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Teaching Algorithms

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Teaching Algorithms

How algorithms are taught

Valerie Sereno

- 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 factsie 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 U T U

1 6 x 3 6 x

9 2 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 = 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.

- 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.