Today was so fun! We did a warm up reviewing Pythagorean theorem, then as a class, we worked through finding the dimensions of the 55″ television at the beginning of act 2.

Students then worked in small groups to answer and discuss whether an 80″ TV is really more then double the area of a 55″ TV. There was struggle, success, frustration, persistence, debate. Standards of mathematical practice abound! Ahh, it was beautiful.

I had a few students who found a more efficient methods for finding the area of each TV:

The student below found the proportional increase from a 55″ to an 80″ and just multiplied the side lengths by the same ratio:

This student calculated the area of each “square” in a 16 x 9 TV, then multiplied it by 144, saving him the effort of finding the length of each side and then the area:

I love how students develop such smart methods when left to their own devices. Its sad to think of all of the times I’ve stifled that creativity by showing them just one method to solve a problem, instead of equipping students with tools and a good understanding of a problem and allowing them to use the tools as they see fit.

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Some great work here! Did they already know the 9 : 16 ratio or was that something discovered together in class?

Thanks! I was really impressed with their work. The aspect ratio was provided in the previous act and they worked to familiarize themselves with what this means and how to use it.

Whoa. Look at all that awesome work! And kudos to the students who came up with quicker methods of comparing the TVs. (Incidentally, “left to their own…devices.” HA!)

This was such a great lesson. Wish I’d seen your post before I did it yesterday/ today! Had to do some deliberate guiding, but I think in the end my kiddos (7th) really “got it,” and more importantly were excited about it 🙂

After reading your blog from yesterday, this is fantastic! Way to change course & do what your students need. Obviously, we’re always trying to do just that, but it’s not easy to turn a lesson around from disappointing to awesome.