Standard place value
Bundling objects into sets of 10 (then 10 tens into one hundred, and 10 hundreds into one thousand, etc.) is the basis of our place value system.
Our system of recorded symbols allocates any given digit a place value depending on its position. The position matches this system of grouping. For example, in 456 the 5 refers to five counts of ten objects.
The power of the place value system is that it makes counting and operating on numbers much simpler than working with individual objects.
Targetted activities can improve the ability of students to anticipate the results of joining or separating sets.
You can read more in the article Is Your Classroom Mental? on the AAMT website.
Students who are in the early stages of learning about place value need to understand the power of grouping ones into sets of 10. They also need to know the way tens and ones groupings are represented in written numerals.
Parking ones and moving tens
An important understanding of early strategic use of place value is what changes (ones, tens or both) in a given calculation. 'Parking ones' refers to the idea of leaving ones unchanged while working on tens.
The power of ten
The place value system was developed as an efficient way to count and record large numbers. Groupings of 10 allow students to efficiently combine, separate or find the difference between two-digit numbers.
Renaming to add and subtract
Combining 10 ones to form a new 10 or decomposing a 10 into ones are procedures. Automation of these renaming procedures eases the memory load in more complex calculations.