Category Archives: Percents

If The Earth Contained 100 People

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I discovered the books, “If the World Were A Village” by David Smith at a local math conference two years ago.  I would love to explore the math in this books with my class but have not come up with a good lesson for it yet.  I am posting about this now to get my links together, inspire myself, and maybe get some ideas from the amazing math teachers that read my blog.

If you have lessons or activities surrounding this concept, please share them in the comments with me!  Once I get something together, I will tell you all about it.

Links I like about 100:

Please share links if you have any.

The Black Death: Percents, Ratios, and Rates

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As much as I love teaching math, sometimes wish I taught social studies.  History is so much fun!

In our 6th grade curriculum the students do a interdisciplinary project on the Middle Ages.  They study the Middle Ages in Social Studies, read period books and fairy tales in Language Arts, create Middle Age art, and even learn popular dances from the Middle Ages in dance class.  With all of the Middle Age fun coursing through the 6th grade, I could not be left out in math class!

The Land Of Matheval

I created “The Land of Matheval” for our Medieval Mathematics Unit.  Matheval was a fictional medieval community comprised of my 25 6th grade students.  I let all of my students pick a person from the Middle Age to become and research.  We were studying percents, ratios, and rates so I wanted to look at the percentages of the different classes of people of the Middle Ages.  To study rates, I decided to focus on the death rate of the Black Death across Europe.

Day 1:  Percent of the Population

When people think of the Middle Ages, they often think of Kings, Queens, and knights.  However, nobility was only about 1% of the population.  In our class we investigated the percentage of the Medieval population that was nobility (1%), monks and priests (5-10%), and commoners (90%).  We then took those percentages and applied them to our 25 6th graders to see how many of each class we would have. We had to do a little rounding and estimating so that we didn’t end up with half a person.  We ended up with 1 member of nobility, 1 monk and 1 priest, and 22 commoners.  The students were quite surprised that there was only one member of nobility among us!

Day 2:  Draw Your Role

I had the students draw their role from a hat to decide if they would be nobility, clergy, or common.  After drawing, we talked briefly about roles of commoners in the Middle Ages.  They had been discussing this in more depth in Social Studies so were already familiar with the roles.  The commoners got to pick a job.  For part of their homework, they were to enter their job and provide a brief description of their responsibilities on a Google Document that  I created.  I told them that since we were such a small community they could not duplicate jobs.

Day 3:  Estimate Your Chance of Survival

After they picked their roles I told them that we would be studying the Black Death.  I explained that many people in Europe died from the Black Death.  For part of their homework that night, they were to go onto their Google Docs and estimate their chance of survival according to the job that they had picked.  This was when the students realized it was NOT a good time to have picked being a rat catcher!

Day 4:  Rate of Death – The Black Death Arrives!

This day was one of those amazing teaching days that you wish you could have every, single day!  I arranged for the art teacher to dramatically interrupt our class to announce that the Pestilence had arrived!  What I didn’t know was that our art teacher was also the director of our school theatre productions OR that the social studies teacher would also join in the fun!  About five minutes into class, the art teacher exploded through our door screaming, “The Pestilence has arrived!” before dropping dead in our doorway.  She was then dragged out by their social studies teacher.  This was immensely entertaining and made QUITE an impression on my students!  With urgency, I told our students that our plans must stop at once today!  We needed to stop everything and learn more about THE BLACK DEATH!

We discussed the spread of the Black Death throughout Europe by analyzing graphs and charts I had on a Powerpoint.  We researched the population of Europe from 1347 to 1352 and discovered that 25 million people had died in 5 years.  We then calculated how many people died each year, each month, and each day!  As we continued on with our calculations, the numbers became more and more manageable (and thus realistic) for the students.  They wanted more, so we then calculated how many people died each hour and finally, how many people died each minute.

We discovered that an average of about 10 people died every minute during that time period in Middle Ages.  What did this mean for Matheval?  For our small class of 12 it meant that we could all be dead from the Black Death in about 60 seconds.  What could I do but set a giant timer on the overhead projector?  At this, the students actually began to panic.  My classroom became a flurry of voices, “The Black Death is here!”,  “I don’t want to die from the Black Death!”, and   “Let’s get out of here!”   Then, they asked me something unexpected.  They asked me, “Mrs. R, can we leave?”  At this point, what could I tell them but, “YES!  If you want to leave – GO!”  At that, they all RAN out of the door, and kept running!  They ran in all directions!  They ran completely across the entire soccer field.  And still, the time was counting down.  When the timer went off I screamed out the door, “TIMES UP!!  You are all DEAD!”  This is when they did something else I did not expect, they all “dropped dead” right where they were.  They were quite the spectacle!  I wish I would have anticipated this, as I would have loved to post those pictures to this post!  But, I was too caught up in the moment.  What else could I do now but loudly sing, “Bring in your dead!  Bring in your dead!”  (You should never miss a chance for a Monty Python moment!)

When the class was back, seated and winded, we discussed what had happened.  At hearing the Black Death was coming, what did all of my students do?  THEY RAN.  What happened to them anyway?  THEY ALL DIED.  But, what did they do in the meantime?  They spread the Black Death across the entire Woodlawn Campus!  We talked about how this was human nature, and many people in Europe probably reacted the same way that they did.  They fled, and they spread the Black Death.

I then opened the Google Doc and we looked at their estimated chance of survival.  After what we learned about the rate of death, we updated their percentages as a class.

It was a fantastic week, it was an amazingly fun lesson, and my students have not stopped begging for more activities like the Black Death!

The Data of Germs and Hand Washing

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Flu season is upon us – and we are working on percents!  What better time to estimate how many germs we have on our hands and investigate how long it really takes to get rid of them?  The CDC (Center for Disease Control and Prevention) defines proper hygiene as vigorous hand rubbing with soap for 20 seconds.  Most of my students were familiar with the 20 second rule, but not convinced of it’s effectiveness.  So, we decided to collect the data and find out for ourselves!

The Set-Up:
I gave them each a squirt of glowing germ simulating lotion which they rubbed onto their hands. We went into the bathroom, turned out the lights, and I shined the black light onto each students hands. This was FUN!  They were quite disgusted with the amount of “germs” on their hands. They were even more surprised to see so many “germs” on their faces, which they had obviously been touching way too much in the five short minutes since they had applied the lotion. It was easy to estimate at this point that the germ count on their hands was at 100%. Let the hand washing begin!

Hand Washing:
The students washed their hands with soap for 5 seconds and then rinsed. I turned the lights off again and we inspected them again with the black light. They were shocked (and disgusted) to see that their hands were still VERY dirty!  Each student then estimated the percent of germs still on their hands.

Rinse and Repeat:
Our goal was to analyze germ data at 5 second intervals for up to 20 seconds.  So we washed, analyzed, estimated, recorded and repeated three more times.

Results:
It took a solid 20 seconds to eliminate the majority of the “germs” from the students hands. The most difficult places to clean were the fingernails and the creases in the palms. The most often missed spot was right around the wrist.  Most of the girls were able to get the estimated percentage of germs down to about 2% while the boys seemed to get stuck at about 10%. The boys found this quite amusing.

Analysis:
After we finally got back to the classroom we loaded all our data into Google Docs and created line graphs.  We then uploaded them to the Handwashing page on our class Wiki.


After we graphed our data in Google Docs we discussed our findings. The kids were surprised that it took so long to wash all of the germs off of their hands even though most of them had either heard about the 20 second rule or knew of a “hand washing” song.  We then picked one of the songs, “Twinkle, Twinkle, Little Star” and sang it as a class while I timed us.  We all enjoyed singing and it took us 23 seconds to sing the song.

In Summary:
This was an extremely engaging and interesting activity!  It did take an entire class period as we only had four sinks and one black light.  But it really brought some fun to a cold winter’s day math lesson.

Looking Forward:
Next year I would like make this like a “Myth Busters” activity. I have since heard Myth Busters did a hand washing episode but could not find it. I would also like the students to do more data analysis and possibly even some comparative analysis.  For this, I am thinking of percent of change between the boys and girls or for each hand washing interval.