to test your mathematical skills!

“Do not worry about your difficulties in

mathematics. I can assure you mine are still greater.” – Albert Einstein

The fact is, Einstein did have problems with

mathematics when he was in school and had to

overcome them in order to pursue his love of

physics. The solution to the problem was Marcel

Grossmann, his classmate.

When Einstein had problems in mathematics, he

would approach Grossmann for help or borrow his

lesson notes – if he missed classes. Grossmann

later became a professor in the subject.

Aims

• Talk about the importance of a growth mind-set in mathematics.

• Provide you with a greater understanding of how mathematics is taught in school.

• Show you the progression of the 4 mathematical

operation methods

• Discuss Maths Mastery• See the importance of mental maths skills and

the strategies children are taught.• Help you understand how you can help your

child at home.

“A lot of scientific evidence suggests that

the difference between those who

succeed and those who don't is not the

brains they were born with, but their

approach to life, the messages they

receive about their potential, and the

opportunities they have to learn.”

― Jo Boaler, Mathematical Mindsets:

Unleashing Students' Potential through

Creative Math, Inspiring Messages and

Innovative Teaching

There is always more than

one way to do things.

We aim to teach children to use mental methods where

appropriate, but for calculations that they cannot do in

their heads they develop and understanding of a range of

written methods they can use accurately and with

confidence.

We teach them a range so they can choose the one they

prefer and proves most accurate for them.

If you teach them a different way that gives them another

option.

The Four Operations

Addition

Subtraction

Multiplication

Division

AdditionColumn Method:

This method remains efficient when adding larger numbers and

decimals. It is a quick and reliable method.

48 + 36 = 84

4 83 6 +

8 4

1 carrying ‘ten’

379 + 92 = 471

3 7 9

9 2 +4 7 11 1 carrying ‘ten’ and ‘one hundred’

Subtraction

Column Method – Decomposition:

This method is the most efficient for subtraction.

However it relies on the children’s understanding

of place value due to the need to ‘borrow’ tens or

hundreds if the number being subtracted is larger

than the number being subtracted from.

Subtraction

6

Column Method – Decomposition:

16

7⁄ 3 9 –3 7

Borrowing ‘ten’ not ‘one’

11⁄2 3 7

8 4 –

1 5 3

Children must keep being referred back to place value – it is 3 tens not just 3.

Borrowing ‘a hundred’

not ten or one

Multiplication

Grid Method:

43 X 6 124 X 32

X 6

4 0 2 4 0

3 1 8

2 5 8

X 3 0 2

1 0 0 3 0 0 0 2 0 0 3 2 0 0

2 0 6 0 0 4 0 6 4 0

4 1 5 0 8 1 5 8

3 9 9 8

This method links directly to the mental method of multiplication.

Multiplication

Expanded Short Method:

4 3 X 64 3

6 x

1 8

2 4 0 +

2 5 8

This method is the next step

on from the grid method.

Children need to have a solid

understanding of place value so

the see it as

40 x 6 and don’t forget the zero.

Multiplication

Short Multiplication:

4 3 X 6

4 36 x

2 5 8

1

This method is the next step on from the expanded

method

Once again children have to

be secure with their place

value and know they are

carrying ‘ten’ not one.

Multiplication

Expanded Short Method for 2-digit x 2 digit:

5 6 x 2 7 =

(Ones 6 x 7)

(tens x ones 50 x 7)

(tens x ones 20 x 6)

(tens x tens 50 x 20)

5 62 7 x

4 2

3 5 0

1 2 01 0 0 0 +1 5 1 2

1

The mathematical language

has changed: -

ones not units

Multiplication

Short Multiplication for 2-digit x 2 digit:

5 6 x 2 7 =5 62 7 x

3 9 24

1 1 2 0 +

1 5 1 2

When multiplying by the ten (20 in this

example) children must remember to put

the place holder ‘0’ in the ones column.

1

Division

Expanded Method – Chunking:

87 ÷ 6 =

6 8 7

6 0 - 6 x

2 7

2 4 - 6 x 4

3

Answer = 14 r 3

divisor or ‘chunks’.

Initially they subtract several

chunks but with practice

children will look at the biggest

multiples of the divisor that they

can subtract.

This method reminds

children the link between

division and repeated

subtraction.

1 4

Division

191 ÷ 6 =

6 1 9 11 2 0 - 6 x 20

7 1

6 0 - 6 x 10

1 16 - 6 x 15

Answer = 31 r 5

Expanded Method – Chunking Hundreds, Tens, Ones ÷ Ones:

Children build up confidence,

using their multiplication

knowledge, to subtract larger

‘chunks’.

0 3 1

Division

Short Division - TU ÷ U:

81 ÷ 3 =

2 7

Answer = 27

This method is the next

step after chunking. It is a

more compact method.

3 821

Links to chunking:3 x 20 = 6080 – 60 = 20 which the ‘2’ represents3 x 7 = 21

No remainder

Division

Short Division – HTU ÷ U:

This method links on from

partitioning but is a more

compact method.

291 ÷ 3 =9 7

3 2 921

Answer = 97

Division

24 x 3

This method links back to

chunking and is used to

reduce errors and children

are using times tables they

are unfamiliar with.

Long Division – HTU ÷ U:

560 ÷ 24 =2 3

2445⁄ 160

4 8 0 - 24 x 20

8 0

7 2 -

8

Answer = 23 r 8

Maths should be real,

practical and fun!

Maths Mastery

The idea of maths mastery was inspired by teaching

approaches developed in Singapore and Shanghai.

Mastery is an inclusive way of teaching that is

grounded in the belief that all pupils can achieve in

maths. A concept is deemed mastered when

learners can represent it in multiple ways, can

communicate solutions using mathematical

language and can independently apply the

concept to new problems.

Teaching for mastery supports National Curriculum

objectives, but spends more time reinforcing number

before progressing to more difficult areas of

mathematics.

Different examples of how we

help children develop mastery.

Application - Problem Solving

Using and applying knowledge and skills

Problem solving requires:

- An understanding mathematical vocabulary

- Being able to interpret the problem

- Establishing what mathematical operations need to

be used.

- The ability to apply the strategies that have been

taught

- Mathematics mastery knowledge in order

- to explain the process

- the reasoning for using that process

- and being able to justify the answer

Real Life Applications

Liam spends £14 altogether on

the Big Wheel and the

Rollercoaster.He goes on the Big Wheel

twice.

How many times does he go on the Rollercoaster?

Mental Mathematics

It is essential children have secure knowledge and recall of mental facts including:

- Place Value including decimals

- Number bonds- Times tables from 0 to 12!- Corresponding division facts.

We generally start each lesson by counting or playing a game designed to recall mental maths facts.

Mental MathematicsMental Maths Strategies:

- Use number bonds to 10, 20 and 100 transferable to

1,000 and decimals

- Use doubles and near doubles- Partition into thousands, hundreds, tens and units- Adding near multiples of 10. Adding the multiple then

add or subtract 1

- Subtracting near multiples of 10. Subtracting the

multiple then subtracting or adding 1.

- These are transferable to multiples of 100, 1,000 etc.

Times Tables

We are working towards pupils at the end of Year 4 being

able to: -

• memorise their multiplication tables up to and including

the 12 times table

• show precision and fluency in their work

• Six Times Table Song

By the end of Year 6 pupils should: -

• be fluent in written methods for all four operations,

including long multiplication and division, and in

working with fractions, decimals and percentages.

• Pupils should read, spell and pronouncemathematical vocabulary correctly.

How you can help at home.Provide fun opportunities to practise maths.

• Playing games – cards, snakes and ladders,

dominoes, Monopoly, Rummikub

• Cooking – let them do it alone!

• Telling the time – get them to plan a journey using a

timetable.

• Pocket Money – let them go shopping

• DIY – let the help, show them a practical use for

angles.

• Online Applications – channel their gaming!

Celebrate their mistakes!

“Every time a student makes a mistake in math,

they grow a synapse.” There”

― Jo Boaler, Mathematical Mindsets: Unleashing

Students' Potential through Creative Math,

Inspiring Messages and Innovative Teaching