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Understanding Scale with Paul Burgmayer

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Scale Work Sheet





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Deborah Hazen's picture

Assessment and this activity

It was illuminating to end our discussion of this mornings activities with the question of how we would assess student understanding of an activity like "How big or small is a water molecule?"

When we posed the question to the class, there were a few "types" of answers.

1. Very, very small.

2. Well, I just went to the sheet and found the answer (a water molecule was on the circuit we traveled downstairs).

3. I looked at the sheet and refered to the size of an atom, a water molecule is made up of 2 hydrogen and one oxygen...

4. I googled it and it is....

5. Well, I thought about how many water molecules I could fit on a .........

Because the exercise was an investigation of scale, my assumption was that Paul wanted us to leave with a sense of the size of a water molecule relative to the size of other objects. Being able to say that a water molecule is about 3x10-10m has great appeal to many students, but for most--it is an answer that doesn't carry with it a whole lot of meaning. We just don't deal in those very small/very large numbers enough to have an intuitive sense of the size. Having the numeric answer be right there on the wall or so easily available on the internet, takes away some of the potential for inquiry for the student who will just want a "right" answer.

"Very, very small" is another response that is ambiguous to evaluate. Very, very small like the ladybug you caught yesterday? Like the piece of cake your brother left on the plate last night? It is hard to measure understanding in this response. In order for everyone in the class to construct a meaningful response to the question and leave with a real sense of the relative size of a water molecule, students must find their own frame of reference to investigate.

Wil's experiences led him to construct a mental model as he thought about wavelengths, microscopes, the smallest bacteria he could view with a microscope and the size of a water molecule. He constructed a story that combined a number of observations, his new story about the relative size of a water molecule built on old experiences--combined them in a novel way (to him) and he was excited enough about his new story to share it with teams as they walked by. Wil was lucky in that his story could be constructed using the information posted on the wall in the hall. My guess is that for many participants, the info on the wall just wasn't "doing it" ---it wasn't supporting their construction of a story. If Paul had shared the scale activity with us one day----sort of a ---"Hey, it really can be hard to wrap your head around really big and really small things, but I think scale is important to building models in science--so I'm going to share one way I look at scale." Then he led us through the hallway exercise and the next day we came in and our assignment wass to come up with our own story/way to wrap our heads around scale--and we shared those stories with each other--then we would have shifted focus for students who were just looking for the "right" answer and made the topic more accessible for everyone.

This is the beauty of inquiry---it makes topics accessible to students with varying readiness, background knowledge, and learning preferences/strengths precisely because it challenges students to find the best way, for themselves, to construct meaning. 

RecycleJack Marine's picture

Music Scale

Here is a wonderful FREE opportunity for anyone:

Woodstock Revisited

For anyone who wonders what is was like,
 and for those who were there...

Wednesday, August 12
6 p.m. – 8 p.m
Penn State Great Valley
Register Here 


August 2009 will mark the 40th anniversary of the Woodstock Festival, three days of peace and music that became one of the most well-known pop cultural events of the 1960s. Woodstock conjures images of rain, music, drugs, rock and roll, dancing, and free love. But what was Woodstock really like?

Find out from those who were there, on Wednesday, August 12 when Michele Hax, contributor to the new book Woodstock Revisited  shares stories and perspectives from everyday people who were there. Hax, a sociology professor, actively participated in the politics of the times and often lectures on the 1960s, and infuses her lectures with a unique perspective by  juxtaposing the sixties with today’s socio-political turbulence.

"What we hope to do is provide a flashback experience, to give everyone a taste of the sixties—and the phenomenon that was Woodstock. We'll do the presentation sixties style, facilitating an open and interactive dialogue about the late 1960s, the legacy of Woodstock, and how it mirrors, or does not mirror, events happening today," says Hax.

 Also at the event, Joanne Hague, author of the new book Woodstock: Peace Music and Memories and founder of the Woodstock Preservation Society, will  display photos she has restored from Woodstock 1969.  

The evening will end with a Woodstock mixer – photos, sounds and snacks from the times. Anyone who was at Woodstock is asked to “come as you were” to share your stories and reminisce with other Woodstock alums.  The evening is free! 

If you were at the Woodstock festival in 1969, we want you to be our special guest.  Please e-mail Suzanne at to let us know you will be attending.


RecycleJack Marine's picture

Bathroom Scale

I liked Paul's lesson about scale, and his visual prersentation was spectactular.

If I think of "A" Scale...I think of my lifetime weight gains and losses. Why does the scale in the bathroom have a different number than the scale in the gym and the scale at Weight Watchers?

But on the other type of scale, I like what Dalia wrote about the FOSS measurement unit. I think it's a great idea about measuring objects on a different scale. I also liked discussing with Jill the lesson on measuring rooms in real feet (chiildren's feet are outlined and used to measure rooms). I once drew an outline of one of my feet and it measured exactly 12 inches from heel to toe.

I like what we did last week in this institute: It allowed for genuine inquiry into each other's "idea box" which are of course chock full of great ideas and memories of great lessons to share with other teachers.

Verolga Nix-Allen's picture

Understanding Scale/Assessment

Wow!  This lesson was really deep.  Most of it went over my head but....................................I reflected on Paul Burgmayer's introduction.  I was so interested in what he was going to say.  However, after a while I was lost because I didn't remember the formula, tools and how to use them.  In retrospect  however, I do remember my introductions given to the General Music class.  My first statement was "picture a world without music". What would the world be like? Why do the supermarkets have music playing while you shop? How does music fit into your world?  These questions generated metacognition upon which I built class discussion of their stories even before we opened a music book.  Some responses were....I whistle while I walk; music helps to pass the time; music can tell the story of what's happening on TV if you're not in the room; without music our world would be dull, uninteresting, not exciting and maybe no meaning. 

Then Joyce comes with the straws and it begins to make a little sense because it was tangible and I could see the relevance between students, the real world, etc. a model we can feel and touch.nd I guess that's a kind of assessment of students nit just doing the process in their head but applying it to a 

Geneva Tolliferreo's picture

7/23 PM: Assessing Understanding Scale

It is the concluding collaboration of Dr. Nix and Dr. Tolliferreo that...

In the real class, with students in elementary, middle, and/or high school grades, this lesson may or not go as smooth as it did in this class of professional educators.  Even with the variables, we were able to complete the lesson, return to the classroom, converse with colleagues briefly, and come back together for a professor led discussion.

How would students who did not understand Math, understand this lesson on 'scale'?  How would they understand Math w/o basic Reading skills, at the very least?  Going through the 'hands on' experience is fun, yet the challenge presents itself when the fun in learning needs to be practical for application and assessment reasons.

Prof. Burgmayer's introduction was engaging, at least for us.  What about the student who knows they are behind the curve and feels defeated before they get started...which in many cases is why they don't get started / with the program?  Thus, challenges in the classroom begin to become apparent.  Now the teacher must share their focus with dealing with disruptive behavior issues. would this lesson be assessed for all our students, including those who may have fun with the lesson, yet not able to apply the mechanics of it?

However, a really savvy teacher would construct an overall assessment and an assessment for each student based on their individual level/need.  And then...what about the student who excels in their areas of interest and disconnects with what they do not have an interest in?  They too must be assessed, and done so w/o fear of failure.

Note:  this is not limited to Special Education students...


Edward Bujak's picture

So the answer is what ?

Geneva, I love your assessment of our scale model lesson and your questions/statements are provoking.

It is the culture of the school that provides for opportunities like this to go outside the classroom and then to return and resettle and focus.  This climate of the school comes from only one place and that is the principal! He/she encourages this and establishes an enforced cause/effect for individuals who abuse any privilege.

I am a math coach and working on principalship cert so I am biased.  I believe the principal is the answer.  I also find myself saying "is isn't about math" too much.  A excellent poem was provided to explain density.  I guess we could have read the poem out loud, but why are these students not seeking extra help to learn math literacy and reading/writing literacy?  I spent about a third of my time tracking students down because they did not show up for pull-out sessions and they never show up before school, after school, or during their lunch period.  This was the same story for the reading/writing literacy coach.  We can provide the opportunities, but I cannot figure out how to force anyone to learn or force anyone to want to learn.   I hear you, but I do not have an answer.  If we did I guess their would be less problems with most schools.

There will be disruptive students regardless of the lesson, regardless of the teacher, regardless of the space, regardless of he didactics, regardless of the multiple intelligences utilized or modalities employed.  It is the teacher and moreso the principal who deals with these few habitual disruptive students and sets the tone of decency, citizenship, and respect in providing a safe learning environment that is least invasive for all students.  Why are we constantly dealing with these repetitive disruptive individuls who do not want to be students?  It typically is the same offending individua across many subjects across many teachers.  I do believe most kids do want to learn and become students.  It is the disruptive individuals who can eaily ruin a class and a school ... if permitted.

Syreeta Bennett's picture

Scale Lesson

I thought the lesson was good. I like how he drew on multiple intelligences. In his lesson there was science, math, literature, etc. I also appreciate the movement and hands-on activities because it drew my interest and allowed me to "see" my thinking.  I beleive that the lesson can promote inquiry, if students then develop other questions. As teachers then with a pacing schedule when do we allow students to answer these questions? Also what  if a student is not interested in the topic or did not  generate any  questions, is the lesson still inquiry? To be honest, it didn't generate any questions for me beyond the lesson. In the lesson, I questioned what I was doing and I was amazed by the dime walk but I didn't generate any inquiry outside the lesson.  So inquiry has to be student generated and come from their interest.

Diedre Bennett's picture

As far as

As far as having an authority figure on a subject, I believe there should be someone who has more knowledge involved.  This person in my opinion serves only as a guide.  We all know the saying you can lead a horse to water but you can't make him drink (he’ll drink when he gets thirsty).  The same applies here, Paul shared his knowledge with us, but it was up to us to make sense of the words coming out of his mouth and from the various activities he had us do.  How else does learning really take place, unless you have a guide to expose you or point out?  I can show you the path but I can't make u walk down it, but if you choose to travel down the path I can't tell you how far to travel down it.



Judith Lucas-Odom's picture


Here Here!  I agree authoritatively! Brie!

Brie Stark's picture

We certainly all teach each

We certainly all teach each other! :)

Geneva Tolliferreo's picture

Tear Drop

This lesson allowed me to see myself in relation to all that exists...

Then I thought about a water drop in relation to a tear drop.  Which weighs the most?  Which has more impact?  Which really weighs the most?

What really is my relation to all that exists...

These are the boxes that opened for me to create this story.


Dalia Gorham's picture


I enjoyed the lesson, I gained many ideas to take back to my classroom.  In math there is a unit on measurement, I will have the children measure printed pictures of items on a larger scale.  I do believe that this will spark inquiry in my students and as a center they would be able to complete an inquiry-based project about scale. I really liked the photos used to introduce the lesson as well as himself.


I believe that inquiry can happen in a classroom with an authority figure/expert. Paul did a great job of answering our questions and guiding us with a question.

Moira Messick's picture

I think Paul did a nice job

I think Paul did a nice job integrating inquiry into an effective lesson.  I like that he set us up with a springboard of information before the "inquiry activity."  His insights into his own life experiences were relevant to establishing the relationship and credibilitiy that he shares with his students.  This allows students to start feeling comfortable about developing their questions.  I found myself asking many questions that I wanted to explore during the period.  My questions were not necesarily the same as the person next to me.  With more time and Paul's guidance, this would have been true inquiry for me.  I look forward to applying his models of scale to cells and forensics this year...

Many thanks to Paul for pushing me outside of my comfort zone with mathematical applications to chemistry.  Today I lived "Confusion is the second step of real learning."

Kathy Swahn's picture


What a fantastic lesson!

Thanks I will find a way to make this lesson a part of my reintroduction to the metric system. I will be going both directions however going from tiny to the solar system.


Diedre Bennett's picture

I enjoyed today's lesson. 

I enjoyed today's lesson.  My learning is best when it is hands-on.  I need to not only hear but see the relationship between objects and ideas. 



RecycleJack Marine's picture

Child vs. Tractor Trailer

This morning's presentation reminds me of something that happened over a decade ago between New Jersey and New York City.

A traffic jam occurred at the entrance to the Holland Tunnel on the New Jersey side, backing up traffic for several miles. A tractor trailer had driven into the tunnel and its top got wedged between the ceiling and the road surface, causing it to get stuck inside. The police copuldn't figure out how to get it out of the tunnel. 

After an hour or so, a young child in one of the cars close to the tunnel's entrance came up with a simple solution, which was shared with the authorities: Let the air out of the truck's tires and then pull it out of the tunnel!

Think about the differences of scale: the child and the truck, the situation at hand and the simple solution.


Judith Lucas-Odom's picture

Scales with Paul

This morning was very cool!  It related to inquiry and what I want to work on, multiple intelligences.  Trying to orchestrate ideas with several layers of inquiry can be overwhelming to the novice learner.  I liked how Paul scaled the lesson for each level of the learner.  Given the makeup of an average class, I would infuse more of a reason why it relates to the student's world as well as the teacher's world and the underlining themes.  It would become a spring board for learning!  Discussion, inquiry learning and yes a little confusion is necessary! 

The authority figure role, the teacher can become the spring board to create stories and the summary of stories that the students can learn! 

Diane Balanovich's picture


I found scale to be challenging for me to understand. It has been a long time since I have worked on scale. The formula's were familiar but the application was difficult for me. I needed to ask assisstance when plugging in the numbers. I thought it related to inquiry because it really allowed the participants to run with their ideas. I'm wondering, what about the students who had little knowledge of the formula's? Would the students be well versed in figuring out the math, so it did not interfer with the science aspect of the lesson? I know as one of the struggling participants, I became frustrated when I did not know where to continue.  I would not have moved on until everyone had a sense of understanding. I guess time was the issue. As a teacher would you continue the lesson another day for struggling students?


The measuring of objects downstairs really put scale into perspective.

Stephen Cooney's picture

couple of good sites on measurement and scale

In the late 50's an MIT undergrad was used to measure the Harvard Bridge over the Charles River.  It is a nice application of 'what is measurement?"


Once you walk you kids through even just a part of the 1000 yard model of the universe, the first 5 planets takes about 150 yards if I remember correctly, you will open their eyes.

RecycleJack Marine's picture

The Scale of Trash in our environment

The party's over.

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