Transcript Cakes and Calculations – Session 1

Welcome to
Mrs Blands Maths
Evening
Life Skill
• Maths is an important life skill. We
want your children to be confident
mathematicians who are able to use
and apply their learning and to
understand that it is fine to make
mistakes along the way.
Aims of tonight:
To share activities/strategies we
teach in this school
To help you feel confident to support
your child at home.
Mental Calculation
The ability to calculate mentally forms the basis
of all methods of calculation. This involves
• instant recall of number facts (+ - x ÷)
• having a secure understanding of place value
and the number system
• having a range of strategies to apply to a
calculation
• understand the language and rules of maths
Written Calculation
Throughout their primary years, children
should progress from informal jottings to
efficient written methods for each of the
four operations.
Standard written methods should only be
introduced when a child has a secure
knowledge and understanding of the
process involved and can clearly explain
the strategies they have used.
It is ok to make mistakes
– this is part of learning!
Addition
Mental Strategies for
Addition
Secure mental addition requires the ability to
•recall key number facts instantly (number pairs to 10, 20 &
100, doubles etc) and to apply these to similar calculations
•recognise that addition can be done in any order and use
this to add mentally different combinations of one and two
digit numbers
• partition two-digit numbers in different ways, including
adding the tens and units separately before recombining
•understand the language of addition including more than,
sum, plus, greater than, total, altogether ….
EYFS to Year 1
• Children need to be confident adding
practically first.
For example
Give a child 3 apples and say how
many will you have if you have one
more?
Year 1 to Year 2
Pictorially
Once a child as a solid understanding
of addition practically they can then
begin to record pictorially.
+
=
• Even when a child moves on to using
written methods if they get stuck
ask them to draw pictures.
• This helps them to understand the
problem!
Written methods for
Addition
Stage 1: The empty number line
The empty number line helps to record the
steps on the way to calculating the total. The
steps often bridge through a multiple of 10.
8 + 7 = 15
48 + 36 = 84
or:
Written methods for
Addition
Stage 2: Partitioning
The next stage is to record methods using partitioning. Partitioning both
numbers into tens and ones mirrors the column method where ones are
placed under ones and tens under tens. This also links to mental methods.
76 + 47 =
70 + 40 + 6 + 7 =
110 + 13 = 123
Subtraction
Mental Strategies for
Subtraction
Secure mental subtraction requires the ability to:
• recall key subtraction facts instantly (inverse of
number pairs to 10, 20 & 100, halves etc) and to apply
these to similar calculations
• mentally subtract combinations of one and two digit
numbers
• understand that subtraction is the inverse of
addition and recognise that subtraction can’t be done
in any order (it has to start with the larger number)
• understand the language of subtraction including
less, minus, take away, difference between etc
EYFS to Year 1
Practical Subtraction
• Taking away using different objects
and materials
• Counting back on number tracks
• Use resources to understand
relationship between addition and
subtraction
Strategies:
Children need to use their
understanding of partitioning
Eg 78 – 27 = 78 – 20 – 7
= 58 – 7
= 51
Written methods for
Subtraction
Stage 1: The empty number line
The empty number line helps to record the steps in
mental subtraction. There are several ways to do this:
• Counting Back - a calculation like 74 - 27 can be
recorded by counting back 27 from 74 to reach 47.
• Counting Up - the steps can also be
recorded by counting up from the
smaller number to find the
difference
Using and applying
Scarves cost £2 each
Gloves cost £3
I buy 2 scarves and 1 pair of gloves, how
much change do I get if I pay with £10?
Multiplication
Mental Strategies for
Multiplication
To multiply successfully, children need to be able to:
• understand multiplication as repeated addition
• group objects and count up in different amounts
• record repeated addition as arrays and on empty number
lines
• understand how to multiply numbers by multiples of 10
Key Stage 2
• know their times tables to 10 x 10
• apply this understanding to more formal methods such as
grid method
Written methods for
Multiplication
Initially multiplication is introduced as
‘repeated addition’ using vocabulary such as
‘lots of’ or ‘groups of’ and real objects or
pictures.
3 lots of 3 = 9
leading to
3x3=9
By the end of KS1
Children count in 2s, 3s, 5s and 10s
They use objects, money, stories and songs to
learn these
eg pairs of socks, playing shop keeper counting
out 2ps
They understand how to record as repeated
addition
Eg 2 + 2 + 2 + 2 = 8
or 4 lots of 2 make 8
or 4 x 2 = 8 this is where they learn the x sign
Year 2 learn their 2, 5 and 10 times tables
By the end of KS1
Children record jumps on an empty
number line
0
+3
+3
+3
3
3 lots of 3
6
9
Year 1 and Year 2
They play games, group objects and
look for patterns on number squares
They learn doubling and halving facts
They learn how to record repeated
addition or multiplication as arrays –
using cubes, peg boards and
pictures.
By the end of KS1
4x2
2x4
Division
Foundation Stage
• Practical activities involving grouping and sharing
• How should we plant the daffodil bulbs in these 3
pots?
• Can we share these cakes out fairly? How shall we
do it?
• I am going to divide this apple in half – how many
pieces do I have?
• Lets sort these toys into 2s – how many groups
have we made?
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
Key Stage 1
• Continue to practically group and
share
• Record in pictures
• Count patterns and equal groups
• Learn alongside multiplication
Share 12 sweets between 4. How
many does each child have
or
Or!
Always ask the class teacher to explain a
method if you need help to support your
child.
The more practical experiences your child
has the greater the understanding the
child will have and they will be more
confident to apply their understanding to
problem solving – which is based on real
life experiences!