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:

http://www.prntr.com/images/mult-table.gif

Learning Objective:

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

## Step 1: Method One: Windowpane Multiplication

## Step 3: Windowpane Multiplication: Step Two

## Step 4: Windowpane Multiplication: Step Three

## Step 5: Windowpane Multiplication: Step Four

Your answer will be read from top to bottom. In this case, 11 * 34 is 374

## Step 6: Method Two: Bowtie Multiplication

## Step 7: BowTie Multiplication: Step One

## Step 8: Bowtie Multiplication: Step Two

## Step 9: Bowtie Multiplication: Step Three

## Step 10: Bowtie Multiplication: Step Four

**Signing Up**

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.

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.

29

x 42

------

18 (2 x 9 = 18)

40 (2 x 20 = 40) *

360 (40 x 9 = 360) **

+ 800 (40 x 20= 800)***

--------

1218

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.