This is how we do it

How am I to teach students to count large numbers? Instead of counting by ones, I can teach students to count large numbers by grouping.  Students should be taught different ways to count as we being 'adults' are counting in different ways too. Initial stage, students count in ones. Next, group large numbers in 5s. Then group of 10s. Most importantly is to teach grouping before we do the counting for large numbers. Learning/teaching materials such as 10 frames or egg trays would be really useful to teach counting of larger numbers.  

10 frames

In Chapter 11 under the 'role of counting' pg 194. ---> 1. Counting by ones. 2. Counting by groups and singles. 3. Counting by tens and ones. According to Thompson (1990) "Each approach helps students think about the quantities in a different way".

How did you learn to do long division? Perhaps your answer would be like mine, the procedural method where we have to multiply and subtract in order to divide. I started paying attention to long division only after Dr Yeap asked "I thought I was dividing, then why am I multiplying and subtracting?" It was then that I realised the complexity of long division. Not all students may be able to understand it. So how should I teach them? Break numbers appropriately to do long division. Long division is not a universal method. Such as 51 divided by 3= breaking the number 51 into 30 and 21 then dividing it by 3. The whole idea is to break the number 51 into manageable numbers that could be easily divided by 3.