Here's what I mean...I gave my students an entrance slip on Wednesday as class started. As they turned them in, I did a quick check of them and sorted them into two piles--"no problem" and "better check it out".
|These assessments are from my "Formative Assessment Toolbox: Place Value Edition" resource. CLICK HERE to see it!|
The same was true with a few of my kiddos who were making some mistakes with expanded and standard form. I need to sit right with them and watch them work--and ask their thinking.
I worked with a few students at a time with my expanded form task cards (actually, to make it more fun, I put the cards in piles and the students took turns picking cards--it's AMAZING how something as simple as letting students flip a card can keep them more engaged!)--and I watched them work on their white boards, asked them questions, and asked them to explain their thinking.
Watching students can help you see exactly what misconceptions students have--and for these place value concepts, several things come to the forefront and need coaching:
- A lack of understanding of our base 10 system (especially once students get past 1,000 numbers get much harder to visualize)
- A misunderstanding of "0" and how having "no" thousands gets represented
- An inability to understand the organization of our number system...that we need three "places" before a comma, then three more and a comma, and so on--and that each of those "groups" or "periods" has a name and follows the pattern of one, ten, hundred.
- The inability to recognize expanded form terms out of order (they might write 50 + 3 + 600 as 536)
- Difficulties reading and writing big numbers and "hearing" the parts. For example, if I say "four hundred thirty-two thousand", students should hear that "432" and know it will come in front of the thousand comma. If I say, "four hundred thirty-two thousand, seven", they should know that they need to write a 0 in the hundreds and tens spots because there are no hundreds or tens. Asking students to read and write big numbers is a great way to check for understanding.
So much of this is tricky whole class--you can present information this way, but when you see how many different ways place value understanding can break down, it becomes more and more clear how our interventions need to be much more personalized.
I have a ton of place value activities in my store so check them out if you are looking for games, lessons, and more. Just type "place value" into the search bar of my store!