Math = Love: Measuring Mass and a Personal Epiphany about Density

## Sunday, October 2, 2016

### Measuring Mass and a Personal Epiphany about Density

My physical science students are currently working on our measurement skill.  We're practicing measuring length, mass, temperature, and volume.  I haven't decided whether I want to include density in this section as well since it is derived from mass and volume or not.  The problem with teaching a science class for the first time (without any training as a science teacher) is that I just don't know what order I should be teaching anything in. I'm definitely learning right along with my students.

(If you haven't been following along with my teaching journey, I'm a high school math teacher who is having to teach a science class this year because of budget cuts.  My school used to have two teachers for each core subject.  Our advanced science teacher retired at the end of this past year, and the school district chose not to rehire that position.  This means our lower-level science teacher is having to teach all of the biology and zoology classes.  The middle school science teacher and I are both picking up a section of physical science to make things work.  I am viewing teaching this class as an adventure, and it's definitely proving to be one!)

This year, we combined our high school and middle school into one building due to budget cuts.  This means that the science lab at the old high school is still full of lab materials.  There were a bunch of triple beam balances in the old lab, so I brought six over to my classroom.

When I was a kid, my parents had a triple beam balance that they used at work.  So, I've used one before, but it's been a VERY long time!  I had an interesting time teaching myself to calibrate the balance.  Let's just say I was twisting the knob the wrong way for way longer than I'd like to admit.

On the car ride to school on the day of our introduction to measuring mass lesson, I started thinking about what I remembered about density from high school.  I was a straight-A student in high school.  I always excelled in science classes.  I excelled in all of my classes.  But, I didn't excel because I had a great conceptual understanding of the concepts.  Instead, I was great at memorizing things for the test and forgetting them soon afterwards.

I remember memorizing that the density of water was 1.  I also remember memorizing that objects with a density greater than 1 will sink and objects with a density less than 1 will float.  Add in the formula for density, density = mass/volume, and you have a list of everything I remember about density from high school.

Back to my car ride.  I started to think about what it meant for water to have a density of 1.  1 what?  I'm always getting on to my math students for not putting units on their answers.  But, here I am talking about the density of water and not even remembering the units.  I started thinking through this the way I hoped my students would.  The unit for mass is grams.  The unit for volume is mL.  So, the units for density must be g/mL.

Then, I had an epiphany.  This must mean that if I have 500 mL of water it should have a mass of 500 grams.  If I have 200 mL of water it will have a mass of 200 grams.  This is the type of thing that's probably obvious to everyone reading this blog, but it wasn't obvious to me.  Now that I've discovered it for myself, I don't see how I never figured this out before.

Once I got to school, I quickly grabbed a triple beam balance, a full water bottle, and an empty water bottle.  I found the mass of the full water bottle and the mass of the empty water bottle.  And, sure enough, the mass of the water was almost identical to the number of mL in the bottle.  (My husband had already warned me that they wouldn't match exactly because the density of water is 1 g/mL only at a specific temperature.)  This was such an exciting moment for me.  Density makes sense now!

I gave my students a list of things to measure the mass of.  These are all things that could easily be found around my classroom!

Contents of Water Bottle.  (Hint: Empty water bottle and full water bottle!)

Dry Erase Marker and Calculator

Ten Bingo Chips

Bottle of Hand Sanitizer and Glue Stick

Remote Control, Deck of Playing Cards, and Pepper Shaker.  I originally planned to have my students measure the mass of the salt shaker, but one of my former students wrote an inappropriate message on it in sharpie...

My kids definitely got a kick out of using the triple beam balances.  They were a bit frustrated with the calibration process, but I think it was good for them to experience that.  I've even spotted some of my physical science kids showing my algebra students how to use the scales!

Here's some pics of my students in action:

1. I'm teaching algebra for kids who need to go at a slower pace this year. I've never taught algebra before. There is no curriculum for the added hands-on stuff I'm trying to include. This is really only my second year teaching high school. All my training to teach math was for the elementary level and over 35 years ago! I relate to your idea that this is an adventure. I'm learning as I go. But I'm proud of myself for taking on such a challenge in my late 50s. And thank you so much, because I use stuff from your site all. the. time.

1. You are an inspiration! Keep up the hard work. I hope this adventure proves to be an amazing experience!

2. I co-teach 8th grade Life Science, and I will have to share your "density epiphany", as we just covered density, mass and volume. So cool!