mailto: richardsinger3@sbcglobal.net
MS WORD FRACTION
FILES THAT YOU CAN DOWNLOAD
Reader
comments are given after information on material.
The book Understanding Fractions consists of six main units.
The
first unit below is sufficient to provide an initial introduction to fractions.
It contains the essence of all the ideas needed to work with fractions. Except
for changing fraction names, it does not relate these ideas to computational
techniques. It also contains that part of the commentary that involves using
these ideas with an average 10-year-old student. These
sample pages are a screen version of the lessons in the booklet Visualizing
Fractions and this booklet is almost identical to Chapter 1
Fractions\Visualizing Fractions with Color pieces.htm
Visualizing
Fractions with Color pieces.docx
Visualizing Fractions Screen Version (Currently Unavailable) This is a version of Visualizing Fraction. Trying
to read other version from the screen involves scrolling in the middle of a
topic. The screen version is designed to avoid the need for such scrolling. It can be accessed as a Microsoft Word file and
examined on line. However I recommend saving it and accessing it from Microsoft
Word if you want to use it.
To use any of the above units you need fraction pieces.
Fraction
Pieces.Doc One of the
most important initial activities for most children is to participate in making
fraction pieces and discussing what they represent. You could use 4-by 6-card
stock to make them. However, this file allows you to use a color printer to
print five pages that can be laminated and then cut to make the recommended set
of a set of pieces.
More materials may be added later, and we are especially interested in adding
accounts that involve the use of the ideas in our books.
READER'S COMMENTS
From: Octavia Randolph
To: Richard Singer
Subject: Understanding Fractions
Understanding Fractions taught me that it is never too late to overcome a math
deficiency. Years of assuming that I could never truly "get"
fractions evaporated in one sitting with this book. I took it with me on a
coast to coast flight and was immediately intrigued with the simplicity and
clarity of the text and visually pleasing graphic demonstrations. I had one
"Eureka" moment after another as I grasped concepts that had always
eluded me with other teaching techniques. I actuall
felt I was learning an entirely different way to think about fractions - a way
that made sense to me. On top of all of this, Understanding Fractions
is written in a way that makes it completely accessible and fun, even for those
of us with serious math deficiencies. I am looking forward to Professor
Singer’s book on Algebra so I can tackle that next!
-Octavia Randolph
Note: Octavia Randolph has a website http://www.octavia.net/ devoted to
Anglo-Saxon England. This site contains a wealth of information about the
people and customs of that time. It also contains an excellent her novel
entitled “The Circle of Ceridwen”.
From: Andrea Rothbart
To: Richard Singer
Subject: some remarks about your fraction materials
Date: March 05, 2000
Richard below are some excerpt of email I have received from a couple of my students:
Note: Andrea Rothbart is a professor of mathematics at Webster University. She the director of the MAT program for teachers of Mathematics. As a visiting lecturer, I discussed a preliminary version of the book with one of her classes. The class consisted mostly of middle school mathematics teachers. The emails which follow come from these students.
From Marissa:
I think that Richard Singer’s fraction unit is wonderful. It seems that often teachers come across educational tools like this and intend on using them but don’t find time to prepare. I think it would be nice if Webster offered a class (maybe just one credit hour) where teachers could be walked through the entire unit and given some pointers.
From Ev:
I have not had a chance to look at his material in depth, but am going to offer it to one student who is still struggling and to one of my daughter’s friends who shudders at the word math. Unfortunately, none of this will probably happen until May. If you are interested in the outcome let me know and I will e-mail you individually sometime during the summer.
From Jon:
Fraction Tiles: I thought that it was a very good presentation, something very basic that I would think that most teachers would use something similar to. It was neat to see something in action like that.
From Nadine:
I enjoyed Richard Singer and the fraction bars. I shared the first chapter with some coworkers at school. I have received feedback from some. Most were delighted with it. we use something similar known as "Dr. Lloyd's Fraction Kit" it used colored coded pieces like the ones Richard used. They are useful for teaching beginning concepts of comparing fractions and equivalency.
From Susan:
Fractions I loved the way how Richard Singer showed the different ways yet, very simple, on how to teach fractions. I love the use of the colors for each fraction. I've thought about that technique and find that it works for those who are struggling with.
From Amy:
I was very interested in Richard Singer's fraction unit. I teach 4th and 5th graders. Therefore, they still need a lot of hands on materials to help their understanding. I will be starting with the 5th grade shortly, and I plan to use some of Richard;s materials. ( I will have to e-mail him to let him know how things went.) I am going to have to work out my approach very carefully, because I am doing division with my 4th graders and I was using place value blocks. When I started to bring them out after the fourth or fifth day, they started to moan. They acted like they didn't need them, when in fact they really did. As I have looked through the information from Richard, I have seen some very useful material. I am anxious to use this in my class.
From Allison:
I am working with one of our 6th grade teachers and she is going to try to use some of this material. I think it could do a lot to help kids understand what fractions are.