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...
- 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
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