Kindergarten Math Readiness 
Counting on and counting backward are useful math concepts. 

Preparing for the learning requirements of arithmetic in first grade, Kindergarten math readiness involves much more than being able to count to 20 ... or any number ... set by education authorities. The ability to do so is a good start.
It does not imply understanding, however. It may be nothing more than counting by memory, in a set, mechanical way. 
What do you do when your child can count from one to 20, flawlessly?
How can you apply that level of knowledge to your child's life experience for future use and appreciation? 
What don't we measure using numbers? 

Our lives are imbued with numbers: time, distance, amount, the acquisition and production of goods.
Numbers are all around us... even when we don't think they are.
When we don't use actual numbers, we often use words that imply numbers...words like more, yesterday, tomorrow, few, many, some.

If your child has a strong number sense, you might want to introduce the idea of counting on. Counting on is an efficient way to add.
Counting on is effective problemsolving. It requires your child to hold the number of objects in one group and to count on from there the objects in the next group to reach the total. 
If 5 red apples exists in a group, adding 2 green apples does not require the development of the equation 5 + 2 = 7. Counting on means counting two numbers beyond 5 to yield the total: (5), 6,7.
Provide many experiences using various combinations to 5. Quick, confident responses will signal adding one more for a total of 6. Work those combinations, using the sort, classify, count approach. 

Increase the number of objects as your child's skill develops. 
In this process, your child will discover, quite quickly, that counting on can begin with either group. With repeated practice, your kindergartener will gain a concrete understanding of the variety of ways his counting skill can be applied.
These activities are part and parcel of kindergarten math readiness.
If, on the other hand, your child doesn't have that level of understanding, he will likely count from one to seven each time the problem is presented. 

More than that, your child will not be able to hold the number contained in the first group from one counting trial to the next. The evidence? She will count the first group from one, repeatedly. 

Holding a number in mind is an aspect of kindergarten math readiness.
If that happens, keep sorting and classifying buttons, cereal, pasta, toys, candy  objects familiar to your child's world. Count the objects in each group. 

For example, take a small quantity of green objects and red objects. Mix them together. If your child sorts by color, you'll have two groups. (Remember, your child may surprise you by producing a sort pattern you didn't anticipate. In that case, use two of the groups for the exercise.) Count how many in each group. How many objects are there, altogether?
One day, your child may discover the principal of counting on! On her own! That will signal a new level of understanding has just been reached. 

Your work with sorting, classifying, and counting will have paid off! 
