I am a huge proponent of application when application is possible. I realize sometimes application is not possible at the level you are teaching. For example, my senior son was working on Calculus the other day and had to recall the exponent rules from Algebra 1 (8th grade for him). He hasn’t needed to use exponent rules in any other class AND when I teach Algebra, I know it’s near impossible to find application for the rules. Clearly they have a purpose, but he didn’t see that purpose until four years later. Application wasn’t possible at the time he was taught the rules.
Surface area and volume, however, is VERY applicable. Last year, I switched my focus from using the formulas to finding online calculators (Read about it here) and just applying the formulas. I created many application type activities, including measuring objects in the classroom. We ended the unit with our robot project (referenced in the book Make Math Not Suck), which the students LOVE!
This year, I wanted to make my life and my student’s lives a little easier. There isn’t ONE calculator online that will calculate every surface area and volume problem we encounter. Teaching students the skills to look for these calculators is a good skill! The issue was the time involved searching for a calculator that would work, then when we did find one, there were some inappropriate ads on some of the pages.
So I fixed it! I created a SURFACE ARE AND VOLUME CALCULATOR that I can give to my students. They still need to know which one to use but they don’t have to search the internet to find one.
Please use this with your classes. Please DO NOT sell this to others or pass it off as your own. I drew each figure on my iPad and I entered each formula in the cells. It took some time! I LOVE when people use my stuff (for FREE) but it upsets me when they take it and sell it on TpT as their own. DON’T BE THAT PERSON!
Here are some quick links to previous posts about surface area and volume applications to use with the calculator and a BRAND NEW remote learning performance event.
Installment three of the area, surface area, and volume application problems. I know some of you have been using these and I hope they are working out well.
Area application can be found here. Surface area application can be found here.
In this post I have included volume application problems and application for surface area and volume of spheres.
I also provide students with candy in boxes and have them calculate the wasted or empty space in the box. This gives them hands-on application and allows them to use their tools. And, student LOVE to eat candy!
The Life Savers box is an amazing find! It’s a trapezoidal prism and we calculate the Life Savers as cylinders with a cylinder removed in the middle. The Mike and Ike’s are also fun because we calculate them as a cylinder with hemispheres at each end. The Kisses container is a triangular prism and we use the cone formula to estimate the volume of each Kiss. Gobstoppers are less fun, just spheres inside a rectangular prism, and the Tootsie Roll container is the least challenging of all with cylinders inside of a cylinder. I have each group work these problems on poster paper and then present them to the class. Giving students the opportunity to share in front of the class is something I try to work into each unit. Please make sure you have a culture of trust and respect in your classroom before you do this with students. It can be damaging to their fragile egos if they are ridiculed or made fun of. And if you chuckled at fragile ego, remember back to high school. What others thought of you mattered at lot!
Here are the application activities I promised. Please let me know if you find them useful. It makes me happy when others can benefit!
I posted some area application problems last week. You can find that post here. I also promised some surface area problems, so here you go. One page is many different problems that you could use as an assignment, assessment, or problem of the day. The second one is one problem broken up into 5 days, perfect for a daily warm-up. This idea of taking one prompt and using it all 5 days, called Focus on the Question, comes from Sue O’Connell in her Putting Practice Into Action book. It’s written more for elementary but the idea can be used with high school. I’ve found this strategy to work better with struggling learners. They have conversation time and it breaks the task down into smaller parts. I always call on a table, and not a person, to allow them to share what they discussed, discovered, and concluded.
I’m currently working on some volume application, which sneaks in some surface area. I will have another one including spheres. Stay tuned.
In Geometry, we teach area as a quick review before surface area and volume. This year, I wanted this topic to be more of a life skill than just a review. I taught students how to use Google cards to find the area of common shapes. A quick search will pull up the following card for almost any shape.
The more important skill I wanted to help my students with was using area. In life, if we can find the information we need and know how to use it, we can solve almost any problem we have. I created some tasks, some based on actual activities I’ve done, to help them use area. I’m sharing them here so you can use them too. Teachers have limited time and sometimes finding a good activity that you don’t have to create is just what you need.
If you use these activities, please share with me on Twitter. It makes my day when someone finds value in what I’ve created. Happy mathing!
Click on the image to view the template.
Stay tuned for surface area and volume application.
I saw this activity on Facebook last year. I don’t know who the teacher is, but the project is posted on North Central Parke Community School Corporation Facebook page.
I created the instructional slide below to facilitate the process with my students. Students had to select an object in the classroom to enlarge or reduce. They needed at least 5 measurements (many students took a lot more than that) and they had to select a scale factor. I provided some supplies but they were welcome to bring others from home. The project had to be completed in the classroom and they had to collaborate with at least one other person.
My students were so engaged, they worked very hard, and they were so proud of their results. Not to mention, they had some a-ha moments during construction. One student in particular made the connection that angles are the same in scaled objects even though the sides change. Now we had investigated and discussed this learning target, but it became evident to her when she was working on her object. YAY!
The first photo gallery includes process photos. I documented our progress on Twitter each day.
The last photo gallery shows the results. They did an amazing job. This is definitely a try again next year project.
I have been doing this activity LONG before computers were a staple in the classroom. (We won’t talk about how many years that’s been!) I love this project now as much as I did when I started.
I used to have a Far Side by Gary Larson desk calendar and each year I would keep the images and use it for this project. I don’t buy the desk calendar anymore, but you can find Larson’s comic’s online.
I take the comics and cut them equally into 3-4 congruent parts (depending on my groups). Students must work in groups of 3-4 to decide on a grid size for their original and a scaled paper size and grid size. Once they’ve worked together to draw this in, they start sketching their drawing box-by-box. We spend about 4 -50 minute class periods on this project.
The students have a lot of fun with this and are proud of their product when finished. It also reinforces teamwork. When one person doesn’t complete their part, a picture is hung up for viewing incomplete. So sad.
Here is the planning guide I use for this project. If you use it, post about about it on Twitter, and tag me @MandiTolenEDU.
For the last 9 years, I’ve had students do a Trig project where they use handmade clinometers to measure the height of an object taller than they are. I love this project because it shows the application of Trig and guides students through a thought process to solve this type of problem.
This year I wanted to shake things up a bit. I wanted them to do the same project, but this time I wanted them to write an angle of elevation word problem. Students struggle with the word problems, and writing them helps them understand the process and required information.
As always, I was blown away by the creativity of some of my students. Their word problems were hilarious! They were problems I would WANT to solve. I took a few and used them on our assessment.
Since we had a recent ice storm, pictures had to be taken inside. It was Homecoming week, so we had some interesting backdrops. Students used the HOCO decorations and wrote their stories around them. Aren’t kids great?
Angle of depression is still giving us issues so maybe next year I’ll have them measure something below them. Maybe from the bleachers or the top of the steps. Hmm… food for thought!