How I Teach Larger Place Value (MUS Beta)

How do you turn 200,000 + 40,000 + 6,000 + 500 into 246,500 instead of 2,465?

Most of my children have had difficulty learning to order these big numbers. Personally, I wonder if this lesson group should be in a later book, but it's in Beta, so we deal with it. Here's what I do.

I have them turn lined paper to the side, so they can write one number in each lined column. I have them write the biggest number first, ie. 200,000. It takes SIX columns to write it out. I mention that you have to think about these big numbers right to left, which is backward from reading, so it makes it hard. I use my fingertip to block out most of the number and say "units", move it to the left slightly, "tens", repeat movement, "hundreds" etc. to teach the names of the places. I tell them that they can count the number of digits to make sure it is the same as the one printed on the page.

Then I have them write the next number (40,000) underneath the first, UNITS FIRST! I know it's backwards from the usual way, but it's what worked for me. That way units end up under units, tens, under tens, etc. I cover the number again, and verbally point out that the units are lined up, then the tens, then the hundreds, etc. Then they write the next number, units first, (6,000), then the next, units first, (500). Then we add the units, the tens, the hundreds, etc, to get the right number. I emphasis that in this kind of problem, the answer must have the same number of digits as the largest (and usually it's the first written) number in the series they are to add.

Some of my older students overheard me teaching this and came to say that it was the hardest part of the book. They also said that when these problems come up (very infrequently) later on, it seems much easier than it does when you are first learning it. I love spontaneous encouragement!

Also, I do not make my students *master* this skill like I do math facts. It is not really used much after these lessons and, like I said at the beginning, it is a higher skill, in my opinion, than is needed at this level. It comes much more naturally later on.