According to my observation, the concept of place value is equally hard for the teachers to make students develop an understanding of the same. Also known as Hindu Arabic system, it is fundamental to all further use of numerics. The multi digit numbers concept is quite tough to understand.
The physical base 10 blocks help students to develop meaningful and conceptual structures for multi digit numbers(English & Halford, 1995) and also understand the analogical relationship between the blocks and numbers (Fuson, 1992). To overcome the difficulty of physical blocks, electronic system is also introduced which includes the grouping and regrouping of numbers and blocks with supported with an audio help.
There are many mental and written strategies for understanding the concepts of the place value system and involving different calculations like addition, subtraction, multiplication, division etc. mental strategies are very important as it records methods which is very useful for future understanding and reference.
According to my observation, students apply and record these mental and written concepts strategies like I added 21+20 to get 41 and then added 5 to get 46, ...