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Teaching Algorithms

Teaching Algorithms. How 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.

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Teaching Algorithms

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  1. Teaching Algorithms How algorithms are taught Valerie Sereno

  2. 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.

  3. 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 factsie 8+7=15 and 15-7=8 • These cannot be applied unless the student has a thorough grasp of basic number facts.

  4. 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

  5. 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

  6. 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.

  7. 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.

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