Today was the first homeschool physics class, and with most first classes in science we went over some basics. We discussed scientific notation, metric units, significant figures and uncertainty. I started by showing the two cartoons you see here. I love the No Cussing! sign (found on this blog https://camarojones.wordpress.com/2008/10/21/the-metric-system/) because we don’t really have any rules in our house about cussing. Nobody gets in trouble for cussing… or I would be in time out all day.The USA is one of the last countries to keep using these archaic units and it drives me nuts. We’ve had a meter stick in our house since the kids could walk, maybe even before then, and we have always measured things in meters or centimeters. But when all the street signs are in miles not kilometers, its hard to understand what a kilometer means. But we need to have a feel for these other units so we went over how to compare them with the ones used in USA. We started with the meter stick, which is just a bit longer than a yard, and for first order estimates you can just remember a meter is approximately a yard or 3 feet. So now you know a board that is 12 feet long is roughly 4 meters long. Which is longer a kilometer (km) or a mile? A mile is longer by quite a bit, there’s roughly 1.6 km in every mile (1.609 to be exact), so if you’re driving in Europe and the sign says 15 km to the next rest area, you know you’ve got about 10 miles to go, you’re just looking for a rough estimate you can use 1.5 km ~ 1mi.
The other unit that causes a lot of confusion is the kilogram (kg) or gram (g), mainly because its a unit of MASS, not weight. But if someone asks for your weight in Europe they are expecting you to give an answer in kg, so really, they are asking for your mass. Mass is the amount of matter that makes up an object. Its the same amount of stuff, no matter where you are. Your mass is the same on Earth, the moon, Mars, everywhere. But your WEIGHT is the force you are exerting on the scale when you step on it and that depends on the force of gravity, so that will be different if you step on the scale on the surface of the moon, or any other planet. In science we make a very clear distinction between mass and weight but in everyday life, they are treated the same so its one of the concepts students can have a lot of trouble with. We’ll get into mass versus weight, later in the class when we discuss gravity but today I just wanted them to know that their mass in kg is roughly half their weight in pounds. 1 lb = 0.454 kg, so if you weigh 120 lb then you have a mass of about 60 kg. A 5 lb bag of sugar is roughly 2.5 kg, etc.
If you have these little math manipulatives around the house, they are 1 cm on a side and have a mass of 1 gram each, so you can actually use them in a balance to find the mass of other objects. Frequently if we read something is 5 grams I’l remind the kids about the cubes and say that’s the same mass as 5 of those little cubes. Just gives them a frame of reference.
OK, so on to the lab activity. To get across the concept of uncertainty in measurement and how to report measurements, the students were asked to measure the length of my living room 3 different ways. The first, was just to estimate the length without moving from the table. I placed a meter stick on the floor and they had to estimate how long it was, to the nearest tenth of a meter. Estimates ranged from 4.5 to 6.5 meters – a pretty big spread in numbers. Next the students measured the length of the floor using their hands, what’s called a hand span – spread out your fingers as much as possible and use the length from the tip of your pinky to the tip of your thumb for your measuring unit. Answers ranged from 25.2 to 36.2 hand spans. We discussed sources of error – hand not being spread out the same each time, repositioning the hand each time and not going in a straight line across the floor. We also discussed how everyone’s hands are different lengths and that would cause some differences in the answers. We made a histogram of our results, but with only 8 students, its not very useful. A bigger class would make for a nicer distribution. Finally, they used meter sticks to measure the length of the floor to the nearest millimeter (mm). Now we got much better results, with a range of 5.600 – 5.730 m, but with 5 of them being within a few mm (thousandths of a m) of the average of 5.646 m. Now is that average of 5.646 m the true length of the floor? Would you bet $50 that it is exact? Probably not, we still had sources of error, repositioning the meter stick each time, still have trouble going straight across the floor (they couldn’t put it against a wall, too much furniture in the way). But we could say with a lot of confidence that the length of the wall is between 5.62 and 5.66 m because most of our measurements fell in that range. So I would report that the length of the floor is 5.64 + 0.02 m, where the plus/minus 0.02 m is what we call the uncertainty in the measurement.
We still had a bit of time at the end of class so I gave them the homework and everyone completed it in class. I gave them the first few worksheets on scientific notation from this handout I found on the web, and this one on significant figures. I liked these worksheets because they had pretty good explanations in front of them so you can use them as a stand alone handout.
Next week the real fun begins when we start playing with the air track and learning about velocity. Students were told to read the first few pages of the Cartoon Guide to Physics if they have it, and then Chapter 2 of Light and Matter.