Transcript Teaching Algorithms - Hassall Grove Public School

Addition in Early Stage 1 and Stage 1 (K-2) are
mostly taught horizontally: 3 + 4= 7 they do not
move into vertical algorithms until late in year 2.
 In early stage 1 (K) all are taught using diagrams
or objects that the students can see and
physically manipulate.
 Students need to know number facts i.e;
knowing numbers before and after, counting
backwards and forwards and skip counting.
 Students learn to use the bigger number and
count on.

 Using
doubles and near doubles; 7 + 8 =
becomes 7 + 7 + 1= 15.
 Using combination s of 10 i.e 4 +6 and 7 +3
and bridging to 10 breaking down
algorithms i. e 17+5, 17+3= 20 then
20+2=22 .
Using related addition and subtraction facts
ie 8+7=15 and 15-7=8
 These cannot be applied unless the student
has a thorough grasp of basic number facts.

The process of trading in addition and
subtraction has changed and is taught as a
vertical algorithm.
 i. e
T U
T U
4 5 +
3 7 _
1 7
1 9

We no longer “borrow and pay back” we “trade”
H T U
H T U
7 6 5 +
7 6 5 _
3 9
3 9
Students MUST have a strong knowledge of
number facts to understand and solve
multiplication problems.
Memorising the times tables means students can
solve more difficult multiplication problems with
much more ease.
 Multiplication does not get taught thoroughly
until stage 2 (year 3)
 So 3 x 4 is basically 3+3+3+3 (or 4+4+4)
(repeated addition)
 Mixed multiplication

T
1
U
6 x
9
T
3
2
U
6 x
3
To put it simply, it is “sharing”
 Division is taught more thoroughly again in
stage 2.
 Is much easier if the student understands
multiplication- as they can be seen as
“related” 4 x 3 = 12 as 12 ÷ 4 = 3
It can also be verbalised as how many times
does 4 go into 12.
Can also be seen as repeated subtraction.
 Division can be the most confusing of all
processes but the best way for students who
are struggling is to draw a diagram.

It becomes difficult when dealing with
“remainders” or “leftovers”- this is taught more
thoroughly in stage 3 (yr 5-6)
r
 4 68
4 67
r
12 144
12 149
As you can see these are solved due to
knowledge of multiplication.


Long Division can be taught but is no longer a
mandatory part of the NSW mathematics
curriculum in primary schools.