I just can’t type “real-life” without quotes because I’m yet to resolve what “real-life” means in a math class. But for this post it means – “Math someone needed to do at their job”. And in this post that someone is my wife – who much to her distain and my joy – does a lot of geometry as a project manager at a construction firm.
So here’s what we need to know: How much cement is needed to make that border? We need the answer in cubic yards because you buy cement in cubic yards.
The image below provides some of the context for the problem – The cement border is being used to circle an existing tree.
I was actually surprised how open the middle was on this problem. Yet students used two main strategies. The first was the standard subtract the areas and multiply by the height, or they subtracted the volumes of both cylinders directly. The second was the find the perimeter, think of the wall as a rectangle (dimensions of 2*pi*r X 1′), find the area of that rectangle and then multiply by the height.
One student using the second strategy used a radius of 14ft and got a solution of 16.2 cubic yards. He told me he knew the answer would be a little too small because of only using the inner radius. Another students used 14.5 and got the same solution as the area subtracting syndicate.
Converting from cubic feet to cubic yards is a great time to practice your perplexed I wonder why you divide by 27? face.
By the way the wall ended up costing around $35000. I can’t believe how long I would have to work to put a wall around a tree 🙁
Posted in #industry, #technology, geometry
Tagged annulus, area, cylinders, geometry, industry, IndustryMath, math1, math2, open middle, real-world, volume
This year I am teaching algebra and geometry again – new school, same subjects. I have decided to do no introduction or ice breaker activities. No syllabus on day 1 (which I never have done) either.
Last year I did the straw bridge challenge and I loved it and definitely recommend it. But I am scrapping it this year due to the time constraints of focusing on CCSS in a district that is still giving the STAR test. So I choose these two activities for their more direct relationship to standards I must teach, as well as their low entry point and interesting hooks.
Day 1 in algebra is going to be my Getting to Vegas problem, which is simply a personalization of a problem Dan Meyer describes here. When I was living in Forestville some friends and I decided to go to Vegas. There are two airports that we could have used – the smaller local airport in Santa Rosa, or the larger airport in San Francisco. Which airport should I have took, or will I take next time? I have screen grabs of all relevant information in the slides.
A couple extensions: How long would the Vegas trip need to be in order for the Santa Rosa airport to be cheaper? (Eventually the more expensive parking at SFO takes over). Or Dan’s scenario of taking a shuttle from Santa Rosa to the San Francisco airport vs. driving directly to San Francisco.
In geometry I’m starting with Dan’s Taco Cart problem. I am just going to go to keep it as Dan vs. Ben, because I am a bit intimated on day1 to follow Fawn’s more interactive implementation allowing students to choose their own paths.
This is an exercise with the Pythagorean Theorem, which is great for day 1 because they have all seen it before.
I had to be absent a couple days last week, and I wanted to the class to learn some new material. We had just spent two days simplifiying radicals, and I wanted them to move onto adding and subtracting. So I decided to make a quick video of myself explaining how to do it.
The next day basically every single student I have told me how much they loved the video. The sub-report talked about how great it was. A couple teachers and a teachers aid all told me at various times throughout the day that they heard I made some great video. Then yesterday a student told me that she learns better from my videos than she does from me (thanks… I think?). And after multiple students asked if the video was online, I figured I should put it online.
And it’s kind of funny because they are nothing special at all – straight up direct instruction. But it seems like some students got something out of them, so who I am to judge? And just like Khan I suppose, I did them in one take so they are not time consuming to create. I ended up making 1 for geometry, and 2 for algebra.
Oh yeah, and I am certainly not going to post them all to this blog.
These are a listing of hastags that I use to catagorize my lessons plans. Each catagory represents a different style lesson plan. My instructional goal is typically to make sure that I use each hashtag at least once a month. The goal of this blog is to share all the lesson plans that I use under each hashtag.
My detailed lesson plans are my Keynote slides. But along with those, I make a quick, calendar-style overview to me a general idea of what I am doing. It’s on this calender where I place the hashtags at the bottom of each day. This allows me to quickly look back at what I have been doing, and know whether of not I am differentiating. For example, here is two weeks worth of my lesson plans in geometry. Notice that I can quickly see whether or not I have differentiated my instruction, without having to analyze each specific lesson plan. The hashtags allow me to get a quick sense of what I have been doing, and what I have not been doing.
-The term “perplexity” is being used as described by Dan Meyer here
Posted in #artistic, #assessment, #collaboration, #error, #game, #graphic organizer, #industry, #kinesthetic, #perplexity, #reasoning, #technology
Tagged artistic, assessment, collaboration, error, game, graphic organizer, industry, kinesthetic, perplexity, reasoning, tactile, technology