So Friday, I approached multiplication of multiple digit numbers with my 5th graders. We had tears, we had fits, we had issues (I have a VERY emotional class). I can work through this. What I am really struggling with is the "Why's." I LOVE this class because they are so knowledge thirsty but they want to know why we multiply the way we do. They want to know why, if you take 234 x 56, you can't take the 4 x 6, the 5 x 3, and then drop down the 2. I tell them because that's not the answer! Because if you take 234 x 56 you don't get 374, it doesn't make any sense! But they get stuck there. They can't get past it. Last year's teacher said that she cried over this classes Math skills. They just plain out don't get it. She said they would pull out the manipulatives and they would get it while they were doing that, and then they would go to the paper, and they couldn't do it anymore. And now they are into multiple digit multiplication when I can't really pull out the blocks and show them an array of 234 x 56. Does anyone have any tips for me? OR feel my pain?
It's too bad you don't have access to some Montessori materials. There's an elementary material called the checkerboard that really helps with double digit multiplication in a nice, hands-on way. http://thelearningark.blogspot.com/2009/01/i-am-obsessed-with-checker-board.html If you do a search for montessori checkerboard, lots of information will come up.
This is my first year teaching 5th grade so I'm not sure if this will work with your students but it did with mine. I used the partial product method to teach multiplication. Break down each part of the number and add it up. For example, 200 x 50, 30 x 50, 4 x 50, 200 x 6, 30 x 6, and 4 x 6, then add up all of the products. It takes a long time and it can be confusing for some, but it makes it clearer for most.
It's all about place value. 234 x 56 is like (200 x 56) + (30 x 56) + (4 x 56). Maybe consider having them do it that way a few times, then go back to the "real" way of doing it... which is really just the reverse-- the 4, then the 30 then the 200. There should be no tears or fits; this is just an extension of math they already know how to do. Just have them take a deep breath and tackle it slowly.
I taught mine with the partial products, too. Some of them preferred that and continued doing it that way, even though it took much longer. It just made more sents to them. I know some people have a lot of success with the lattice method--maybe something to look into?
I actually did that and they got upset and said it was more confusing that way. I think I'm going to try the Lattice Multiplication method on Monday and then if that doesn't seem to go well, I'll try the other method again when they've calmed down a bit. Holybajoly though, when these guys don't understand something, the tears!!!
I have to admit that I am relieved to know that I am not the only one having this problem. I tried to do a math tower with them the other day (a game on of the other teachers told me about) and they could not multiply or divide. They are also having a terrible time rounding and doing decimal place values. I had them make huge place value charts on Friday, so I'm hoping this helps. I have to think of more creative things to do. The math books we use are terrible. I wish they had Everyday Math because then they would all know those different methods to multiply. I would love to teach them, but at this point, I feel like it would only confuse them.
Can you back up the multiplication to smaller numbers until they understand the importance of place value when multiplying? Maybe write some word problems using their names and everyday objects to actually put the numbers in context. My last two classes have really struggled in math and those two strategies worked for us. For my groups that don't have a good grasp of multiplication, use two different methods that show partial products: the area model (using boxes) and complete multiplication (shows partial products in a column). We associate each model with a teacher (i have a co-teacher... he's tall and skinny, so his way is complete mult. and I'm wider and like to draw, so area model is mine ) and make them practice both ways so they can check themselves. Good luck, I completely understand what you're going through!
Place value, place value, place value. For years I've stressed the importance of this, especially to the early elementary teachers. The kids need hands-on experience for years before moving on to paper and pencil.
I would most definitely suggest NOT introducing the lattice multiplication method yet. These kids need to understand the place value first, or you are just going to have more tears and frustration. Remember, it is not about just getting the right answer. Without that number sense, math is going to continue to be a struggle for them. You said you can't use manipulatives. I bet you can, even if you have to get big sheets of butcher paper and have them draw 30 groups of 256 (you might want to start with smaller numbers!) Just don't push it. Make absolutely certain they understand what single digit multiplication is, even if that takes a few days. Just my :twocents:
I definitely recommend teaching the partial products way---I call it Place Value Multiplication. It makes alot of sense to most kids. After you've practiced that awhile, then you can teach lattice, which most kids seem to get. I would do the place value way first--then lattice....
It's a hard skill for them...it just is.... We are using Math Expressions--it's different...but I like a few things about it....for one when we are subtracting 422-388; we refer to the 2 in the tens place as 20; the 8 in the tens place as 80..we then ungroup the 400; to 300 and add the 100 to the 80---thus making it 380....I think this will help these students as they learn 2 digit x. You might want to go back and review with them what the numbers actually mean...especially if they are low to begin with.
Place value is the most important concept they have to understand-and I definitely recommend the partial product method over the lattice. The kids like Lattice, because it is easy (they only multiply single digits) but place value is not enforced in that method. I spend a few days with the partial product method, then introduce the traditional method. It makes the transition easier.
My son had been doing the lattice method for two years in his homework. I had to check his answers with traditional math. I did not understand the lattice method until it was explicitly taught to me in one of my education courses. lol
I think you need to back track, spend time MASTERING everything they need to know to do multiplication problems like this. Have them prove to themselves that they know what they are doing by starting with the basics. Maybe set up a new rule. No saying "I can't" anymore, that may help them see that they CAN do it.
