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 love taking boring problems from the book and turning them into fun learning experiences. A boring word problem was the beginning of this task.
The actual prompt (which I can’t seem to find anymore) gave two popcorn containers, one a cylinder and one a cone, and asked the relationship between the volumes.
I saw an opportunity to construct three-dimensional figures AND eat popcorn. Oh yeah, we could discover the formula for the volume of a cone and have some great mathematical conversations too.
I’ve been doing this project for quite a few years. I originally posted it on my Infinitely Teaching blog. I have updated the Google Slide I give to students and I now encourage them to begin with the cone and move to the cylinder. This simplifies the process significantly.
Here are some pictures of our recent process. My favorite comment overheard by a student was “This is so much fun!” I want math to be fun so this is a success.
Here is a link to the Google Slide I give students with instructions and a scoring guide. If you use this, please let me know about it. It makes my day when others find my contributions useful!