<br><font size=2 face="sans-serif">Three robust ideas are surfacing about
using manipulatives in adult math classes </font>
<br>
<br><font size=2 face="sans-serif">1. Manipulatives (movable objects) can
deepen the mathematical knowledge and understanding of students at ALL
ages and levels. </font>
<br>
<br><font size=2 face="sans-serif">2. You can use almost anything as manipulatives
(coins, chips, paper plates, candies, pattern blocks...) </font>
<br>
<br><font size=2 face="sans-serif">3. Manipulatives can help people communicate
and reason mathematically. </font>
<br>
<br><font size=2 face="sans-serif">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: </font>
<br><font size=2 face="sans-serif">Show visually:</font>
<br><font size=2 face="sans-serif">12 divided by 4</font>
<br><font size=2 face="sans-serif">1/2 divded by 4</font>
<br><font size=2 face="sans-serif">1/2 divided by 1/4</font>
<br><font size=2 face="sans-serif">2/3 divided by 1/4</font>
<br>
<br><font size=2 face="sans-serif">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. </font>
<br>
<br><font size=2 face="sans-serif">There's a great resource called the
National Library of Virtual Manipulatives http://nlvm.usu.edu/en/nav/vlibrary.html</font>
<br>
<br><font size=2 face="sans-serif">Mary Jane</font>
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<td width=40%><font size=1 face="sans-serif"><b>"Kathie Daviau"
<daviauk@billings.k12.mt.us></b> </font>
<br><font size=1 face="sans-serif">Sent by: specialtopics-bounces@nifl.gov</font>
<p><font size=1 face="sans-serif">09/20/07 11:58 AM</font>
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<div align=center><font size=1 face="sans-serif">Please respond to<br>
specialtopics@nifl.gov</font></div></table>
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<div align=right><font size=1 face="sans-serif">To</font></div>
<td><font size=1 face="sans-serif"><RS-Metternich@wiu.edu>, <specialtopics@nifl.gov></font>
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<div align=right><font size=1 face="sans-serif">cc</font></div>
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<div align=right><font size=1 face="sans-serif">Subject</font></div>
<td><font size=1 face="sans-serif">[SpecialTopics 705] Re: Components of
Numeracy</font></table>
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<br><font size=2 color=#000080 face="Arial">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.</font>
<br><font size=2 color=#000080 face="Arial">Kathie </font>
<br><font size=2 color=#000080 face="Arial"> </font>
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<hr></div>
<br><font size=2 face="Tahoma"><b>From:</b> specialtopics-bounces@nifl.gov
[mailto:specialtopics-bounces@nifl.gov] <b>On Behalf Of </b>Rebecca Metternich<b><br>
Sent:</b> Thursday, September 20, 2007 9:30 AM<b><br>
To:</b> specialtopics@nifl.gov<b><br>
Subject:</b> [SpecialTopics 704] Re: Components of Numeracy</font>
<br><font size=3 face="Times New Roman"> </font>
<br><font size=2 color=blue face="Arial">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.</font>
<br><font size=3 face="Times New Roman"> </font>
<br><font size=2 color=blue face="Arial">I am enjoying the discussion.</font>
<br><font size=3 face="Times New Roman"> </font>
<br><font size=2 color=blue face="Arial">Rebecca Metternich </font>
<br><font size=3 face="Times New Roman"> </font>
<br><font size=3 face="Times New Roman"> </font>
<br><font size=3 face="Times New Roman"> </font>
<br><font size=3 face="Times New Roman"> </font>
<br><font size=3 face="Times New Roman"> </font>
<div align=center>
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<hr></div>
<br><font size=2 face="Tahoma"><b>From:</b> specialtopics-bounces@nifl.gov
[mailto:specialtopics-bounces@nifl.gov] <b>On Behalf Of </b>Rose Steiner<b><br>
Sent:</b> Wednesday, September 19, 2007 6:31 PM<b><br>
To:</b> specialtopics@nifl.gov<b><br>
Subject:</b> [SpecialTopics 699] Re: Components of Numeracy</font>
<br><font size=2 color=blue face="Arial">Kate (and others),</font>
<br><font size=2 color=blue face="Arial">You mentioned </font><font size=2 color=#000080 face="Arial"> "we
had the appropriate manipulatives for –halves, quarters, eighths, sixteenths,
thirds, sixths, twelfths, fifths, and tenths." </font>
<br><font size=2 color=#000080 face="Arial">What exactly do you consider
the appropriate manipulatives for these fractions? Are there <b>inexpensive</b>
ones that work well? So many of our sites in Montana have limited
funds and I am sure we are not alone.</font>
<br><font size=2 color=#000080 face="Arial">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).
</font>
<br><font size=2 color=#000080 face="Arial">I look forward to trying your
10 pages with my students. ;-)</font>
<br><font size=3 face="Times New Roman"> </font>
<br><font size=2 color=#000080 face="Arial">Thanks</font>
<br><font size=2 color=#000080 face="Arial">Rose Steiner</font>
<br><font size=2 color=#000080 face="Arial">I am enjoying this great discussion
on the special topic of numeracy...</font>
<br><font size=2 color=blue face="Arial"><br>
</font>
<br><font size=3 face="Times New Roman"> </font>
<br>
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