Do your students have a hard time remembering the formulas for the volume of cylinders, cones, and spheres? Well, if that describes you, then you have come to the right place my friend.
I’m going to share a sequence of learning that has helped my students memorize these formulas. Every year when I teach this topic just about every kid can remember the formula after going through this process. I know that I sound like an infomercial, but that’s genuinely how I feel about this topic in particular. If you follow these simple steps then you’ll have your students feeling success with the formulas for volume in no time.
What I want my students to be able to do with the volume of cylinders, cones, and spheres
First, let’s get clear on what we’re aiming for with this topic. I want my students to be able to solve problems like the one above. Ultimately, they have to be able to produce the formulas for volume on their own and use them in different situations. Also, they need to be able to take the formula and turn it into the height formula or the radius formula.
Some students struggle to memorize formulas. Some even lack an understanding of what a formula is. That can spell certain doom if this topic is taught in a traditional way. But with some conceptual understanding, mnemonic devices, and repetition, you can get almost all students to memorize the formulas.
When I plan for each topic I make a list of I can statement. I let that list inform my instruction and we move from one objective to the next. The statements have to be simple, kid friendly, and not be too much at a time. They build on each other. When a student masters each one as you go, they will get to a level of mastery.
Using I can statements to organize learning
The following list are my I can statements for this topic. I spend as much time as I need on each statement to get students near proficiency. Then we practice more over the course of the unit they reach success.
- I know the formulas for finding the volume of cylinders, cones, and spheres
- I can find the volume of a cylinder.
- I can find the volume of a cone.
- I can find the volume of a sphere.
- I can find the volume of cylinders, cones, and spheres in real world problems.
We use a lot of these I can statements in our interactive notebooks. Students check off the objective when they have shown they can do it. We go back and look at the I can statements at the beginning or end of class almost every day. (If you’re not doing something like this now, I’d love you to try this with your students. It has really helped my students see what their goals are with the topic and it gives them a chance to talk about their learning.)
You can get this I Can Statement sheet ⇑ ⇑ ⇑, plus the rest of my I Can Statements for 8th grade math by clicking HERE. Enter your email and it’ll be on it’s on way to your inbox.
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#1- I know the formulas for finding the volume of cylinders, cones, and spheres.
Sometimes we expect kids to just memorize things. Unfortunately, (or maybe fortunately!) not everyone has the memory of Sheldon on Big Bang Theory. Most of us have a memory that needs a lot of help to transfer information to long term memory. To facilitate this someone invented mnemonic devices and graphic organizers. Both of these aides make remembering things doable for us mere mortals.
Most of my experience as a teacher has been working with students who don’t do well on tests for myriad reasons. Some of them have crazy home situations, some of them are academically behind, and some of them are disenfranchised with school.
For most of these students, I could spend a lot of time feeling sorry for them. However, I find that my pity doesn’t breed success for them. Instead, I commit myself to work really hard to give them opportunities to be successful in math. Hopefully tasting that success changes the way they look at themselves as students. So with volume formulas, I searched and searched for strategies and approaches that would help them memorize and understand these formulas.
I’m always looking for and experimenting with methods that get kids to be successful with difficult topics without compromising the math. For volume of cylinders, cones and spheres, that included using discovery learning and a graphic organizer. The discovery activity gave the students a basis for the math and helped them to see the patterns in the formula. I wrote an entire post about this discovery lab here.
Next, I used a graphic organizer to help students organize the parts of these formulas, as well as look for patterns:
How to use this graphic organizer for memorization
The graphic organizer above was so key to my students’ success. You can get your own free copy of the graphic organizer by clicking here. As you can see, it breaks the different parts of the formulas down. There are aspects to the formula that all 3 shapes have, like V=, pi, and r. Then, there are a few differences. The cylinder is the whole one, while the formulas for spheres and cones have fractions. The formulas for cones and cylinders have height in them. The radius is squared for the cone and cylinder and is cubed for the sphere. Using words, all of that seems really complicated. But put it in a graphic organizer and practice setting it up every day, and it becomes doable.
We followed this process with the graphic organizer to memorize the formulas:
- Complete a discovery activity.
- Teacher introduces the graphic organizer and models filling it out.
- Students practice filling out a blank graphic organizer every day during the unit.
- When practicing, teacher asks students questions about how to remember each part.
- Have students create and fill out their own graphic organizer. Prompt them to create this themselves as a tool during testing.
This has worked for years with my students and I believe it can do the same for yours. This graphic organizer builds a place in students’ brains to remember these formulas.
This year all of my students were able to write down the formulas on the test, even though I put the shapes in a different order on the test than the graphic organizer. They got to a point where they had internalized the formulas. Hooray!
Practicing finding the volume of cylinders, cones, and spheres
Once students have a foundation with the formulas, we turn to using them. To me this is a skill that they just need to practice. If my teaching calendar permits I spend one day on each figure. When they spend an entire class period on each figure they become very confident and start to tell me how easy each one is. Building that confidence helps them overall as students and not just with this topic.
#2-4: I can find the volume of a cylinder, I can find the volume of a cone, I can find the volume of sphere
I teach each figure on a different day. The process for each one looks very similar. We start out with a foldable in our interactive notebook that gives an example of how to find the volume of a cylinder, cones, or sphere. Then, I model some problems on the whiteboard that I get from my task cards.
Next, students solve some problems on their own. Then, we go over those problems together. Finally, I give them an assignment to do (see more about these activities & assignments in this post).
During the final practice work, I usually sit at my horseshoe table to help kids individually and to have students come check their answers as they go. This way I can give students immediate feedback and adjust based on how they’re doing. Whatever their practice looks like, having immediate feedback is so important in this step.
#5: I can find the volume of cylinders, cones, and spheres in real world problems
After we’ve spent three days practicing finding the volume, we spend a day or two practicing with real world situations. What this really means is word problems. The word problems can add a little bit of complexity because they might ask which shape has more volume or which situation will work better. Really this is another opportunity for students to practice their problem solving skills with a backdrop of volume of cylinders, cones, and spheres.
We use the C.U.B.E.S. strategy to analyze word problems, and we always read with a pencil in our hands (you can grab the presentation we use and read more about it in this post on teaching simple probability). Students can be so used to finding the volume that they overlook what the question is actually asking. They just want to show off their newly acquired skill and rush for an answer. You really have to slow them down and get them to see what the question is asking, and the C.U.B.E.S. strategy is helpful to do just that. At this point in our learning I model a few problems and then have students practice on task cards with a partner.
Common misconceptions
Since solving volume problems is a skill, most students get good at it rather quickly. But a few things can throw them off.
We all know the biggest enemy of students when they are practicing this concept. It has to be the dreaded diameter, and the fact that it’s different than the radius. They struggled with this in 7th grade when finding the area and circumference of a circle, and now it’s back in 8th grade to give you nightmares. It’s astonishing how long it takes them to really get that each part of the formula stands for something specific and you can’t just put a diameter in the place of a radius. So- something to keep an eye on!
Another misconception that I see happens when the shape is turned on its side. You would think you just turned the whole world upside down by putting a cylinder on its side.
To help students see that regardless of the direction a cylinder is facing, you still solve in the same way, make sure you do this a couple of times. This helps to build their understanding of what they are doing and not just make them robots. Asking lots of questions about the different parts of the shapes and what they represent with real objects helps them think about what they’re doing too.
Take-aways and getting to work
Nothing beats a graphic organizer and lots of repetition when you want students to memorize something. Also, you can build their confidence as they learn something new and use that confidence the next time something is difficult for them to do.
The I can statements that I used with my students might be perfect for you. I hope you check out this print and go version of these here (plus 20 other 8th grade topics!) But remember, these are certainly are not set in stone and you might need to add or subtract based on your situation (that’s why I also included a blank template in that download).
You can grab everything I use to teach the volume of cylinders, cones, and spheres here (see pic below). Also, check out 11 more teaching volume activities and ideas here.
Thanks so much for reading! Until next time!
