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Posts Tagged ‘Surface Area’

My students rock. We just finished a 3-4 day unit on Surface Area that ended with a quiz that only 3 students out of 70 did not pass – amazing progress!!!!

I started out the volume unit by handing-out a warm-up worksheet that asked students to count the number of cubes that made up each figure. There was an example at the top of the page that also showed students that it was cubic centimeters so answer with the units cm^3. I got fantastic questions immediately:

Are we counting the faces or are we counting the cubes?

Score 1 for a successful surface area unit yet again. I explained we are counting the CUBES, I saw many students erasing their previous answers. They finished the problems in about 3 minutes once they realized it was simply counting up boxes. We went around the room answering the questions making sure to include the correct units (hey, it’s cm^3 because they’re little cubes!).

Next I directed their attention to my desk, and asked them to turn their warm-up paper over and SILENTLY write down their prediction on which container held more and give a reason why. I stated again the need to not shout out because they don’t want to share their answers with their neighbors. I held up each Tupperware for them and its corresponding name (neighboring  high schools).

My demonstration table

I asked students to raise their hands for each Tupperware, we started with St. Joes. In the first class nobody raised their hand (interestingly, in the honors class about a third believed it was the biggest which shows they are different kinds of thinkers, but I digress). Instead of just moving on I asked if somebody would raise their hand and explain why they did NOT pick St. Joes. The volunteer’s responses included words like deep and short. I reenforced the word Height and when they explained that it was in fact wide I used the word Base. I continued to use those words over and over until the students started to include them in their own descriptions.

As expected, we became split on Masterman and P E&T and it was time to figure out how we were going to measure this! I held up my marshmallows and explained these were my kind-of-cubic centimeters like in the warm-up activity and we were going to count how many cubes filled it up. I asked why this wasn’t perfect and students explained that they were cylinders, wouldn’t fill up the perfectly, could we have half layers?, smushy, etc. And we agreed upon no smushing and a good estimate. I also asked if I could just dump a bunch in and they emphatically responded NO! I must build a layer on the bottom and build carefully.

Good.

I had a student volunteer and a supervisor (both rooting on opposite teams) to come up and measure P E&T while I measured Masterman for the class (it was clear). I found there were 6 marshmallows on the bottom layer and I showed this to students and asked if I could find a shortcut. I decided to look at how many layers could I fit and noticed there were four (I stacked four marshmallows on the side and showed students). About half the class shouted, TWENTY-FOUR MARSHMALLOWS WILL FIT!

Score. How did you get that number? I multiplied. Why? Ummmm. Okay, let’s see if you’re all right! And then I proceeded to fill up the Tupperware and WOW, 24. And then I asked them use the terms base and height to explain their shortcut and they explained they multiplied base by height.

The next awesomeness happened when skinny ol’ P &ET ended up with 25 marshmallows and we were flabbergasted on how the two different shapes could hold such a similar amount! And then students started to realize that maybe ones fatter base made up for the shorter height. The conversation was mind-blowing and it occurred in all three class periods.

So when time to show them the volume formula for rectangular prisms and cubes it was super easy for them to see we just get the area of the base and multiply the height. They wrote down the formulas I put on the board and did the following two pieces of classwork, exit ticket, AND completed their homework. Mind you, we did all this in a short day – which means 38 minutes. WOW.

They continued to show me they understand the concept of volume when we moved onto more figures including cones and pyramids which we compared to cylinders and prisms and saw how their volume was related (I put figures inside of other figures and asked questions like which holds more to reenforce similarity/differences) and thus the formulas would be related. It’s been a very successful and exciting 2 weeks of learning for us!

Unfortunately – I only have 10 days left of student teaching. Which means I am going to do some AWESOME things for the next 10 days to get the most out of the last few days – up next, Pythagorean Theorem (looking for projects!)

Sources: All worksheets (except Molly-made exit ticket) taken from: http://www.superteacherworksheets.com/volume.html

My Links: Classwork:http://www.scribd.com/fullscreen/73201749?access_key=key-1f62a6i45ii2q5u5p4zf. http://www.scribd.com/fullscreen/73201750?access_key=key-2kgmvw3emrxadclicsrr

Homework:http://www.scribd.com/fullscreen/73201751?access_key=key-mdrtsl9v0wki7bwwuh6

Exit Ticket: http://www.scribd.com/fullscreen/73201835?access_key=key-rishm72tbtyzsvm7aqf

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I focused on surface area this week with my juniors in my catch-all-test-prep-this-should-definitely-be-illegal class. (To put my two cents in on forcing students to take Algebra 2 as well as a PSSA prep class… well a post for another time I suppose).  The past two weeks we were covering area and perimeter and I was astounded at the lack of understanding. Many misconceptions were evident but the most alarming was the inability to use the test prep formula sheet. For example, many students were unable to identify the triangle on their paper and match it to the triangle on the formula sheet and thus find the correct formula. I thought it might be because they were using a right triangle and the height was measured different, but when the test came and I matched the shapes to their formula sheet I was still surprised at the number of students who could not match the shapes. Thus the test on area and perimeter became a test on something totally different.

Only about 5 students in each class were still struggling with identifying parts of a shape and the rest of the students were starting to get frustrated and bored. I decided to move forward and try to squash area misconceptions during surface area, since we would still continue to use the area formulas for the shapes again and again.

Why I believe this unit worked so effectively had to with the use of scaffolding in their warm-ups, manipulatives, and lots of classwork practice time with limited homework. For each day I focused on two shapes and had the warmup focus on finding the area of the 2-D shapes that would ultimately make up the 3-D solids. For example, for the rectangular solid their warm-up was to find the area of three rectangles that later in the lesson we would put together to build the 3-D solid.

I made sure that for each shape they saw the deconstruction of the solid into their familiar shapes and I had cut out my own nets and taped and colored them to pass around the classroom for further understanding. What captivated the students most was asking them what shapes they believed made up the 3-D solid. For example with the cylinder they all noticed the two circles for the bases but most did not guess that the “middle” was actually a rectangle. When we got to the cone it was pretty cool how excited they were to guess what the 2-D shape would be. I used that as a great moment to say, “This is a funky shape- which is why it has a funky formula.” So the students didn’t really moan and groan at the obnoxious cone formula because they saw (sort of) where it came from.

Finally I made sure to have a practice sheet for the last 15 minutes of class everyday. I wanted students to practice the formulas in front of me and immediately after learning about it. I also read this blog about Results Only Learning Environment and the role of homework. Since homework completion and cheating are two huge obstacles to overcome I decided to focus on classwork and if students needed more time they could complete the rest of the worksheet at home. This way I could monitor who is doing their own work, the struggles they are having as well as ensure they are getting the practice I desire.

Overall I was very pleased with this unit and hoping to follow some of these teaching themes that worked to help me in the Volume Unit I start on Wednesday.  All suggestions, resources, and what you’ve done in the past for surface area and volume would be greatly appreciated as well!

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