M1N2 - Understanding "place values"

M1N2. Students will understand place value notation for the numbers 1 to 99. (Discussions may allude to 3-digit numbers to assist in understanding place value.)

I have written about this standard previously. In that entry, I discussed different rules of our numeration system. In this post, I want to discuss a bit about what it means to understand "place value."

When you ask young children problems like 24 + 32 before they learn addition of two-digit numbers formally, they would often say something like this: "I know 20 and 30 is 50 and 4 and 2 is 6. So, the answer is 56." So, does this child understand "place value"? It is difficult to say. English number words beyond 20 has a very distinct and easily recognizable pattern. 21 is read "twenty one," 22 "twenty two," etc.. Young children easily notice that "twenty" and "one." Thus, they can easily "decompose" the number words into "twenty" and "two," but that is not enough to say they understand our number system. Understanding of our number system requires not only recognizing 21 is made up of 20 and 1, but also 21 is made up of "2 tens and 1." Because children are often familiar with the decade number words, "ten, twenty, thirty, forty, fifty, sixty, ..." they can determine that "twenty and thirty is fifty." Children who understand "place value" can say that 20+30 is the same things as 2 tens plus 3 tens, thus 2+3=5 tens.

Clearly understanding of "place value" is important for children's understanding of computational algorithms starting in Grade 2. However, this understanding is one of the important goals when we have children think about how to solve problems like 20+30 in Grade 1 (M1N3g). The focus of M1N3g is not to develop computational strategies but really to deepen their understanding of our number system.