‘Blogging and Twitter are all about sharing ideas, and hopefully growing as a result. In this, my 100th post, I share a creation I made in response to Paul Salomon‘s Imbalance Challenge. As he notes on his ‘blog, these challenges emerged when he wondered how he could shift his young students to some deeper thinking from their conversations about equivalence.

From the image below, can you rank circle, square, and triangle from lightest to heaviest?

Thanks to those who share with me. I hope some of my offerings help others think and grow, too.

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Square>triangle>circle

For the 3 on the previous post, I could “see” the order by visual comparison, but I had a harder time with this one visually. I came up with an order by using algebra and inequalities. Would you expect students to be able to visualize this figure, or use any means necessary? My order is c<t<s.

Dennis, I used algebra & inequalities to create it. The original challenge was given to 5th graders, but I was trying to leverage up the problem to a middle or high school level. The symbolic manipulations, I hoped, helped extend the problem into a broader realm beyond visualization.