# Interactive Algebra Lessons and Experiments

I've never had any trouble bringing things in to my geometry, trig, or calculus courses. I think it's very important to do so that students have something that sticks out to them years later. Unfortunately, my problem is that I can't seem to think of anything for algebra. Sure I can talk to my classes about functions that model real world situations, but I can't actually bring in a rocket that's modeled by a certain function, or a car traveling at a certain rate, etc.

So I'm looking for ideas or things that you bring in to show your algebra classes. Thanks.

I'm motivated by these videos and this professor. https://www.youtube.com/watch?v=97oTDANuZco

• Instead of bringing something to the classroom, why not take your group outside – say, to some field – and make them form a ring and, say sing songs? Just beware of mosquitoes – they are vectors of some serious diseases! Apr 23 '14 at 19:45
• (I know, I know – this is a lame joke. BTW: there's a better one, but untranslatable into English. In Polish, we call a field using the word meaning body (so we say – literally – about e.g. the "body of complex numbers"). There's then the joke about a (male) student approaching his (female) friend and making some comments about "wanting to have a body"; she replies "if you want to have a body, you need a ring first!") Apr 23 '14 at 19:48
• And more seriously: this is not a "real" thing, only a virtual one, but did you consider using Geogebra to do some (interactive) visualizations? Also, what level of education do you mean exactly – when saying "algebra", do you mean "solving equations" or "studying abstract algebraic structures"? Apr 23 '14 at 19:50
• The joke is much appreciated. I haven't heard that one. And it might actually be a good idea to take the class outside (if only that were feasible more often)
– jon
Apr 24 '14 at 14:31
– jon
Apr 24 '14 at 14:32

I made "logarithm sticks" for my college algebra class.

I bought some dowels at home depot and cut them to the following lengths:

• $\log_{10} 10$ feet
• $\log_{10} 12$ feet
• $\log_{10} 15$ feet
• $\log_{10} 20$ feet

etc. Then I labeled them as such with stickers, so they look like small flags.

Then when you put the stick that is $\log_{10} 20$ next to the one that is $\log_{10} 10$, they add up to the same length as the $\log_{10} 200$ stick. This visually demonstrates the logarithm multiplication rule. More specifically it tries to convince them that $\log_{10} 15$ is a number which is actually the part that is hard for them.

The numbers I actually chose were 10, 12, 15, 20, 30, 50, and then all the products you can generate from those numbers. Make sure you make more of the smaller ones, and make lots of 10s, 100s, and 1000s because those make sense first: they are 1, 2, and 3 feet long. I recommend this list:

• 10, 12, 15, 20, 30, 50, 100, 120, 150, 180, 200, 240, 300, 360, 450, 500, 600, 750, 1000

I haven't done this yet, but you could make a different-sized set by just using a different base -- then you could maybe visually motivate the change-of-base formula?

• Thanks! This is exactly the type of thing I wish I could think of more often.
– jon
Apr 25 '14 at 2:30
• In school we had a huge slide rule, which was hung from the blackboard... Apr 28 '14 at 3:21
• @vonbrand When my college algebra class has an extra day, I often spend it having them create simple slide rules, by drawing on yardsticks. Their calculators work quite nicely as log tables. ;) Apr 28 '14 at 10:20