Does the upside down division method work for everything - just about :)

    The upside down division method can be used to teach just about everything. OK, I exaggerated a little, but I use it to teach kids prime factorization, simplifying algebraic fractions, greatest common factor, least common multiple, and factoring polynomials. Teaching students one way to solve so many different types of problems makes it much easier for them to remember. I am sure that most of you are already very familiar with upside down division. If you are not, it is the cake method many people use for prime factorization, but upside down. See Sarah's post to explain the birthday cake method. The only problem I have with the cake method is if I don't start in just the right place the problem goes off the paper.This is not an issue with upside down division, you can keep dividing all the way down to the bottom of the paper.

    Initially, I teach this when finding prime factorization of numbers. Here is a foldable for their interactive notebooks. I needed to review divisibility rules with my kids before this lesson. 

I love prime factorization because it helps the kids review their multiplication tables with smaller numbers. They should know them but so many of my kids don't.  :(

 I like how this method doesn't take up as much space as the factor trees do.

I have started making more of my notes fill in the blanks. It saves so much time. However, I don't like to have them all written for them.

   I do a quick review of short division with the kids. Many of them have never seen this before.

     We use this method again when simplifying algebraic fractions.

 Here's a foldable we used for simplifying fractions.

I usually draw a fraction bar between the numbers. I forgot to do that on this foldable.

    Before we do upside down division with fractions, we have written fractions in expanded form and simplified to find the answer. They are familar with the exponent rules already.

     Next I use this with Greatest Common Factor and Least Common Multiple. 

I originally had this foldable as one foldable, but I decided to cut it in half and have a separate page for GCF and LCM. The students have already learned the other two methods for finding GCF. They have also covered exponent rules 

as well.

Instead of circling the common factors, the students place a large G over the numbers. It is an added visual for the kids.

Upside Down Division for LCM is also called the Ladder Method. I never knew that until I started writing this post. You learn something everyday:)

On LCM the students draw a large L around the numbers as an added visual.

     Lastly, we factor polynomials using Upside Down Division. 

My Pre-Algebra students always have difficulty with this topic. Using the Upside Down Division makes it so much easier for them to understand.

     

Download documents from this post here:

Upside Down Division - Prime Factorization Booklet

Upside down division - Simplifying Fractions

Upside Down Division - GCF and LCM foldable

Upside Down Division - Factoring Polynomials

I am so happy to have all of this written and saved in one place. I litterally had to search everywhere to consolidate all the pieces. I hope there is something new for you to use.

Til next time,

Jan :D

It's almost Pi Day !!!!!

Pi Day is almost here. Check out my Pi Day Pinterest Board:)

Pi Day Pinterest Board

Enjoy, Jan

The evolution of an Interactive Notebook page for Graphing Systems of Equations

     February has been a crazy month. My hubby had a big birthday, so family and friends were in town and we were very busy. PARCC testing is right around the corner for my kiddos at school and I am trying to get them as prepared as possible. (This is another post that I do plan to write soon.) February just got away from me and I can't believe that I had only one post this month.

     I started pulling together ideas for my interactive notebook pages on graphing systems of equations, not thinking that this would be a big deal to make. Was I wrong. I just can't seem to get the page to fit and the foldables aren't lining up. So I thought I would let you see my evolution of this page.

     I decided to use a matchbook foldable instead of the flat organizers I've been using lately. Then I tried to put all the information on the page.

     The information just wouldn't fit on the page.

     This has all the information that I wanted on the page but it was too crowded for my liking, so I went back to the drawing board.

 Still too crowded. Wasted another piece of paper. UGH!

   What a mess!!!!

Maybe a different foldable will work. Which one to choose?

I can't get this foldable to line up correctly front to back. The lines are off. 

  FRUSTRATING:(

     I finally became so irritated with using up my pages in my notebook that I made a copy so I could make mistakes on the copies. If you would like to use these blank pages here is a copy of. 

blank half graph half ruled notebook page
And if you want the systems matchbook:
systems small matchbook 

     Tomorrow is another day. I was hoping to get this post finished in February but it has now turned into 1:30 am, March 1st, so I will try again tomorrow. Who knew one page of a notebook could make me so crazy.

Til next time, which will hopefully be tomorrow,

Jan