Skip to main content

Exploring Surface Area

We spent a couple of days exploring surface area recently! We haven't done much with surface area in past years, so approaching this was new for me, a well as for the students. We started out with various shaped boxes (rectangular prisms) and I asked the students to visualize and then draw what the boxes would look like if they were taken apart and laid flat (without all the separate flaps and such). Most students took about 5 minutes to complete their drawings, depending on how detailed they chose to be, and for the most part, they did a very good job drawing their nets. They then spent a few minutes comparing their nets with their group members, deciding whether they were correct (even if they were drawn differently), and determining whether anyone appeared to be missing anything (some students did draw only five sides, and their group members were able to help them figure out what was missing).


After drawing their nets, the groups had two tasks - to find the surface area of their particular box and to determine a formula for the surface area of rectangular prisms. We have already studied area, so the only thing we discussed before they set upon their tasks was the actual meaning of the term surface area. So, they set off measuring (asking if they should measure in centimeters or inches - I said it was their choice) and calculating.
Most groups determined their surface area by the end of the class period, but none of the groups were able to decide upon a formula. We continued the next day, and while some groups were able to write a formula that reflected a correct understanding of the concept (though not written correctly "variable-wise"), others were stumped. Even though they were stumped about writing a formula, the "stumped groups" were able to explain to me HOW they had found their surface area. Most of them explained that they found the front and multiplied by 2 because the back is the same, and that they found the top and multiplied by 2 because the bottom was the same, (and the same idea for the sides), and then they added those three sums together. Other groups found the area of all six surfaces and added them all. One group found the area of the 3 different sides, added them and then multiplied by 2.  Based on our conversations, I know that they all had a correct way to find the surface area, but writing a formula was difficult. Some groups were very close with their formulas, but had to be guided toward naming the length, width, and height with different variables.



One group actually finished fairly quickly (correct formula and all!), so they then worked on determining the surface area of a triangular prism (I had a Toblerone box on hand to use)....they found that surface area fairly quickly too!


In the end, several groups wrote good formulas, which were shared and discussed with the class. The students really seemed to enjoy this activity - it was challenging but achievable:)  Giving the students the chance to explore the concept and to construct a formula based upon their understanding of surface area was a great use of class time!


Comments

Popular posts from this blog

Memory Wheels - First Day, Last Day, and Any Day in Between!

This post has been moved to:  http://www.cognitivecardiowithmsmm.com/blog/memory-wheels-first-day-last-day-and-any-day-in-between

Love to Doodle (and a freedbie)

Exponents Color by Number For most of my school life as a student (and even as an adult, during PD), I have really liked doodling! During lectures, discussions...it would help me focus, but also give me something to make me look busy, so I wouldn't get called on in class! I always hated being called on and almost never participated voluntarily:) I liked to draw cubes, rectangles, squiggly lines, etc, and color in different parts of the doodles. Download this freebie:-) I really wanted to make some color by number activities. Since I am not good at creating actual pictures, I decided to make my color by numbers similar to my random drawing/doodling. My Exponent Color by Number is most similar to my past doodles, but I thought it was a little too random, so I started using actual shapes. The Integer Operations Color by Number (freebie), as well as most of my other color by numbers are more structured, but so much fun for me to make! Computerized doodling! Anyone else

Differentiation and the Brain - Introduction

It's summer-time and time to get some reading done! Myself and my Tools for Teaching Teens collaborators are going to read and review Differentiation and the Brain, How Neuroscience Supports the Learner-Friendly Classroom , by David A. Sousa and Carol Ann Tomlinson.We will each be reviewing different chapters, and those blog posts will be linked together as we go. If you're interested in learning more about this book, check back and follow the links to the different chapters:) I'm going to give a quick review of the book introduction here, and then later today I'll be reviewing Chapter 1. According to the authors, differentiation is brain-friendly and brain-compatible! They describe the rise, fall, and rise of differentiation, starting with the one-room schoolhouses, where teachers taught all subjects to all students, of all ages, and HAD to differentiate - there was no other way! As the country's population grew, public schools grew, and students were separat