In the latest blog post on Dan Meyer's blog, he talks about how we can numerically quantify a negative times a negative integer in real world applications. He was at a conference in California and one of his colleagues asked this question,"How can we quantify a negative time a negative integer in real world applications?" He thought it was a good idea to pose this question on twitter and see what other people had to say about this topic. Within the first day he received over 100 tweets answering this question. He went on to talk about two different techniques that can create two very different classrooms and two very different teachers. I was perplexed by the idea so here is what I said to him:
[Makeover] Checkerboard Border
In this blog post Dan Meyer, he discusses an idea of showing students a picture of a checkerboard border for a few seconds. After he has shown them, he asks them to make a guess of how many blue squares are in the checkerboard. They don't have to be right, they just need to make a guess. He suggests to them to make an extremely high guess and an extremely low guess. Then he gives them some smaller checkerboards to recreate on their own. Next, he tells them that the smaller checkerboard has 88 blue tiles. So, then he brings their attention back to the big checkerboard border. So some of his students might try to derive equations to figure out the number while others might apply the first method that they used. Then he tells them that the big checkerboard has 408 blue tiles. So he then asks the students to reveal their guesses and the student with the closest guess gets one clap.
"Hi, I am a edm310 student at the University of South Alabama and I agree with you. I think if you give students something easy to start with and get them engaged, then by the end of it once you deliver the “hard part of the problem” they will have already invested a lot of time so they will work harder to finish. I think that if you start out with the hard part then most f your students will give up without even trying to solve the problem."