Archive for January 2012
Teachers – how are you handling significant figures? I’m a bit at odds with my textbook and I’m wondering what the rest of the world is doing. I’ve discussed my issues with our chemistry teacher, he tends to agree with me, but it’s just the two of us. Let me explain.
I teach from Holt Physics. The book treats sig figs mostly okay. When they provide numbers for problems, they are always precise. Usually the numbers are in scientific notation, so you know where you stand with your given information. The book does state that 1500 could be 2 or 3 or 4 significant figures because we don’t know about the two trailing zeroes. I tell the students to err towards caution in those cases and treat that number as though there are 4 sig figs. The book correctly states that the answers are rounded to the least significant number of figures. You all know what I mean.
Here is where we part ways. I teach my students to carry an extra place while doing calculations. For example, if I’m dividing 35 by 62, my working answer is 0.565. If this is my answer to the problem, I would round this to 0.57. If I’m using this number in another calculation, I would use all three digits. The textbook rounds this here along the way even when it is used later. I’ve even seen problems where they have rounded more than once in the same problem. (There is no way I can remember the actual problem right now.) The results are often an error of about 10% difference between my answer key and my calculations.
While we are at this, I have a question I’m stuck on. Suppose you read a meter stick and you get a reading of 8.65 cm. That is three significant figures. Now you move a little ways up the ruler and read 22.40 cm. The accuracy of the ruler hasn’t changed, but I’m now working with 4 significant figure versus 3 before. I wouldn’t round the second number, it is as accurate as the device, but the first number isn’t 8.600. How do you account for this when you are dealing with the significant figures of a problem?
In the last couple of weeks we’ve done some new LEGO Robot Challenges and I’m really pleased at how they turned out.
First was my LEGO version of the Hungry Hippo game. The students were tasked with creating a robot that drives around gathering balls and marbles. The robot that collects the most points worth of marbles and balls in 60 seconds wins the challenge. The balls are the colored balls that are included in the robot kits. The large balls are worth 5 points each, the marbles are worth 2 points. Students had to come up with a strategy and then build to that strategy. The best design drove around with a scoop on the front that shoveled the captured balls into a bin on top. Many designs had rotating claws in front to direct the balls into a pen.
About a week into the challenge, students were tasked with doing a design review with another group. They had to critique the other groups’ project and suggest ways to improve the design, then have the same done for their project. All of the groups felt they got something out of the design review process.
The arena was our own Octagon I created out of 1×4’s. Each side of the octagon was 24″ and the sides were held together with masking tape. It was sturdy enough that the robots could bump into the walls and trigger a touch sensor. The plan was to have the robots go head to head in the arena, but they all locked up so badly that each robot did individual one minute runs.
The latest challenge was a rope climb. I first showed the kids a couple short videos on the space elevator and we had a short discussion on the cost benefits of such a system. They were given a short week (4 days) to design a robot that could climb up a rope. I hadn’t tried this before so I didn’t know what to expect. I had a few robots climbing the rope within 30 minutes, so I had to up the ante. Basically, they got a C if the robot climbed the rope. If the climber carried a 0.5 kg weight up the rope, the group got a B. If the robot managed to carry a full kilogram weight up the length of the rope, the students earned the A. Only one group managed the A using an innovative design of tires and belts.
I’m going to challenge them to go back to the drawing board on this one and see who can carry the most weight up the rope. After that, we are going to do Robot Wars in the Octagon. The goal is to disable your opponent or remove them from the ring. It should be fun.