Easy Multiplication!




If you are a teacher or student who needs a new way to teach or learn multiplication, LOOK NO FURTHER!
This Instructable will teach you 2 basic ways to multiply large or small numbers, but only require basic knowledge
of multiplication of numbers up to nine. You can print out a multiplication chart if you need at:

Learning Objective:
By learning these two multiplication techniques, teachers and students will be able to multiply two numbers faster and easier.

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Step 1: Method One: Windowpane Multiplication

This method is by far, the coolest multiplication method I have ever seen, and it keeps the numbers nice and separate, so you don't get mixed up on where the place values are (I always get mixed up when multiplying the traditional way).

Step 2: Windowpane Multiplication: Step One

Construct the shape shown above:

Step 3: Windowpane Multiplication: Step Two

Write the numbers that you want to multiply on the top edge, and the edge on the right (In my case, 11 * 34).

Step 4: Windowpane Multiplication: Step Three

Multiply the 1 and the 3, the one and the 4, etc. When you are done, it should look like the photos above.

Step 5: Windowpane Multiplication: Step Four

Add the numbers that are within the same "strip" within the lines (The four, The 3 and the four, the 3, etc.)
Your answer will be read from top to bottom. In this case, 11 * 34 is 374

Step 6: Method Two: Bowtie Multiplication

This method is pretty cool, but not as easy as the other one, but the end result looks like a bow-tie.

Step 7: BowTie Multiplication: Step One

 Write out a multiplication problem just like you would write it out the traditional way.

Step 8: Bowtie Multiplication: Step Two

Multiply the 4 and the 1. Write it down in the spot you would put it if you were adding the 2 digits.

Step 9: Bowtie Multiplication: Step Three

Multiply the two numbers, like you did last time. But be careful--The 1 up there is in the tens place value, so that 1 is actually a 10. SO 4 * 10 is 40. Write that down on the paper, again, as if adding.

Step 10: Bowtie Multiplication: Step Four

Multiply the 30 and the 1. Write it down as if adding.

Step 11: Bowtie Multiplication: Step FIve

Multiply the 30 and the 10. Write it down as if adding. Your paper should now look like this if you were following along correctly. If it doesn't, check your work and fix what's wrong.

Step 12: Bowtie Multiplication: Step Six

WHOA!!! We're adding! Remember when I told you to write them down as if you were adding? This is where that part comes in.

Step 13: Bowtie Multiplication: Step Seven

Add the digits, and if you did all the steps correctly, you should've gotten 374. Both Windowpane multiplication, and Bow-tie multiplication both yield an answer of 374, which means both are correct, and effective.

Step 14: Now What?

Now that you know two great ways to multiply, you can learn Vedic Maths, which provide neat tricks to multiply, add, subtrct, divide, etc.

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    12 Discussions


    7 years ago on Introduction

    These are fine and often used in schools, but i have heard high school teachers vocally complain when students learn only these alternative methods and not the traditional algorithm, because they will need knowledge of the algorithm to solve algebra problems. So students should learn these alternate ways AND the algorithm - but from understanding the concept first, not the algorithm first.

    8 replies

    Reply 7 years ago on Introduction

    These were meant for elementary-middle school students who need a "crutch" to stay with the class, and not fall behind. But I'd expect that, by high school, the kids should know how to multiply the traditional way, and make their teachers happy. ;)


    Reply 7 years ago on Introduction

    I'm a middle school math teacher and this method is the bane of my existence.
    The problem is that once students have a method that works for them it is really difficult to get them to consider any other way of doing things. They've been told that this method is just fine so they see no reason to reconsider multiplication. So your expectation that students learn the traditional method often only comes true with a lot of personal struggle. Struggle that is much more difficult that simple math instruction.

    Please at least consider the partial products method. Students only need basic facts and they will also be learning something about multiplying by powers of 10. Plus it includes honest number sense.

    The problem with the lattice method is that while you are able to see and maybe understand place value, the reason it works for kids who are behind is that they don't need to understand anything. They are just pushing numbers around. This is never a good idea.


    Reply 6 years ago on Introduction

    I hate to say it, since I am going through the described situation, but it's true. :(


    Reply 7 years ago on Introduction

    Thank you for saying this. I agree with what you're saying. The reason the algorithm is taught is because it is the most efficient way to multiply. And the reason it often fails is because it's often taught without the understanding of the concepts behind it. This is one reason I love how Singapore Math teaches math.

    When you say the partial products method, do you mean what the author calls the bowtie method? I do like that method, especially as a stepping stone toward the algorithm.


    Reply 7 years ago on Introduction

    When I say partial products this is what I mean.
       x 42
         18   (2 x 9 = 18)
         40 (2 x 20 = 40) *
       360 (40 x 9 = 360) **
    + 800 (40 x 20= 800)***

    With the partial products method  the confusion of "carrying" a number to the tens place or hundreds place is eliminated.

    FIrst the weirdness of telling kids who just learned that the 4 (of 42) and the 2 (of 29) are in the tens place and called forty and twenty - of now telling them that they are a 4 and 2 and just multiply by four and multiply by two - that is absent from this method.

    * Second kids are reinforcing place value and the idea that multiplying big numbers is not a big deal. ** Third lets reinforce the idea that the only facts we need to know are the on the times table up to 9x9. Everything else is just a repeat by powers of 10. 2x2 is the same as 2x20 - just ten times bigger. This means that we add a place value make it one place bigger. PLEASE don't say "add a zero" . Imagine how that screws up kids who are working with decimal places - adding a zero doesn't change the values at all if it is behind the decimal. Not to mention that adding a zero doesn't change the value of anything (additive property of zero) what you mean is that you are adding a place value.

    *** Third we start to understand multiplying by powers of ten. (20 x 40 = 800) is the same as saying 2x4 is 8 with two powers of ten or two place values or even two zeros but just don't say adding two zeros.

    Yes there is a little extra leg work here but teaching the lattice method requires lots of "draw this, and connect that, and the numbers go diagonal" that is overhead too. It just doesn't have any number sense behind it. Everything here provides a useful concept for the future. All that being said this method will not work forever. And will cause some tears in middle school when kids have to abandon it. (imagine multiplying 3.14 x 2.25 - that would be 9 rows of numbers to add up, some to the 4th power of ten). However it is much easier to transition to the traditional algorithm from this partial products algorithm.


    Reply 7 years ago on Introduction

    this is how I, and most other children learn. The "Bowtie" method in this ible is similar.


    Reply 7 years ago on Introduction

    Your partial products method looks suspiciously like my bow tie method, i=without the lines.


    Reply 7 years ago on Introduction

    Yep! In first grade, our teacher taught us the Bowtie method because it used mostly everything we knew before: single-digit multiplication, and adding. In third grade, before the DSTP, the teacher taught us lattice if we're really crunched for time, or we're stuck on multiplying large numbers. It works because it IS just pushing numbers around, which is faster because it requires no thought.


    6 years ago on Introduction

    I am actually in a 6th grade pre-algebra class, and the traditional method is the only way to correctly multiply decimals or numbers with decimals. But I sure wish it was as easy as lattice, or window-pane, but if you do it the traditional way your results will be better with decimals.