2.  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.  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.

4.  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.  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 1 6 x 3 6 x 9 2 3

6.  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.

7.  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.