Counting by ones, counting by tens, and counting by groups and singles:

I was rather curious about how these methods of counting can be used to coordinate concepts and oral and written names for numbers.

Since this is not my area of expertise, I searched Google under the key words "counting oral written" to get these possible sources:

http://books.google.com/books?id=xqd4O1Za1kQC&pg=PA68&lpg=PA68&dq=counting+oral+written&source=web&ots=N-DMsE1Zb7&sig=q-_seFfVH6awL3st195ly-XoV9I&hl=en
http://books.google.com/books?id=eAcCAAAAYAAJ&pg=PA56&lpg=PA56&dq=counting+oral+written&source=web&ots=i07MIq_xvl&sig=qBSRA57r93eUTHWSRJRVEYBEIPA&hl=en
http://books.google.com/books?id=_p1DAAAAIAAJ&pg=PA262&lpg=PA262&dq=counting+oral+written&source=web&ots=toeNtE4gYR&sig=u0t4bQO4U_QZ32kG_Q7b-wtwevQ&hl=en
http://books.google.com/books?id=_p1DAAAAIAAJ&pg=PA262&lpg=PA262&dq=counting+oral+written&source=web&ots=toeNtE4gYR&sig=u0t4bQO4U_QZ32kG_Q7b-wtwevQ&hl=en

In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search.

I hope this helps. Thanks for asking.

Counting by ones, counting by tens, and counting by groups and singles are different methods of counting that can help coordinate concepts and oral and written names for numbers. Let's look at each method individually and see how they can be applied:

1. Counting by ones:
Counting by ones is the most basic and intuitive method of counting. It involves incrementing the count by one for each number in a sequence. For example, counting from 1 to 10 would go like this: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. This method is fundamental in developing number sense and understanding the concept of quantity.

When using counting by ones to coordinate concepts and oral and written names for numbers, it helps establish a direct correspondence between spoken numbers and their written representations. It also reinforces the order and sequence of numbers. Children typically learn to count by ones first, and it provides a solid foundation for further mathematical concepts.

2. Counting by tens:
Counting by tens involves incrementing the count by ten for each number in a sequence. For example, counting from 10 to 100 would go like this: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100. This method is efficient for larger numbers and helps develop an understanding of place value.

Counting by tens allows for grouping numbers into sets, which helps simplify calculations and mental math. For instance, if you need to add 30 and 40, you can count by tens: 30, 40, 50, instead of counting individual numbers. It also helps with skip counting, where you count numbers in a sequence but only include every nth number, such as counting every tenth number.

3. Counting by groups and singles:
Counting by groups and singles combines both the concepts of counting by ones and counting by tens. It involves counting objects in groups of ten and then counting the remaining objects individually if there are any left. This method is useful for developing a deeper understanding of place value and can help with more complex calculations involving larger numbers.

For example, if you have 27 apples, you can count them by groups of ten (20) and then count the remaining ones individually (21, 22, 23, 24, 25, 26, 27). This approach allows for efficient counting while still maintaining accuracy. It also highlights the idea of bundling groups of ten and the value associated with it.

In summary, counting by ones, counting by tens, and counting by groups and singles are different methods that contribute to coordinating concepts and oral and written names for numbers. Counting by ones establishes the foundation, counting by tens introduces place value, and counting by groups and singles combines both for a more comprehensive understanding of numbers and their representations.