Transcript Title Slide

Session 1
Setting the Scene
Why is it all so different today?
•A
desire to do something different to counter the
nations phobia around mathematics
• Development of understanding of effective
methods to teaching mathematics since mid
1990s
• Exploration of effective approaches from some
of the most successful education systems in the
world
• Extensive research and trialling
There is no “right” way to work!
Children exposed to a range of methods – if you
get an answer, then the method works.
Methods selected will depend upon the situation
and the numbers involved, including when to
use calculators. Efficiency is as important as
accuracy.
Children make decisions about methods and
draw on a range of strategies and approaches
when applying Maths is context.
Children in same class could be using different
methods to others depending on their ability,
confidence and stage of mathematical
development.
ALSO…
Maths is also about more than correct
answers! Real mathematicians are more
than calculators.
Maths is about reasoning, explaining,
testing, visualising, using the correct
vocabulary.
Maths is more than just number.
Mathematical paper folding
Correct use of mathematical vocabulary is
key importance
Children work in meaningful collaboration
– it is not just copying!
Communication can lead to development
and clarification of ideas and concepts
Key Concepts
Structured representations of
number
Digit Cards Calculation
Place value underpins out whole counting
system
Language associated is at odds with
concept e.g. 17 – “seventeen” – automatic
to put the 7 as the first digit
Give digits the correct value e.g. 157 is not
“one five seven” but one hundred and fifty
seven
How to Partition in Addition
25 + 12
20
5
10
20 + 10 = 30
5+ 2 = 7
30 + 7 = 37
2
Or….
25 + 12
10
25 + 10 = 35
35 + 2 = 37
2
How to Partition in Subtraction
25 - 12
10
25 - 10 = 15
15 - 2 = 13
2
Numberline Golf
Numberline Golf
Clubs
2
Strength 0.5
4
6
1
8
3
10
5
7
Numberline Golf
56
Clubs
2
Strength 0.5
4
6
1
8
3
10
5
7
Numberline Golf
56
10 x 5
Clubs
2
Strength 0.5
4
6
1
8
3
10
5
7
Numberline Golf
56
10 x 5
Clubs
2
Strength 0.5
6x1
4
6
1
8
3
10
5
7
Numberline Golf
Numbertracks and numberlines cement
the understanding of the continuous
number system
Numbertracks and numberlines support all
kinds of calculation
Numbertracks and numberlines link to
mental methods of calculation
123456789
10
1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 10
The Numberline!!
16 + 8
16 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
16
17
18
19
20
21
22
23
24
The Numberline!!
16 + 8
16 + 2+ 2 + 2 + 2
16
17
18
19
20
21
22
23
24
The Numberline!!
16 + 8
16 + 4 + 4
16
17
18
19
20
21
22
23
24
The Numberline!!
67 - 32
67 - 10 - 10 - 10 - 2
-2
35
-10
37
ANSWER!!!
-10
47
-10
57
67
Why don’t you go straight to
vertical methods?
Incorrect lining up of columns
Lack of understanding of size of numbers,
therefore reasonableness of answers
Recognising when calculations are better
carried out mentally
Forgetting about carried 10s/100s
Vertical methods require more
understanding than numberlines
Also…
33 + 17
33 + 17
33
+17
I need to know that
the digits represent
tens and units.
I need to know that
I have to set them
out with digits in
the correct
columns.
33 + 17
33
+17
I have to know that
I start from the
units column.
I have to know
where the answer
for the units
column goes.
33 + 17
33
+17
0
1
I have to know
what happens to
the carried ten.
33 + 17
33
+17
0
1
I have to know that
I am dealing with
tens now to help
me check that my
answer makes
sense, even
though it looks like
I am working with 3
and 1
33 + 17
33
+17
0
1
I need to
remember to add
in the carried ten
I have to know how
to write the 50 in
the context of this
answer – what
happens to the 0?
33 + 17
33
+17
5 0
1
I need to
remember to add
in the carried ten
I have to know how
to write the 50 in
the context of this
answer – what
happens to the 0?
Common errors for this question include…
33
33
33
+17
+17
+17
41
410
4010
33
+17
40
0
33
+
17
347
33 + 17
I need to start at
33.
33
33 + 17
I partition 17 into
10 and 7.
I add 10.
33
43
33 + 17
I add 7.
I get my answer.
33
43
50
Place Value Challenge
+
+
Place Value Challenge
Fun and engaging
Catering for different learning styles
Recording is not always the focus –
learning about concepts is
Focus on using and applying
A few things about multiplication
and division
Multiplication as an Array
2x4=8
4 lots of 2 = 8
4x2=8
2 lots of 4 = 8
Arrays are quite common –
ice cube trays, egg boxes,
chocolate boxes, medicine
wrapping, tiles etc.
Multiplication by 10
7 x 10 = 70
Multiplication by 10
7 x 10 = 70
Multiplication by 10
7 x 10 = 70
BUT WE DIDN’T JUST ADD A 0!
Multiplication by 10
7 x 10 = 70
BUT WE DIDN’T JUST ADD A 0!
If you add a 0, that means
7+0=7
Multiplication by 10
H
T
U
Multiplication by 10
H
T
U
7
Multiplication by 10
H
T
7
U
7
Multiplication by 10
H
T
7
U
7
0
Multiplication Tables
Three for free!
If you know 3 x 5 = 15, you also know
5 x 3 = 15
15  5 = 3
15  3 = 5
Division
Share 8 sweets between two children.
Division
Share 8 sweets between two children.
Division
Share 8 sweets between two children.
Division
Share 8 sweets between two children.
Division
Share 8 sweets between two children.
Division
Share 8 sweets between two children.
Division
Share 8 sweets between two children.
Division
Share 8 sweets between two children.
Division
Share 8 sweets between two children.
Division
Share 8 sweets between two children.
4 sweets in each pile
Division
Share 9 sweets between two children.
Division
Share 9 sweets between two children.
Division
Share 9 sweets between two children.
Division
Share 9 sweets between two children.
Division
Share 9 sweets between two children.
Division
Share 9 sweets between two children.
Division
Share 9 sweets between two children.
Division
Share 9 sweets between two children.
Division
Share 9 sweets between two children.
Division
Share 9 sweets between two children.
Division
Share 9 sweets between two children.
Division
Share 9 sweets between two children.
Is it 4 or 5? Or
does it matter
as long as I
have the
bigger pile?
Division
Divide 9 sweets between two children.
Division
Divide 9 sweets between two children.
Division
Divide 9 sweets between two children.
Division
Divide 9 sweets between two children.
Division
Divide 9 sweets between two children.
Division
Divide 9 sweets between two children.
4 groups and
one left over.
4r1
Repeated Subtraction (Grouping)
8  2 can be thought of as
8–2=6
6–2=4
I’ve taken 2
away 4 times, so
4–2=2
the answer is 4!!
2–2=0
-2
0
-2
2
-2
4
-2
6
8
Repeated Subtraction (Grouping)
9 2 can be thought of as
9–2=7
I’ve taken 2 away 4
times, so the answer is
7–2=5
4!! I have one left over.
5–2=3
3–2=1
-2
0
1
-2
3
-2
5
-2
7
9
Repeated Addition (multiplication)
2 x 4 can be thought of as
2+2+2+2
+2
0
+2
2
+2
4
+2
6
8