Volume and Surface Area
Volume and Surface Area is my last unit before Probability and Statistics. That means, it gets the best problems!
Magformers
A couple of years ago I wrote some grants for math toys in my classroom. The next couple of lessons are based on those.
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Surface Areas of Prisms and Pyramids
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Using magformers, we explore surface area and volume using manipulatives. Here is the activity I created.
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Platonic Solids and Euler's Theorem
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Using magformers, we explore creating platonic solids. Here is the activity I created.
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The following lessons are Magformer-free.
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Guatemalan Sink Hole
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Fun little lesson from Robert Kaplinsky about volumes of cylinders. I do this in the same class period as Girl Scout Cookies.
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Girl Scout Cookies
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3 Act lesson from Dan Meyer about volumes of rectangular prisms.
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Soup Can Packaging
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How do you break into a new market if you're a soup company? Marketing and... packaging. This task combines trig, circles, compound shapes, and surface area. It's a great problem for multiple solution methods but the same answers (open middle). Link here.
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Gas Station Fuel Tank
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Gas station fuel tanks are basically cylinders we bury in the ground. When we fill them using tanker trucks, we first put a stick in the top to see how full it is. How much fuel do we need to add to the tank? Circles, trig, compound shapes, volume, dimensional analysis--this problem is what some might call "rich". I made a presentation for it. Here is the link to the task. I adapted this problem from Tom Reardon.
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Glasses
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Volumes of pyramids, cones, and composite shapes. But wait! There's more. The real brilliance of this gem from the Math Assessment Project is that it asks students to figure out when a glass, made of composite shapes, is half full. The task starts low floor and then works all the way to the tippy top of the ceiling. Extension number 3 is wicked hard for most students. Here is a link to the pdf I use.
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Gumball Machine
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From the spectacular Robert Kaplinsky. Our estimates always end up being off because spheres don't pack very tightly. This leads to a discussion of sphere packing density. Here's the presentation I use.
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I took this problem from Emaths. The numbers in the original problem were meant to be easier but it caused confusion with my students who were in track. I've revised the problem to include lengths on standard high school and NCAA tracks. This is a great 2 or 3 day task: circles, trig, dimensional analysis, volume, composite shapes. I love it! Here's the link.
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