It is important for children to achieve competency with numbers because of the relevance of numeracy and application of mathematical operations in everyday life.
In my school, teachers would play the CDRom to Nursery children, learning the concept on “Whole Numbers” teaching number words as they recite the poem “One, Two, Boo!” and singing “The Number Rumba”. Through this activity and some followup, they are able to differentiate the ordinal and cardinal sense of a number.
Number Sense Development
The common concepts taught to preschoolers in Singapore are:
1) Simple “Addition & Subtraction”
Children learn to add and subtract just by counting together at first and then, with practice, fairly quickly learn to recognize by memory. For example, children can learn to play with dominoes or with two dice and add up the quantities, at first by having to count all the dots, but after a while just from remembering the combinations. Children can play something like blackjack with cards and develop facility with adding the numbers on face cards.

Is it effective to draw sticks for counting? 
It is important to practice counting things with children. Counting can be incorporated into daily activities: counting money, counting toys or game parts, counting Cuisinaire rods or Unifix cubes, counting on a monthly calendar, counting how many utensils are needed for dinner, etc. Children can count candy, poker chips, the hearts (spades, clubs, diamonds) on face cards in a deck of cards, dots on dice, beans, or pennies. Games like Chutes and Ladders or Monopoly will give lots of practice counting.
Children often have trouble learning "transition" number names, such as the number that comes after the 9s in the two digit numbers; e.g., after 29, 39, 49, even though they can count by tens: 10, 20, 30, 40, etc. It takes extra practice to learn this. You have to help them understand that what comes after, say, 69, when counting by one's (70) is the same thing that comes after 60 (70) when counting by 10's. They need lots of practice to understand that when you finish the forties you go into the fifties, when you finish the twenties you go into the thirties. So give extra practice in counting, starting at 7 in each "decade"; i.e., 27, 28, 29, 30, 31, 32 or 57, 58, 59, 60, 61, 62, 63.

Model Drawing is an effective teaching aid to help children understand the problem. 
2) The Relationships of More, Less, and Same
Learning how to put numbers in order and compare them in less than and greater than guidelines is an important math skill. The important ideas are to make sure we use discrete materials that are movable when teaching this concept to children. Then, emphasize moving left to right when comparing groups is also essential in developing this concept. I would usually model estimating prior to actual comparing. For instance, I would initially cue students to differences in groups by using groups that are unlike in many attributes (size, shape, color), gradually fade these differences and have students compare groups with like attributes. Eventually, the learning objective would be to invite children to identify if a given group of objects has more than, less than or the same number of objects when compared to another group of objects.
2) Numeral Writing and Recognition
Most nursery children are able to count to twenty or even higher and kindergarteners up to 100; and most recognize numerals to twenty in isolation and can match one to one. I agree with the book that in most cases this concept is taught using matching exercise such as matching sets (count the number of cubes first) with numerals or words.

Number Lines 
3) Counting on and Counting back
I felt that this skill can only be practiced if children have strong recognition of number sense. Number lines is a great tool to enhance this development.
The uncommon concept is:
Anchoring Numbers to 5 and 10
Tens frames are a great tool for teaching guided math lessons. The tenframe provides a spatial representation that supports children’s visual understanding of “fivereferenced, tenreferenced, and doublesreferenced conceptions of numbers up to ten and the development of mental imagery for such numbers. It also supports development of partitions of ten.
Teachers should start off by using 5 frames to make sure that students learn the complements of 5. Then they can move on to using 10 frames. These frames can be used to teach students at the concrete, pictorial and abstract level. Use two color markers (if you don’t have these then just spray paint some lima beans so they are twocolored). See the ideas and links below for resources.
More Ideas and Games: