Integrated mathematics scheme: IMS T2 - National STEM Centre

Unit 1, page 1
Comment
Negative numbers has been considered a difficult topic in the
past. The use of a calculator makes it into a topic that can be
handled and explored by most children. The key to the
whole thing lies in considering whether a larger number is
being taken from a smaller. Many of the physical explanations
confuse the issue so we use them as applications
rather than explanations. Once children understand that
+ 1 + -1 = 0 the rest can be developed easily. A helpful aid
is to make red and blue cards 1+11,1-11with [Q] on the back
of both cards, showing that a + 1 and -1 together can be
treated as zero. This leads to the following explanations of
addition and subtraction of negatives.
(i) 3 + 5 ... (+1, +1, +1) + (+1, +1, +1, +1, +1)~ +8
(ii) -3+-5 ... (-1,-1,-1)+
(-1, -1, -1, -1, -1)~-8
(iii) - 3 + 5 ... -1 -1 -1
+1 +1 +1 +1 +1~ +2
tit
000
(iv) +3+-5 +1+1+1
-1-1-1-1-1~-2
t t t
000
From (iii) it is clear that adding - 3 has the same effect as
subtracting 3, and this leads to all the required subtraction
results.
(v) 4-3~4+-3~1
(vi) - 2 - - 3~ - 2 + 3~ 1
(vii) 2 - - 3~ 2 + 3~ 5
(viii) -4 -7~ -4 + -7~ -11
The subtraction can be confirmed by the calculator and also
by 'take away reasoning' as follows.
1