Select Page New standards call for an increased emphasis on understanding place value, rather than just, for example, identifying the digit in a certain place value position (eg., In the number 345, what digit is in the hundreds place?).  In Texas, both the 1st and 2nd grade TEKS contain wording that indicates students should be able to think flexibly about place value.

1.2.B Use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many hundreds, so many tens, and so many ones

2.2.A Use concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way as a sum of so many thousands, hundreds, tens, and ones

It’s that phrase in more than one way that sets the current standards apart from previous ones. Traditionally, we have only taught decomposing by place value in one way–the way the digits are written. So, for example, 43 would be always be decomposed as 4 tens and 3 ones. The new standards are saying that students should understand that the same number can be decomposed into 3 tens and 13 ones, or 2 tens and 23 ones. Why is this important? Look at the second example pictured above. Isn’t that what we do when we regroup to subtract? Think about subtracting 43 – 18. Because I don’t have enough ones to subtract, I need to trade one of my tens for 10 ones, which gives me 3 tens and 13 ones.

Notice that both the 1st and 2nd grade standards stress concrete and pictorial models. It is absolutely essential that students experience place value concepts with hands-on materials to fully understand that a ten and 10 ones represent the same value. My firsties are using linking cubes to compose 2-digit numbers in multiple ways. Linking cubes are the most concrete material to use for place value, because you can physically break a ten apart into 10 ones. While still concrete, base-10 blocks are more abstract, because the rod, which represents a ten when working with whole numbers, can’t be broken into 10 ones. Place value disks are even more abstract, but they allow us to work with larger numbers.    