Transcript Number line method

Welcome to our
Mathematics Evening
Please take a seat
First of all – 10 questions
whiteboards ready!
What is 134 less than 207?
What is 207 minus 134?
What is 207 subtract 134?
What is the difference between 207 and
134?
Can you decrease 207 by 134?
From 134 how many more to make 207?
What is 207 take away 134?
What is the remainder when 134 blocks
are removed from a pile containing 207?
I had 207 books and lost 134 of them,
how many does this leave?
I have £207 and spend £134, how much
do I have left?
Subtraction Vocabulary
• You have just seen 10 different ways of
asking the question 207-134
• There are other pieces of subtraction
vocabulary as well
• The answer was 73
• You don’t always see the word subtraction
when you have to subtract.
This evening we aim to…
Take an in depth look at subtraction. By…
• Showing you how the children need to
develop their subtraction skills through the
year groups and levels.
• Looking at the non-mental methods we teach
and the order in which we teach them.
• Showing you which mental maths facts are
crucial to each stage.
Why are we doing this?
• From your feedback after last year’s
calculation night, more parents
commented that they felt less comfortable
practising subtraction with their children
than addition.
• Also pupils (not just our pupils, pupils
nationally) find subtraction harder than
addition for any two given numbers.
How do the children’s
subtraction skills
progress?
Level 1
• Understand subtraction as take away.
• Use practical and informal methods to subtract a one
digit number from a one digit or two digit number
8-5= 7-3= 15-6 =
23 – 8 =
• Subtract a multiple of 10 from any 2 digit number
43-10= 67-10= 56-10=
• Find the difference by counting up
• Begin to recognise the inverse
10-4 =6
6+4 = 10
• Solve simple one-step problems
• Record calculations using number sentences that
include the appropriate symbols
The story of 5 teddy bears
1
2
3
4
5
Once there were 5 teddy bears
1 fell off the shelf …
… then there were 4
5 - 1
1
2
= 4
3
4
10 – 2 = 8
10 – 3 = 7
Finding the
difference between 2
numbers
7
What is the
difference between
2 and 7?
6
5
4
The difference is 5.
3
2
2
1
1
The red tower has
5 more blocks
1
2
3
4
1
2
3
4
5
6 7
8
9 10
What is the difference between
4 and 10?
The difference is 6
There are 6 more yellow blocks
1
11
21
31
41
51
61
71
81
91
2
12
22
32
42
52
62
72
82
92
3
13
23
33
43
53
63
73
83
93
4
14
24
34
44
54
64
74
84
94
5
15
25
35
45
55
65
75
85
95
6
16
26
36
46
56
66
76
86
96
7
17
27
37
47
57
67
77
87
97
8
18
28
38
48
58
68
78
88
98
9
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100
Level 1
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Count backwards from any number to 20
Say the number that is one less than any number to 20
Count back in 10s
Know by heart subtraction facts for numbers up to 5
Recognise that subtraction has to be done in a particular order
Calculate by taking away objects or by counting back on number
line
Find the difference by counting on
Write number sentences using symbols
Use objects, pictures and number sentences to answer a problem
Answer subtraction calculations using known facts
Understand and use words that link to subtraction
Break for Mental Work
• You are about to participate in a Year 1
Mental and Oral Starter (this usually lasts
for around ten minutes at the beginning of
every maths lesson, throughout school)
which will help you with the skills needed
for subtraction later!
• You will need your number fans
• By Miss Chapman
Year 2
• Subtract mentally a one digit number or a
multiple of 10 from any two digit number
• Use practical and informal written methods
to subtract two digit numbers
• Derive and recall all addition and
subtraction facts for each number to 10
• Recognise subtraction as the inverse of
addition
Level 2
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Count back in equal steps of 2, 5 and 10
Partition numbers to 100 beyond
Derive and recall all addition and subtraction facts for each number to at
least 10, all pairs with totals to 20 and all pairs of multiples of 10 with totals
up to 100
Subtract by partitioning 56-6
Subtract 10 from a two digit number
Subtract a multiple of 10 from a two digit number
Subtract by counting back or finding the difference by counting on
Subtract the nearest multiple of 10 and adjust
Partition the number to be subtracted 43-23
Choose how to solve a problem and explain the method
Record working out for subtraction problem
Understand the relationship between subtraction and addition. Say the
subtraction that matches an addition sentence visa versa
Explain how they know to use subtraction to solve a problem
Inverse
• Addition is the inverse of subtraction.
• Answers can be checked by using the
inverse operation.
• We can solve ‘missing number’ problems
by using the inverse method.
25 – 19 = 6
19+6 =25 6+19 = 25
Can you turn these addition number
sentences into subtractions?
• 6+2=8
• 9+7=16
• 23+41=64
• 39+22=61
•8 – 2 = 6
• 16-7 = 9
• 64- 23 = 41
• 61-39=22
Can you make a different
subtraction?
This method can be used to check
answers.
9+4=13
Check an answer by turning it into a subtraction
13-4=9 or 13-9= 4
Solve a missing number
problem
+7=15
The children use the numbers they
have been given!
8 +7=15
15-7= 8
It is an addition, so start at the end
and turn it into a subtraction…
Subtract the nearest multiple of
10 and adjust
52 – 9 =
Subtract the nearest multiple of 10
and adjust
First subtract
ten.
2
53
4
But that’s one
too many, so
now add one
back.
Now you’ve subtracted 9 from 52 by
subtracting ten then adding 1 back.
1
11
21
31
41
51
61
71
81
91
2
12
22
32
42
52
62
72
82
92
3
13
23
33
43
53
63
73
83
93
4
14
24
34
44
54
64
74
84
94
5
15
25
35
45
55
65
75
85
95
6
16
26
36
46
56
66
76
86
96
7
17
27
37
47
57
67
77
87
97
8
18
28
38
48
58
68
78
88
98
9
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100
Subtraction – Level 2
Using a blank number line to solve
calculations and problems. Also
known as finding the difference.
74-27=
Lets find the difference!
53 – 25 = 28
+5
25
+10
+10
30
40
+3
50
10+10= 20
5 + 3= 8
53
Try these
76 – 43
102 – 84
302 - 153
Use number line method.
Start at the lowest number.
Add on to the next multiple of ten.
Then add to the ten below the final number.
Then add on to the final number.
Remember to COUNT ON NOT BACK
Try it with decimals, it can become complicated.
SUBTRACTION – Mental Facts are Crucial
Number line method
- Must know (not be able to work out but know) your number
bonds to ten
4+6=? as well as 7+?=10 and 1+?=10
Because you always add upto the next multiple of ten
- You also need to know which multiple of ten comes next.
e.g. 60 is the next multiple of ten after 54
- You need to be able to add ten and small multiples of ten.
Number Line Method
• Some pupils continue to use it into L3, 4, 5
• Can become very complicated depending
how efficiently it is used (especially with
decimals)
• We don’t discourage pupils from using it if
they are using it properly.
2nd break for Mental Work
• This Mental and Oral Starter helps
develop place value.
• By Mrs Asvadi
Level 3 Expectations
• Subtract a two digit number from another
(mentally)
• Subtract a three digit number from another
(written)
• Subtract an amount of money from
another (written)
• To solve 1 or 2 step problems where these
calculations are needed
Level 3
• Understand the value of each digit in a 3 digit number
• Partition to 100 beyond simple tens and ones
e.g. 54 = 40+14 or 30+24
• Know by heart subtraction facts for numbers up to 20
• Subtract 2 digit numbers using an efficient method
• Record the steps of subtraction method
• Check answer using inverse
• Use subtraction to solve problems
Expanded decomposition
As the children progress through level 3 AND
have a thorough understanding of place value
and partitioning, we start to teach them the
more ‘standard methods’
Try these
765 – 543
402 – 284
3092 - 1534
Use the expanded decomposition method.
SUBTRACTION – Mental Facts are still Crucial
Expanded Decomposition Method
Must be know the subtraction facts
9-4
13-6
17-6
and others
Must be able to subtract a tens number from another (upto
200)
80-30
120-40
170-90
and others
Must be able to subtract a hundreds number from another
400-200
800-200
300-200
and others
Subtraction – compact
decomposition
Efficient for all subtractions.
Can get ‘messy’ if performing
a calculation like 2004 - 997
Try these
765 – 543
402 – 284
3092 - 1534
14.16 – 12.95
62.2 – 35.95
Use the compact
decomposition method.
SUBTRACTION – Mental Facts are Crucial
Compact Decomposition Method
Must be know the subtraction facts to twenty
9-4
13-6
17-6
and others
Must understand that in the example below
they are really subtracting 30 from 70
and not 3 from 7 (even though they
really are subtracting 3 from 7!)
Subtraction – compact
decomposition
PROs and CONs
•You never have to do a subtraction that is harder than 18-9
•You must understand your ‘place value’ for the method to
have any relevance to you or real life
•You must know your number facts upto 20 – 10
(any number to twenty subtract any number
upto ten)
•Can become ‘messy’ when you have a
thousands number on the top.
Level 4 Expectations
• To subtract thousands numbers
• To subtract decimals to 2 decimal places
• To use subtraction as a part of wider
problem solving
• To solve 1 or 2 step problems where these
calculations are needed
(From L4 onwards the method must be efficient)
Level 5 Expectations
• To subtract one decimal from another,
where the decimals do not have the same
number of digits
12.1 – 8.45 31.98 – 2.345
19 – 4.8
• To solve two or more step problems with
these calculations.
Which method is best?
Which method is best?
• Actually it depends on the question asked!
• Knowledge of number facts (addition and
subtraction) underpins all calculations, no
matter how large or involved (i.e.
decimals) the numbers are.
Thank you for taking part
• We hope it has been useful
• This PowerPoint will be placed on the
school website.
• Please feel free to ask any questions, to
members of staff, about the calculation
strategies used.