Lattice Multiplication: A Weird-Looking But Super-Simple Way to Multiply Big Numbers

lattice multiplication method

Lattice multiplication is one of those weird-looking math techniques that makes parents cover their eyes and say, “Oh for crying out loud, what have they come up with NOW?”

That was me for a while. And I even like visual math, a lot.

I decided it was time for me to give lattice multiplication a chance, and wow, am I glad I did. This is a solid math tool that has a lot to recommend it. I’m impressed.

First–the pros and cons, then I’ll show you how to do it.

Pros And Cons Of Lattice Multiplication

The cons: It looks weird. I guess that could be a pro or a con, depending. It can also take a long time drawing the grid, especially for kids with fine motor challenges.

Also, unlike other visual models, Lattice Multiplication doesn’t model the concept of multiplication. It gives another way to multiply big numbers, but doesn’t actually make the concept of multiplication easier to understand.

The pros: It makes it super simple for even young kids to multiply REALLY big numbers, including numbers with decimals.

And (*cough*) it’s kind of fun…

The most important “pro”, for me, is that it makes tricky multiplication, with big numbers or decimals, super easy for kids.

I believe the end goal should still be the traditional algorithm for multiplying big numbers, but lattice multiplication can be a fun “filler” tool to give kids success while they are learning the trickier skills.

How To Do Lattice Multiplication

I think it will be easiest to start by watching this short video.

Starting to have a sense of it? Let’s do one together. Draw a grid like this on your paper to multiply 34 x 17.

lattice multiplication grid

Multiply each top digit by the number on the side. Write the answer in the box, with the tens and the ones digit divided by the diagonal line. If there is no tens digit, write a zero there.

When all the boxes are filled in, add the numbers in the diagonals, starting at the lower right corner. Then read the number from left to right for the answer: 34 x 17 = 578

Now let’s try a larger multiplication problem: 4213 x 529. Feel free to try this on paper first before you scroll down.

Multiply each digit by its criss-crossed counterpart and write the answer in its box.

lattice multiplication - long multiplication

Now all you need to do is add them up. Start in the lower right corner as before. This time, you’ll notice that adding gets some larger, 2-digit numbers. When this happens, just carry the one to the next diagonal over (to the left).

When you’ve added them all up, you’ll have a grid that looks something like this:

lattice multiplication multiplying big numbers

Now write all the digits from left to right. The answer to 4213 x 529 is 2,228,677!

Lattice Multiplication With Decimals

If you are multiplying numbers with decimals, you will solve in exactly the same way. There is just one final step of knowing where to put the decimal in your final answer.

Here is my favorite way to know where to put the decimal with the lattice method:

Once kids understand a bit more about how decimals work, they can also simply count decimal places to find where the decimal goes, much the same way we learned in school. Watch how easy this guy makes it look:

Lattice multiplication is a great technique to have in your math toolbox, and it may be just the thing your kid needs to do long multiplication simply and quickly.

Have a question or thought about lattice multiplication? Leave a comment below!

lattice multiplication math strategy

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