Division is EASY, you get more information than multiplication or factoring and yet students find it hard and confusing. The way it is taught is what makes it hard and confusing. Most students never even realize that the symbol itself actually MEANS make a rectangle, tell me the other side; the same way they often never get that the symbol for square root means make a square count one side. Long division is universally hated by 6th graders because it is taught 100% rules and process without any conceptual understanding that what we are doing is keeping track of how many times one number is contained in another by subtracting.
Here are some kids who would be in second grade learning these concepts with problems because they can see what they are doing. Because they have both had several lessons I went backwards starting with a stretch and then getting easier and easier.
Here is some more practice with polynomials; often we start with algebra because it's "generic math". The concepts are THE SAME and many kids note that the algebra is actually easier than base ten mathematics. This starts off with factoring but quickly moves to division concepts:
And ends with negative expressions which are slightly off topic for this page.
Take a look at this simple chart. It shows what you get and what you have to give when doing these three operations. Multiplication and factoring both involve the sides of a rectangle when you look at it conceptually. Where do you get the most information? When you get the rectangle and one side all you have to give is the other side...so really which one is EASIEST? Then why do we teach it last?
Here is a primer so to speak, covering the three concepts that are intertwined so intrinsically you cannot easily separate them when you are doing concept based teaching, yet text books in public (and private) schools have somehow managed to do so...
Then here is a screencast where I get a little carried away showing exactly how those who used CONCEPT based teaching should NOT do it:
Also beware of using multiplication tables to drill multiplication facts into your students, between the non-clever use of multiplication tables and long division there is often very little love of math left in them by the time they reach those intrepid few who are tasked with the job of teaching them algebra.
There is a short 4 page worksheet for beginner division on the Password Protected PDF's Page. Get a password. They're cheap. Here is a short screencast on how to use said worksheet:
The password will get you into pages showing percentages, 3rd and 4th power algebra and more, plus more pdf's and also buying a password keeps this site up and makes it possible for me to spend the time required to keep putting up new topics and information.
Also be sure to visit the blog, there are lots of videos and entries there that are FREE, that can help you introduce these concepts and make it not only easy but also FUN. Playing with rectangles makes what was "complex" math assessable to students of all ages and skill levels. When they see the pictures the scare factor and hard factor disappear almost magically, although it's NOT magic it's math.
This page will have a more shortly.
Bonus sample lesson:
Now, for just $19.99, you can get Divinely Dandy non-Difficult Division, (DDnDD) which will show you how to use your base ten blocks to make division super easy and even fun. The information contained in this PDF can be found nowhere else at any price....
Just send $19.99 to:
"There are two ways to do great mathematics. The first is to be smarter than everybody else. The second way is to be stupider than everybody else -- but persistent." -- Raoul Bott
Crewton Ramone chose door number two.