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Developing Mathematical Thinking in Addition and Subtraction. Aim of presentation. To encourage staff reflection on approaches to teaching addition and subtraction. To stimulate professional dialogue. To use as a CPD activity for staff individually or collegiately. - PowerPoint PPT Presentation
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Developing Mathematical Thinking in Addition and
Subtraction
Aim of presentation
To encourage staff reflection on approaches to teaching addition and subtraction.
To stimulate professional dialogue.
To use as a CPD activity for staff individually or collegiately.
Relevant Experiences and Outcomes
I can use practical materials and can count on and back to help me to
understand addition and subtraction, recording my ideas and solutions in
different ways. MNU 0-03a
I can use addition, subtraction, multiplication and division when solving
problems, making best use of the mental strategies and written skills I have
developed. MNU 1-03a
Having determined which calculations are needed, I can solve problems
involving whole numbers using a range of methods, sharing my approaches
and solutions with others. MNU 2-03a
I can use a variety of methods to solve number problems in familiar contexts,
clearly communicating my processes and solutions. MNU 3-03a
Progression
5
5
3
3
8
5
3
8
Empty Number Lines
3+ 5 = 5 + 33+ 5 = 5 + 3
Commutative property–Early level progression: ‘understand the idea that 3+4 is the same as 4+3
(commutative)’
28
28
3
3
31
28
3
31
Empty Number Lines
3+ 28 = 28 + 33+ 28 = 28 + 3
Commutative property enables you to start adding
from the larger number
34
Empty Number Lines – Addition Counting on – no crossing of tens
boundary34+2
334+2
3+10
+1
44 54
+10+1 +1
55 56 57
34
+10+3
44 54
+10
57
34
+20+3
54 57
Jumps of 10 and 1
Use the known fact 4+3
Add 20 in one jump
Increasing efficiency of approach
37
Empty Number Lines – AdditionCounting on – crossing of tens
boundary37+2
537+2
5+10
+1
47 57
+10+1 +1
58 59 60
37
+10+3
47 57
+10
37
+20
57 60
Jumps of 10 and 1
Add on 5 by bridging through the ten
Add 20 in one jump
+1 +1
61 62
+2
+3 +2
62
60 62
Increasing efficiency of approach
37 47 5734
-3
37 47 57
-10
34
-10
37
Empty Number Lines – Subtraction
Counting back – not crossing of tens boundary
57-2357-23
47 57
-10-1
3635
-3
-20
Jumps of 10 and 1
Using known facts 7-3=4
20 in one jump
34
-10-1-1
Increasing efficiency of approach
32 52
-3 -2
27
32 42 52
-10-10
32
Empty Number Lines – Subtraction
Counting back – crossing of tens boundary
52-2552-25
42 52
-10-1
3130
-3
-20
Jumps of 10 and 1
Bridge through a ten.
20 in one jump
29
-10-1-1-1-1
2827
-2
3027
Increasing efficiency of approach
47
+10
50 60 70
+10
73
47
Empty Number Lines – Subtraction Consider subtraction as counting
on73-4773-47
+10
50 60
+1 +1 +1
70
57
+3
+20
Jumps of 10 and 1
Jump to multiples of 10
Add 20 in one jump
+10+1 +1 +1
73
+3
71 7248 49
47 50 70 73
+3 +3
Increasing efficiency of approach
73-47 becoming 47+ ? = 73
73-47 becoming 47+ ? = 73
a a+3
3
3
a
3+a
3
Empty Number Lines
a + 3 = 3 + aa + 3 = 3 + a
a
Moving from specific to general.Commutative property - numbers can
be added in any order
a a+b
b
b
a
b+a
b
Empty Number Lines
a + b = b + aa + b = b + a
a
Commutative property - numbers can be added in any order
3 + 4 + 7
= 4 + 3 + 7
= 4 + (3 + 7)
= 4 + 10
=14
Using commutative and associative properties for addition.
Development and progression FIRST Level - ‘understanding and using commutative and associative properties when
calculating‘
Commutative property – swap the numbers round – change the order
Associative property – it does not matter how you group the numbers ie which calculation you do first What about
subtraction with 2
numbers and more than 2 numbers?
Next stepsWhat
informationwillyou
share with
colleagues?
What might you or your
staff do differently in
the classroom?
What else can you do as to improve learning and
teaching about number
What impact will this have on your
practice?
