Download Key Stage 1 Maths Evening for Parents

Welcome to our Maths
Workshop for parents – thank
you so much for coming!
There is a selection of maths resources arranged
on the tables around the edge of the hall –
please
feel
free
to have
look –and
have
a much
Welcome
to our
Maths
Workshop
foraparents
thank
you so
‘play’!
for
coming!
Using models and images in maths is essential in
helping the children understand underlying
patterns and principles of maths.
Learning, Growing
and Succeeding Together
Oh no!!!
etc.
add
and
How many more?
plus
double
more than
altogether
increase
sum
total
The Downley Staff – and guests!
Mental Recall of Number Bonds …
This is REALLY IMPORTANT!!!
Number bonds to 10
eg, 10 + 0 = 10, 9+ 1 = 10….
Addition facts for numbers up to 10
6+0=6; 5+1=6; 4+2=6…
Numbers bonds to 20  19+1; 18+2; 17
+3
All addition facts to 11, 12 , 13 …20
Multiples of 10 and multiples of 5 which
add up to 100…
70 + 30, 45 + 55 etc
Doubles and near doubles
6 + 6 = 12, 6 + 7 = 13, 6 + 5 = 11
35 + 35 = 70, 35 + 36 = 71 etc
‘Sums!!!’
Writing operations and solving problems using
‘informal methods’
17 + 5 = ?
Firstly, encourage mental strategies
(starting with the higher number, counting on, looking for
pairs which make 10, verbal discussion about the method
used to get an answer, checking!)
On Monday morning, Beech get 4 housepoints,
Chestnut get 3, Oak get 6 and Willow get 7. What is
the total number of housepoints given?
Find the total
7
Double 8 =16
8
8
7 and 3 are bonds to 10
3
Total is 16+10 = 26
Use knowledge of place value and adding on 10 to a
number
Simple, informal jottings… use of a number line
17 + 5 = ?
X
17
18
19
20
21
22
23
24
If another way has been used, encourage discussion about the
method and talk about how effective it is.
The importance of
understanding
PLACE VALUE
PLACE VALUE – Tens and Units…
25
293
2 Tens and 5 Units
2 Hundreds, 9 Tens and 3
Units
What is the value of each underlined digit in the following
numbers?
28
158
49
317
84
708
60
965
Can you add single units to
any number?
Can you add multiples of 10
to any number
Can you add multiples of 100
to any number?
What would 10 more than this
number be?
What about 1 more? 10 less?
Explain how you know.
What numbers are covered?
How do you know?
This is a section from
a hundred square.
63
What are the missing numbers?
Explain how you know.
This is a section from
a hundred square.
What are the missing numbers?
45
48 + 1 =
139 + 1 =
299 + 1 =
48 + 10 =
139 + 10 =
299 + 10 =
48 + 100 =
139 + 100 =
299 + 100 =
48 + 3 =
139 + 6 =
299 + 9 =
48 + 30 =
139 + 60 =
299 + 90 =
48 + 300 =
139 + 600 =
299 + 900 =
Being able to split a number into Hundreds, Tens and Units is
VERY IMPORTANT!
This is called
‘partitioning’ and ‘recombining’
28  2 tens and 8 units
28 =
20 + 8
49  4 tens and 9 units
49 =
384 
616 
902 
40 + 9
7 tens and 3 units =
6 tens and 2 units
3 hundreds and 7 units =
200 + 50 + 6 =
500 + 10 + 9 =
Different ways of adding up
– mentally and with
jottings…
Using a ‘mental’ or empty numberline
24 + 47=
47 + 24 =
47 + (20 + 4) =
+10
+10
+1
+1
+1
+1
X
47
57
67
68
69
70
71
Getting quicker…
24 + 47=
47 + 24 =
47 + (20 + 4) =
+20
+4
X
47
67
71
And more difficult…
38 + 74 =
74 + 38 =
74 + (30 + 8) =
+30
+8
X
74
104
112
A different strategy…
26 + 42 =
Add the tens together and then add the units together
2 6
+
4 2
(20 + 40) + (6 + 2) =
60 + 8 =
68
Larger numbers – crossing the hundreds boundary…
97 + 76 =
Add the tens together and then add the units together
9 7
+
7 6
(90 + 70) + (7 + 6) =
160 + 13 =
173
Vertical Layouts –
Formal Written Methods
(Year 4 ish)
Only starting this when confident with stages so far!
Wherever possible, children should be encouraged solve
problems mentally. Vertical addition should be used as the
problems become too complicated to solve mentally…
500 + 123
Easy! - a
MENTAL
calculation!
367 + 256
Tricky!
A written calculation!
But I still need
MENTAL
skills!!!
First steps (using partitioning)
236 + 421 = ?
2 0 0
+
3 0
+
6
4 0 0
+
2 0
+
1
6 0 0
+
5 0
+
7
=
6 5 7
The ‘Expanded’ method
4 6 9
+
3 8 5
1 4
1 4 0
7 0 0
8 5 4
The Compact Method – ‘Carrying’
4 6 9
+
3 8 5
8 5 4
1
1
subtract
minus
How many fewer
is…..than….?
take away
difference
between
decrease
leave
reduce
How much
less is..?
Number bonds up to 10
Eg, 3 - 0 = 3, 5 - 1 = 4….
10 - 0 = 10, 9 - 1 = 8
Numbers bonds up to 20
All bonds to 11, 12 , 13 …20
Multiples of 10 up to 100…
70 - 30, 100 – 20 = 80 etc
It is important that children move away from the language of ‘take away’ in
Key Stage 2 and move towards ‘subtraction’.
Counting back…
…on a numberline
Simple, informal jottings… use of a number line
7-5=?
2
7
-5
At Key Stage 1, children will count back on the
numberline to find the answer.
Counting on…
…with a numberline
You buy an item for £8.
You give a £20 note to the shopkeeper.
What is the change?
You buy an item for £15.56
You give a £50 note to the shopkeeper.
What is the change?
Subtraction – Think of it as ‘finding the difference’
20 – 8 =
20
8
20 – 8 =
20
8
20 – 8 = 12
20
Count on…
From 8 to 20…
12 steps
8
It’s really easy to jot a
numberline to count on…
20 – 8 = 12
10
2
8
10
20
20
8
12
What is the difference between 74 and 47?
20
3
4
74
47
50
70 74
47
27
27
You buy an item for £15.56
You give a £50 note to the shopkeeper.
What is the change?
4p
15.56
15.60
£4
40p
16.00
£30
20.00
50.00
Then total all the jumps  4p + 40p + £4 + £30 = £34.44
Jumps can be labelled with pounds and pence notation, or with decimal notation,
leading to
0.04 + 0.40 + 4.00 + 30.00 = 34.44 = £34.44
Decrease 100 by 43
1
0
4
0
3
1
4
3
-
SUBTRACTION MISCONCEPTIONS
Decrease 100 by 43
7
43 50
57
50
100
100
43
57
775 – 292 =
-
7
2
7
9
5
2
5
2
3
775 – 292 = 483
775
292
8
292 300
400
75
700
775
483
The link between addition
and subtraction
+
=
-
=
+
=
-
=
-
-
+
Number triangles are BRILLIANT.
Know 1 FACT, know 4 FACTS!
They will help you a lot with addition and subtraction…
Example
5 + 4 = 9
9
Complete…
___ + ___ = ___
4 + 5 = 9
___ + ___ = ___
9 - 5 = 4
5
4
9 – 4 = 5
___ + ___ = ___
___ + ___ = ___
11
15
___ - ___ = ___
___ – ___ = ___
___ - ___ = ___
6
8
___ – ___ = ___
___ + ___ = ___
14
___ + ___ = ___
10
___ - ___ = ___
___ – ___ = ___
Can I solve this mentally?
Yes!
CHECK!
Can I solve this mentally?
NO
1. Estimate
2. Numberline
3. Add jumps
4. CHECK!
multiply
times
arrays
lots of
double
multiples
repeated addition
double
product
scale up
Can you draw an
image to show …
4x2
4x2
4 sets of 2
4x2
4 lots of 2
2+2+2+2
4x2
4 lots of 2
0
2 +
2 +
2
4
2 +
6
2
8
4x2
4 times 2
4x2
4 two times
4+4
4x2
4 multiplied by 2
ARRAYS
Fast, mental recall of
times tables is
really,
really,
really
IMPORTANT!
Multiplying by 10
It is important that multiplying by 10 is not
thought of as a case of ‘adding zeros’. It
isn’t an inappropriate expression because
adding zero actually leaves a number
unchanged and the ‘add a zero rule’ fails
when, for example, 0.2 is multiplied by 10
(‘adding a zero’ results in 0.20).
Children need to understand that when you
multiply by 10 the digits move one place to
the left, leaving an empty space which is
filled by zero (a place holder).
Multiplication facts
Children will struggle with multiplication if they can’t recall
multiplication facts.
Knowing a multiplication table is much more than being able
to recite it in order. It also means children should be able to
respond quickly to oral or written questions phrased in a
variety of ways, e.g.
• What are seven fives?
• What is 7 times five?
• 5 multiplied by 7 is…
• How many fives in 35?
• What would I multiply by five to get 35?
• What are the factors of 35?
divide
share
quotient
group
remainders
decimals
divisor
fractions
12  3 = 4
Sharing
There are three children and 12 cakes. How many can
they each have, if I share them out equally?
Sharing 12 things equally into 3 piles.
How many in each
12  3 = 4
Grouping
There are 12 cakes. How many children can have three
each?
(How many threes are there in 12?)
Language and division
• The  sign represents both the sharing and
grouping aspects of division
• Encourage the children to read this as
‘divided by’ rather than ‘shared by’,
• Even easier – ‘HOW MANY!’
12  3 = ?
HOW MANY three’s make 12?
4 three’s make 12
4 x 3 = 12
Know 1 fact, know 4 facts!!!
4 x 3 = 12
12 ÷ 3 = 4
3 x 4 = 12
12 ÷ 4 = 3
4 x 3 = 12
12 ÷ 3 = 4
3 x 4 = 12
12 ÷ 4 = 3
12
÷
4
÷
x
3
x
=
÷
x
=
÷
=
=
Number triangles are BRILLIANT.
Know 1 FACT, know 4 FACTS!
They will help you a lot with
multiplication and division
Example
2x4=8
8
Complete…
___ x ___ = ___
4x2=8
___ x ___ = ___
8÷2=4
2
4
8÷4=2
___ ÷ ___ = ___
6
8
___ x ___ = ___
___ x ___ = ___
24
45
___ x ___ = ___
4
___ ÷ ___ = ___
___ ÷ ___ = ___
___ ÷ ___ = ___
___ x ___ = ___
___ ÷ ___ = ___
9
___ ÷ ___ = ___
Look for
patterns and
relationships
too!
100  50 = 2
100  2 = 50
100  5 = 20
100  20 = 5
100  10 = 10
You’ll be laughing if you remember these
simple facts…
• dividing any number by 0 gives an answer of 0
eg, 6 ÷ 0 = 0
0 ÷ 59 = 0
• dividing any number by 1 leaves the number unchanged
e.g, 12  1 =12 1,346 ÷ 1 = 1,346
Order does matter
16  2 does not equal 2  16
• division is the opposite of multiplication
eg, 3 x 4 = 12 so 12 ÷ 4 = 3
• there will be remainders for some division calculations
eg, 11 ÷ 2 = 5 and a remainder of 1
Division and number
lines/repeated subtraction
(getting close to ‘chunking’)
18  3 = 6
0
3
6
9
12
15
18
Generally speaking, children are happier and
more accurate when counting forwards…
So think of 18  3
As ‘How many 3s are in 18?’
0
3
6
9
12
15
18
Problem solving
1. I have 26 eggs. If 6 eggs fit in one box,
how many boxes will I need for
ALL the eggs?
2. There are 26 children in a P.E lesson. If teams
of 6 are needed, how many full teams can be
made?
The same basic calculation will be
needed, but how we deal with the
remainder will be different.
So we need to calculate 26 ÷ 6
r2
0
6
12
18
24
26
So the answer is 4 r 2
If we need to box up all the eggs, this means we need 5 boxes (but only 4 will be full)
If we need teams of 6 children in P.E., we can only have 4 teams, with
2 children left out.
Fractions!
A whole session by itself but…
3
4
Know that it is possible to divide a smaller
number by a larger number
Know that the line in the middle of a
fraction means ‘divided by’
Know how to work out a fraction as a
decimal on a calculator
http://www.woodlands-junior.kent.sch.uk/maths/
Very well done everyone!
Thank you for your time!
A favour please…