Friday, February 28, 2014

Conquering Volume!

Y'all, teaching middle school math can be hard some days! Don't get me wrong, I love my job, but there are some things that kids just have a plain old tough time understanding. One of those things is the difference between volume and surface area. They don't understand conceptually where the formulas come from, therefore can't figure out how to solve the problems. I don't want to be that teacher who just tells them to use the chart and plug in the values, I want them to understand WHY that formula makes sense.

I SO wish that students aren't told to find volume by multiplying length x width x height. It takes me a full day to explain the formula V = Bh is the real formula for prisms. The one that they learn in elementary school only works for rectangular prisms, so that is fine until they get to my class, but most students feel like their whole life was a lie when that is no longer on the formula chart! I feel like I have to start from scratch and tell them that volume is a stack of 2D objects. We need to find the area of the base first. If I had a nickel every time I corrected a student regarding "b" (which is just base) or "B" (which is AREA of the base), I could have retired this week.

Literally, I am emotionally exhausted from saying, "what does big B stand for?"

Students respond with, "BASE!"

Me: "No. You don't get to say base loudly because it is a capital letter."

Students: "Oh, right! AREA of the base!"

My lord. I hope they still remember next week when we have a test.

One thing I wanted to share that they were JUST NOT GETTING was why we multiply by 1/3 for volume of a pyramid (and cones for that matter). I had finally sold them on the formulas for prisms and cylinders and they totally understood it conceptually. YES! But, then we hit a wall with pyramids. They wanted to know why we multiply by 1/3. Or divide by 3. Yes, we had a conversation that those were the same thing. Minds were blown. It wasn't enough for me to tell them that it takes the volume of 3 pyramids to make a prism. I had to show them.

I started with one of these:

Then, we made 2 more and taped them together at their apexes.

And, folded them up!

This TOTALLY helped them to visualize what I was saying. I love being able to let them PROVE things. It's the best. Love being able to use my washi tape too. It's the little things, right?

Here are some foldables that I created to use this week as well and are now in my TPT store! Click the pictures to go to the listing. 

How was your week?


  1. I love it! What a great visual. :)

  2. love your visual.
    I also love that you wrote this. I think I can start helping with this is sixth grade. We too only use rectangular prisms, but V=Bh is on their formula chart for the first time.
    Hmm... you really have me thinking about how I teach volume!
    Hodges Herald

    1. Coming from 6th grade, I totally understand!

  3. As one of those 5th grade teachers who will be teaching volume soon, I pledge to teach them that volume is additive. So they will indeed learn V=Bh in my class. Prepped and ready with toms of foam cubes. Great post- I feel your pain!

  4. This is a great idea!! We only do rectangular prisms in 5th and rectangular prisms and cylinders in 6th, but I have been working with my 5th graders on the idea that it is the Area of the Base times the height just this week. I found some great CCSS resources that work on this. Thanks!

  5. Love this visual! I usually show the relationship between pyramids and prisms with water...can fill a prism 3 times with water from pyramid with same base and height.

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