Transcript Addition – Mid stages - Little Melton Primary School

Welcome to
Little Melton Primary School
Calculations
Addition and Subtraction
2011
This evening we will:
• Outline the features of our calculations policy.
• Focus on the strategies used to develop the
children’s understanding and application of
addition and subtraction.
• Identify key areas where you can help your child
with their maths.
• Share classroom resources and approaches.
• And of course – DO SOME MATHS!
What can a numerate child do?
By the age of 11 they should:
• Have a sense of the size of number and where it fits into the number
system.
• Know by heart addition and subtraction facts to 20, multiplication
and division facts to 10 x 10, doubles and halves, complements to
100, multiply and divide by 10 and 100.
• Use what they know to figure out answers mentally.
• Calculate accurately and efficiently, both mentally and on paper,
using a range of strategies.
• Recognise when it is appropriate to use a calculator (and when it is
not) and be able to use one effectively.
• Explain their methods and reasoning using correct
mathematical terms.
• Judge whether their answers are reasonable and have
strategies for checking them where necessary.
• The aim is for children to do mathematics in their
heads, and if the numbers are too large, to use pencil
and paper methods to avoid losing track.
• To do this children need to learn quick and efficient
methods, including
appropriate written methods.
Learning written methods is not the ultimate
aim.
•Our maths teaching aims to develop children’s mental
strategies and then written methods that derive from and
support these mental methods.
We want the children to ask themselves:
• Can I do this in my head?
• Can I do this in my head using drawings
jottings?
• Do I need to use a pencil and paper procedure?
• Do I need a calculator?
or
Calculations policy
Our school Calculations policy shows how the methods progress
across the year groups. Some children may be ready for the year
appropriate method, others may be consolidating the previous
year’s or being extended.
How do you add and subtract?
61 + 45
5735 + 3657
83 - 68
5002 - 4996
538 -295
7800 -5600
362 + 39
267 + 267
2.5 + 2.7
5735 + 3990
5.1 – 2.78
Addition – Early stages
• Practical activities and discussions.
 Recognising numbers.
 Count objects up to 10.
 Find one more than a number.
 Count in ones and tens.
 Relate addition to combining two groups of objects.
 Count along a number line to add numbers.
 Begin to use + and = signs in a number sentence.
Addition – Mid stages
•Mental Strategies and Informal Methods
 Looking for pairs that make 10 then 20, 30 etc.
16 + 12 + 4=
 Using a number square, count on the units then the tens.
 Adding ‘nearly’ numbers – To add 9 add 10 then subtract 1
32 + 9 =
32 +10 = 42 -1 = 41
 Using a number line, bridging through a multiple of 10 e.g 27 + 8
+3
+5
_______________________________________________
27
30
35
Addition – Mid stages
• Formal Methods start to emerge:
 Add using partitioning: 47 + 34 = 40 + 7 +30 + 4=
Add units 4 + 7 = 11
Add tens 40 + 30 = 70
Total
70 + 13 = 81
 Expanded Method: 47 + 34 =
TU
47
34
11 (7 + 4)
70 (40 + 30)
81
Addition – Later stages
• Standard Methods
 Label columns and carry below the line:
Th H T U
3587
HTU. th
124 .90
+ 675
+117 .25
4262
242 .15
111
11
Now it is your turn!
• Try using one of the methods shown to answer these:
1. I have £257 in one bank account and £468 in another. How
much is there altogether?
2. A sunflower measures 1.94m. By Friday it has grown 38cm. How
tall is it now?
Subtraction – Early stages
• Practical activities and discussion
 Count backwards in number rhymes or stories.
 Count back from a given number.
 Begin to relate subtraction to take-away.
 Find one less than a number.
Counting back in tens.
Count backwards along a number line to take away.
Begin to use the – and = signs to record mental
subtractions.
Subtraction – Mid stages
•
Mental Strategies and Informal Methods
 Using a number square, partition the number, then count back the units then the tens.
 Subtracting ‘nearly’ numbers – To take 9 take 10 then add 1
32 - 9 =
32 -10 = 22 +1 = 23
 Using a number line, bridging through a multiple of 10 e.g 63 – 26
37
-10
47
-10
57
-3
60
63
-3
 Recognise when to count on: when 2 numbers are close together e.g.106 – 98
+6
=8
_________________________
98
100
106
+2
Subtraction – Mid stages
• Methods which lead to Standard Methods
 Can also use counting on:
+22
+100
+74
374
- 178
___________________________________
178
200
300
374
 Expanded Method – Exchanging 10
43 – 27 =
T
U
T
U
40 + 3
30 + 13
20 + 7
20 + 7
10 + 6 = 16
• This leads to understanding how the standard written method works.
= 196
Subtraction – Later stages
•Standard methods
 Complementary addition e.g. 6467 – 2684 = 3783
2684 + 16 (2700) can be refined to + 316 (3000)
+ 300 (3000)
+ 3467 (6467)
+ 3467 (6467)
3783
= 3783
 Standard decomposition layout will be introduced via partitioning into
HTU where exchange can be clearly shown.
Now it is your turn again!
•
Try using one of the methods shown to answer
these:
1. There are 83 children on the playground. 37 go in for their
lunch. How many are left outside?
2. A sports stadium holds 9010 spectators. 5643 people attend a football match. How
many empty seats are there?
This evening we will:
• Outline the features of our calculations policy.
• Focus on the strategies used to develop the
children’s understanding and application of
multiplication and division.
• Identify key areas where you can help your child
with their maths.
• Share classroom resources and approaches.
• And of course – DO SOME MATHS!
How do you multiply and divide?
57 x 2
742 ÷ 2
78 ÷ 2
43 x 50
36 x 25
700 ÷ 4
8 x 19
5.4 ÷ 6
18 x 15
17 ÷ 5
34 x 7
Multiplication – Early stages
• Practical activities and discussions.
 Counting in twos, fives and tens.
 Using activities to recognise doubles and halves.
 Using equipment to give lots of practice of making groups.
Multiplication – Mid stages
•Mental Strategies and Informal Methods
 Using arrays.
●●●●
2 x 4 means 2 lots of / groups of 4
●●●● 2 x 4 = 8
OR 4 x 2
is 4 lots of / groups of 2
●●
4x2=8
* Therefore demonstrating
●●
that multiplication can be
●●
done in any order.
●●
 Partitioning e.g.
4 x 13 =
4 x 3 = 12
4 x 10 = 40 Total 12 + 40 = 52
 Counting on using times tables.
They really need to know tables!!
Multiplication – Later stages
• Methods which lead to Standard Methods
 Use what is already known to help with what is not known:
if 3 x 4 = 12 then 30 x 4 = 120 and 30 x 40 = 1200
7 x 0.8 = we know 7 x 8 = 56 therefore 10 x smaller = 5.6
 The grid method:
1, First partition and put numbers in grid
2, Multiply each number together, remembering to use existing knowledge.
3, Total each row or column and then add together.
x
300
20
6
40
12000
800
240
2
600
40
12
= 13040
= 652
Total = 13692
Multiplication – Later stages
• Standard Methods
 Short multiplication
Long multiplication
HTU
48
HTU
67
x7
x36
5 6 (7 x 8)
4 2 (6 x 7)
2 8 0 (7 x 40)
3 6 0 (6 x 60)
336
2 1 0 (30 x 7)
1 8 0 0 (30 x 60)
2412
 Extend to decimals with up to two decimal places.
 Higher attaining children will move to formal methods of multiplication
carrying numbers underneath..
Now it is your turn!
• Try using one of the methods shown to answer these:
1. How many legs do 36 spiders have?
2. A concert hall has 124 rows of chairs, each row has 32 chairs.
How many chairs are there altogether?
Division – Early stages
• Practical activities and discussion
 Counting back in tens, twos and fives.
 Know halves ... half of 6 is 3
Division – Mid stages
•
Mental Strategies and Informal Methods
 Counting on and back using tables.
 Understanding division as sharing
e.g If 20 sweets are shared between 4 people how many will each get?
 Understanding division as grouping
e.g. How many groups of 5 are there in 20? (Use apparatus and tables)
 Using arrays:
10 divided into 2 groups = 5 in each group
●●●●● ●●●●●
OR 10 divided into 5 groups = 2 in each group
●●
●●
●●
●●
●●
Division – Mid stages
• Methods Strategies and Informal Methods
 Repeated subtraction: 12 ÷ 3 means how many 3’s in 12, therefore keep subtracting 3’s 12 - 3 = 9, 9 – 3
= 6 etc.
__-3____-3____-3____-3___
0
3
6
9
12
How many 3’s? = 4
 Start to understand remainders and if you need to round up or down.
e.g If I have 14 eggs, how many egg boxes will I need?
14 ÷ 6 = 2 remainder 2
2 full egg boxes and 2 in the other
Answer = 3 egg boxes
Division – Mid stages
• Methods Strategies and Informal Methods
 Chunking - Use times tables and partitioning:
93 ÷ 6 =
60 ÷ 6 = 10
(partition 93 using 6x table knowledge)
33 ÷ 6 = 5 r3
= 15 r 3
977 ÷ 36 = 977
- 720 (20 x 36)
257
- 180 (5 x 36)
77
- 72 (2 x 36)
5
 Extend to 4 digit numbers and decimals.
 Introduce ‘bus shelter’ when secure.
Answer = 27 r5
Now it is your turn again!
•
Try using one of the methods shown to answer
these:
1. 72 children were put into teams of 6 for sports day. How many teams were there?
2. 168 children and 19 adults are going on a school trip.
Each minibus holds 15 passengers. How many
minibuses will be needed?
Remember:
Can you explain the
method you used?
How did you do
it?
Which method
did you use?
Will this method work
for all of these
calculations?
What skills were you
using?
Talk me through
your workings.
How can you help at home?
Talk about how
you do maths.
Give praise and
encouragement.
Make sure maths is fun!
Ask your child to
explain.
Be positive!
Booklets for parents
• Helping your child with addition, subtraction,
multiplication and division.
Thank you for attending – your interest
means a lot to us and your children!