## Sunday, October 28, 2012

### In Search of the Perfect Man

Do your students hate fractions as much as mine do?  At this point in my career, I've decided that the evolutionary cycle has altered our children's genes in a way that the minute they see a fraction in any problem, they immediately write  "IDK"  and then skip right over it.

Well, this week I had my students literally BEGGING to do more fraction work! It was an amazing site to behold!! What is it that caused this "genetic" transformation to occur? My students were in search of the perfect man!

This project has everything a teacher could hope for: an introduction that had the students literally begging to find out the "answer", an intense buy in from my students ("Can I take this home and work on it?"),  and LOTS of contextual practice for changing mixed numbers to improper fractions, multiplying fractions,  and adding and subtracting fractions with different denominators.

It all started when I saw this: the Vitruvian man with a list of the proportions Leonardo DaVinci categorized as perfect. The list included things like:

• the length of the outspread arms is equal to the height of a man
• from above the chest to the hairline is one-seventh of the height of a man
• the maximum width of the shoulders is a quarter of the height of a man
• the distance from the elbow to the tip of the hand is a quarter of the height of a man
Now, my sixth graders are not ready for the formal study of proportions yet, but we have been reviewing adding and subtraction fractions, have been learning about multiplying fractions and about transforming mixed numbers into improper fractions, and learning about cross checking our multiplication problems. It seemed that all this would work nicely into a "Perfect Man" project.

I recruited five male teachers to help - one for each period.  All I had to tell them is that my students were looking for the perfect man and they readily volunteered. :) One teacher came into each period and the students measured them so they could do their calculations.  They all happen to be "hams" in the best sense of the word, so they really had the students going by the time they left the room. Here's the form we used to record the measurements:

In Search of the PERFECT Man Blank

If you'll notice, there's six columns, instead of five. That's because one of my sixth grade boys insisted that - since they are now in middle school - the boys really should be referred to as "men". :) With that, we decided to add one of the sixth grade boys to the list as well.

After the students recorded the measurements in each period, I typed up the list and brought it in the next day.

In Search of the PERFECT Man
We talked about how to determine if someone was perfect in a particular area. The students decide that if the real measurement equaled the answer to the problem they set up (for instance 1/2 times the height), then the person would receive a "0". If the measurement was greater, they would put a +, along with the difference in the column and if the measurement was less, they would put a - .  Finally, students would add and subtract the numbers in the right-most column to determine which man came closest to "0" (closer to perfection). I know that sounds confusing, so here's one of the recording sheets...

Then I set the students loose.  It's rare to have 100% engagement 100% of the time, but that's what I had! I gave them very little direction about how to solve the problems, but they quickly figured out how to set up their equations ( I heard lots of "you have to multiply the fraction DaVinci said by ____'s  height..." and saw the use of lots of different strategies we had discovered to make multiplying fractions easier. They understood what each number meant and whether they had to multiply or add or subtract them. It was awesome!)

At the beginning of the fraction work, things went slowly as students worked their way through the correct strategy to use and then through the initial practice of setting up and solving the equations they set up, but as the period wore on, students became faster and much more confident in their ability to use fractions. I think they were even surprised at how adept they became at using the fractions in their calculations.

This was one of the best lessons I've ever done involving the real-life use of fractions. I can't wait to bring out the data again when we get to proportions.... I think the already deep understanding of the data will aid in helping the students understand setting up and solving proportions.

If you would like to try this with your students, you can use the blank recording sheet above and the calculations sheet I'll paste below.  If you try it, I'd love to hear how it went for you and I would love to hear of any modifications you made so I can try those next year.
In Search of the PERFECT Man Calculation Sheet

1. I love this application for fractions. I have a Vitruvian man lesson too! But it is slightly different. It comes later in the 6th grade curriculum. Your kids would love it since it will "build" onto this!

http://ispeakmath.wordpress.com/2011/02/21/da-vincis-vitruvian-man-ratios-mean-median-mode-frequency/

And this isn't the Vitruvian man, but was similar - and fun! We also had "mystery guests"
http://ispeakmath.wordpress.com/2011/02/26/linear-equations-plotting-and-predicting-measurements/

1. Julie, I just took a look at your Vitruvian man lesson. It looks awesome! I can't wait to use it with my kids! I like your mystery guest idea too.... You always have soooooo many good ideas!

2. We are doing fractions right now and you are exactly right... IDK all of the time. Once I get done with multiplying/dividing I plan on doing this!! Thank you!!

3. Very cool. Thanks for sharing!

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Jamie
MissMathDork

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