# [Numeracy 136] Re: Starting with intensive study of fractions

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Charlie charlie at durangoaec.org
Wed Feb 10 13:38:16 EST 2010

Thank you for sharing your book, Kate. It looks like an amazing
resource, worth printing, using, and sharing with colleagues. After
taking a quick glance, I really like the egg carton manipulative idea
for fractions and the human digits idea.

Charlie Love
GED/ESOL Instructor
701 Camino del Rio, Room 301
Durango, CO 81301
phone: 970-385-4354 ext. 110
fax: 970-385-7968
charlie at durangoaec.org

On Feb 9, 2010, at 9:01 AM, Kate Nonesuch wrote:

> Hi Andrew--"Human Fractions" is a way to model many basic ideas

> about fractions--meaning of denominator and numerator,

> equivalencies, etc. Also gives time for social interaction, much

> repetition in an interesting context, etc.

>

> You are going to ask the class to sort themselves into groups that

> meet the criteria you call out, for example, "pairs in which half

> the people are wearing glasses." Start by saying that there will

> nearly always be a few people left over who can’t make that pair

> (e.g., three people all wearing glasses), and they should come to

> see you immediately (you have a job for them). Then ask the class

> to get into pairs in which half the people are wearing glasses.

>

> Start with the group that doesn’t fit the criteria: What fraction of

> the people in this group is wearing glasses? Ask them to be your

> assistants in checking out the rest of the activity.

>

> Ask one assistant to pick a pair to come forward. Ask the class to

> check that half the people in the pair are wearing glasses. Write

> the fraction on the board. (Two people in the group, so the bottom

> number is 2. One person wearing glasses, so the top number is 1.)

> Ask the assistant to pick another pair, and ask the class to check

> that half that pair is wearing glasses. Ask the second pair to join

> the first, so that the two people with glasses stand beside each

> other. Write the fraction of the new group wearing glasses. (Four

> people in the group, so the bottom number is four. Two people

> wearing glasses, so the top number is 2.) The fraction is 2/4. In

> this new group, do we still have half the people wearing glasses?

> Ask the assistant to bring in another pair, and repeat. You can ask

> another assistant to write the fraction, 3/6. Repeat until all the

> pairs have joined. When all the pairs have been joined to the

> review the equivalent fractions written on the board.

>

> Other suggestions for forming groups: Ask students to get into

> groups where 1/3 of the people are wearing watches; where 2/3 of the

> people are wearing sneakers; where 1/4 of the people are wearing

> shorts; where 4/5 of the people are wearing pants; where 3/4 of the

> people are wearing some piece of black clothing; and finally, to

> find many equivalents for 1, ask for groups of any size where all of

> the people are students, or all are men or all are women, etc.

>

> This idea is taken from my book, Changing the Way We Teach Math,

> available free at http://www.nald.ca/library/learning/mathman/mathman.pdf

>

> Kate Nonesuch

> Kate Nonesuch

> Victoria, BC

> kate.nonesuch at viu.ca

>

>

> Do you or anyone else have any other recommended activities for

> making the abstract concept of fractions more concrete? I would like

> to spend a couple more weeks on approaching them various ways and

> really make sure that they are clear before moving on to decimals

> and percents.

> Thanks~~

>

> Andrew J. Isom

> Math Specialist

> Center For Literacy

> North Philadelphia Community High School

> (215)744-6000 ext. 210

>

>

>

>

>

>

> -----Original Message-----

> From: numeracy-bounces at nifl.gov on behalf of numeracy-request at nifl.gov

> Sent: Mon 2/8/2010 12:36 PM

> To: numeracy at nifl.gov

> Subject: Numeracy Digest, Vol 2, Issue 9

>

> than "Re: Contents of Numeracy digest..."

>

>

>

>

> Today's Topics:

>

> 1. [Numeracy 116] Re: Personal Introduction (Linda Shilling-

> Burhans)

> 2. [Numeracy 117] Re: introductions (Linda Shilling-Burhans)

>

>

> ----------------------------------------------------------------------

>

> Message: 1

> Date: Mon, 8 Feb 2010 09:43:10 -0500 (Eastern Standard Time)

> From: "Linda Shilling-Burhans" <lshilling at cvabe.org>

> Subject: [Numeracy 116] Re: Personal Introduction

> To: "The Math and Numeracy Discussion List" <numeracy at nifl.gov>

> Message-ID: <4B7022FE.000004.02644 at LSHILLING-BU-PC>

> Content-Type: text/plain; charset="utf-8"

>

> Hello Arnold,

> This sounds fantastic. It has never failed that when an adult

> student weak

> in math comes in it all goes back to fractions. Sounds like you have

> the

> secret. I have been working with one adult for a year (though he is

> not

> putting in intense time to the study) but he just keeps saying he

> just doesn

> t get it.

> As it turns out, I will be in Sarasota in April (who from the north

> won't

> be?). Do you have any material that reflects your teaching style?

> Best,? ? ? ?

> Linda

>

> Linda Shilling-Burhans

> Community Coordinator

> Central Vermont Adult Basic Education

> 802-222-3282

>

> -------Original Message-------

>

> From: arnoldbailey

> Date: 2/6/2010 4:10:07 PM

> To: 'The Math and Numeracy Discussion List'

> Subject: [Numeracy 108] Re: Personal Introduction

>

> Sounds as if you have your work cut out for you. I tutor Title 1

> children in

> math and I found a very high success rate by starting them out with

> intensive studies of fractions. I found that by teaching them how

> fractions

> are simply division problems and giving them an easy way to remember

> Numerator and Denominator positions, conversion from fraction to

> division

> problem and division to fraction, and the various other combinations

> the

> children find Algebra rather simple. I have several 3rd Grade

> students with

> IEP's that were D and F students, now doing 5th Grade math and

> middle school

> basic Algebra. Once the light clicks and they grasp the concept of

> fractions, their confidence rapidly increases as does their interest.

>

> Arnold

>

> Sarasota, Florida

>

> -----Original Message-----

> From: numeracy-bounces at nifl.gov [mailto:numeracy-bounces at nifl.gov]

> On Behalf

> Of Andrew Isom

> Sent: Friday, February 05, 2010 9:33 AM

> To: numeracy at nifl.gov

> Subject: [Numeracy 107] Personal Introduction

>

> Hello all!

>

> It's nice to e-meet you all. My name is Andy and I am in a position

> title

> "Math Specialist" for an community literacy organization in

> It's an interesting position for the fact that I actually work with

> youth

> ages 16 - 21 who attend an "accelerated" school for students who are

> behind

> on their credits and therefore at risk of dropping out. Many of our

> students

> have been placed here by a probation officer and we have many teen

> mothers,

> but we do have students who have made their way here through other

> means.

>

> It is an exciting position for me because I have taught high school

> and

> middle school math in the city for 4 years prior to taking this

> position,

> having come here through Teach For America and being placed as a

> Algebra I

> and II teacher at a large comprehensive high school in North Philly.

> It was

> an immensely deflating position because many of the students needed

> intensive remediation, but due to the fact that our old "CEO" Paul

> Vallas

> (now in New Orleans making the same bad policy decisions) decided

> that all

> schools in the city should strictly adhere to a "core curriculum".

> This

> meant that I had to be on the same page in the same textbook as

> every other

> math teacher in every other school in the city, despite the specific

> needs

> of my students.

>

> At the school I am placed at all of our students are given the TABE

> and we

> have a wide range of ability levels, but most students are well

> below their

> grade level. We also place students by ability level, but they are

> usually

> placed more based on their literacy score than math, and they almost

> always

> score lower on their math. So, this position has offered me the time

> and

> freedom to explore remediation strategies for students with profound

> misconceptions. I have had some small successes but also floundered

> wildly

> in my attempts. I spend a great amount of my time and energy seeking

> the

> best possible ways to assist them in their development of their

> numeracy

> skills. I have so much to learn still, and am therefore very excited

> the prospect of learning from a talented and dedicated community of

> like-minded colleagues!

>

> Sorry for the long windedness (you might think I were a drama

> teacher!) and

> I look forward to future e-discussions and discovery of new resources!

>

> Best wishes~~

>

> Andrew J. Isom

> Math Specialist

> Center For Literacy

> North Philadelphia Community High School (215)744-6000 ext. 210

>

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> Email delivered to charlie at durangoaec.org

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