Teaching AlgorithmsHow algorithms are taught

Valerie Sereno

Simple Addition and Subtraction.

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.

Addition and Subtraction algorithm strategies.

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.

TRADING 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

Multiplication 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 U T U 1 6 x 3 6 x 9 2 3

DIVISION 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 = 3It 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.

DIVISION 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.