Engineering Forum - 3D Imaging

Wow, has it been a while since my last post.  Blogging hasn't been my priority since I have been teaching since the beginning of the semester.  It's March Break now though so I thought I would try to fit in some blogging.

3D Imaging Technology

Last night, I attended this year's Engineering Innovations Forum at the Ontario Science Centre with a few of my Engineering friends.  The topic of discussion was 3D imaging technology.  The presenters talked about 3D scanning and modelling for Construction Design, Forensic and Medical applications.  There is some really cool and interesting tech out there.  Particularly interesting to me was the discussion of Photogrammetry (using photographs to find measurements and model in 3D).  Eugene Liscio, president of AI2 3D talked about how taking pictures with any digital camera can be used to generate a 3D model which he uses in Forensic applications.  He mentioned the Autodesk app 123D Catch, which can create a 3D model from photographs with any Apple mobile device.  Pretty neat.  Now how could I use this in my classes?  Something to think about over the next week...

3D Printing Technology

Turning 3D computer models into tangible objects for the Medical field was the theme for another one of the presenters.  You must check out the pictures at this link for 3D Printed casts.  They look awesome.

Breathing

Anyways, the presenter talked about how he was involved in designing a mask to be used to analyze breathing in sleep studies.  He needed to find the optimal spot for the microphone so it picked up the sound of breathing from the nose and mouth at the same time.  To find where to put it, they went outside when it was cold and snapped a picture of the condensing breath.  They used this to find the ideal location of the microphone.  The picture he showed us looked something like this (red lines indicate direction of breath):

Application problem time!  My Grade 10's are starting the unit on solving linear systems so I could get them to overlay an axis and grid on the picture and determine the location of the ideal microphone spot.  Here is a screencap of a Geogebra model of it that I threw together.  I didn't scale it to the size of the face but that would be necessary to solve the problem:

Also, here's a link to a Desmos graph of the same thing.

This could be a quick activity to show the students how this stuff can actually be used in real-life.

And then they could use their answers to design a mask which could be printed on the school's 3D printer.... ok maybe that's not that realistic yet.  It would be AWESOME if every school had a 3D printer.  Only $2500 each!  Somebody needs to get on that.  Real-world problem solving to the MAX.

This is why I still go to Engineering events when I can.  It gives me some ideas for presenting concepts in new ways and helps me stay current with the technology that's out there.  Engineering PD is teaching PD for me as a math/science teacher.

Day 9 - Crossing the Chasm

The problem... 

Experiment with designs and materials to build a structure that enables a truck to cross a chasm (between 2 desks).    

Why?

• Build an intuitive understanding of forces and load paths
• Make use of the engineering design process
• Encourage collaboration, knowledge construction and real-world problem solving

Ode to the Bridge Builder...

While reading this blog post, feel to play what I like to think of as the Anthem of Civil Engineers: Ode to the Bridge Builder by the awesome Kyle Gabler from the awesome game World of Goo (available for desktop, iOS, Wii and more)


Bridges are awesome (I use the word awesome a lot when I talk about Civil Engineering stuff because it is all awesome.  Big + heavy + awe-inspiring = awesome).  

The bridge building challenge has been a key go-to for physics and science teachers.  Usually it goes something like:  use the provided materials (toothpicks, spaghetti, balsa wood) to span the gap between two desks.  The team with the bridge that supports the most weight is the winner.  Its Collaborative nature also makes it a standard team-building exercise.  I want to pull this classic into the 21st Century by tweaking the challenge a bit.

Into the 21st Century...

The modifications I would make are as follows:

• Success Criteria: Bridge is able to support the weight of a (weighted toy) truck crossing over it while satisfying the constraints.  
• The usual challenge of building the bridge that supports the most weight isn't representative of Real-World Problem Solving.  Instead, if a teacher chooses to make it a competition, the winner may be the cheapest bridge (the ethics of the lowest bidder standard is a good discussion topic in classes!)
• Instead of providing the students with the materials to build the bridge, provide them with nothing.  They will have to experiment to find out what materials are best to use.
• Real constraints!  Set a material price limit.  I would set this very low (a few dollars?) to prevent them from using just a straight 2x4 or steel which would be acceptable based on the success criteria.
• Make the span huge.  Note: huge is a relative term.  It depends on how long you want students to spend on it!

Time to Play...
Students may want to dive straight into the building of the bridge but it should be stressed that they should do some research and planning before building.  This doesn't have to be boring research though.  It can be hands on and engaging.

Having the students decide what materials to use supports Knowledge Construction.  Students will have to experiment with a host of materials, taking into account their strength, weight, and cost.  They will also need to decide what to affix the members together (if it even ends up being constructed with multiple members).  

Physically experimenting with different designs can be time consuming, and time is money.  Student can experiments with different designs using simulations instead.  I say the more fun, the better.  Save the boring simulations for the pros (at least in younger grades).  Although World of Goo is not your typical physics simulation program, it helps develop an intuitive understanding of structural design (as long as they are reflecting on what they build and how they can improve their designs while playing).  Another (free) web-based game that is more specifically for bridge design is called Cargo Bridge.  Ultimately, the groups should decide what simulation program they would like to use.  

Screenshot from World of Goo

Curriculum Connections...

I see this activity as at the beginning of a physics course or at the beginning of a unit on forces.  It is a good formative assessment for a teacher to learn about students' preconceptions about forces and building.  During the design process, students can analyse the external forces in the structure, a part of the grade 12 physics curriculum.  If done at the beginning of the unit, the teacher can use it as context for the rest of the unit.  

1. Collaboration: entry - adoption - adaptation - infusion - transformation
2. Knowledge Construction: entry - adoption - adaptation - infusion - transformation
3. Real-World Problem Solving & Innovation: entry - adoption - adaptation - infusion - transformation
5. Self-Regulation: entry - adoption - adaptation - infusion - transformation
6. Use of ICT for Learning: entry - adoption - adaptation - infusion - transformation


Future blog topics...

• Formalize the engineering design process

Day 6 - The neXt Desk

The Problem...

What is the best way to move the neXt Desk?

Why?

• Opportunity for students to demonstrate real-world problem solving skills
• Illustrate the usefulness of several math concepts

I'm posting this a day late but it's because I was at the Connect 2013 conference yesterday and today. Great few days connecting with representatives from different school boards and vendors.  The neXt Desk is an art installation that is a symbol for the TCDSB's Project neXt and the neXt Lesson.  This is a picture of it set up at the Connect 2013 conference in Niagara Falls (which I'll definitely blog about later).

Ask the questions...

In an art class, students might critique the effectiveness of the piece in challenging how we normally look at desks but I thought it would be cool to turn the piece into a math problem as well. 

I would start by giving the students the picture.  Tell them they are the moving crew responsible for moving the sculpture! What might they want to know about it?  What if the only information they had was from the picture?  What would they want to know before agreeing to move the piece?  Students could work in groups and may come up with entirely different sets of questions.  Some examples may be as follows:

• How tall is the piece? 
• How much does the entire piece weigh? 
• The piece comes apart into sections.  How many sections should it come apart in for two people to be able to carry it? (I came up with this because I did this multiple times in the past few days)
• How much tension are in the cables?
• Would the piece stand if the cables weren't there?

How can we find the answers...

Then, in groups, students can discuss how are they going to solve the problem posed.  This may take some research and data collection.  Some possible methods are described below:

• How tall is the piece? They could scale the picture from the size of one desk that they measure in the school.  If they had access to the piece, they could just measure it.
• How much does the entire piece weigh? Students could estimate/measure the weight of one desk and multiply.  But then what is their method for weighing one desk?  Look it up or find a scale and somehow measure it?  What about hardware and connectors?  Does their contribution to the total weight matter?
• The piece comes apart into sections.  How many sections should it come apart in for two people to be able to carry it? They may ask questions such as: what is a reasonable weight that 2 people are able to carry? What are the size constraints such that it would fit through a regular door?  It takes more time to take it apart into more sections.  What is a good balance between weight and time to construct/deconstruct?
• How much tension are in the cables? This is hard!  At least I think so.  Even with a Civil Engineering degree.  I think it is still an interesting question to pose.  Students could try building a scale model and directly measuring tension (but this  brings into question problems with scaling up loads, one of the many causes of the Quebec Bridge Disaster of 1907).   They could also come up with a range of possible values based on the weight of the structure.  Another method would be to compare the different sets of cables: which ones would have the most/least tension and make some assumptions for them.  Another interesting method would be if the students had access to the sculpture, they could theoretically pluck the cables and measure the frequency of the vibration.  They could then calculate the tension using the length, density and diameter of the cable.  I have done this with my guitar students to find out how much compression their guitar neck is resisting.  Another topic for another day...
• Would the piece stand if the cables weren't there? They might look at the tension in the cables.  They might try (safely) experimenting with a desk in the classroom to see how strong it is.  If you are wondering, the answer is yes it does stand but it ain't pretty!

Educated guessing...

Before actually applying their calculations, students should hypothesize what their answers would be.  This is an important part of solving real-world problems.  Know the answer before you find the answer! This is one of 3 Engineering Tenants I learned in my undergrad (which I will dedicate another blog entry on problem-based learning to).

What I like about questions like this is that I (as the teacher) dont necessarily need to know the answer.  To move it, we took the sculpture apart into 4 segments of 5 desks to move it but maybe there is a better way!  


What if...

Once the students have a good understanding of the sculpture you can take it one step further by asking questions such as:

• Why might the artist have used 20 desks?
• How tall would the piece be if there were 10,25,30,50 desks?  What assumptions would you have to make?  This can turn it into a geometry (something I didn't explore but another good way to go with the sculpture) or even a calculus question (rate of change of perimeter to diameter).
• What are some limitations of increasing the number of desks?

Curriculum...

Depending on the grade level and questions the students ask, the investigation can cover topics such as measurement, scaling, relationships between variables (weight of sculpture vs. number of desks, height of sculpture vs. number of desks).

21C...

Though it may not be a real-world problem that the students themselves face, it is one that we had to face moving it and the artist had to face when designing and building it!  Next time the neXt Desk needs to be moved from its location at the TCDSB headquarters to another conference, have some students test out some of their ideas!  (Only with adult supervision.  The piece is not the easiest or safest thing to move)  


1. Collaboration: entry - adoption - adaptation - infusion - transformation
3. Real-World Problem Solving & Innovation: entry - adoption - adaptation - infusion - transformation




A final point.  Obviously this is a TCDSB specific sculpture but the problems students are solving should be specific!  This problem may engage students from Cardinal Carter who walk by the sculpture every day but may not for a student who hasn't seen the piece before.  Teachers should seek out opportunities for investigations such as these in their own school communities.  Put on those math goggles and see what you can find.


Future Lesson Ideas:

• Guitar String Tension vs Pitch