Teaching multiplication actually starts in 3rd grade. Children generally arrive in 4th grade classrooms with the ability to count by twos, fives, and tens. Our challenge is take them from that basic level of knowledge clear through understanding and applying the standard multiplication algorithm.
This is something that I regularly accomplish for my entire class – including those with math IEP's – by winter break. How? It all begins with a very strong foundation in math facts up to 10 x 10 (at a minimum)… and most often, through 12 x 12.
Just the Facts!
Automatic recall of math facts is what puts kids on the path toward mastering the standard multiplication algorithm and is a critical part of teaching multiplication. But first, kids must understand why we need to multiply.
I always begin my elementary math lesson plans for multiplication with very simple story problems. This sets the stage for kids to be able to picture what multiplication is all about.
For example, we’ll begin with a story problem as simple as this:
“Kenny hands out two pencils to each person in class. How many pencils does he hand out?”
We’ll write the algebraic equation on the board like this: 2 x 24 = ___. Then we’ll fill in the blank.
Story problems this simple make it very clear what we are accomplishing with multiplication and they form the basis for the next step, which is to understand multiples of each number. For that, we get to have a whole lot of fun!
Video tips: math songs
Rockin' the Standards
To teach multiples, I introduce songs and my kids sing and dance their tails off. Of course, I sing and dance along with them! The songs are easy to find. I use the ones from “Rockin’ the Standards,” which can be found on YouTube or iTunes.
I introduce one song a week until we’ve worked our way through all of them. Using their voices as well as moving their bodies really reinforces the understanding and retention of numeric multiples and makes teaching multiplication a breeze.
Meanwhile, I reinforce the same multiples concepts as we work on number strings (also called “related problem sets”) every morning during whiteboard math. I start with the multiples they know (two, five and ten) then add in the others as they pick them up:
- Threes come along pretty quickly
- Fours are just double twos
…so these are added into my number strings early on.
Take note: What I outlined just above with fours is one of those little tricks that I teach children as we go along. Pretty soon, these little tricks are things they don't have to remember at all, but things that they simply know and can explain… and it all happens through repetition and application.
After we work our way through learning the multiples using “Rockin' the Standards,” we start teaching multiplication with flashcards.
Flashcards and math facts
The kids are horrible at flashcards at first. They get better very quickly as they learn to apply the multiples in this new setting.
I send packets of flashcards home. Meanwhile, I'm constantly advising parents through verbal discussions and my newsletters to work with their children every night.
We always set a class goal of everyone knowing their math facts by Thanksgiving. It’s pretty common to meet that goal, except for one or two kids, and any stragglers will certainly know them by winter break. They know (from hearing me talk constantly about it) that mastery of the facts is critical for learning the multiplication algorithm.
Video tips: using math flash cards
This outlines the process that occurs in my room from mid-September (just after the beginning of school) through November. It takes about two months to move kids from knowing only multiples of two, five and ten through knowing their math facts up to 10 x 10 and frequently, 12 x 12.
When a student learns learns all of her facts, I award one of my multiplication mastery certificates.
Next, I'll discuss moving beyond math facts to actually teaching multiplication using different algorithms:
- Area (matrix) model
- Partial product
Area model (open array) multiplication
We spend about three weeks using the open array or area model for multiplication. This is a great way to decompose numbers in multiplication problems so that kids can really understand place value. It's most effective to teach area and perimeter at the same time.
Take a look at this video to see how it's done.
Video tips: area model multiplication
I'll only use the area model for problems up to four digits by one digit, or two digits by two digits. Beyond that, it begins to get a little too confusing. Besides, it’s unnecessary for them to go further with this model before moving on to the next step in teaching multiplication.
Don't get stuck overusing the developmental stages on the way to the standard algorithm! Don't let kids get too comfortable with them before moving on.
Partial Product Multiplication
Next, for about two weeks, we work on the partial product algorithm. This is when the kids really start to understand what they are doing with the multiplication algorithm, which is why I use it only briefly.
I use it just long enough for the students to really understand how place value works in teaching multiplication. If I use it any longer, the children start to get too comfortable with it and hesitate to move on.
Here a video example of how it's done.
Video tips: partial product multiplication algorithm
By the time they can accurately calculate two digits by two digits or two digits by three digits using the partial product algorithm, they are ready to move on.
What we've covered to get to this point
Let's pause to recap our progress. By now, my students have built a very firm foundation:
- They understand multiples (counting by 2's, 3's, etc.)
- They have mastered their multiplication facts through 10 x 10 at a minimum
- They know the open array (area model) algorithm
- They have learned the partial product algorithm
They are now primed to master the standard algorithm with about only one week of work.
Teaching multiplication: standard algorithm
The standard algorithm requires a lot of mental math, and I really work on reinforcing this during my early morning number strings sessions involving related problem sets, as noted earlier. During these sessions, I’m constantly showing them tips and tricks about mental manipulation of multiplication sets.
Here's an example of a related problem set. In this particular instance, I might uncover one problem at a time and discuss them as we go — although it’s not unusual for me to give them two or three at a time to see how they do.
10 x 13: We discuss and remind each other how to multiply by 10 (remove the zero, multiply, then add the zero back on).
11 x 13: We add one more 13 to the answer above which they can do in their heads.
9 x 13: We subtract 13 from the first problem, which, again, they can do in their heads. But I do ask them also to prove their thinking by using their personal whiteboards. Most will “stack and subtract.”
3 x 13: Those who are paying attention know that this is simply 3 x 10 plus 3 x 3.
13 x 13: They will quickly determine that this is the first problem plus the fourth problem.
19 x 13: This is the first problem plus the third problem added together.
If they get the last two, I congratulate them on decomposing the problem into its components in order to solve them in their heads (or with a minimum of written calculation).
Video tips: teaching the standard algorithm
So by winter break, I'm done teaching multiplication except for review. All of my kids, including those with math IEPs, have mastered multiplication up to and beyond grade-level standards. They are very solid: they get it, they can explain it, and they can teach others.
In fact, my students can and do teach adults who visit the room how to use the standard multiplication algorithm to solve problems involving:
- 4 digits x 1 digit
- 2 digits x 2 digits
- and 3 digits x 2 digits
This entire process of teaching multiplication is accomplished with a ton of enthusiasm, lots of fun, plus a few other tricks:
- I let my kids write a lot of the story problems that we use in class.
- I celebrate publicly every achievement that they make and hand out multiplication mastery certificates.
- I use their names in all of my story problems which helps them stay engaged. They love seeing their names in print!