### Partial Products Multiplication

I picked up on my own some better ways multiplication and division. Hope this helps you in your teaching.

Do your kids struggle with multiplication? Do you pull your hair out when you have to teach it? Maybe this method can help.

When I was in junior high, I discovered a different way to do multi-digit multiplication. I honestly can't remember what book I read, or where I learned it, other than I know it wasn't what was taught by my math teachers.

But as soon as I taught myself the method, I was hooked. I switched completely to using that new method and never looked back.

The partial products methods (although at the time I learned it, I had no idea that's what it was called) improves on the traditional method of multi-digit multiplication in two main ways.

**All multiplication is done first, then addition at the end.**The current method requires the student to switch back and forth between multiplication and addition. Keeping each operation together prevents errors in calculation.**Rechecking work is****quick and easy**since the products of each pair of digits is visible in the process of working out the problem. This simply isn't possible with the current method.

My own children use the partial product method when they multiply, and they like that they can recheck their own work without having to totally rework their problems. I like it as well because when they make an error in their work, I can see quickly where in the process they went wrong.

Personally, I think it would be fantastic if this method were taught in the mainstream of math education as a primary method rather than an alternate (if it's even taught at all). I think the partial product method is far superior to the traditional method of multiplication that is taught now and that children would suffer much less over their math homework if they learned this method.

### Short Division

You'll notice that the short division method really isn't substantially different from the long division method most of us learned in school. However, the written procedure is different, and in my opinion, much simplified, making the process less daunting. And like the partial products method, short division allows you to check your work and uncover errors more quickly than the traditional long division method.

Stacey says

As a math teacher I have also used lattice mulitplication for children who struggle with style that is main stream for teaching multiplying. Partial products is great also. You can also use a partial product method for division.

Marilyn Williams says

Wow-love the new multiplication method-we need so badly to change over to help Algebra students get the distributive property. Spent 3 years in elementary school in English schools and we did ALL math on graph paper with large squares, only allowed to place one digit or symbol in each square. I'm going to use this method with the grid paper – and I prefer an "x" for the place holder-also I'm now wondering if counting the digits behind to know number of place holders could transfer into helping students understand how many digits are behind the decimal in multiplying decimals??

Jamie Thomson says

I just want to say thank you for the great maths tips. I'm 34 and have 3 children, 14, 11 & 6. I have long lost touch with my maths, so I've been using your site and tips as much, if not more than my kids!! I've found them really helpful, as has my 11 year old especially. I'm going to recommend your site to my friends, as even I, an older "student" in maths can follow your method!!

Thank you, Jamie.

Fern says

This is how I was taught to divide in school. We were taught short division first and when everyone had got the hang of that, we were taught long division. I know a lot of people who use other methods or use short division every time, but personally I use short division when I'm dividing by a single-digit number and long division when it's more than one digit.

Phyllis says

Thanks for taking the time to share this. I will use it with my math-challenged son next week. I will let you know how it goes.

I love your blog!

-Phyllis

Phoebe @ Getting Freedom says

I absolutely love your math videos! I've never seen short division before, but always assumed it existed. Why else would division be called "long division"?

.-= Phoebe @ Getting Freedom´s last blog ..Kitchen Oil Sprayer =-.

Dan M says

Nice post. It reminded me of 360's list of 25 ways to multiply. It doesn't seem that there are as many truly different ways of doing division, but I suspect that if you look closely at the different multiplication techniques listed there you might find some alternatives to the usual division methods as well.

Amanda Schoolfield says

Wow…honestly never learned to do short division like this. Looking forward to showing it to my 2 oldest students today! Thanks!

.-= Amanda Schoolfield´s last blog ..Bun in the Oven =-.

Cara R. says

Thanks for another informative video. I can't wait to show this to my kids (and DH) and watch their eyes grow wide. LOL!

.-= Cara R.´s last blog ..SPRING BREAK! =-.

flutemom says

i was taught this method in school, i think. or else, i just learned it on my own. at any rate, i rarely use long division for anything, as the short form is easier to work with. i was surprised to read the other comments of folks who have never done division this way. i thought everyone knew about it, but apparently not. i enjoy doing mental math problems, and often challenge my older girls to figure things out 'in your head', especially percent off on a sale price for something in the store. if the product is 20% off, instead of multiplying the price by .2 and subtracting it from the original price, multiply by .8, as that's the price you'll actually pay. then you don't have to figure out one number, remember it while you subtract it from your first number, and then come up with your answer. example (if you're confused trying to figure that out)- say the sweater costs $20 and is 30% off. that means you'll pay 70% of the price. so 20 x .7 = $14

Heather says

Wow!!! Thanks so much for the simpler versions of "long" multiplication and division! My poor son has struggled with the changing steps of previous "old school" ways. I cannot wait to show him this.

Gerry Gunn says

Woke up dreaming that short division might be one small step in the right direction towards helping American children improve at math. So I had to look it up, which is why I found this site.

I grew up in England and learned short division years before being taught long division. It works with bigger numbers too.

I have other ideas and will do further research.

Melanie Carroll says

Joy, This is so awesome. I was never shown this in school. I have a daughter in the 3rd grade. We are using Singapore math which introduces long division this year. It totally blew my 3rd graders mind and we just skipped it for now. I'll be going back now and trying with this method. Thank you for sharing!!!

Ann says

Excellent!

Pablo U says

This method is great if your kid knows the pitagoric table perfectly, here in Argentina, division is teach using approximations, its easier than the way I learn when I was a 8 y/o kid.

http://imageshack.us/photo/my-images/541/divide.png/

I do like the way you teach how to multiply in another video, its cleaner and less prone to errors.

Jolyn says

This fascinates me and I wish I'd had these videos five years ago. We are a military family and when we lived in Italy 2004-2007 we sent our now 15yo to Italian schools where they taught short division. I'd seen short division before, or heard of it, rather, and always associated it with "cerebral" people as the one family I knew in my high school who practiced this method were super-smart people. I didn't even know what it was called! I called it "horizontal" division (vs. vertical) and was completely lost in trying to help my son with his homework, not wanting to introduce the method that I knew that would only confuse him more.

Now I am wondering why Singapore math teaches the "inferior" methods versus these? We are getting ready to start Singapore (8yo and 6yo); we're currently using Teaching Textbooks but for many reasons I'm deciding to make the switch, not wanting them to be behind and wanting the "head math" that Singapore encourages. I'd actually like to teach both methods (for Multiplication and Division)… but do you recommend starting with the "better" one and then showing the method SM uses, or showing both methods and letting the child choose which they prefer? (This is our first year homeschooling, can you tell? 😉

Jon says

One thing to note with partial products multiplication is that the number of rows you should have to add up at the end should match the number of digits on each row multiplied together. For example a 2 digit number times a 2 digit number gives 4 numbers to add up, 2 digit by 3 digits gives 6, 3 by 3 gives 9. I find this a useful way to make sure you don't miss combinations, especially when multiplying larger numbers.

On the division I personally prefer the approximations technique as illustrated by the Argentina reference above. It is not necessarily better, just how I work things out in my head, so good to teach people a technique that matches their natural instinct.

Precious Crafts says

I'm facing some challenges in teaching my kids division. I will give this method a try. Wish me luck! And thanks a lot for sharing!

jeremiah says

thank you i have been strugleing in division

sue says

We are teaching multiplication and division this way in the public school where I teach in 3rd, 4th, and 5th grades. More kids are having greater success and deeper understanding of the math. I'm sold on the method. Parents are having a tough time because they do not understand it and it is different from the algorithm they learned as kids. They think that because it is hard for themselves to get it, it must be more difficult for kids, when the reality is that kids are developing a deeper conceptual understanding than their parents have of what these operations are about. I LOVE it!

becky says

http://www.youtube.com/watch?v=x2UG0YzT2UA

this is by far the easiest method to multiply.

At school we call it the z box method because you draw boxes with z's in them

Joy says

@Fern, I've really discovered recently how differently people have been taught the basic operations of multiplication and division. I was always taught long division in school, and ended up learning short division on my own. I thought it was a much simpler way of doing things and I really wonder why my school didn't teach it that way at all.

So far I've found very few people who were even familiar with short division, but I have a feeling there are more out there than I thought.

It's too bad more kids aren't exposed to multiple methods of doing math like you were so they can choose the one that works best for them.

Fern says

@Joy,

Hm – that's curious. Perhaps it's taught differently in England? My primary school certainly were VERY big on teaching us different methods for things – I can remember endless lessons being taught to do addition/multiplication/division in different ways but I've always preferred the 'standard' methods.

I'm in the highest maths set in my school in a class doing an extra GCSE, but hardly anyone in my class can do long division (which I only discovered when we were being taught dividing polynomials). Many people denied they'd ever seen such a method before or couldn't remember it if they ever had – a symptom of the calculator generation?

Denise says

've really discovered recently how differently people have been taught the basic operations of multiplication and division. I was always taught long division in school, and ended up learning short division on my own. I thought it was a much simpler way of doing things and I really wonder why my school didn't teach it that way at all.

So far I've found very few people who were even familiar with short division, but I have a feeling there are more out there than I thought.

It's too bad more kids aren't exposed to multiple methods of doing math like you were so they can choose the one that works best for them.

Joy says

@Melanie Carroll, We use Singapore too for elementary math. Such an awesome curriculum!

Have you seen how I teach my kids multiplication? It's different from the regular method, but it's OH so much easier for student and teacher. The only trouble is the examples in Singapore for multiplication are with the traditional, inferior method. But my kids know how to ignore that and just think the partial products way.

http://fivejs.com/a-better-way-to-multiply-the-partial-products-method/

Joy says

For multiplication, I always taught my kids 'my' way first (which is most intuitive anyway I think), and then showed them the traditional method. By that point, the can recognize the idiocy of the traditional multiplication method

As for the division though, if my kids weren't doing the remainders in their head already, I'd probably have gone through long division first since short division is really just skipping written steps. It's not as different from the traditional method as partial products is.