Transcript What strategies could you use?

Developing Mathematical Thinking
in Addition and Subtraction
Checking
Understanding
What strategies could you
use?
Count up from /
back from.
Empty number
line actual or
imagined
round and
compensate
eg 42 – 30 then +1
Subtraction
42 - 29
Decomposition
?
conserve number ie 42 – 29 = 43 - 30
29
42
30
43
Strategies for calculation
 2704 + 3562
 2704 + 5998
 2704 + 96
They all start
with the same
number
How would your
pupils solve these?
• 5006 – 3562
• 5006 - 99
• 5006 – 4958
Efficiency of calculation
– it depends on the
relationship between the
numbers involved
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
Should it make a
difference if this
was written
horizontally as
6000 – 2369?
Is decomposition
the most sensible
strategy here?
Checking Understanding
Subtract:
Do you
encourage and
discuss informal
jottings which
pupils use?
6,000
– 2,369
Do pupils develop
understanding of
the process using
practical
material?
How can we encourage understanding and develop learning?
Applying Strategies
A concert is taking place. 6003 tickets are
on sale. 5997 tickets sell in a week. How
many tickets remain on sale ?
Is decomposition
the most sensible
strategy here?
How can we help
pupils in solving
word problems?
Development and progression FIRST Level - ‘solving word problems
involving the four number operations‘
Time – a further
complication.
A common error –
2h 40 mins. Why?
George took 7 hours 55 minutes to travel
from Glasgow to London.
Eric took 9 hours 15 minutes to drive the
same journey.
How much longer did Eric take?
How can we encourage understanding and develop learning?
Properties of Number
Inverses
The inverse of + is eg family of four facts
Do you encourage
your pupils to
make the links?
5+2 = 7
2+5 = 7
7–2 = 5
7-5 = 2
Knowing one fact
means you know four.
Properties of Number
Identity: An important mathematical concept
identity of + and - is 0
2+0=2
e.g.
6-0=6
+0=
-0=
x+0=x
Does it matter
how many
items are in the
cup?
Progression
to formal
algebra
a-0=a
Support for progression in mathematics
http://www.ltscotland.org.uk/curriculumforexcellence/mathematics/outco
mes/moreinformation/developmentandprogression.asp
Next steps
What might you
or your staff do
differently in the
classroom?
What impact will this
have on your practice?
What else can you do as to
improve learning and teaching
about number
What
information
willyou
share with
colleagues?