Surface Area – Educational Aspirations

Last year I taught a lesson on surface area that bombed. I thought it’d be great to have students measure the surface area of a state using a scale model. This task was found in my course adopted resource pack. Looking back, it wasn’t a bad idea or problem but the execution was far less than stellar. The problem asked students to find the surface area of the state of Nevada. They were given a model and a scale at the bottom.

Screen Shot 2020-02-02 at 4.26.05 PM

The class completed this mostly in whole group (which in hindsight was not the greatest idea). I asked students to use the scale to find the surface area. Students used rulers and decided to find the area by dividing the shape into one rectangle and one triangle. After giving students about 10 minutes I surveyed the class and the answers were all over the board. Some debated on the word “approximate” as the class was asked to find the approximate surface area. Other students thought the 0-100 km was a guideline and could be rounded. While others decided to neglect the missing piece near the southern border of the state. Needless to say it didn’t go as well as planned. Looking back, one of the problems was that this activity was completed whole group. Students didn’t get time to discuss with each other what or how to measure. There wasn’t a determination of what to do with the missing piece in the south and how to divide up the state. The class eventually came to a consensus that there was one right answer and we moved on. I put a note in my planner to do things differently next year.

So it is now next year (2020) and I have a different class. This year I gave the same problem, but did things a bit differently. I first front-loaded information about the state itself as a whole class discussion. The class discussed the shape of Nevada and how it’s not exactly one rectangle and one triangle. I reinforced that we can’t just neglect the small corner of Nevada. It may be helpful to find that area as well. Students were then randomly selected and placed in small groups of 2-3 students per group. I asked the students what was meant by the scale in the bottom left and how they could use it to help them find the area. Student groups had time to discuss and report out how they would use it. Some students even found that the 0-100 km was actually 1 centimeter. I then gave each group a ruler/straightedge to help construct shapes within the state itself. Students had approximately 15-20 minutes to discuss and find the surface area using the tools that they were provided. Students were busy slicing up the state and using a straightedge to find the approximate surface area.

The class then came back as a whole and each group submitted a response. I received all the responses and students were given time to think about their submission and possibly make a change. It’s interesting how peer pressure and consensus will sometimes make you second guess a decision. In this case students mostly received affirmation and there was justification that came along with that decision. All but one group was in the ballpark and that group didn’t initially convert the scale. There answer ended up being extremely small compared to others. Some of the groups decomposed like this:

Screen Shot 2020-02-02 at 4.48.21 PM

The majority of the class was within the approximate range and it was a productive discussion. If you’re wondering, the surface area is approximately 278,000 square kilometers. So now you can win a trivia contest.

I put a note in my planner to use this method next year. Last year it bombed and this year was much better. Part of teaching is improving your craft and I had more than a couple pieces of humble pie last year. I tend to hear the phrase best practice thrown around in the field of education. I’m more of the mindset of emphasizing better practices and looking forward to tweaking this even more to make it a better experience next year.

My fourth grade class has been exploring a measurement unit for the past few weeks. We’ve been discussing the difference between area and volume. This has been a bit challenging as many students can apply area and volume formulas but struggle when finding surface area. Students were confusing area and volume and weren’t sure when to use a specific formula. The idea of area being squared and volume cubed has been emphasized but still not cemented. It seemed that students knew much more about the formulas and not as much about the conceptual understanding. To strengthen students’ understanding my class started a surface area activity late last week. Click the image below for the template.

Students were asked to pick one box in front of the classroom. I had many different boxes to choose from. Many of them were board games or boxes I borrowed from other teachers. It’s near the end of the school year and some teachers are moving classrooms so there were plenty of boxes. All of the boxes were rectangular prisms. Once students picked a box they took a picture and then found the dimensions. Students then took one piece of butcher paper and created a net based on the dimensions found earlier.

Photo May 20, 11 22 59 AM Photo May 20, 11 23 08 AM

Students created the net and then wrapped up the box. Students were able to immediately identify whether their measurements were off or on target. It took some groups multiple attempts to find a correct solution. After students wrapped up their box they took a picture. Before and after pictures were sent to me via Showbie. I printed them out and the students placed them on their sheets.

final

It would have been great to print these out in color, but at this time of the year our school’s color printer is out of ink. After the activity students reflected on how their perception of area has changed over the past week. After listening to a few student reflections I’m deciding to keep this activity for next school year.