Regarding Place Value:

I have had a few conversations about place value as it relates to number and numeracy, and I thought I would share a couple basic concepts that may help with your students' mastery of place value. I have been working on identifying some interventions for number and numeracy, so this is relevant to that also:

The emphasis of simple games is really important in engaging students toward quantitative thinking. Since a prerequisite for understanding place value is understanding ten and multiples of ten, games that reinforce place value mastery often emphasize and involve the number ten in one way or another. Using base-ten blocks, for example, is a common and effective introductory method for showing students how groups of ten, when put together, represent other quantities with names like "30," and "70," and "120." But one thing those base-ten blocks to is leave the training wheels on... Students can count each "one" on every base ten block. For example, if they count the spaces between the notches in a ten block, they count ten ones. If they count all the squares on the hundred block, they can count ten sets of ten, or one hundred ones. This is not a bad thing for introductory lessons, but the next step would be to eliminate the notches so students can see and grasp REPRESENTATIONS of ten without counting, such as with Cuisinaire rods. That serves as a bridge to grasping the number value in symbolic form. For example, if a student sees "172," and they can grab a representation of 100 (base ten 100 square), seven tens (cuisinaire rods), and two ones (Cuisinaire), without having all the notches to count, that is one short step away from recognizing 172: "1" as 100, the "7" as seven tens, and the "2" as two ones.

Other things besides Cuisinaire rods can be used to represent tens and hundreds (there is a neat Unifix cube trick you can do on your hands; I can show you if you don't already know this).

The more opportunities children have to use representations of quantity without being allowed to count by ones to find the answer, the more confident (and eventually, fluent) they will be with their learning of place value.

I hope this is at least a little helpful. Let's keep these discussions going!

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