1. Show an open hardtop suitcase that you're taking on vacation (full of clothes). Close it, then get a student volunteer to come up and lift it.
2. Then open the suitcase, and talk about how you always get sucked into buying stuff when on vacation while tossing a bunch of tacky souvenirs and other knickknacks you've bought on vacation into the suitcase.
3. Then ask another volunteer to sit on the suitcase to help cram it shut and do up the locks (you want it visibly too full, and for them to see things are getting compressed).
4. Ask the original volunteer to lift the suitcase again. Is it heavier? (yes).
5. Ask the class - did the mass change? (let them debate it out until they come up with a consensus of yes, it increased).
6. Then ask the class if the volume changed (no, it's the same volume inside).
7. Is it more or less dense? (at this point, only a few students will know it's more dense, so state it is more dense - if you put more mass into the same volume, it's more dense).
8. Write these principles on the board.

Principle B: If you pack the same mass into a smaller volume, it's more dense. Common experience: crushing Styrofoam (ie. everyone's put teeth marks on a Styrofoam cup sometime or another)

1. Show a block of Styrofoam. Get a hyper volunteer to jump on it until it's crushed a bit.
2. Then ask the class if it's mass changed. (No, it'd still weigh the same on the scale).
3. Then ask the class if it's volume changed. (Yes, it's squished, it's smaller now).
4. Is it more or less dense? (let people hash it out awhile then say, yes, it's more dense, and write the second principle on the board).

Principle C: Just because something has more mass doesn't mean it's more dense. Common experience: Styrofoam packing chips, paper clip

1. Preparation: stuff a big, big plastic bag with Styrofoam packing chips until, to you, it feels obviously heavier than a paper clip.
2. Then get a student volunteer to hold the bag in one hand, and the paper clip in the other, and say which feels heavier. (If you have a strong bag, and some time to kill, it's fun to have the students toss the bag around the room at this point to get an idea of its weight).
3. Now ask the students which is more dense, the paper clip or the bag of Styrofoam chips. (At this point, I got an almost unanimous class vote for the paper clip since it was obviously metal).
4. Then ask if you could assume something was more dense just because it had more mass.
5. Write the third principle on the board.
6. Ask how you could tell if some substance was denser than another substance. Try to avoid saying much here - let them debate it out and ask questions. (It depends on how much mass is packed into a volume - if you had the same volume of two things, then the one with more mass would be denser).
7. At this point, the students ruminated & asked me case scenarios (ex. if I smashed the bag down to be really, really small - could it be denser than the paper clip).

• What sorts of things could happen in the numerator or denominator to increase a ratio
• What sorts of things could happen in the numerator or denominator to decrease a ratio