I bet many of your students are weak in this skill too. Just last week, I had to take a detour from my planned math lessons and revisit something they should have learned in second grade - how many tens are in a 3-digit number. It was a simple question, or so I thought...
"What is the total number of tens in the number 238?"
All of their hands shot up in the air and all of them thought the answer was 3.
"No, I don't want to know what number is in the tens place. If we were going to build the number 138 and we only had tens rods and ones blocks, how many tens would we need?"
They stared at me like I was speaking in tongues. No one had an understanding that 2 hundreds is the same as 20 tens. So I got out the math blocks. We counted by tens. We figured it out. We practiced with pictures of math blocks, We did it forwards and backwards. They were ready, right?
So, I wrote a problem on the white board...
238 - 57
I asked them how we could solve this problem. Note that I did not ask them to find the answer. I wanted to know how they would tackle the problem itself. Not one of them could verbalize the idea that you would need to move one of the hundreds from the hundreds place and convert it into tens in order to subtract the 50. Nor did anyone see that there were 23 tens from which you could subtract 5 tens. I got all kinds of things like...
"Cross off the two and cross off the three and put a one above it and then you have thirteen which is bigger than five."
I prodded them to explain their ideas and again, they just stared at me. Clearly they had been shown the algorithm either by a parent or a teacher, but they had no understanding of what the procedure meant or why they were doing it.
I'm sure my class isn't the only group of 8-year olds who get stuck when it comes to understanding what regrouping means. That's where expanded form comes in. When you break a problem down into expanded form before subtracting, it all becomes very clear. This is what it looks like...
Now students are forced to see the value of each digit and therefore, understand what is being moved from one column to the next. It's the logical step between concrete and abstract and it's missing from a lot of math instruction. If your kids don't have a solid understanding of regrouping and why they are doing it, try using the expanded form model before the standard algorithm. I think you'll find that it really helps!
A few resources you might like:
