multiple column multiplication woes
Here’s our challenge – and I’m sure some of you have been there too:
Despite knowing the times tables and fully understanding the process of multiple column multiplication inside and out …. mistakes are still being made.
A while ago, I created simple divided up graph paper on the computer so that I could print up as many copies as we wished or needed. She would solve her problem on the section on the graph paper – really was amazing in how it fixed the problem of column confusion and errors caused by messiness or accidental carry overs in wrong spots. Well, I think too much confidence came in and then the paper was ditched. Slowly with more difficult problems, the slipping and sliding of columns has been recurring again.
The workbook doesn’t give enough room to solve the problems so numbers get squished and messy. In unit 28 they start giving you vertical separating lines in the workbook… but that wasn’t even enough to help.
As you see here, while it looks somewhat clear, something is still going funny:
Math is my weakest of all areas personally. I love Math U See …. but I’m just thrown by the way that they put the carry overs underneath amongst the rows instead of up top. I understand why it’s better than piling on top …. but it’s a lot to manage down there ! It’s hard to teach an old dog new tricks… and I learned the other way. Trying to be flexible on this one!
The answer key I find rather headache inducing. As you see…. they aren’t fans of putting the place holder zeros down there…. wow, that’s a lot of rows and spaces to follow around when you’re trying to figure out why your child’s answer was incorrect with them.
So with frustration, I pulled out more of my handy dandy graph paper that I made – and had the happy thought to USE COLORED PENCIL CRAYONS to represent each line in the problem (including their own carryovers.) As you can see here, you can EASILY see everything 4x in red, everything 5x in orange and everything 3x in purple. But even more awesome… is that when it comes time to add the columns in pencil, those new carryovers are in pencil too so they are really obvious. Being in graph paper vs just vertical line guides… is that every number is only allowed to occupy one square space. In her other multiplication problems we have super teeny weeny numbers squished in all over the place, you couldn’t tell which column they were meant to go in, or if they were a duplicate accidental number, or at what point in the problem solving that particular number showed up exactly. With this method we see everything – and you know what…. all the problems that were incorrect previously, were corrected perfectly instantly on this math graph paper. Sooooo happy. Better yet…. she was even happier. Feeling good, confident…. we just needed a bit of visual organization. BOTH of us. I needed it too big time.
Another helpful bit of advice that I heard this summer at a Diane Craft convention lecture was the helpfulness of bringing any ‘problem and solution’ together to life through illustrations and color. Pebbles and I are both very right brained, so we gave this a try on a few tricky ones to test the theory.
She made up her own story.
In this case, she turned the 6 into a cat and the 9 into a flower.
In another one she made the 7 into a bird, and the 6 into a cat again.
Yup, we have another cat in this one. (I will always see ‘6’ as a cat now!)
“6 cats times 8 people equals 48 songs.” I can hear it now … yikes!
Diane Craft says that it doesn’t matter what the story is – just has to create a picture to put in your mind. Put it up in a higher spot and look up at it daily. Before you know it, you’ll never think of 6×9 the same way again! Totally works.