Three robust ideas are surfacing about using manipulatives in adult math 
classes 

1. Manipulatives (movable objects) can deepen the mathematical knowledge 
and understanding of students at ALL ages and levels. 

2. You can use almost anything as manipulatives (coins, chips, paper 
plates, candies, pattern blocks...) 

3. Manipulatives can help people communicate and reason mathematically. 

It's one thing to be able to find the answer to 2/3 divided by 1/4 by 
following the rule we all learned ...2/3 x 4/1 = 8/3 =2 2/3. It's another 
thing to be able to show it with objects.  Most of us who teach basic math 
know how to work out the symbolic math.  A few months ago, in a pd 
workshop, we posed the challenge to teachers after lunch: 
Show visually:
12 divided by 4
1/2 divded by 4
1/2 divided by 1/4
2/3 divided by 1/4

There was a lot of buzz as small groups worked out the problems with 
objects.  The tables were strewn with plastic chips, cubes, and pattern 
blocks, but one group raided the cucumber slices on two uneaten salads to 
show all 4 scenarios. I wish I could attach the photo. Manipulatives 
become a way of life if we routinely challenge ourselves and our students 
to "do the math" by connecting symbolic notation, visual models, and real 
life situations. 

There's a great resource called the National Library of Virtual 
Manipulatives http://nlvm.usu.edu/en/nav/vlibrary.html

Mary Jane





"Kathie Daviau" <daviauk at billings.k12.mt.us> 
Sent by: specialtopics-bounces at nifl.gov
09/20/07 11:58 AM
Please respond to
specialtopics at nifl.gov


To
<RS-Metternich at wiu.edu>, <specialtopics at nifl.gov>
cc

Subject
[SpecialTopics 705] Re: Components of Numeracy






I have made brownies (one pan for each class) and asked how to cut the 
brownies so each person gets exactly the same size piece.  This develops 
fractions, measurement and rulers, area, prime numbers and factors, and 
great verbalization of a math problem.  And… any activity involving food 
will be successful.
Kathie 
 

From: specialtopics-bounces at nifl.gov 
[mailto:specialtopics-bounces at nifl.gov] On Behalf Of Rebecca Metternich
Sent: Thursday, September 20, 2007 9:30 AM
To: specialtopics at nifl.gov
Subject: [SpecialTopics 704] Re: Components of Numeracy
 
I have used inexpensive paper plates and cut them apart.  You can have a 
set for each student.  A fun activity would be to bring in a bag of apples 
and plastic knives.  After a trip to the restroom to wash hands, students 
could cut up their apple, discuss the fractions represented, and finish 
with a nutritious snack.
 
I am enjoying the discussion.
 
Rebecca Metternich 
 
 
 
 
 

From: specialtopics-bounces at nifl.gov 
[mailto:specialtopics-bounces at nifl.gov] On Behalf Of Rose Steiner
Sent: Wednesday, September 19, 2007 6:31 PM
To: specialtopics at nifl.gov
Subject: [SpecialTopics 699] Re: Components of Numeracy
Kate (and others),
You mentioned  "we had the appropriate manipulatives for –halves, 
quarters, eighths, sixteenths, thirds, sixths, twelfths, fifths, and 
tenths." 
What exactly do you consider the appropriate manipulatives for these 
fractions?   Are there inexpensive ones that work well?  So many of our 
sites in Montana have limited funds and I am sure we are not alone.
We have used egg cartons (12 and 18 egg size) for many of these fractions. 
 But to do all of these, our class would need to make some adaptations to 
the cartons (i.e. cover up some of the egg slots so that are not a part of 
the whole, etc). 
I look forward to trying your 10 pages with my students.  ;-)
 
Thanks
Rose Steiner
I am enjoying this great discussion on the special topic of numeracy...

 
 
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