Helping Our Children To
Achieve
Welcome
Maths is FUN!
How Maths teaching has changed
- To give children the chance to explore ways of
finding an answer, and being able to explain why
it works
- To give them the key skills needed to solve real
world problems and examples
- To provide opportunities to apply these skills in
practical situations
Developing understanding
 Prompting thinking & questioning
 Providing opportunities to manipulate, experience and see
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(use of resources)
Develop thinking through investigation
Reasoning and making connections
Engaging in talk
Enabling learning through drawing attention to.
Encouraging children to make links and generalise
Changing attitudes towards Maths . . .
Right then, time for
a warm up!
5
12
21
Which is the odd one out, and
why?
No hands up!
1 min talk to a neighbour!
Everyone has generalised!
FS and KS1 Mental Arithmetic
The emphasis in KS1 is on mental
arithmetic BUT based on practical
activities. Useful things to practise at
home include:
• Doubles and halves
• Bonds of 10, 20 and 100
• Adding 2 small numbers
• Adding or subtracting
• Using different vocabulary
KS2 Mental Maths
HTU
Times tables and division facts
Number bonds up to 100
Doubling and Halving
Rounding and estimating
x 10, x 100
(DON’T ADD A 0!)
STRONG MENTAL CALCULATION
STRATEGIES
 Quick recall of
 Number bonds to 20, 50 and 100.
 Times tables knowledge
 2x, 5x, 10x
 3x, 4x,
 6x, 8x, 9x
 7x
When ready, the children will move on to
more formal written methods.
Moving to written procedures too fast
can mean:
• Children add/subtract the digits in a
column by rote, without understanding
what their value is, or what a sensible
answer is likely to be
• Children who rely on written procedures
can be more likely to look for a calculator
when stuck, not a mental strategy
• Children can hide their understanding of
mathematical concepts behind having a
good memory for procedure.
Written Methods
for larger numbers, or too many numbers to deal with mentally
We will attempt to touch on as many written
methods as we can in the time we have. Please stay
at the end and ask if you are unsure or have any
further questions.
resources to support
understanding
Addition
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Counting on using objects
Counting on using number line / tracks
Counting on using a hundred square
Blank number line (bridging)
Partitioning
Column addition
Addition
48 + 35
ADDITION: Number tracks /
lines
3+2=
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1
2
3
4
5
6
7
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8
9 10
and 2 more
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3
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5
Addition : Number lines
38 +26
10
38
10
48
1
1
1
58
59
60
1
61
1
62
427 + 358
300
427
50
727
3
777
5
780
785
1
63
64
ADDITION : partitioning
 36 + 45 = 30 + 40 + 6 + 5  Use of dienes blocks can
support this.
 = 70 + 11
 = 81
 or
 36 + 45 = 36 + 40 + 5
 = 76 + 5
 = 81
 Stage 2: Partitioning continued
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 Partitioned numbers are then written under one
another. This mirrors the column method and also
links mental methods.
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ADDITION : Vertical : column
addition
47
 76
110
13
123
Try these out on your table using
the resources
2 more than 9
5 + 8 =
Total of 25 and 41
74 plus 27
134 + 217 =
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Subtraction
Counting back using objects
Counting back using a number line
Counting back using a hundred square
Blank number line
Partitioning
SUBTRACTION: Number lines
5 – 2 =
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0 1 2 3 4 5 6 7 8 9 10
2 less
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3
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5
SUBTRACTION:
 73 – 26 =
+4
0
26
+40
30
-4
0
26
+3
70
-40
30
73
-3
70
73
SUBTRACTION
 COUNTING BACK
 85 - 37 =
48
-7
55
Or finding the difference
-30
85
Counting on
 354 – 188 =
354 – 188 =
12
188
154
200
354
End of year 4
This method would be supported with practical apparatus. Once confident this then
leads to the column method. The amount of time spent teaching and practising the
expanded method will depend on how secure the children are in their recall of number
facts and with partitioning.
Example: 563 − 241
Expanded method
500  60  3
 200  40  1
300  20  2
leading to
563
 241
322
Start by subtracting the ones, then the tens, then the hundreds. Refer to subtracting
the tens, for example, by saying ‘sixty take away forty’, not ‘six take away four’.
Examples : try these!
 Find 2 less than 7
 What is 27 – 13?
 62 – 45 =
 Take away 19 from 96
 72 – 46
 What’s the difference between 87 and 105?
 How would you tackle this number sentence? Can
you explain your method?
Multiplication
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Doubles – objects / beadstring
Counting in steps of 2,5,10
Counting objects
Pictures
Number lines
Times tables
Arrays
Grid method
Arrays and numberline
 Children represent by drawings, counters, cubes
and begin to link to number line as repeated addition
8 x 23 = 8 x 10 + 8 x 10 + 8 x 3
= 80 + 80 + 24
= 184
This develops into the grid method.
8 x 23 =
X
8
10
80
10
80
3
24 =184
leading to
X
8
20
160
3
24
=
184
Multiplication
Double 7
5 times 6
Times
3 lots of 4
23 x 7=
13 x 24= Repeated
Addition
Division
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Halving
Sorting hoops and objects
Pictures
Related times tables facts
Division
‘84 sweets shared equally between 6 children’
How many 6’s go into 84?
84 divided by 6?
84 shared by 6?
There is no need to
divide! Use your
tables knowledge!
Examples
As with multiplication, division is recorded as arrays, number lines or number
sentences.
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16  8 = 2
0
8
16
(I start at zero and count in 8s until I get to 16)
Remainders
Number lines can also be used for more complex calculations, where the pupil is
working with multiples of the divisor.
33  9 =
9x1=9
9x1=9
9x1=9
6 left (remainder)
xxxxxx
0
9
18
27
33
so 33  9 = 3 r 6
196  7 =
7x10=70
0
7x10=70
70
7x8=56
140
196
so 196  7 =28
Place value understanding is needed to count on in multiples of the divisor.
Use of ‘I know’ boxes
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I know:
10 x 7 = 70
SO
20 X 7 = 140
(I HAVE 56 LEFT)
8 LOTS OF 7=56
SO
196  7 = 28 ( AS I KNOW 28 X 7 = 196)
Helping at home
…And Some Don’ts!
Some Dos…
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Play (maths) with your child
There are opportunities for impromptu
learning in games with real people that you
can't get from a DS or Xbox
Let your child win or be better than you
Otherwise all they learn is that you are
better at maths than them
Recognise that there is more than one
way of doing calculations
You may have learned one method, but
children are actively encouraged to seek out
alternative methods in school and choose
one which works for them, no matter how
long winded
Be an actor
Get excited about maths and your child will
get excited too
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Don't expect them to understand after
you've explained it once
It is normal for a child to 'get it' one day,
and then in a different context not know
how to find an answer
Don't tell them you are hopeless at
maths
You may remember maths as being hard,
but you were probably not hopeless, and
even if you were, that implies to your child,
“I was hopeless at maths, and I'm a
successful adult, therefore maths is not
important”
Don't get into an argument over
homework
It will be something that your child has
covered in class, and if they really can't do it
without a lot of tears and frustration, leave
it and LET US KNOW!
Ideas taken from Maths for Mums and Dads
Eastaway, R. and Askew, M. (2010)
Helping at home KS1/ FS
• Play board games
• Cook – measuring and weighing
• Look at numbers in the environment e.g.
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telephone keys, number plates, door numbers,
book pages, sleeps until Christmas!
Money
Comparing heights
Birthdays, Months of the year, Days of the week
Time
Props around the house KS2
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A prominent clock- digital and analogue is even better. Place it somewhere where you can talk
about the time each day.
A traditional wall calendar-Calendars help with counting days, spotting number patterns and
Board games that involve dice or spinners-helps with counting and the idea of chance
A pack of playing cards- Card games can be adapted in many ways to learn about number
bonds, chance, adding and subtracting
A calculator- A basic calculator will help with maths homework when required, there are also many
calculator games you can play, too.
Measuring Jug-Your child will use them in school, but seeing them used in real life is invaluable.
Also useful for discussing converting from metric to imperial
Dried beans, Macaroni or Smarties- for counting and estimating
A tape measure and a ruler- Let your child help when measuring up for furniture, curtains etc
A large bar of chocolate (one divided into chunks)- a great motivator for fractions work
Fridge magnets with numbers on- can be used for a little practice of written methods
Indoor/outdoor Thermometer- especially useful in winter for teaching negative numbers when
the temperature drops below freezing
Unusual dice- not all dice have faces 1-6, hexagonal dice, coloured dice, dice from board games
all make talking about chance a little more interesting
A dartboard with velcro darts- Helps with doubling, trebling, adding and subtracting.
Ideas taken from Maths for Mums and Dads Eastaway, R. and Askew, M. (2010)
Homework!
• Related to classwork
• Use method shown in class
• Check with teacher if unsure!
• It’s the child’s responsibility to complete their
homework!